International Journal of Engineering and Technical Research (IJETR) ISSN: 2321-0869 (O) 2454-4698 (P) Volume-7, Issue-12, December 2017 RPI 1% to 5% – Mathematical Reasoning of Economic Intervening Principle Based on Yin Yang Wu Xing Theory in Traditional Chinese Economics (II) Yingshan Zhang  the various categories of commodity retail price index weighted average income. Look from the definition, the commodity retail price refers to (RPI) and consumer price index (CPI) both are similar, this is, commodity retail price index statistics scope is wide than the consumer price index, and the different aims of both statistical and RPI compiled the purpose is to grasp the changes in prices of goods market, and compiled on the basis of various other derived counsel, for studying market circulation and the national economic accounting.The CPI is mainly to see inflation levels.Of course, look from the China statistical yearbook, both trends are almost synchronous, has a high degree of correlation. A microcosm of the macro economy as RPI is headed. RPI index is commodity the price of the last link in the process of circulation.According to the law of supply and demand rule, it is known: what is the price of high demand and increase supply, demand for lower prices to increase supply decrease.If commodity retail price overall level continues to increase, in the case of other factors unchanged, people's consumption atrophy, reduced demand, this leads to a lot of unsold goods, supply, direct impact on corporate profits and the future market is likely to enter the vicious circle.So how do you solve this problem, the general government will implement a proactive fiscal and monetary policy, increase spending on people's livelihood, measures such as increasing the income of people and to expand domestic demand to stimulate consumption, to solve the problems about circulation field, the market into a virtuous cycle.But the problem is not so simple, if the RPI index rise is due to the circulation of money increase inflation pressure, are much more difficult to solve, you need to shrink in circulation currency, such as raising interest rates and other measures to solve them.Because both the RPI and CPI trend with synchronicity, so it is said, the RPI is a miniature of the macro economy. Internationally, RPI data applications also is more, in the United States, the ministry of commerce investigation into national commercial sampling every month, summarize from commodity retail price index, and on the basis of paying close attention to the macro economy is headed.The RPI statistical product range is wide, pay by cash or credit card form of retail goods were included in the survey, including furniture, electrical appliances, supermarket sales of goods and medicine, etc., but excludes services consumption. Through the growth rate of price index to calculate the rate of inflation, prices can be respectively by the consumer price index (CPI), the producer price index (PPI), the retail price Abstract— RPI (Retail Price Index) is useful in understanding economic disease. By using mathematical reasoning based on Yin Yang Wu Xing Theory in Traditional Chinese Economics (TCE) , this paper demonstrates the treatment principle:“Don’t have economic disease cure cure non-ill” (不治已病治未病) . It means that for the RPI inflation rate of industry economic society, the normal range of theory is [0.8789%,5.2241%] nearly to [1%,5%] , and the center is 2.7047% nearly to 3% . The first or second transfer law of economic diseases changes according to the different RPI inflation rate whether in the normal range or not. Assume that the range of the RPI inflation rate is divided into four parts from small to large. Both second and third are for a healthy economy. The treating works are the prevention or treatment for a more serious relation economic disease which comes from the first transfer law. And both first and fourth are for an unhealthy economy.The treating works are the prevention or treatment for a more serious relation economic disease which comes from the second transfer law. Economic disease treatment should protect and maintain the balance of two incompatibility relations: the loving relationship and the killing relationship. As an application, the Chinese RPI inflation rate is used for the wood subsystem how to do works based on studying the sick subsystem of steady multilateral systems. Index Terms— Traditional Chinese Economics (TCE), Yin Yang Wu Xing Theory, steady multilateral systems, incompatibility relations, side effects, medical and drug resistance problem I. INTRODUCTION RPI (Retail Price Index) is useful in understanding economic disease. Teach in retail prices of commodities is the last link in the process of the flow of goods in the price index, it covers all industrial, commercial, catering and other retail enterprise groups to the urban and rural residents, organ selling prices of consumer goods and office supplies, reflect a certain period retail price change trend and degree of index data. RPI index statistics of major commodities, including food, beverages, tobacco, clothing shoes and hats, textiles, Chinese and western medicines, cosmetics, books, newspapers, magazines, cultural and sports supplies, daily necessities, household appliances, jewelry, fuel, building decoration materials and mechanical and electrical products, such as 14 categories.In each class, in several categories and points within the class divided into small classes, the program is to small class first, then in the class, major categories, finally by Yingshan Zhang, School of Statistics, Faculty of Economics and Management, East China Normal University,Shanghai,P. R. China 6 www.erpublication.org RPI 1% to 5% – Mathematical Reasoning of Economic Intervening Principle Based on Yin Yang Wu Xing Theory in Traditional Chinese Economics (II) economic disease, the condition of inflation rate is a Yin condition, little is a Yang condition. If the RPI rose is too large, it shows that the inflation has become the economic instability, the central bank will be a tight monetary policy and fiscal policy paying risk, resulting in the uncertain economic outlook. As a result, the index of high rise is often not welcome by the market. In the past 12 months, for example, the RPI roses 2.2%, that means, the cost of industry making rose by an average of 2.2% more than 12 months ago. When the cost of living increase, your money value drops. That is to say, a 100-yuan notes, only can buy $97.70 worth of living goods except for services. Generally when the RPI inflation rate  1% , it is called plus, is INFLATION. And when the RPI inflation rate  5% , it is treated as a SERIOUS plus, is a SERIOUS INFLATION. In this paper, the rate of inflation can be considered as the price level rises rather than the currency quantity rises from the basic concept of RPI. It is because the RPI is the direct reflection of living standards, although the price level increase is difficult to be controlled directly. The RPI is a general parameter linking together the complexity of relations between subsystem pairs of economic social system, economic social system itself, the capabilities for intervention reaction and self-protection of the economic social system as an economy and mind as a whole, related to the environment, food, health and personal history, air, water, earth, climate, season, etc. RPI is as useful in understanding economic disease as the average is in statistics, or as the expected value is in probability calculation. The economic social system as an economy begins to activate the necessary mechanisms to restore this parameter to its appropriate range. If the economic social system as an economy is unable to restore optimal RPI levels, the economic disease may become chronic and lead to dire consequences. Zhang etc [15-23] have started a great interest and admired works for Traditional Chinese Economics (TCE), where, through mathematical reasoning, they demonstrate the presence of incompatibility relations, which are predominant in daily life, yet absent in traditional Aristotelian Western logic. Many people as Western persons are beyond all doubt the Yin Yang Wu Xing theory is superior to the traditional true-false logic, which does not contemplate incompatibility relations, which Zhang [19] has expertly explained from a mathematical standpoint. The work Zhang [15,16] has started, allows many people like Western person to think of a true re-foundation of mathematical language, to make it a better suited tool for the needs of mankind economic social system and the environment. Although so doing, Zhang [18] also brings to light the difficulty of establishing the values of both the intervention reaction coefficients 1 , 2 and the index (RPI), and the gross national product (GNP) as conversion price index. In order to examine the retail business development situation, general use of RPI, its formula is as follows: RPI  a1 (P1t / P10 )  a2 (P2t / P20 )  ...  an (Pnt / Pn0 ), (1) where the type of digital and t , n is the number in the subscript, P* as the representative of retail business goods prices, an is the weight. Both the rate of RPI inflation and the RPI are two different concepts. Calculation method of the rate of RPI inflation through the calculation of the RPI changes: The rate of RPI inflation (price rises)   100%, (2) base price level where the price rise level from low to high, to base the level of prices for base. One of the base period is selected one price level as a reference, so that you can put the other periods of price level with a comparison between base level to measure the current level of inflation. Note on the type, the rate of RPI inflation is not a price index, which is not a price rise, but the price index to rise. In fact, what is said above is just one of the three methods (CPI,PPI,RPI) of measuring inflation index reduced living consumption laws, but it is the most commonly used for studying the retail business economy, in addition to Gross Domestic Product (GDP) and consumer price index (CPI) or producer price index (PPI) conversion method. The RPI is the government measure of inflation one of the data. Popular speaking, the RPI is the price of the retail goods on the market growth percentage. As an important indicator, observe the level of inflation in China, much attention has been paid to also for such an important indicator, as a new era of youth, more objective view should be observed. First of all, let the RPI be met. The RPI is to reflect the retail goods, related to the retail goods calculated price, retail business index usually observed inflation as an important indicator. Levell [1] has found that there is the important relation between the RPI and the CPI. The RPI plays a key role in the CPI. So the central bank can minimize the inflation by taking certain predictive measures to keep the input prices under control. Because of the relation between the RPI and the CPI, the normal range of the RPI inflation rate can be obtained from the normal range of the CPI inflation rate. It is found that the normal range of the CPI inflation rate is from 2% to 5%. There are a lot of evidences (e.g., experimental identification for probability and real applications) to support this viewpoint, such as, Crone etc [2], Pauhofova etc [3],Funke etc [4], Formica etc [5], Fan etc [6], Adams [7], Hausman [8], Nahm [9], Moosa [10], Zhao [11], Daniel [12], Anonymous [13-14], and so on. It is believed that the normal range of the RPI inflation rate is from 1% to 5%. It is because the RPI is more sensitive than the CPI at the low RPI inflation rate, so changes in the wider range at the low RPI inflation rate. Thus the retail business economic social system identifies an important indicator for an economic social system health: the value of RPI inflation rate, which, under normal conditions, ranges from 1% to 5%. Outside this range (low:Yin condition; high: Yang condition), economic disease appears. Almost always, when there is current price level - base price level self-protection coefficient 3 as parameters with due accuracy. In this paper, the introduction of a parameter such as a RPI will be suggested, in order to facilitate the understanding and the calculation of the values of both the intervention reaction coefficients 1 , 2 and the self-protection coefficient 3 . This paper ventures to suggest this with all due to respect, because it be believed that the path Zhang [15,16] has started, 7 www.erpublication.org International Journal of Engineering and Technical Research (IJETR) ISSN: 2321-0869 (O) 2454-4698 (P) Volume-7, Issue-12, December 2017  ( x)  in such an understandable way from the mathematical point of view, will be very useful for all mankind searching for tools to understand the mechanisms of economic social system. The article proceeds as follows. Section 2 contains a parameter model and basic theorems, in order to explain both the intervention reaction coefficients 1 , 2 and the self-protection coefficient | x  0.027047 | , x  (0.08,0.6) (0.6  x)( x  0.08)  x  0.027047  (0.6  x)( x  0.08) , 0.6  x  0.027047;    0.027047  x , 0.08  x  0.027047.  (0.6  x)( x  0.08) 3 through the introduction of a parameter model to study the normal range of a RPI inflation rate, while the first or second transfer law of economic diseases is demonstrated in Section 3, proved through the concept of both relation diseases and a relationship analysis of steady multilateral systems. Furthermore, if the range of RPI inflation rate is divided into four parts, for the economy in every part, the prevention or treatment method of economic diseases as treatment principle of TCE is given in Section 4. As an application, the Chinese RPI inflation rate is used for the wood( X ) subsystem how to do works based on studying the sick subsystem of steady multilateral systems in Section 5 and conclusions are drawn in Section 6. (3) A parameter model is considered as  ( x)  1/ 2 , x  (0.08, 0.6).  ( x)  1/ 2 (4) Theorem 2.1 Under model (4), the following statements hold. (1) The one that 0   ( x )  1 / 2  1 is equivalent to the other that 0   ( x)   ( x)  1 / 2 1   ( x) 2  ( x)   ,  ( x) is a monotone decreasing function of x if x  (0.08, 0.027047] or a monotone increasing function of x if x [0.027047, 0.6) ; and  ( x) is a monotone decreasing function of  ( x) if  ( x) [0, ) ; and  ( x) is a monotone decreasing function of  ( x) if  ( x)  (0,1] . where II. PARAMETER MODEL AND BASIC THEOREMS The concepts and notations in Zhang [21] are start and still used. (2) Let   ( 5  1) / 2  0.61803399 be the gold number.  ( x)  Denoted 0  0.5897545123 , namely healthy number. It is If 1   ( x)  0 , then 1  0 1   ( x)    02   ( x) 2  1; 2  ( x) 2 0 1  0 1   ( x)  ( x)     0   ( x )  1; 2  ( x) 2 2  02  ( x) 1  0 1   ( x)  ( x)    1. 2  ( x) 3 2  03  ( x) 2 0 can make the healthy balance , and conditions 1  3 2  13 2 1  2 3  1  2 3 hold if 1  0 , 2  0 and 3  0 . Assuming 0  0.68232780, namely unhealthy number. It because the healthy number (3) If 0   ( x)  0 and , 1  0 1   ( x)  ( x)     02   ( x ) 2  0; 2  ( x) 2 0  ( x) 1   ( x) 1   0     0   ( x )  0;  ( x) 2  ( x) 2 2  02 1  0  ( x) 1   ( x)    1.  ( x) 2 2  ( x) 3 2  03 is because under a poor self-protection ability, the unhealthy number 0 can make the poor healthy balance conditions hold: then and 0  1   ( x)  0 , 2   ( x) 2 where there 0  c 1 , are 3  c ( x) 1  3   ( x)(1  c)  0, 2  13   ( x)2 (1  c)  0 , (4) 1  3  3  0 / 2  0.34116390, 2  1 3  1 3  ( 0 ) / 2  0.23278561 1  2 3  1   2 3 2 Taking and ( 1  2 3 )   ( x)  c ( x)3  1  2 3  1  c ( x)3 , wh and 1 if 1  0 , 2  ( 0 )  0.46557123 and 3  0 . 2 Thus 0    0 . 2 | ( 1  2 3 )  (1  2 3 ) | 2(1  c) 03  (1  c)0.41024. (5 ere 1  1   ( x)  0 , 2   ( x) 2 3  c ( x) where 0  c  1 , there are ) A parameter model of a RPI inflation rate in a mathematical sense based on Yin Yang Wu Xing Theory of TCE is reintroduced by using the functions  ( x) and  ( x) of the RPI inflation rate x described as follows. Taking and 1  3   ( x)(1  c)  0, 2  13   ( x)2 (1  c)  0 and ( 1  2 3 )   ( x)  c ( x)3  1  2 3  1  c ( x)3 if firstly, Let x  (0.08, 0.6) be a RPI inflation rate, where the values 0.08 and 0.6 are the minimum and maximum acceptable the RPI inflation rate. Denoted the value 0.027047 is the target as the expectation of the RPI inflation rate. Define a function  ( x) of the RPI inflation rate x in below: 1 c   ( x) 1   ( x)  0;  ( x) 2 2  ( x)3 1  3   ( x)(1  c)   ( x) / 2, 2  13   ( x)2 (1  c)   ( x)2 / 2 and secondly, ( 1  2 3 )   ( x)  c ( x)3  1  2 3  1  c ( x)3 where 8 this inequality range to meet www.erpublication.org RPI 1% to 5% – Mathematical Reasoning of Economic Intervening Principle Based on Yin Yang Wu Xing Theory in Traditional Chinese Economics (II) | ( 1  2 3 )  (1  2 3 ) | ( 0 )3  0.31767 0c 1   ( x)  0 ; 1   ( x)  ( x) 1 in which    ( x) 2 2 2  ( x )3  (0.010552)   (0.049013)     ( x)  if (4) The condition x [0.008789, 0.052241] equivalent to each of the following conditions: 1   ( x)   (0.008789)   (0.052241)=02  0.34781,  (0.027047)  0   ( x)  2  ( x) 1  3   ( x)(1  c)   ( x) / 2, 2  13   ( x)2 (1  c)   ( x)2 / 2 thirdly, ( 1  2 3 )   ( x)  c ( x)3  1  2 3  1  c ( x)3  (0.008789)   (0.052241)  0   ( x)  and | ( 1  2 3 )  (1  2 3 ) | 203  0.41024 where 0c this inequality 1 1   ( x)  ( x)   1 2 2  ( x)3  ( x) 2 range in which to 0   ( x)  0 ;  (0.014201)   (0.042994)  0   ( x)  ( 1  2 3 )   ( x)  c ( x)3  1  2 3  1  c ( x)3 inequality range 1 1   ( x)  ( x) c   1 in which 2 2  ( x)3  ( x) 2 to 0   ( x)  0 . meet if nearly to 0 if 0  c  1   ( x)   ( x)  1 in which 3 2 [ 03  0.20512, 0) 1 1   ( x)  ( x) 0c    1 in which 2 2  ( x)3  ( x) 2 2 respectively 0   ( x)  0 . if (c).The value [( 1  2 3 )  (1  2 3 )] is included in the interval [ 03  0.20512, 0) 1 1   ( x)  ( x) c   1 in which 3 2 2  ( x)  ( x) 2 0   ( x)  0 . # respectively instead of the normal range of a RPI inflation rate. The equivalence of Corollary 2.1 shows that TCE is The scientific which is from TCM (Traditional Chinese Medicine). Zhang etc [21] has already determined: an economy is said a healthy mathematical complex system when the intervention reaction coefficient 1 satisfies 1  1  0 . In logic and if Corollary 2.1 Under model (4), the following statements hold. (1) For any 0  d  1 , there is an unique solution u  (0.08, 0.027047) and there is also an unique solution v  (0.027047, 0.6) , such that  (0.027047)  0   ( x)  practice, it's reasonable that  ( x)  1 / 2 1/ 2 energy for intervening mathematical complex subsystem can transmit to other mathematical complex subsystems which have neighboring relations or alternate relations with the intervening mathematical complex subsystem. The condition 1  0 can be satisfied when 2  13 and 3  1 for  1   (0.027047). (2) The condition x [0.01,0.05] is equivalent to each of the following conditions:  (0.027047)  0   ( x)  a mathematical complex system since 1  2  1 implies 1   ( x)   (0.01)   (0.05)= 0.32103, 2  ( x) 1    0.61803  0 . In this case, 2   2  0.38197 . If 1/ 2  (0.01)   (0.05)  0.60899   ( x)   1   (0.027047).  ( x)  1/ 2 (3) The condition x [0.010552, 0.049013] equivalent to each of the following conditions:  (0.027047)  0   ( x)  1  2 is near to 1 if the input and output in a complex system is balanced, since a mathematical output subsystem is absolutely necessary other subsystems of all consumption. In case: 1  2  1 , all the 1   ( x)   (u )   (v)  (1  d ) / (2d ), 2  ( x)  (u )   (v)  d   ( x)  and is equivalent to that x[0.008789, 0.052241] . In other words, in Theory of TCE, the normal range of the RPI inflation rate is considered as x[0.008789, 0.052241] nearly to x[0.01,0.05] . Of course, little difference of the two intervals which makes the diagnosis of disease as a result, there may be no much difference as a suspect. In fact, TCE uses the rule 0  1  1 from Yin Yang Wu Xing Theory 1   ( x)  0 . (b). The value [( 1  2 3 )  (1  2 3 )] is included in the interval Taking which has the capabilities of both intervention reaction and self-protection. From Corollary 2.1, the condition 0  1  1 the following statements hold. (a). The absolute value | ( 1  2 3 )  (1  2 3 ) | is  ( x) 1   ( x), 2   ( x)2 3  c ( x) where 0  c  1 for an economic society economy. In particular, when c is nearly to 1/2, there are 1  3   ( x)(1  c)   ( x) / 2, 2  13   ( x)2 (1  c)   ( x)2 / 2 and 2  ( x) 1/ 2  1   (0.027047). #  ( x)  1/ 2 Remark 1. In west, through experiment or through practice observation, by using the relation between the RPI and the CPI, many researchers [1-14] can obtain the normal range of the RPI inflation rate as x [0.01,0.05] from the normal range of the CPI as x [0.02,0.05] . But in TCE, from Yin Yang Wu Xing Theory, Zhang etc [21] have already determined: 0  1  1 for the normal range of a healthy and this is  (0.027047)  0   ( x)   (0.014201)   (0.042994)  ( 0 )2 / 2  0.23279, 1  3   ( x)(1  c)   ( x) / 2, 2  13   ( x)2 (1  c)   ( x)2 / 2 | ( 1  2 3 )  (1  2 3 ) | ( 0 )3  0.31767 is 1/ 2  1   (0.027047).  ( x)  1/ 2 (5) The condition x [0.014201, 0.042994] equivalent to each of the following conditions: meet if finally, where 1/ 2  1   (0.027047).  ( x)  1/ 2 this assumptions is set up, then the intervening principle: “Real disease with a healthy economy is to rush down its son and virtual disease with a healthy economy is to fill its mother” based on “Yin Yang Wu Xing” theory in image mathematics [20] , is quite reasonable. But, in general, the ability of self-protection often is insufficient for an usual mathematical complex system, i.e., 3 is small. A common is 1   ( x) 1   (0.010552)   (0.049013)   0.30902, 2  ( x) 2 9 www.erpublication.org standard is   1  1 22 International Journal of Engineering and Technical Research (IJETR) ISSN: 2321-0869 (O) 2454-4698 (P) Volume-7, Issue-12, December 2017  1 and (1  2 3 )  ( 1  2 3 ) at the same time if 2 0 2 of condition the loving principle which all losses are bear in mathematical complex system. Thus the general condition is often 1  0.61803  3  0.5  2  0.38197 . Interestingly, they are the killing relationship and the loving relation at the same time. But neither are the others. The RPI inflation rate must be precise calculation to keep at least 6 decimal places can ensure correct because of its sensitivity to the diagnosis of disease. Remark 2. Western Economics is different from TCE because the TCE has a concept of Chi or Qi as a form of energy. From the energy concept, that one organ or subsystem of the economic society is not running properly (or disease, abnormal), is that the energy deviation from the average of the organ is too large, the high (real disease) or the low (virtual disease). But there do not exist these concepts of both real diseases and virtual diseases in Western science. For the normal range of a RPI inflation rate of some economic society as x [0.008789, 0.052241] , in TCE, if x  0.052241 , the economy is considered as a real disease since the RPI inflation rate is too high; if x  0.008789, the economy is considered as a virtual disease since the RPI inflation rate is too low. Thus TCE identifies an important indicator for an economic society's health: the value of the RPI inflation rate, which, under normal conditions, ranges from 0.008789 to 0.052241 . Outside this range (too low: Yin condition; too high: Yang condition), disease appears. Almost always absolutely, when there is a virtual disease, the condition of the RPI inflation rate is a Yin condition; when there is a real disease, the condition of the RPI inflation rate is a Yang condition. Remark 3. Obviously, when applying the hypothesis of Theorem 2.1 and Corollary 2.1 to other fields rather than economic society's health, it is necessary to identify a global parameter in each field that is able to yield a general Yin or Yang condition in relation to the average behavior of the studied phenomenon, and that maintains the equations at a sufficiently simple level of writing and application. In fact, let x  (min, max) where the values min and max are the minimum and maximum acceptable the index x . Denoted the value t0 is the target as the expectation of the index x such all near to the golden numbers. It is the idea to consider the unhealthy number 0  0.68232780 since the poor 3  1 / 2  0 / 2  0.34116390 can make the following condition of self-protection ability unhealthy balance conditions holding 1  3  3  0 / 2  0.34116390, 2  1 3  1 3  ( 0 ) 2 / 2  0.23278561 1  2 3  1   2 3 if 1  0 and 2  ( 0 )2  0.46557123 . By Theorem 2.1 and Corollary 2.1, the interval x [0.01,0.05] implies the following condition 1  1   ( x)  0.60899   (0.01)   (0.05) ; and the interval x [0.010552, 0.049013] implies the 1  1   ( x)     (0.010552)   (0.049013) ; and the interval x [0.008789, 0.052241] implies the following condition 1  1   ( x)  0   (0.008789)   (0.052241) , 1  0 where  (0.008789)   (0.052241)   02 since 2 0 following condition (1  03 )  ( 0  03 ) ; and the interval x [0.014201, 0.042994] implies the 1  1   ( x)  0   (0.014201)   (0.042994) , following condition where  (0.014201)   (0.042994)  1  0 ( 0 ) 2  2 0 2 since ( 0 )3  (1  0 ) . The last one is the healthy interval in an economic society's self-protection ability poor conditions. The interval range than the normal economic society health requirements is too strict. Only the first three interval ranges can be considered as a normal economic society health. If keep two decimal places, then first three intervals are the same as x [0.01,0.05] . This shows that range x [0.01,0.05] is stable. The interval as the normal range of a RPI inflation rate may be also appropriate. To conservative estimates, one of the first three interval ranges with the largest length is used, i.e., x [0.008789, 0.052241] , as the theoretical analysis of the normal range in this paper. In fact, the range x [0.008789, 0.052241] is better than the range x[0.01,0.05] because that  (t0 )  1 . In Eqs.(3) and (4), replace 0.08,0.6, 0.027047 by min, max, t0 , respectively. The 0  1   ( x)  1 equivalent condition of can a healthy economy be obtained as where x [u, v], min  u  t0  v  max,  (u)   (v)  0  1   ( x)  (1/ 2) /[( x)  (1/ 2)]   (t0 )  1 and  (t0 )  0   ( x)  (1   ( x)) / (2 ( x))  02   (u)   (v)   (u)2   (v)2  2   ( x)2  1   ( x)  1.# III. RELATIONS OF STEADY MULTILATERAL SYSTEMS 0   (0.008789)   (0.052241) 3.1. Energy Changes of a Multilateral System In order to apply the reasoning to other fields rather than society economy's health, Zhang etc [21] has started a steady multilateral system imitating society economy. A most basic steady multilateral system is as follows . and  (0.008789)   (0.052241)  1  0   2 , which 0 2 0 satisfy the healthy balance conditions 1  0 ,  2   and 3  c0 where c  1 . In other words, the or the range parameter 1   ( x)  0 x [0.008789, 0.052241] is the healthy condition of both which comes from the balance (1  2 3 )  ( 1  2 3 ) relationship if 1  2  1 . In other words, there is a 3 1  3 , 2  13 , 10 www.erpublication.org RPI 1% to 5% – Mathematical Reasoning of Economic Intervening Principle Based on Yin Yang Wu Xing Theory in Traditional Chinese Economics (II) Theorem 3.1 [20] For each element x in a steady multilateral system V with two incompatibility relations, there exist five equivalence classes below: to be the unseen vital force that nourishes steady multilateral systems’ economy and sustains steady multilateral systems’ life. It is also believed that an individual is born with an original amount of Chi at the beginning of steady multilateral systems’ life and as a steady multilateral system grows and lives, the steady multilateral system acquires or attains Chi or energy from “eating” and “drinking”, from “breathing” the surrounding “air” and also from living in its environment. The steady multilateral system having an energy is called the anatomy system or the first physiological system. And the first physiological system also affords Chi or energy for the steady multilateral system's meridian system (Jing-Luo (经络) or Zang Xiang (藏象) ) which forms a parasitic system of the steady multilateral system, called the second physiological system of the steady multilateral system. The second physiological system of the steady multilateral system controls the first physiological system of the steady multilateral system. A steady multilateral system would become ill or dies if the Chi or energy in the steady multilateral system is imbalanced or exhausted, which means that 1   ( x)  0, 2   ( x)2  0 and 3  c ( x)  0 . X  {y V | y ~ x}, X S  {y V | x  y}, X K  {y V | x  y}, K X  { y V | y  x}, S X  {y V | y  x}, which the five equivalence classes have relations in Figure 1. # It can be proved by Theorem 3.2 below that the steady multilateral system in Theorem 3.1 is the reasoning model of Yin Yang Wu Xing in TCE if there is an energy function  (*) satisfying  ( X K )   ( X S )   ( X )   ( K X )   (S X ). It is called Yin Yang Wu Xing model, denoted by V 5 . The Yin Yang Wu Xing model can be written as follows: Define V0  X ,V1  X S ,V2  X K ,V3  K X ,V4  S X , corresponding to wood, fire, earth, metal, water, respectively, and assume V  V0  V1  V2  V3  V4 where Vi  V j  , i  j . And take   {R0 , R1 , Rr   Vi  Vmod (i  r ,5) , r  {0,1, 4 i 0 , R4 } satisfying , 4}, Ri * R j  Rmod (i  j ,5) , For example, in TCE, a society economy as the first physiological system of the steady multilateral system following the Yin Yang Wu Xing theory was classified into five equivalence classes as follows: wood( X )={industry, PPI (the Producer Price Index) or RPI (Retail Price Index) , liver, bravery, soul, ribs, sour, east, spring, birth}; xiang-fire( X Sx )={agriculture, AAF (the total output value of where Vi  V j  {( x, y ) : x Vi , y V j } is the Descartes product in set theory and Ri * R j  {( x, y) : u V such that ( x, u)  Ri , (u, y)  R j } is the multiplication relation operation. The relation multiplication of * is isomorphic to the addition of module 5. Then V 5 is a steady multilateral system with one equivalent relation R0 and two incompatibility relations R1  R41 Agriculture forestry Animal husbandry and Fishery) , pericardium, the triple energizer, nerve, the blood, bitter taste, the south, summer, growth}; earth( X K )={ commerce, CPI (the Consumer Price Index), and R2  R31 where Ri1  {( x, y ) : ( y, x)  Ri } is the inverse operation. The Yin and Yang means the two incompatibility relations and the Wu Xing means the collection of five disjoint classification of V  V0  V1  V2  V3  V4 . spleen, stomach, willing, meat, sweetness, center, long summer, combined}; metal( K X )={science-education, GBR (the General Budget Figure 1 in Theorem 3.1 is the Figure of Yin Yang Wu Xing theory in Ancient China. The steady multilateral system V with two incompatibility relations is equivalent to the logic architecture of reasoning model of Yin Yang Wu Xing theory in Ancient China. What describes the general method of complex systems can be used in society complex systems. By non-authigenic logic of TCE, i.e., a logic which is similar to a group has nothing to do with the research object [20], in order to ensure the reproducibility such that the analysis conclusion can be applicable to any complex system, a logical analysis model which has nothing to do with the object of study should be chosen. The Tao model of Yin and Yang is a generalized one which means that two is basic. But the Tao model of Yin Yang is simple in which there is not incompatibility relation. The analysis conclusion of Tao model of Yin Yang cannot be applied to an incompatibility relation model. Thus the Yin Yang Wu Xing model with two incompatibility relations of Theorem 3.1 will be selected as the logic analysis model in this paper. Western Economy is different from TCE because the TCE has a concept of Chi or Qi (气) as a form of energy of steady multilateral systems. It is believed that this energy exists in all things of steady multilateral systems (living and non-living) including air, water, food and sunlight. Chi is said Revenue), lung, large intestine, boldness, fur, spicy, west, autumn, accept}; water( S X )={army-economic,GDP (the Gross Domestic Product), kidney, bladder, ambition, bone, salty, the north, winter, hiding}; jun-fire( X Sj )={President or Governor, Finance (right of making money), heart, small intestine, bitter taste, whole economy, throughout the year, overall growth}. jun-fire( X Sj ). fire( X S )= xiang-fire( X Sx ) There is only one of both loving and killing relations between every two classes. General close is loving, alternate is killing. In every category of internal, think that they are with an equivalent relationship, between each two of their elements there is a force of similar material accumulation of each other. It is because their pursuit of the goal is the same, i.e., follows the same “Axiom system”. It can increase the energy of the class at low cost near to zero if they accumulate together. Any nature material activity follows the principle of maximizing so energy or minimizing the cost. In general, the size of the force of similar material accumulation of each other is smaller than the size of the loving force or the killing force in a stable complex system. The stability of any complex system first 11 www.erpublication.org International Journal of Engineering and Technical Research (IJETR) ISSN: 2321-0869 (O) 2454-4698 (P) Volume-7, Issue-12, December 2017 needs to maintain the equilibrium of the killing force and the loving force. The key is the killing force. For a stable complex system, if the killing force is large, i.e., 3  c ( x) becomes larger by Theorem 3.3 below, which intervention on the first physiological system, the second physiological system is able to get food. Energy concept is an important concept in Physics. Zhang [17] introduces this concept to the steady multilateral systems or image mathematics [20] and uses these concepts to deal with the steady multilateral system diseases (mathematical index too high or too low). In mathematics, a steady multilateral system is said to have Energy (or Dynamic) if there is a non-negative function  (*) which makes every subsystem meaningful of the steady multilateral system. Similarly to Zhang [18], unless stated otherwise, any equivalence relation is the liking relation, any neighboring relation is the loving relation, and any alternate relation is the killing relationship. Suppose that V is a steady multilateral system having an energy, then V in the steady multilateral system during a normal operation, its energy function for any subsystem of the steady multilateral system has an average (or expected value in Statistics), this state is called as normal when the energy function is nearly to the average. Normal state is the better state. That a subsystem of the steady multilateral system is not running properly (or disease, abnormal) is that the energy deviation from the average of the subsystems is too large, the high (real disease) or the low (virtual disease). In addition to study these real or virtual diseases, TCE is also often considered a kind of relation diseases. The relation disease is defined as the relation of two sick subsystems. In general, a relation disease is less serious if the relation satisfies one of both the loving relationship and the killing relationship of the steady multilateral system. In this case, in general, the RPI inflation which means rate x [0.008789, 0.052241] needs positive exercise, then the loving force is also large such that the force of similar material accumulation of each other is also large. They can make the complex system more stable. If the killing force is small, i.e., 3  c ( x) becomes smaller by Theorem 3.3 below, which means little exercise, then the loving force is also small such that the force of similar material accumulation of each other is also small. They can make the complex system becoming unstable. The second physiological system of the steady multilateral system controls the first physiological system of the steady multilateral system, abiding by the following rules. Attaining Rule: The second physiological system of the steady multilateral system will work by using Attaining Rule, if the first physiological system of the steady multilateral system runs normally. The work is in order to attain the Chi or energy from the first physiological system of the steady multilateral system by mainly utilizing the balance of the loving relationship of the first physiological system. In mathematics, suppose that the economy of X is healthy. If X is intervened, then the second physiological system will attain the Chi or energy from X directly. Suppose that the economy of X is unhealthy. If X is intervened, then the second physiological system will attain the Chi or energy from X indirectly. If virtual X is intervened, it will attain the Chi or energy (Yang energy) from the son X S of . If real X is intervened, it will attain the Chi or energy (Yin energy) from the mother S X of X . # X 0  1   ( x)  1. This relation disease is less serious because Affording Rule: The second physiological system of the steady multilateral system will work by using Affording Rule, if the first physiological system of the steady multilateral system runs hardly. The work is in order to afford the Chi or energy for the first physiological system of the steady multilateral system, by mainly protecting or maintaining the balance of the killing relationship of the steady multilateral system, to drive the first physiological systems will begin to run normally. In mathematics, suppose that the economy of X is healthy. The second physiological system doesn’t afford any Chi or energy for the first physiological system. Suppose that the economy of X is unhealthy and the capability of self-protection is lack, i.e., 3  c ( x)  0 and 0  1   ( x)  0 . The second this relation disease can not undermine the loving order or the killing order of the steady multilateral system. The less serious relation disease can make the intervention increasing the sizes of both the intervention reaction coefficients 1 , 2 and the self-protection coefficient 3 . But the relation disease is more serious if the relation not only doesn’t satisfy the killing relationship of the steady multilateral system, but also can destroy the killing order, i.e., there is an incest order. In this case, in general, the RPI which inflation rate x[0.008789, 0.052241] means 0  1   ( x)  0 . This relation disease is more serious because the relation disease can destroy the killing order of the steady multilateral system if the disease continues to develop. The more serious relation disease can make both the intervention reaction coefficients 1 , 2 and the self-protection coefficient 3 decreasing response to physiological system will afford the Chi or energy for X directly, at the same time, affording the Chi or energy for other subsystem, in order to protect or maintain the balance of the killing relationship, abiding by the intervening principle of “Strong inhibition of the same time, support the weak”, such that the capability of self-protection is restored, i.e, 3  c ( x)  0 and 1  1   ( x)  0 , to drive the first intervention. There are also many relation diseases which cannot destroy the loving order or the killing order of the steady multilateral system although the relation doesn’t satisfy strictly the loving relationship or the killing relationship of the steady multilateral system, i.e., there is not an incest order. These relation diseases are called rare since they are hardly occurrence for a healthy economy. physiological system beginning to work.# The Chi or energy is also called the food hereafter for simply. In order to get the food, by Attaining Rule, the second physiological system must make the first physiological system intervened, namely exercise. It is because only by 12 www.erpublication.org RPI 1% to 5% – Mathematical Reasoning of Economic Intervening Principle Based on Yin Yang Wu Xing Theory in Traditional Chinese Economics (II) The purpose of intervention is to make the steady multilateral system return to normal state. The method of intervention is to increase or decrease the energy of a subsystem. What kind of intervening should follow the principle to treat it? Western mathematics emphasizes directly mathematical treatments on disease subsystem after the disease of subsystem has occurred, but the indirect intervening of oriental mathematics of TCE is required before the disease of subsystem will occur. In mathematics, which is more reasonable? Based on this idea, many issues are worth further discussion. For example, if an intervening has been implemented to a disease subsystem before the disease of subsystem will occur, what relation disease will be less serious which does not need to be intervened? what relation disease will be more serious which needs to be intervened? 3.2. Kinds of Relation Disease of Steady Multilateral Systems For a steady multilateral system V with two incompatibility relations, suppose that the subsystems X , X S , X K , K X , S X are the same as those defined in Theorem 3.1. Then the relation diseases can be decomposed into the following classes: Definition 3.1 (involving 相及 and infringing 相犯 ) Suppose that both X The relation disease between X serious if X X X X and X K is called more is a virtual disease but X K is a real disease at the same time. The more serious relation disease between X K is also called an insulting relation. It means that X X and has been harmed by X K through the method of incest. The relation disease between X and X K is called rare if is a real disease and so is X K at the same time, or if X X is a virtual disease and so is X K at the same time. The rare relation disease implies that they cannot destroy the killing order from X to X K although real X cannot kill real X K or virtual X cannot kill virtual X K . The relation disease between serious if KX X X , X K and K X is called more is a real disease, and X K is a virtual disease but is also a virtual disease at same time, i.e., not only real X multiplies in virtual X K , but also insults virtual K X by using the method of incest. It is because the energy of real X is too high. The more serious relation disease between X , X K , and is KX also called a multiplying-insulting 乘侮 relation. and X S having the loving relationship fall ill. Consider a relation disease occurred between XS . serious if The relation disease between The relation disease between and serious if and X S is called less SX is a virtual disease and so is X S at the same time. X X X , X K , and S X is called more is a real disease, and X K is a virtual disease but is also real disease at same time, i.e., not only real multiplies in virtual X K , but also real S X insults virtual X K The less serious relation disease between virtual X and virtual X S is also called a mother’s disease involving in her by using the method of incest. It is because the energy of virtual X K is too low. The more serious relation disease son. The mother is the cause of disease. The relation disease between X and X S is also called less between serious if X The less serious relation disease between real X and real X S is also called a son’s disease infringing upon its mother. X and X S is called rare if X is a real disease but X S is a virtual disease at the same time, or if X is a virtual disease but X S is a real disease at the same time. The rare relation disease implies that they cannot destroy the loving order although real X cannot love virtual X S or virtual X cannot love real X S .# Definition 3.2 (multiplying insulting 相侮 ) Suppose that both 相乘 X and and X K having 3.3 First Transfer Laws of Diseases of Steady Multilateral Systems with a healthy Economy the killing relationship fall ill. Consider a relation disease occurred between X and X K . The relation disease between serious if X X Suppose that a steady multilateral system V having energy function  (*) is normal or healthy. Let x be the RPI and X K is called less is a real disease and X K is a virtual disease at the same time. The less serious relation disease between and X K is also called a multiplying relation. , X K , and S X is also called a multiplying-insulting relation. Only the more serious relation disease can destroy the killing relationship order of the Yin Yang Wu Xing system. All the therapeutic principles need to prevent the more serious relation disease occurrence in the first place.# The disease of multiplying-insulting relation will result in more than three subsystems falling-ill. Generally, three or more subsystems falling-ill, it will be difficult to treat. Therefore, the multiplying-insulting relation disease should be avoided as much as possible. In Chinese words, it is that“Again and again, not only to the repeated to four” 只有再一再二，没有再三再四 -Allow one or two subsystems fall ill, but Don’t allow three or four subsystems fall ill. is a real disease and so is X S at the same time. The son is the cause of disease. The relation disease between X 3  c ( x) inflation rate of V . Taking X and where 1   ( x), 2   ( x)2 , 0  c  1 and  ( x) is defined in Eqs.(3) and (4). The healthy economy means that the conditions 0   ( x)  1 and 0  c  1 hold, which is 13 www.erpublication.org International Journal of Engineering and Technical Research (IJETR) ISSN: 2321-0869 (O) 2454-4698 (P) Volume-7, Issue-12, December 2017 x [0.008789, 0.052241] condition 1 +2 3  1  2 3 . That c  0 implies that equivalent to the normal the or range healthy All first transfer laws of diseases with a healthy complex system are summed up as Figures 2 and 3.# Remark 4. Theorem 3.2 is called the transfer law of occurrence and change of diseases with a healthy economy, simply, the first transfer law. For a real disease, the first transfer law is along the loving relationship order transmission as follows: the body is without the ability of self-protection, i.e., 3  c ( x)  0 . Of course, the body cannot be healthy. It is because for any x  0.027047, when c  0 , there are real X  real X S  virtual X K  virtual K X  real S X  real X . For a virtual disease, the first transfer law is against the loving relationship order transmission as follows: less 1 +2 3 = ( x)  c ( x)3   ( x)  1  1  c ( x)3  1  2 3 , such that the healthy condition 1 +2 3  1  2 3 cannot less conditions 0  1   ( x)  1 and 0  c  1 . In this case, almost always, the less serious relation disease will occur and change. If the disease continues to develop, the change can make a more serious relation disease occur. The occurrence and change of diseases with a healthy economy has its transfer law: The first occurrence and change of the loving relationship and the killing relationship after the loving relationship disease. In other words, the following statements are true. (1).If a subsystem X of a steady multilateral system V falls a virtual disease, the transfer law is the first occurrence of the virtual disease of the mother S X of X with a less serious relation real disease of the bane K X of X X virtual X X the best state of X secondly the virtual disease of the prisoner X K of X to disease of the bane K X of X X disease of the mother S X of X , and after the c  1 , implies the non-existence of any side effects issue if the treatment principle of TCE is used. Therefore any disease that causes side effects issue occurrence in the first place dues to the non-best state of self-protection ability, i.e., 3  c ( x)   ( x)   .To follow or utilize the , and fourthly the real running of the first transfer law can make both  ( x)  1 and 0  c  1 . At this point, the paper advocates to follow or utilize the first transfer law. It is in order to avoid the side effects issue occurrence for the healthy economy. # with a less serious relation disease between real S X and real X 1   ( x) the greater the use. In other words again, if Side effects of treating problems were the question: in the treating process, destroyed the balance of the normal subsystems which are not sick or intervened systems. The energy change of the intervened system is not the true side effects issue. The energy change is called the pseudo or non-true side effects issue since it is just the food of the second physiological system of the steady multilateral system for a healthy economy. The best state of the self-protection coefficient, 3  c ( x)   ( x)   , where with a more serious relation X for a healthy economy. self-protection , and thirdly the virtual disease between virtual K X and real 3 3  c ( x) where c  1 which is 3  c ( x)  0 where 0  c  1 will tend to be the best state, i.e.,  ( x)  1 and 0  c  1. # X real disease of X S with a less serious relation disease between virtual X K and real less the treatment principle of the loving relationship disease is to use continuously abiding by the first transfer law, then all of both the intervention reaction coefficients 2 1   ( x), 2   ( x) and the coefficient of virtual X , and finally the new remission virtual disease of the subsystem X itself, and for the next round of disease transmission, until disease rehabilitation. (2).If a subsystem X of a steady multilateral system V encounters a real disease, the transfer law is the first occurrence of the real disease of the son X S of X with a less X rare tending to be small at the same time. In other words, the way can make all of both  ( x) and c tending to be large. It is because the running condition of the loving relationship ( 1  2 3 )  (1  2 3 ) is the stronger the use, which dues with a less serious relation disease between virtual X S and serious relation disease between real X S and real more tending to be large and the value (1  2 3 )  (1  c  ( x)3 ) , and thirdly the real disease of the prisoner X K of , and fourthly the virtual disease of the son X S of less To follow or utilize the running of the first transfer law is equivalent to the following method. For dong so, it is in order to protect or maintain the loving relationship. The method can strengthen both the value ( 1  2 3 )  (  ( x)  c ( x)3 ) with a more serious relation disease between real X K and virtual rare of the first transfer law is after the virtual disease of a less serious relation disease between real K X and rare and Corollary 2.1, the running condition is nearly equivalent to both 0  1   ( x)  1 and 0  c  1. The best-state condition , and secondly the S X with more virtual X  virtual S X  real K X  real X K  virtual X S  virtual X . The transfer relation of the first transfer law running is the loving relationship, denoted by  . The running condition of the first transfer law is both (1  2 3 )  (1  2 3 ) and 3  c ( x)  0 . By Theorem 2.1 hold. By using Corollary 2.1 and Theorems 2.1 and 3.1, the following Theorem 3.2 can be obtained as the transfer law of occurrence and change of diseases with a healthy economy. Theorem 3.2 Let the RPI inflation rate x [0.008789, 0.052241] which is equivalent to the disease between virtual S X and virtual rare , and finally the new abated real disease of the subsystem X itself, and for the next round of disease transmission, until disease rehabilitation. 14 www.erpublication.org RPI 1% to 5% – Mathematical Reasoning of Economic Intervening Principle Based on Yin Yang Wu Xing Theory in Traditional Chinese Economics (II) between real X S X and virtual X K , and finally the new abated 3.4 Second Transfer Laws of Diseases of Steady Multilateral Systems with an unhealthy Economy real disease of the subsystem X itself with a less serious relation disease between virtual X K and real X , and for the Suppose that a steady multilateral system V having energy function  (*) is abnormal or unhealthy. Let x be the RPI next round of disease transmission, until disease rehabilitation. All second transfer laws of diseases with an unhealthy economy are summed up as Figures 4 and 5.# Remark 5. Transfer law of Theorem 3.3 is called transfer law of occurrence and change of diseases with an unhealthy economy, simply, the second transfer law. For a virtual disease, the second transfer law is along the killing relationship order transmission as follows: 1   ( x), 2   ( x)2 and 3  c ( x) where 0  c  1 , and  ( x) is defined in inflation rate of V . Taking Eqs.(3) and (4). The unhealthy economy means that the conditions 0  1   ( x)  0 and 0  c  1 hold, which is equivalent to the abnormal range x[0.008789, 0.052241] . From [20] and by using Corollary 2.1 and Theorems 2.1 and 3.1, the following Theorem 3.3 can be obtained as the transfer law of occurrence and change of diseases with an unhealthy economy. Theorem 3.3 Let the RPI inflation rate x [0.008789, 0.052241] which is equivalent to the conditions virtual X  virtual X K  virtual S X  virtual X S  real K X  virtual X . rare rare rare more less For a real disease, the second transfer law is against the killing relationship order transmission as follows: real X  real K X  real X S  real S X  virtual X K  real X . rare rare rare more less The transfer relationship of the second transfer law running is the killing relationship, denoted by  . The running condition of the second transfer law is both ( 1  2 3 )  (1  2 3 ) and 3  c ( x)  0 . 0  1   ( x)  0 and 0  c  1. In this case, almost always, the rare relation disease will occur and change. If the disease continues to develop, the change can make a more serious relation disease occur. The transfer of disease with an unhealthy economy has its transfer law: Only there is the transfer of the killing relationship. In other words, the following statements are true. (1).If a subsystem X of a steady multilateral system V falls a virtual disease, then the disease comes from the son X S of X . By Theorem 2.1 and Corollary 2.1, the running condition is equivalent to both 0  1   ( x)  0 and 1  c  0 . That 3  c ( x)  0 means the lack of capability of self-protection. Of course, it is the basis condition of running the second transfer law. The stopping condition of the second transfer law is both ( 1  2 3 )  (1  2 3 ) and 3  c ( x)  0 , which is the The transfer law is the first occurrence of the virtual disease of the prisoner X K of X with a rare relation disease between running condition of the first transfer law, or, the existence condition of capabilities of both intervention reaction and self-protection. To follow or utilize the running of the second transfer law is equivalent to the following method. For dong so, it is to protect and maintain the killing relationship of the steady multilateral system. The method can strengthen all of both 1  3   ( x)(1  c) and 2  13   ( x)2 (1  c) virtual X and virtual X K , and secondly the virtual disease of the mother S X of X after the virtual disease of X K with a rare relation disease between virtual X K and virtual S X , and thirdly the virtual disease of the son X S of X with a rare relation disease between virtual X S and real K X , and finally the new tending to be small at the same time. In other words, using the method can make c tends to be large for a fixed  ( x)  0. It is because the transferring condition of the killing relation disease ( 1  2 3 )  (1  2 3 ) is the weaker the use, which remission virtual disease of the subsystem X itself with a less serious relation disease between real K X and virtual X , and for way can make both disease between virtual S X and virtual X S , and fourthly the real disease of the bane K X of X with a more serious relation dues to 3  c ( x) is the greater the use. The transferring the next round of disease transmission, until disease rehabilitation. (2).If a subsystem X of a steady multilateral system V falls a real disease, then the disease comes from the mother S X of X . time such that the killing relation disease cannot be transferred. In other words again, if the treatment principle of the killing relationship diseases is to use continuously abiding by the second transfer law, then the coefficient of self-protection will tend to be the occurrence state, i.e., 3  c ( x)  0 where 1  c  1   ( x)  0 , and the 2  ( x )3 coefficients of intervention reaction also will tend to the healthy state, i.e., 0  1   ( x)  1 , such that The transfer law is the first occurrence of the real disease of the bane K X of X with a rare relation disease between real X 1  3  0 and 2  13  0 at the same and real K X , and secondly the real disease of the ( 1  2 3 )  (1  2 3 ) .# Medical and drug resistance problem is that such a question: beginning more appropriate medical treatment, but is no longer valid after a period. In the state 1  3   ( x)(1  c)  0，2  13   ( x)2 (1  c)  0 , by son X S of X after the real disease of the bane K X of X with a rare relation disease between real K X and real X S , and thirdly the real disease of the mother S X of X with a rare relation disease between real X S and real S X , and fourthly the virtual disease of the prisoner X K of X with a more serious relation disease Theorem 3.2, any medical and drug resistance problem is 15 www.erpublication.org International Journal of Engineering and Technical Research (IJETR) ISSN: 2321-0869 (O) 2454-4698 (P) Volume-7, Issue-12, December 2017 For the unhealthy economy where x  a or x  b , the treatment principle is the method for doing so in the following: The primary treatment is to increase or decrease the energy of X directly corresponding to x  a or x  b respectively, and the secondary treatment is to increase the energy of X S or X K while to decrease the energy non-existence if the treatment principle of TCE is used. But in the state 1  3   ( x)(1  c)   ( x)，2  13   ( x)2 (1  c)   ( x) , by Theorem 3.3, the medical and drug resistance problem is always existence, even if the treatment principle of TCE has been used. In other words, the lack of capability of self-protection, i.e., 3  c ( x)  0 , implies the possible existence of a medical and drug resistance problem, although the treatment principle of TCE has been used. At this point, the paper advocates to follow or utilize the second transfer law. It is in order to prevent and avoid the medical and drug resistance problem occurrence for the unhealthy economy.# of K X or S X , respectively.# The primary treatment is in order to protect and maintain the loving relationship, abiding by TCE's ideas “Virtual disease with an unhealthy economy is to fill itself” and “Real disease with an unhealthy economy is to rush down itself”. It is because the method for dong so is not only greatly medical diseases of their own, but also provides the pseudo side effects as the food for the second physiological system. The method is to promote the first physiological system running since the second physiological system controls the first physiological system. And it is also to improve the loving relationship to develop since the loving relationship mainly comes from the first physiological system. The loving relationship to develop can strengthen both that 1  2 3   ( x)  c ( x)2 tends to be large and that IV. TREATMENT PRINCIPLE OF TCE In order to explain treatment principle of TCE, the changes in the RPI inflation rate range can be divided into four parts. From [20] , Corollary 2.1 and Theorems 2.1, 3.2 and 3.3, it can be easily proved that the following theorem is true. Theorem 4.1 Suppose that the subsystem X of a steady multilateral system falls ill. Let x be the RPI inflation rate of the steady multilateral system. Denoted the parameters of the normal range as follows a  0.008789, b  0.052241, t0  0.027047. Then the following statements are true. (1) Suppose that x  a as virtual, in which X falls a virtual disease with an unhealthy economy. The primary treatment is to increase the energy of the subsystem X directly. And the secondary treatment is to increase the energy of the son X S of X , and at the same time, to decrease the energy of the 1  2 3  1  c ( x)3 tends to be small at the same time. In other words, the way can make all of both  ( x) and c tend to be large, at least, c greater than zero for an unhealthy economy and 0   ( x)  1 , such that the economy from unhealthy to healthy, or the first physiological system works, or, the occurrence of capability of self-protection, or, the running of the first transfer law, or, the stopping of the second transfer law. The secondary treatment is in order to protect or maintain the killing relationship, abiding by TCE's ideas “Don’t have disease cure cure non-ill” and “Strong inhibition of the same time, support the weak”. By the second transfer law in Theorem 3.3, the more serious relation disease is the relation disease between virtual X S and real K X , or between real S X and prisoner K X of X S . (2) Suppose that x  [a, t0 ) as virtual-normal, in which X will fall a virtual disease with a healthy economy. The primary treatment is to increase the energy of the mother subsystem S X of X which is an indirect treating for X . And the secondary treatment is to increase the energy of X itself, and at the same time, to decrease the energy of the prisoner X K of X . (3) Suppose that x [t0 , b] as real-normal, virtual X K respectively. Abiding by TCE's idea ‘Strong inhibition of the same time, support the weak”, it must be done to increase the energy of X S or X K while decrease the energy of K X or S X in which X will encounter a real disease with a healthy economy. The primary treatment is to decrease the energy of the son subsystem X S of X which is an indirect treating for X . And the respectively. Abiding by TCE's idea “Don’t have disease cure cure non-ill”, it must be done to prevent or avoid the more serious relation disease between virtual X S and real K X , or between secondary treatment is to decrease the energy of X itself, and at the same time, to increase the energy of the bane K X of X . (4) Suppose that x  b as real, in which X encounters a real disease with an unhealthy economy. The primary treatment is to decrease the energy of the subsystem X directly. And the secondary treatment is to decrease the energy of the mother S X of X , and at the same real S X and virtual X K occurrence respectively. The method for doing so can improve the killing relationship to develop since real X S or X K can kill virtual K X or S X respectively. The killing relationship to develop means that both 1  3   ( x)(1  c) and 2  13   ( x)2 (1  c) tend to be small at the same time. In other words, the way can make, for fixed  ( x) , c tending to be large, at least, greater than zero for an unhealthy economy, such that the economy from unhealthy to healthy, or the first physiological system works, or, the occurrence of capability of time, to increase the energy of the bane X K of S X . # Remark 6. Treatment principle of Theorem 4.1 based on ranges of the RPI inflation rate is called the treatment principle of TCE, since it is in order to protect and maintain the balance of two incompatibility relations: the loving relationship and the killing relationship. 16 www.erpublication.org RPI 1% to 5% – Mathematical Reasoning of Economic Intervening Principle Based on Yin Yang Wu Xing Theory in Traditional Chinese Economics (II) self-protection, or, the running of the first transfer law, or, the stopping of the second transfer law. For the healthy economy where x  [a, t0 ) or best state, or, the non-existence of side effects, or, the non-existence of medical and drug resistance issue. # so in the following: The primary treatment is to increase or decrease the energy of S X or X S corresponding to x  (a, t0 ] or Suppose that M 2 as issued in the circulation of money and GDP x [t0 , b] , the treatment principle is the method for doing V. CHINESE RPI FOR THE WOOD SUBSYSTEM as Gross Domestic Product in Chinese from 1990 to 2014, the annual RPI and the annual RPI inflation rate can be measured in Table 1. Also watching Table 1, the state of the RPI inflation rate is: real, real, real, real, real, real-normal, for 1991-1996, respectively.During this period of time, large-scale goods have been made. It means that the subsystem wood( X ) of the economic social system with an unhealthy economy encounters a real economic disease since the RPI inflation rate belongs to “industry” of wood( X ). Also watching Table 1, the state of the GBR inflation rate is:virtual, virtual-normal, real, real-normal, real-normal, real-normal, for 1991-1996, respectively. x [t0 , b] respectively, and the secondary treatment to increase the energy of K X or X while to decrease the energy of X or X K , respectively.# The primary treatment is in order to protect and maintain the loving relationship, abiding by TCE's ideas “Virtual disease with a healthy economy is to fill mother” and “Real disease with a healthy economy is to rush down its son”. It is because the method for dong so is not only greatly medical diseases of their own, but also provides the pseudo side effects as the food for the second physiological system. The method is to promote the first physiological system running since the second physiological system controls the first physiological system. And it is also to improve the loving relationship developing since the loving relationship mainly comes from the first physiological system. The loving relationship developing can strengthen both that 1  2 3   ( x)  c ( x)2 tends to be large and that It means that the subsystem metal( K X ) of the economic social system with a healthy economy encounters an expected real economic disease since the GBR inflation rate belongs to “science,education, and public facilities” of metal( K X ). There are two subsystems wood( X ) and metal( K X ) which 1  2 3  1  c ( x) tends to be small at the same time. In other words, using the way can make all of both  ( x) and have the killing relationship and fall a real disease or an expected real disease. By Definition 3.2, the relation 0  c tending to be large, the best, all equal to 1 for a economic disease is rare because real-normal metal( K X ) cannot kill real wood( X ) which cannot destroy the balance of healthy economy, such that the capability of self-protection is in the best state, or, the non-existence of side effects issue, or, the non-existence of medical and drug resistance problem. The secondary treatment is in order to protect or maintain the killing relationship, abiding by TCE's ideas “Don’t have disease cure cure non-ill” and “Strong inhibition of the same time, support the weak”. By the first transfer law, the more serious relation disease is the relation disease between real X and virtual K X or between virtual X and real X K corresponding to real X or virtual X the killing relation from metal( K X ) to wood( X ). If metal( K X ) is intervened such that it is from real to virtual, then there is a more serious disease to occur since virtual metal( K X ) cannot kill real wood( X ). Thus the mainly root-cause is the real disease of the subsystem wood( X ). So, at present the most serious problem is to treat the subsystem wood( X ) falling a real disease for an unhealthy sub-economy. It is the case in (4) of Theorem 4.1 for wood( X ). By (4) of Theorem 4.1 again, the primary treatment is gotten to decrease the energy of the subsystem wood( X ) directly. And the secondary treatment is gotten to decrease the energy of the mother water( S X ) of wood( X ), and at the same , respectively. Abiding by TCE's idea “Don’t have disease cure cure non-ill”, it must be done to prevent and avoid the more serious relation disease between real X and virtual K X or between virtual X and real X K occurrence corresponding to real X or time, to increase the energy of the bane earth( X K ) of virtual X respectively. Abiding by TCE's idea “Strong inhibition of the same time, support the weak”, it must be done to increase the energy of K X or X while decrease the energy of X or X K respectively. water( S X ). In fact, the Chinese government did just that. For 1993-1999, not only had decreased gradually the financial amounts of investment in the manufacture (to decrease the energy of the subsystem wood( X ) directly), but also had decreased investment in the Army , such as, big disarmament, a freeze on a large number of military engineering, etc. (for decreasing the energy of water( S X )) while had increased little The method for doing so can improve the killing relationship developing since real K X or real X can kill virtual X or virtual X K respectively. The killing relationship developing also means that both 1  3   ( x)(1  c) and 2  13   ( x)2 (1  c) tend to be small at the same time. by little the workers’ wages, the social security and social welfare, such as, the public accumulation fund for housing construction, pension funds, medical insurance, unemployment insurance, etc.(to increase the energy of earth( X K )). In other words, using the way can make, for fixed  ( x) , 0  c tending to be large, the best, equal to 1 for a healthy economy, such that the capability of self-protection is in the 17 www.erpublication.org International Journal of Engineering and Technical Research (IJETR) ISSN: 2321-0869 (O) 2454-4698 (P) Volume-7, Issue-12, December 2017 Also watching Table 1, the state of the RPI inflation rate is: virtual, virtual, virtual, real-normal, virtual, virtual, virtual-normal, for 1997-2003, respectively. During this period of time, mass goods cannot be made. Supplies are still scarce. Rush on still appear on the market. It means that the subsystem wood( X ) falls a virtual disease for an unhealthy economy since the RPI inflation rate belongs to the “industry” of wood( X ). But also watching Table 1, the state of the CPI inflation rate is virtual-normal, virtual, virtual, virtual, virtual, virtual, virtual, for 1997-2003, respectively. It means that the subsystem earth( X K ) of the economic It means the subsystem wood( X ) is mainly with a healthy sub-economy. It is because the manufacture of large-scale goods or the normal RPI inflation rate belongs to“industry” of the subsystem wood( X ). But the Finance inflation rate is continuously smaller than a 6  2.9515% (deflation) from 2004 to 2008 as virtual, except for 2005 year's normal state. It means the whole economy still is unhealthy. Its some subsystem still has encountered a virtual disease. Observation of the whole economic and social five subsystems, it can be found that there is a virtual disease state of the subsystem earth( X K ). There are two subsystems wood( X ) and earth( X K ) which social system with an unhealthy economy encounters a virtual economic disease since the CPI inflation rate belongs to“commerce” of earth( X K ). have the killing relation. But the subsystem wood( X ) is real-normal and the subsystem earth( X K ) falls a virtual There are two subsystems wood( X ) and earth( X K ) which disease. By Definition 3.2, the relation disease between real wood( X ) and virtual earth( X K ) is less since real wood( X ) can have the killing relation and fall virtual diseases. By Definition 3.2, the relation disease between virtual wood( X ) and virtual earth( X K ) is rare since virtual wood( X ) cannot kill virtual earth( X K ) which cannot destroy the killing order from wood( X ) to earth( X K ). Now the subsystem earth( X K ) kill virtual earth( X K ) which cannot destroy the killing order can be intervened such that it is from virtual to real-normal. So, at present the most serious problem is to treat the subsystem earth( X K ) falling a virtual disease for an unhealthy from wood( X ) to earth( X K ). But if the subsystem earth( X K ) is intervened such that it is from virtual to real, there is a more serious relation disease between virtual wood( X ) and real earth( X K ). It is because the virtual wood( X ) cannot kill the sub-economy of earth( X K ). It is the case in (1) of Theorem 4.1 for earth( X K ). real earth( X K ) which can destroy the balance of the killing The X K as relation from wood( X ) to earth( X K ). in theorem 4.1, using (1) of Theorem 4.1 again, the primary treatment is gotten to increase the energy of the subsystem earth( X K ) directly. And the secondary treatment is So, at present the most serious problem is to treat the subsystem wood( X ) falling a virtual disease for an unhealthy sub-economy. It is the case in (1) of Theorem 4.1 for wood( X ). By (1) of Theorem 4.1, the primary treatment is gotten to increase the energy of the subsystem wood( X ) directly. And the secondary treatment is gotten to increase the energy of the gotten to increase the energy of the son metal( K X ) of earth( X K ), where ( X K )S  K X in Figure 1, and at the same time, to decrease the energy of the bane wood( X ) of earth( X K ),where K ( X )  X in Figure 1. K In fact, the Chinese government did just that. For 2004-2014, not only had increased the financial amounts of investment in commerce, such as, strengthen the support for the WTO trade, etc. (to increase the energy of the subsystem earth( X K ) directly), but also had increased investment in son fire( X S ) of wood( X ), and at the same time, to decrease the energy of the prisoner metal( K X ) of fire( X S ). In fact, the Chinese government did just that. For 1999-2008, not only had increased gradually the financial amounts of investment in the manufacture (e.g.,to invest in real estate, to increase the energy of the subsystem wood( X ) directly), but also had increased to make money, and investment in the agriculture, such as, exempt from the agricultural taxation, increase of agricultural land expropriation compensation, etc. (to increase the energy of j X science, education and public facilities, such as to build high speed rail, etc. (to increase the energy of metal( K X )) while had reduced the industrial support, such as, the appreciation of the RMB, etc. (to decrease the energy of wood( X )). Therefore, again application of nature for the treatment principle of TCE by the Chinese government had brought the 2004-2014 economic taking off again. Also watching Table 1 again and again, the state of the RPI inflation rate is: virtual, virtual, virtual, for 2012-2014, respectively. It means that the the subsystem wood( X ) is a happen virtual disease for an unhealthy sub-economy. It is because the manufacture of large-scale goods or the RPI inflation rate belongs to“industry” of the subsystem wood( X ). The virtual disease of wood( X ) is not because of its low energy, but because of its energy is too high to make producing products too much, so much so that there is no way to sell products, low profit of industrial production. In the TCE, this disease is Yang irritability turned to deficiency x fire( X S ) including jun-fire( X S ) and xiang-fire( X S )) while had decreased in the science and education, such as, a small amount of teachers and researchers for a raise, schools and research institutions self-sustaining, etc.(to decrease the energy of metal( K X )). Therefore, application of nature for the treatment principle of TCE by the Chinese government had brought the sustained and rapid growth of industry economy for 1991-2008. Also watching Table 1 again, the state of the RPI inflation rate is: real, real-normal, real-normal, real-normal, real, virtual, real-normal, real, for 2004-2011, respectively. During this period of time, large-scale goods have been still made. But a lot of society problems begin occurring. 18 www.erpublication.org RPI 1% to 5% – Mathematical Reasoning of Economic Intervening Principle Based on Yin Yang Wu Xing Theory in Traditional Chinese Economics (II) disease. This disease is not the current urgent problems since it cannot destroy the killing order balance of the economy. But if this virtual-normal disease of wood( X ) is continuously to develop, by Theorems 3.2 and 3.3, the virtual wood( X ) will make its mother subsystem water( S X ) falling a comes from the first transfer law in Theorem 3.2. And both first and fourth are for an unhealthy economy with a virtual or real disease respectively. The treating works are the prevention or treatment for a more serious relation disease between virtual X S and real K X or between virtual X K and virtual economic disease when it encounters an economic disease. In fact, the economic indicators of GDP which belongs to the subsystem water( S X ) is beginning to decline. real S X respectively. Each of both more serious relation diseases comes from the second transfer law in Theorem 3.3. Economic disease treatment should protect and maintain the balance or order of two incompatibility relations: the loving relationship and the killing relationship. The method for doing so can make the 3  c ( x) tending to be large. Abiding by TCE's idea “Don’t have economic disease cure cure non-ill”, the prevention and treatment of the current work is the need to prevent the virtual disease of the subsystem water( S X ) for a healthy economy. In other words, using the method can make all of both  ( x) and c tend to be large, at least, greater than zero for an unhealthy economy; or, the best, equal to 1 for a healthy economy. The following way can make the capabilities of both intervention reaction and self-protection become in the best state, the non-existence of side effects issue, the non-existence of medical and drug resistance problem, and so on. (1) Suppose that x  a  0.8789%, as virtual, in which X falls a virtual disease with an unhealthy economy. In order to protect or maintain the loving relationship, abiding by TCE's idea “Virtual disease with an unhealthy economy is to fill itself” (虚则补之) , increase the energy of X directly. In order to protect or maintain the killing relationship, abiding by TCE's idea “Don’t have disease cure cure non-ill” (不治已病治未病) , do a preventive treatment for the more So, at present the most serious problem is to treat the subsystem water( S X ) falling a virtual disease with a healthy sub-economy of the subsystem of the subsystem water( S X ) . It is the case in (2) of Theorem 4.1 for water( S X ). The S X as X in (2) of Theorem 4.1, the primary treatment is gotten to increase the energy of the mother subsystem metal( K X ) of the water( S X ), where S( S )  K X in Figure 1. And the secondary treatment is gotten to increase the energy of the water( S X ) itself while decrease the energy of the X prisoner fire( XS ) of the water( S X ) ,where (S X ) K  X S in Figure 1. In fact, the Chinese government also is doing just that. Since 2015, not only has increased continuously investment in science, education and public facilities, such as, One Belt and One Road, etc. ( for increasing the energy of metal( K X )), but serious relation disease between virtual X S and real K X . Through the intervening principle of “Strong inhibition of the same time, support the weak” (抑强扶弱) , increase the also has increased to military spending (to increase the energy of the water( S X )) while has reduced the number of making energy of the son X S of the energy of fire( xiang-fire( x XS ) XS ) including jun-fire( (2) Suppose that a=0.8789%  x  t0  2.7047%, as virtual-normal, in which X will fall a virtual disease with a healthy economy. In order to protect and maintain the loving relationship, abide by TCE's idea “Virtual disease with a healthy economy is to fill its mother” (虚则补其母) , increase ) and ). Therefore, again and again application of nature for the treatment principle of TCE by the Chinese government will lead to economic continue to glory since 2015.# the energy of the mother S X of X . The treating way is an indirect treating for X . In order to protect and maintain the killing relationship, abiding by TCE's idea“Don’t have disease cure cure non-ill” (不治已病治未病) , do a preventive treatment for the more serious relation disease between virtual X and real XK . VI. CONCLUSIONS This work shows how to treat the diseases of a economic society by using the RPI inflation rate x .For the RPI inflation rate, the normal range of theory is [0.8789%,5.2241%] nearly to [1%,5%] , and the center is 2.7047% nearly to 3% . The first or second transfer law of economic diseases changes according to the different economic society's RPI inflation rate whether in the normal range or not. For the normal range, the first transfer law in Theorem 3.2 runs; For the abnormal range, the second transfer law in Theorem 3.3 runs. Assume that the range of economic society's RPI inflation rate x is divided into four parts from small to large. Both second and third are for a healthy economy with a virtual or real disease respectively. The treating works are the prevention or treatment for a more serious relation disease between virtual X and real X K or between virtual K X and real X while decrease the energy of the prisoner K X of X S . money, and reduced the agricultural support, such as, reduce the purchase price of agricultural products, etc. (to decrease j XS X Through the intervening principle of “Strong inhibition of the same time, support the weak” (抑强扶弱) , increase the energy of X itself while decrease the energy of the prisoner X K of X . (3) Suppose that t0 =2.7047%  x  b  5.2241%, as real-normal, in which X will encounter a real disease with a healthy economy. In order to protect or maintain the loving relationship, abiding by TCE's idea “Real disease with a healthy economy is to rush down its son” (实则泄其子) , decrease the energy of the son X S of an indirect treating for X . respectively. Each of both more serious relation diseases 19 X . The treating way is www.erpublication.org International Journal of Engineering and Technical Research (IJETR) ISSN: 2321-0869 (O) 2454-4698 (P) Volume-7, Issue-12, December 2017 d  ( x) ( x  min)(max  x)  (t0  x)[(max  x)  ( x  min)]  [( x  min)(max  x)]2 dx A ( x  min)(max  x)  (t0  x)[(max  x)  ( x  min)]  [( x  min)(max  x)]2 [( x  min)(max  t0 )  (t0  x)(max  x)]   0. [( x  min)(max  x)]2 In order to protect or maintain the killing relationship, abiding by TCE's idea “Don’t have disease cure cure non-ill” (不治已病治未病) , do a preventive treatment for the more serious relation disease between real X and virtual KX . Through the intervening principle of “Strong inhibition of the same time, support the weak” (抑强扶弱) , decrease the energy of X . (4) Suppose that x  b  5.2241%, as real, in which X encounters a real disease with an unhealthy economy. In order to protect or maintain the loving relationship, abiding by TCE's idea “Real disease with an unhealthy economy is to rush down itself” (实则泄之) , decrease the energy of X directly. In order to protect or maintain the killing relationship, abiding by TCE's idea “Don’t have disease cure cure non-ill” (不治已病治未病) , do a preventive treatment for the X  ( x)  ( x) And Through the intervening principle of “Strong inhibition of the same time, support the weak” (抑强扶弱) , decrease the This article has been repeatedly invited as reports, such as People's University of China in medical meetings, Shanxi University, Liaocheng University, Xuchang College, and so on. The work was supported by Specialized Research Fund for the Doctoral Program of Higher Education of Ministry of Education of China (Grant No. 200802691021).  ( x) 1/ 2 1   ( x)    ( x)  . 1   ( x)  ( x) 2  ( x) If x  min or x  max , then  ( x)  0. If x  t0 , then  ( x)   ,  ( x)  0 , and Thus and  ( x)  1. 0   ( x)  1 0   ( x)   will be equivalent to each other. It is because  ( x) is a monotone decreasing function of x if and  ( x) x  (min, t0 ]  ( x)  (0,1] since is a monotone decreasing function of if monotone decreasing function h(  ( x))   ( x)  ( x) is from dh(  ( x)) 1  (1)  ( x) 2  (1   ( x))[2  ( x)]   ( x)  2    0.  3  ( x) 4 d  ( x) 2  2  ( x) Furthermore, there is 1  0  ( x) 1   ( x)   1  ( x) 2 2  ( x)3 2  03 since h(  ( x))   ( x ) is a monotone decreasing  ( x) 2 function of  ( x) where 0  0   ( x) .The proof of the monotone decreasing function h(  ( x))   ( x )  ( x) 2 is from x  (min, t0 ] or a monotone increasing function of x if x [t0 , max) ; and  ( x) is a monotone decreasing function of  ( x) if  ( x) [0, ) ; and  ( x) is a monotone decreasing function of  ( x) if  ( x)  (0,1] . In fact,  ( x) monotone decreasing function of  ( x) where 0  0   ( x) . Similarly,there is 1  0 1   ( x)  ( x)    0   ( x)  ( x) 2  ( x) 2 2  02 since h(  ( x))   ( x) is a monotone decreasing  ( x) function of  ( x) where 0  0   ( x) . The proof of the Proof of Theorem 2.1. Let min  0.08, max  0.6, t0  0.027047. (1) Firstly, from Eqs.(3) and (4), by equal ratio theorem,  since then f (  ( x))  (  ( x)   ( x)3 )  (1   ( x)3 )  f ( 0 )  0 because of monotonicity of f . Thus 1   ( x)   ( x) 2 . 2  ( x) By the result of (1), there is 1   ( x) 1  0 2 2 since is a  ( x )  ( x)     0   ( x) 2  ( x) 2 0 APPENDIX 1/ 2  ( x) [0, ) (2). Let the function f (u)  (u  u3 )  (1  u3 ), u  (0,1] . Then f (u) is a monotone increasing function of u since f (u)  1  6u 2  0 . On the other hand, from [20], there is f ( 0 )  ( 0  03 )  (1  03 )  0 . Hence, if  ( x)  0 , ACKNOWLEDGEMENTS  ( x)  1/ 2 if 1  (1)  ( x)  (1   ( x))[1]  d  ( x) 1    0.  2 d  ( x) 2   ( x) 2  2  ( x) while increase the energy of the bane X K of S X .  ( x)  since d  ( x) (1 / 2)[1] 1    0. d  ( x) [ ( x)  1 / 2]2 2[ ( x)  1 / 2]2 more serious relation disease between real S X and virtual X K . X is a monotone increasing function of x if d  ( x) ( x  min)(max  x)  ( x  t0 )[(max  x)  ( x  min)]  [( x  min)(max  x)]2 dx ( x  min)(max  x)  ( x  t0 )[(max  x)  ( x  min)]  [( x  min)(max  x)]2 [(max  x)(t0  min)  ( x  t0 )( x  min)]   0. [( x  min)(max  x)]2 And  ( x) is a monotone decreasing function of itself while increase the energy of the bane K X of energy of the mother S X of  ( x) x [t0 , max) nd is a monotone decreasing function of x if since 20 www.erpublication.org RPI 1% to 5% – Mathematical Reasoning of Economic Intervening Principle Based on Yin Yang Wu Xing Theory in Traditional Chinese Economics (II) | g (u ) || 2cu 3  u  1| 0.31767, u [ 0 , 0 ) dh(  ( x)) 1  (1)  ( x)3  (1   ( x))[3 ( x) 2 ]  2  ( x)  3    0.  4 d  ( x)  ( x) 6 2  2  ( x) 1 1 u c  1 since 2 2u 3 1 u 1 | g (u ) || 2u 3 (c  3 ) | 2u 3   u 3  ( 0 )3  0.31767. 2u 2 (3). It is similar to the proof of (2). (4). Let the following function g (u)  (u  cu3 )  (1  cu 3 ), u, c  (0,1]. Then g (u ) is a monotone increasing function of u since g (u)  1  6cu 2  0 where 0  c  1 . On the other hand, g (u)  2(c  1)u 3  f (u), where f (u)  (u  u 3 )  (1  u 3 ), u  (0,1] is the same as that in (2). Therefore, if  ( x)  0 , then In particular, from the proof of (3), there is that 1 u g (u )  2u 3 (c  ) is a monotone increasing function of u  (0,1] . When c is nearly to 1/2, not only the following results can be obtained directly 1  3   ( x)(1  c)   ( x) / 2, 2  13   ( x)2 (1  c)   ( x)2 / 2 ,but also the following statements can be obtained. (a). g ( 0 )  (1  2c)( 0 )3 and g (u )  2u 3 (c  1  u ) are nearly 2u 3 g (  ( x))  0,| g (  ( x)) | 2(1  c) 03 , since g (  ( x))  g ( 0 )  2(c  1) 03  f ( 0 )  2(c  1) 03  0. The condition g (  ( x))  0 implies that ( 1  2 3 )   ( x)  c ( x)3  1  c ( x)3  1  2 3. to 0 if 0  c  1  u  1 in which u [ 0 ,1) . 3 2u 3 (b). g ( 0 )  2(1  c)  and 2u The c(u )  1  u is a monotone decreasing function of 2u 3 u  (0,1] since 2u nearly (u  cu3 )  (1  cu3 ) . 2u 3 1 u , then 2u 3 3 3 1 u g (u )  2u 3 (c  3 )  0 which implies (u  cu )  (1  cu ) .  (t0 )  0   (u)   (v)  (1  d ) / (2d ), By  (u )  and For is that 3   | g (u ) || 2cu  u  1| ( 0 )  0.31767, u [ 0 ,1) if 1 u 1 since 0c  one result  (u )  1 / 2 1/ 2 of d  (1) in is  (v)  1 / 2 1/ 2 Theorem equivalent   (v). 2.1, to d  0 ,  (u )   (v)  (1  0 ) / (2 0 )  02 ( 0 )3  1  0 . The others can be obtained through the calculated directly from the result of (1) by SAS. # 1 u 1 u | g (u ) | 2u 3 ( 3  c)  2u 3 ( 3 )  1  u  1  0  ( 0 )3  0.31767. 2u 2u 2 Proof of Theorem 3.2 Let a  0.8789%, b  5.2241%, t0  2.7047%. (1).If a subsystem X of a steady multilateral system V falls And two is that | g (u ) || 2cu 3  u  1| 2 03  0.41024, u  [ 0 , 0 ) 1 1 u   1 since 0c 2 2u 3 1 u 1 u | g (u ) | 2u 3 ( 3  c)  2u 3 ( 3 )  1  u  1  0  2 03  0.41024. 2u 2u the since ( 0  03 )  (1  03 ) . For d  0 ,  (u )   (v)  (1  0 ) / (2 0 )  ( 0 ) 2 / 2 , since 3 2u 3 is a monotone decreasing function of  (u)   (v)  (1  d ) / (2d ) u  ( 0 ,1] , there are, Thus  ( x) x  (min, t0 ) or a monotone increasing function of x  (t0 , max) if 0  (1  d ) / (2d )   . since 2u 3 ; if there is also an unique solution v  (t0 , max) , such that 2u Because the balance solution of 1  u  1 is u  0 2u 3 2 1 u  is a monotone decreasing function of and c(u )  1 u 1  2u 3 2 1 u 1.  u  [  0 ,1)  0  2u 3 2 u [ 0 , 0 ) . respectively, Taking u   ( x) , the desired are gotten. # Proof of Corollary 2.1.Let min  0.08, max  0.6, t0  0.027047. (1). From the proof of (1) in Theorem 2.1, for any 0  d  1 , there is an unique solution x  (min, t0 ) and If 0  c  c(u ) , i.e., 0  c  u  [ 0 , 0 )  1   03  0.20512, 0 to 1 1 u c  1 in which 2 2u 3 1 1 c(u )  (3u 4  2u 3 )  4 (3  2u )  0, , u  (0,1]. 2 2u If c  c(u) , i.e., c  1  u , then 1 u )  0 which implies 2u 3 g ( 0 )  (1  2c)( 0 )3 are nearly to respectively, if  03  0.20512, 0 1 1 u  1 in which u [ 0 , 0 ) . 0c  2 2u 3 (c). g ( 0 )  2(1  c) 03 and g ( 0 )  (1  2c)( 0 )3 are if c  1  u . Denoted the function 1  u by c(u ) . 3 3 g (u )  2u 3 (c  2 3 0 (5). Consider the function g (u)  2cu 3  (1  u) is the same as in (4). Easy to know that g (u)  0 if and only 2u if if a virtual disease, denoted by 0 , which means that there is a force such that its energy  ( X ) decreases, i.e., changed by the increment  ( X )    0 . By the Intervention Rule in [20], its capability of intervention reaction can make the And three is that 21 www.erpublication.org International Journal of Engineering and Technical Research (IJETR) ISSN: 2321-0869 (O) 2454-4698 (P) Volume-7, Issue-12, December 2017  ( X )2   ( X )1   ( X )  (1  2 3 )  (1  c ( x)3 )  (1   ( x) 3 )  0, increment  (S X )  1  0 , in which its absolute is large, mother S X of to fall a virtual disease by a negative X  ( S X )2   ( S X )1   ( S X )  ( 1  13 )  (  ( x)  c  ( x) 2 )  (  ( x)   ( x) 2 )  0,  ( K X )2   ( K X )1   ( K X )  ( 1  3 )   ( x)(1  c)  0, denoted by  , and also can make the son X S of X to fall a virtual disease by a negative increment  ( X S )  2  0 , in which its absolute is small,   ( X K )2   ( X K )1   ( X K )  ( 2  13 )   ( x)2 (1  c)  0,  ( X S )2   ( X S )1   ( X S )  ( 2  13 )    ( x) 2 (1  c)  0  . denoted by  . Diseases of the loving subsystems have the same direction of X . At the same time, its capability of intervention reaction can make the bane K X of X to fall a real disease by a large It means that the first physiological system of the steady multilateral system runs normally. From the idea of TCE, by the Affording Rule, the second physiological system of the steady multilateral system will not work to afford for. It is because there is a full Yin food  ( X )2  (1  2 3 )  (1  c ( x)3 )  0 for the second increment  ( K X )  1  0 , denoted by  , and also can make the prisoner X K of physiological system if the subsystem X falls a virtual disease or is intervened for a healthy economy by the Attaining Rule. By Theorem 2.1 and Corollary 2.1, the RPI inflation rate x [a, b] makes 1   (x)  0 such that ( ( x)   ( x)3 )  (1   ( x)3 ) , to fall a real disease by a little increment  ( X K )  2  0 , denoted by  . Diseases of the killing subsystems are the opposite direction of X . The bane K X of X is the biggest victim since its increment X  ( K X )  1  0 is large. therefore the first transfer law is the first occurrence of the virtual disease of the mother S X of X if a subsystem X of a On the other hand, if the RPI inflation rate x [a, b] , by Corollary 2.1, there is 1  1   ( x)  0 such that steady multilateral system V falls a virtual disease. From Figure 2 and by Definition 3.1, the relation disease between virtual S X and virtual X is less serious since virtual 1 +2 3   ( x)+c ( x)3  1  2 3  1  c ( x)3 . Thus, c  [1   ( x)] / (2  ( x)3 )  0, x  t0 . It means SX that the economy is healthy such that there is the capability of self-protection of the steady multilateral system. By the Self-protection Rule in [20], its capability of self-protection can make the biggest victim as the bane K X of X restored by a fixed increment  ( K X )1   3  0 , denoted by 0 . By the Intervention Rule in [20] again and from Theorem 3.1, its capability of self-protection can make the mother X K ( 2  13 )   ( x) (1  c)  0 denoted by  , and also can make the son S X of K X to fall a 2 ( 2  1 3 )    ( x) (1  c)  0 .  by a negative increment  (S X )1  2 3  0 , in which its absolute is small, and finally X will encounter a sick which is different from the disease direction of X , i.e., changed by the increments  ( K X )2   ( K X )   ( K X )1  ( 1  3 )   ( x)(1  c)  0,  ( X K )2   ( X K )   ( X K )1  ( 2  1 3 )   ( x)2 (1  c)  0, At the same time, its capability of self-protection can make the bane X S of K X to fall a real disease by a large increment  ( X S )1  13  0 , denoted by  , and also can make respectively. At the same time, the son X S of X also falls a virtual ill which is the same disease direction of changed by the increment X , i.e.,  ( X S )2   ( X S )   ( X S )1  ( 2  1 3 )    ( x)2 (1  c)  0, since 1  c  0. Therefore the transfer law is secondly the real disease of the bane K X of X after the virtual disease of the of K X to fall a real disease by a little increment  ( X )1  2 3  0 , denoted by  . Diseases of the killing subsystems are the opposite direction of K X . All these mother S X of changes consist of the following Figure 2. From Figure 2 or from Theorem 3.2 in [20], if 3  1   ( x) , i.e., c  1 , its capabilities of of X X , and thirdly the real disease of the prisoner X K , and fourthly the virtual disease of the son X S of X , against the loving relationship order transmission. In fact, watching Figure 2, K X is real, X K is real, X S is intervention reaction and self-protection can make the subsystems X S , X K and K X be restored at the same time, but X , secondly By Theorem 3.1 in [20] , the victim K X or X K of denoted by  . Diseases of the loving subsystems have the same direction of K X . the subsystems , 2 disease X . ( 1  3 )   ( x)(1  c)  0  ( X K )1  13  0 , in which its absolute is large, the prisoner X treatment principle of TCE is used. Thus the self-protection coefficient 3 will near to small such that firstly of K X to fall a virtual disease by a negative increment virtual can love virtual If the disease continues to develop, it will lead to undermine firstly the best state of the capability of self-protection of the steady multilateral system, i.e., c  1 , since any disease that causes side effects in the first place dues to the non-best state of self-protection ability, i.e., 3  c ( x)   ( x)  1 , where 0  c  1 , even if the virtual, X is virtual, and S X is virtual. The order of the and S X will decrease their energies. In transfer law of diseases must be against the loving relationship order transmission. It is because (1  3 )  (2  13 )  (2  13 )  (1  2 3 )  (1  2 3 ). mathematics, from Theorems 3.1 and 3.2 in [20] , the final increments can be obtained as follows: 22 www.erpublication.org RPI 1% to 5% – Mathematical Reasoning of Economic Intervening Principle Based on Yin Yang Wu Xing Theory in Traditional Chinese Economics (II) On the other hand, if the RPI inflation rate x [a, b] , by Theorem 2.1 and Corollary 2.1, there is 1  1   ( x)  0 such that The result is obtained from (1  2 3 )  ( 1  2 3 ) since ( 1   2 3 )  ( 1   2 3 )  ( 1  3 )   ( x)(1  c)   ( x) 2 (1  c)  (  2  1 3 ). 1 +2 3   ( x)+c ( x)3  1  2 3  1  c ( x)3 . In other words, the diseases are transferred from real K X Thus, to virtual S X against the loving relationship order if X is the means that the economy is healthy such that there is a good capability of self-protection of the steady multilateral system. By the Self-protection Rule in [20], its capability of self-protection can make the biggest victim as the prisoner X K of X restored by a fixed increment cause of diseases or X is intervened. It implies that the mother S X of X will obtain the best Yin (negative) energy if the energy of X decreases. Watching Figure 2 and by Definitions 3.1 and 3.2, the relation disease between real K X and virtual X is less serious since real K X can kill virtual between virtual virtual X X X  ( X K )1  3  0 , denoted by 0 . By the Intervention Rule in [20] again and from Theorem 3.1, its capability of self-protection can make the son K X of X K to fall a real disease by a large increment , but the relation disease and real X K is more serious since  ( K X )1  13  0 , denoted by  , and also can make cannot kill real X K which will destroy the killing order from X to X K of the Yin Yang Wu Xing system if the the mother X S of X K to fall a real disease by a little increment  ( X S )1  2 3  0 , denoted by  . Diseases of the loving disease continues to develop. Finally the relation disease between virtual X S and virtual X is also less serious since virtual X makes that the loving order from subsystems have the same direction of X K . can love virtual X S . The less serious relation disease between virtual X S and virtual X At the same time, its capability of self-protection can make the prisoner S X of X K to fall a virtual disease by a negative X increment  (S X )1  13  0 , in which its absolute is to X S will be restored large, denoted by  , and also can make the bane easily. The transferring way of strengthening the loving relationship can make the new virtual disease of X remission since  ( X )2  (1  c ( x)3 )     ( X ) . of X K by  . Diseases of the killing subsystems are the opposite direction of X K . All these changes consist of the following Figure 3. From Figure 3 or by Theorem 3.2 in [20], if 3  1   ( x) , i.e., c  1 , its capabilities of changed by the increment  ( X )    0 . By the Intervention Rule in [20], its capability of intervention reaction can make the son X S of X to fall a real disease by intervention reaction and self-protection can make the subsystems S X , K X and X K restored at the same time, but the a large increment  ( X S )  1  0 , denoted by  , and subsystems  X and X S will increase their energies. In mathematics, from Theorems 3.1 and 3.2 in [20] , the final increments can be obtained as follows:  ( X )2   ( X )1   ( X )  (1  2 3 )  (1  c ( x)3 )  (1   ( x)3 )  0, also can make the mother S X of X to fall a real disease by a little increment  (S X )  2  0 , denoted by  X to fall a virtual disease by a negative increment  ( X )1  2 3  0 , in which its absolute is small, denoted Despite of the positive way, the system will be still for the next round of disease transmission, until disease rehabilitation. (2). If a subsystem X of a steady multilateral system V falls a real disease, denoted by 0 , which means that there is a force such that its energy  ( X ) increases, i.e.,  c  [1   ( x)] / (2  ( x)3 )  0, x  t0 . It  ( X S )2   ( X S )1   ( X S )  ( 1  13 )  (  ( x)  c ( x) 2 )  (  ( x)   ( x) 2 )  0,  ( X K )2   ( X K )1   ( X K )  ( 1  3 )    ( x)(1  c)  0, .  ( K X )2   ( K X )1   ( K X )  ( 2  13 )    ( x)2 (1  c)  0, Diseases of the loving subsystems have the same direction of X. At the same time, its capability of intervention reaction can make the prisoner X K of X to fall a virtual disease by a  (S X )2   ( S X )1   ( S X )  ( 2  13 )   ( x) 2 (1  c)  0  . absolute is large, denoted by  , and also can make the bane K X of X to fall a virtual disease by a negative increment It means that the first physiological system of the steady multilateral system runs normally. From the idea of TCE, by the Affording Rule, the second physiological system of the steady multilateral system will not work to afford for. It is because there is a full Yang food the second  ( X )2  (1  2 3 )  (1  c ( x)3 )  0 for  . Diseases of the killing subsystems are the opposite direction of X . The prisoner X K of X is the biggest victim since its increment physiological system if the subsystem X falls a real disease or is intervened for a healthy economy by the Attaining Rule. By Theorem 2.1 and Corollary 2.1, the RPI inflation rate makes 1  1   ( x)  0 such that x [a, b] negative increment  ( X K )  1  0 , in which its  ( K X )  2  0 , in which its absolute is small, denoted by  (  ( x)   ( x)3 )  (1   ( x)3 ) . Therefore the transfer law  ( X K )  1  0 is the scope of big changes. is the first occurrence of the real disease of the son X S of 23 X if www.erpublication.org International Journal of Engineering and Technical Research (IJETR) ISSN: 2321-0869 (O) 2454-4698 (P) Volume-7, Issue-12, December 2017 a subsystem X of a steady multilateral system V falls a real disease. From Figure 3 and by Definition 3.1, the relation disease between real X and real X S is less serious since real X can Finally the relation disease between S X and serious since real S X can love real disease between real S X and real love real X S . If the disease continues to develop, it will lead to undermine firstly the capability of self-protection of the steady multilateral system, i.e., c  1 since any disease that causes side effects in the first place dues to the non-best state of self-protection ability, i.e., 3  c ( x)   ( x)  1 order from S X to ( 2  1 3 )    ( x) 2 (1  c)  0 . By Theorem 3.1 in will encounter a sick respectively which is different from the disease direction of X , i.e., changed by the increments  ( X K )2   ( X K )   ( X K )1  ( 1  3 )    ( x)(1  c)  0, which its absolute is small, denoted by  . Diseases of the loving subsystems have the same direction of X . At the same time, its capability of intervention reaction can make the bane K X of X to fall a real disease by a large , i.e., changed by the increment since 1  c  0. Therefore the first transfer law is secondly the virtual disease of the prisoner X K of X after the of the bane K X of mother S X of X X X increment  ( K X )  1  0 , denoted by  , and also , and thirdly the virtual disease , and fourthly the real disease of the can make the prisoner X K of X By Corollary 2.1 and Theorem 2.1, the RPI inflation rate x  [a, b] makes that 0  1   ( x)  2   ( x)2  0 such that diseases must be along the loving relationship order transmission. It is because (1  3 )  (2  13 )  (2  13 )  (1  2 3 )  (1  2 3 ). ( 1  2 3 )  (1  2 3 ). In this case, the steady The result is obtained from (1  2 3 )  ( 1  2 3 ) since ( 1   2 3 )  ( 1   2 3 )  ( 1  3 )   ( x)(1  c) multilateral system V is abnormal or unhealthy. The unhealthy means the lack of self-protection ability. Thus the self-protection coefficient 3  c ( x) will near to small   ( x) 2 (1  c)  (  2  1 3 ). such that firstly 0  (1  3 )   ( x)(1  c)   ( x)  1 and secondly 0  ( 2  13 )   ( x)2 (1  c)   ( x)2  2 , i.e., c  0, if the disease In other words, the diseases are transferred from virtual X K of diseases or X X is the cause is intervened. It implies that the son X S of continues to develop. Consider in the worst state: 3  c ( x)  0 , i.e., c  0 , where 0  1   ( x)  2   ( x) 2  0 . Its X will obtain the best Yang (positive) energy if the energy of X increases. Watching Figure 3 and by Definitions 3.1 and 3.2, the relation disease between real X and virtual X K is less serious since real X KX capability of self-protection cannot make the biggest victim as the bane K X of X restored. In mathematics, from Theorems 3.1 and 3.2 in [20] , the final increments can be obtained as follows: can kill virtual X K , but the relation disease between virtual K X and real cannot kill real X X  ( X ) 2   ( X )1   ( X )  (1   2 3 )  (1  c  ( x)3 )    0, is more serious since virtual  ( S X ) 2   ( S X )1   ( S X )  ( 1  13 )  (  ( x)  c  ( x) 2 )   1  0,  ( K X ) 2   ( K X )1   ( K X )  ( 1  3 )   ( x)(1  c)   ( x)   1  0, which will destroy the killing order of the Yin Yang Wu Xing system from K X to X X  ( K X )  1  0 is large. is real, and X S is real. The order of the transfer law of to real X S along the loving relationship order if to fall a real disease by a little increment  ( X K )  2  0 , denoted by  . Diseases of the killing subsystems are the opposite direction of X . The bane K X of X is the biggest victim since its increment , along the loving relationship order transmission. In fact, watching Figure 3, X K is virtual, K X is virtual, S X is real, will be restored easily. The transferring virtual disease by a negative increment  ( X S )  2  0 , in  (S X )2   ( S X )   ( S X )1  ( 2  1 3 )   ( x) 2 (1  c)  0 real disease of the son X S of makes that the loving denoted by  , and also can make the son X S of X to fall a Respectively since 1  c  0. At the same time, the mother S X of X also falls a real ill which is the same disease X X increment  (S X )  1  0 , in which its absolute is large,  ( K X )2   ( K X )   ( K X )1  ( 2  1 3 )    ( x) 2 (1  c)  0, direction of The less serious relation X positive way, the system will be still for the next round of disease transmission, until disease rehabilitation. This completes the proof.# Proof of Theorem 3.3. Let a  0.8789%, b  5.2241%, t0  2.7047%. (1).If a subsystem X of a steady multilateral system V falls a virtual disease, denoted by 0 , which means that there is a force such that its energy  ( X ) decreases, i.e., changed by the increment  ( X )    0 . By the Intervention Rule in [20], its capability of intervention reaction can make the mother S X of X to fall a virtual disease by a negative small such that firstly ( 1  3 )   ( x)(1  c)  0 , and secondly ( 2  13 )   ( x)2 (1  c)  0 , and finally X is also less way of strengthening the loving relationship can make the real X disease of remission since 3  ( X )2  (1  c ( x) )     ( X ) . Despite of the where 0  c  1, even if the treatment principle of TCE is used. Thus the self-protection coefficient 3 will near to [20], the victim X K or K X of X X  ( X K ) 2   ( X K )1   ( X K )  (  2  13 )   ( x) 2 (1  c)   ( x) 2   2   0,  ( X S ) 2   ( X S )1   ( X S )  (  2  13 )    ( x) 2 (1  c)    2  0. . 24 www.erpublication.org RPI 1% to 5% – Mathematical Reasoning of Economic Intervening Principle Based on Yin Yang Wu Xing Theory in Traditional Chinese Economics (II) It means that the first physiological system of the steady multilateral system runs hardly, such that the final increments of self-protection are similar to the increments of intervention reaction. The hard running is not only because the killing order has been destroyed, but also the loving order cannot be running. From the idea of TCE, by the Affording Rule, the second physiological system of the steady multilateral system will work. It is because a steady multilateral system would become ill or dies if its Chi or energy in the steady multilateral system is imbalanced or exhausted. The purpose of the second physiological system working is to increase the energy of the system, and restores the order of the killing relationship of the Yin Yang Wu Xing system. By Theorems 3.3 and 3.4 and Corollary 3.2 in [20], the method of “Strong inhibition of the same time, support the weak”, i.e., to increase energy of virtual X while to reduce energy of real X K , should be used in this case: x  [a, b] Of course, the virtual disease of comes from the son X S of X since any virtual disease always comes from its son by Theorem 3.2 in [20]. In order to cure the virtual X , by Affording Rule, the increment  ( X )13  [(1  2 3 )  ( 1  3 )]1  (1  c ( x)3   ( x)(1  c))1  0 must be very big. For example 1   ,which means righteousness to defeat evil, this treatment can make the increment  ( X K )13  [(1  2 3 )  ( 1  3 )]1  (1  c ( x)3   ( x)(1  c))1  0 be very small. In fact, by Affording Rule and from Theorems 3.1-3.4 of [20], the all final increments can be obtained as follows:  ( X K )14   ( X K )13   ( X K )2  [(1  2 3 )  ( 1  3 )]1  ( 2  13 )  [(1  2 3 )  ( 1  3 )  ( 2  13 )]  [(1  2 )  3 ( 1  2 )  ( 1  3 )]  0,  (S X )14   ( S X )13   ( S X )2  ( 1  2 3 )  (  ( x)  c ( x) 2 )   1  0,  ( X S )14   ( X S )13   ( X S )2  ( 2  13 )    ( x)2 (1  c)    ( x) 2    2  0, which is equivalent to that 0  1   ( x)  2   ( x)2  0, such that ( 1  2 3 )  (1  2 3 ). It is because the  ( K X )14   ( K X )13   ( K X )2  ( 2  2 3 )   ( x) 2 (1  c)   ( x) 2    2   0,  ( X )14   ( X )13   ( X )2  [(1  2 3 )  ( 1  3 )]1  (  2  13 ) inequality ( 1  2 3 )  (1  2 3 ) makes the absolute  [(1  2 3 )( 1  3 )  ( 2  13 )]  [(1  2 )  3 ( 1  2 )  ( 1  3 )]  0. value of their increments (1  2 3 )1 becoming large . By Definitions 3.1 and 3.2, consider the lack of self-protection ability, from Figure 4, for a virtual X , its capability of intervention reaction can make many relation diseases occurrence. Only the relation between virtual X and real X K can be considered as more serious, since virtual X X to XK Therefore, the transfer law is the first occurrence of the virtual disease of the prisoner X K of X ; secondly the virtual disease of the mother S X of of X X , thirdly the virtual disease of the son X S , and finally the real disease of the bane K X of X . In fact, watching Figure 4, X K is virtual, S X is virtual, X S is which will destroy the killing order from virtual, and K X is real. The order of the transfer law of of the Yin Yang Wu Xing system if the disease diseases must be along the killing relationship order transmission. It is because [(1  2 )  3 ( 1  2 )  ( 1  3 )]  ( 1  2 3 )  ( 2  13 )  ( 2  13 )  [(1  2 )  3 ( 1  2 )  ( 1  3 )]. cannot kill real XK , X continues to develop. By Affording Rule again, abiding by the treatment principle of “Strong inhibition of the same time, support the weak”, the intervention of the second physiological system is to increase the energy of virtual X while to reduce the energy of real X K . If an intervention force on the subsystem X of The result is obtained from (1  2 3 )  ( 1  2 3 ) since [(1  2 )  3 ( 1  2 )  ( 1  3 )]  ( 1  2 3 )  1  2 3  3 1  2 3   2  1  2 3  3 1  2 3  2  ( 1  2 )  3 1  0, and steady multilateral system V is implemented such that its energy  ( X ) has been changed by an increment ( 1  2 3 )  (2  13 )  (1  2 )  (1  2 )3 =(1  2 )(1  3 )  0. 0  ( X )  1  0 , denoted by  , and at the same time, another intervention force on the subsystem XK other words, the diseases are transferred from virtual X to real K X along the killing relationship order transmission. of steady multilateral system V is also implemented such that its energy  ( X K ) has been changed by an increment By Definition 3.2, the relation disease between virtual X and virtual X K is rare since the relation cannot destroy the 0  ( X K )  1  0 , denoted by  , then from Theorem 3.4 killing order from X and X K although virtual in [20], all other subsystems: S X , K X and X S can be restored at the virtual X K . The rare relation disease between virtual the same time, and the subsystems X and XK In will increase and virtual X K makes that the killing order from and decrease their energies by the same size but the direction opposite. In mathematics, from Theorems 3.1, 3.3 and 3.4 in [20] , the final increments can be obtained as follows: cannot kill X X X to X K will be cured difficultly. Although rare refractory disease, but their disease transmission is natural since they are all virtual. By Definition 3.2, the relation disease between virtual X K  ( X )13  [(1  2 3 )  ( 1  3 )]1  [(1  c ( x)3 )   ( x)(1  c)]1  0, and virtual S X , or between virtual S X and virtual X S , is also  ( X )  [( 1  2 3 )  ( 1   2 3 )]1  0, 1 S 3 rare. Thus the disease transmission from virtual X K to virtual  ( X K )13  [(1  2 3 )  ( 1  3 )]1  [(1  c ( x)3 )   ( x)(1  c)]1  0,  ( K X )13  [( 2  13 )  ( 2  13 )]1  0, SX ,  ( S X )13  [( 2  1 3 )  ( 2  13 )]1  0. or, from virtual S X to virtual X S , is also natural since they are all virtual. Only the relation disease between virtual X S and real K X is All these changes consist of the following Figure 4. more serious since virtual X S cannot kill real K X , which will 25 www.erpublication.org International Journal of Engineering and Technical Research (IJETR) ISSN: 2321-0869 (O) 2454-4698 (P) Volume-7, Issue-12, December 2017  ( X )2   ( X )1   ( X )  (1  2 3 )  (1  c ( x)3 )    0,  ( X S )2   ( X S )1   ( X S )  ( 1  13 )  (  ( x)  c ( x) 2 )  1  0, destroy the killing order from X S to K X of the Yin Yang Wu Xing system if the disease continues to develop. Finally the less serious relation disease between real K X and virtual X makes that the killing order from K X to X  ( X K )2   ( X K )1   ( X K )  ( 1  3 )    ( x)(1  c)    ( x)   1  0,  ( K X )2   ( K X )1   ( K X )  ( 2  13 )    ( x)2 (1  c)    ( x)2    2   0,  ( S X )2   ( S X )1   ( S X )  ( 2  13 )   ( x) 2 (1  c)   ( x) 2    2  0. will means that the first physiological system of the steady multilateral system runs hardly, such that the final increments of self-protection are similar to the increments of intervention reaction. The hard running is not only because the killing order has been destroyed, but also the loving order cannot be running. From the idea of TCE, by the Affording Rule, the second physiological system of the steady multilateral system will work. It is because a steady multilateral system would become ill or dies if its Chi or energy in the steady multilateral system is imbalanced or exhausted. The purpose of the second physiological system working is to increase the energy of the system, and restores the order of the killing relationship of the Yin Yang Wu Xing system. By Theorems 3.3 and 3.4 and Corollary 3.2 in [20], the method of “Strong inhibition of the same time, support the weak”, i.e., to decrease energy of real X while to increase energy of virtual K X , should mainly be used in this be restored easily. The transferring way of strengthening the killing relationship by the second physiological system can make the new virtual disease of X remission since virtual X will get the positive increment 1 if  ( X )4  [(1  2 )  3 ( 1  2 )  ( 1  3 )]  0, 1    0 . Despite of the positive way, the system still will be for the next round of disease transmission, until the disease rehabilitation. (2). If a subsystem X of a steady multilateral system V falls a real disease, denoted by 0 , which means that there is a force such that its energy  ( X ) increases, i.e., changed by the increment  ( X )    0 . By the Intervention Rule in [20], its capability of intervention reaction can make the son X S of X to fall a real disease by a large increment  ( X S )  1  0 , denoted by  , and also can make case: x  [a, b] which is equivalent to that X to fall a real disease by a little increment makes negative increment  ( X K )  1  0 , in which its absolute is large, denoted by  , and also can make the bane K X of X to fall a virtual disease by a negative increment  ( K X )  2  0 , in which its absolute is small, denoted by  . Diseases of the killing subsystems are the opposite direction of X . The prisoner X K of X is the biggest victim since its the killing order from K X to ( 1  2 3 )  (1  2 3 ). In this case, the steady multilateral system V is abnormal or unhealthy. The where i.e., V is Its capability which will destroy of the Yin Yang Wu Xing also implemented such that its energy  ( K X ) has been changed by an increment  (K X )  1  0 , denoted by 0 , 3  c ( x)  0 , i.e., c  0 , 0  1   ( x)  2   ( x)2  0 . X X denoted by 0 , and at the same time, another intervention force on the subsystem K X of the steady multilateral system small such that firstly 0  ( 1  3 )   ( x)(1  c)   ( x)  1 , and Consider in the worst state: large. multilateral system V is implemented such that its energy  ( X ) has been changed by an increment  ( X )  1  0 , unhealthy economy implies the lack of self-protection ability. Thus the self-protection coefficient 3  c ( x) will near to c  0, if the disease continues to develop. (1  2 3 )1 becoming system if the disease continues to develop. By Affording Rule again, abiding by the treatment principle of “Strong inhibition of the same time, support the weak”, the intervention of the second physiological system is to decrease energy of real X while increase energy of virtual K X . If an intervention force on the subsystem X of the steady By Corollary 2.1 and Theorem 2.1, the RPI inflation rate x  [a, b] makes that 0  1   ( x)  0, such that , increment serious, since virtual K X cannot kill real increment  ( X K )  1  0 is the scope of big changes. 0  ( 2  13 )   ( x)2 (1  c)   ( x)2  2 the ( 1  2 3 )  (1  2 3 ) From Affording Rule, this is just the working method of the second physiological system. By Definitions 3.1 and 3.2, consider the lack of self-protection ability, from Figure 5, for a real X , its capability of intervention reaction will make the many relation diseases occurrence. Only the relation disease between real X and virtual K X can be considered as more loving subsystems have the same direction of X . At the same time, its capability of intervention reaction can make the prisoner X K of X to fall a virtual disease by a secondly 0  1   ( x)  0, such that ( 1  2 3 )  (1  2 3 ). It is because the inequality  (S X )  2  0 , denoted by  . Diseases of the the mother S X of It then from Theorem 3.4 in [20], all other subsystems: X K and of X S can be restored at the same time, and the subsystems self-protection cannot make the biggest victim as the prisoner X K of X be restored. KX X and will decrease and increase their energies by the same size but the direction opposite. In mathematics, from Theorems 3.1, 3.3 and 3.4 in [20] , the final increments can be obtained as follows: In mathematics, from Theorems 3.1 and 3.2 in [20] , the final increments can be obtained as follows: 26 www.erpublication.org RPI 1% to 5% – Mathematical Reasoning of Economic Intervening Principle Based on Yin Yang Wu Xing Theory in Traditional Chinese Economics (II)  ( X )13  [(1   2 3 )  ( 1  3 )]1  [(1  c  ( x)3 )   ( x)(1  c)]1  0,  ( S X )13  [( 1   2 3 )  ( 1   2 3 )]1  0, disease transmission from real K X to real X S , or from real X S  ( X K )13  [(  2  1 3 )  (  2  1 3 )]1  0, to real S X , is also natural since they are all virtual. All these changes consist of the following Figure 5. Of course, the real disease of X comes from the mother S X more serious since virtual X K cannot kill real S X , which will  ( K X )13  [(1   2 3 )  ( 1  3 )]1  [(1  c  ( x)3 )   ( x)(1  c)]1  0,  ( X S )13  [(  2  1 3 )  (  2  1 3 )]1  0. Only the relation disease between real S X and virtual X K is destroy the killing order from X K to S X of the Yin Yang Wu Xing system if the disease continues to develop. But the less serious relation disease between virtual X K and of X since any real disease always comes from its mother by Theorem 3.2 in [20]. In order to cure the real X , by the Affording Rule, the intervention of the second physiological system must make the increment  ( X )3  (1  2 3 )1  (1  c ( x)3 )1 to X K will be restored easily. The transferring way of strengthening the killing relationship by the second physiological system can make the new real disease of X remission since real X will get a negative increment  ( X )14  [(1  2 )  3 ( 1  2 )  ( 1  3 )]  0 if real tending to be very small, for example 1   , which means righteousness to defeat evil, this treatment makes the increment  ( K X )3  (1  2 3 )1  (1  c  ( x)3 ) 1 tending to be very big. In fact, by Affording Rule and from Theorem 3.1 of [20], the all final increments are as follows  ( K )   ( K )   ( K )  [(1    )  (    )]  (     )  Th 1 X 4 1 X 3 2 3 1 3 1 2 1 3  ( S X )14   ( S X )13   ( S X ) 2  (  2  1 3 )   ( x) 2 (1  c)   ( x) 2    2   0,  ( X K )14   ( X K )13   ( X K ) 2  (  2   2 3 )    ( x)(1  c)    ( x)   1  0, is unhealthy where 0  c  1 and ( 1  2 3 )  (1  2 3 ) . Since x  a means that the RPI inflation rate is too lower than the normal state, thus the subsystem X has encountered the virtual disease. From Theorem 3.2 and Corollary 3.2 in [20], the subsystem X was considered as virtual. When the capability of self-protection is nearly to the best state, i.e., 3  c ( x)  ( X )14   ( X )13   ( X ) 2  [(1   2 3 )  ( 1  3 )]1  (  2  13 )  [(1   2 3 )( 1  3 )  (  2  1 3 )]  [(1   2 )  3 ( 1   2 )  ( 1  3 )]  0. erefore, the transfer law is the first occurrence of the real disease of the bane K X of X ; secondly the real disease of the X , thirdly the real disease of the mother S X of and finally the virtual disease of the prisoner X K of X X , . where c  1 , if you increase the energy of the subsystem X directly, then its capabilities of both intervention reaction and self-protection can make the subsystems S X , K X and X K In fact, watching Figure 5, K X is real, X S is real, S X is real, and X K is virtual. The order of the transfer law of diseases must be against the killing relationship order transmission. It is because [(1  2 )  3 ( 1  2 )  ( 1  3 )]  ( 1  2 3 )  (  2  13 )  (  2  13 )  [(1  2 )  3 ( 1  2 )  ( 1  3 )]. restored at the same time, but the subsystems [(1  2 )  3 ( 1  2 )  ( 1  3 )]  ( 1   2 3 )  1   2 3  3 1   2 3   2  1  2 3  3 1   2 3   2  ( 1   2 )  3 1  0, therefore the subsystem cannot kill the real real X X although the real . The rare relation disease between and real X K makes that the killing order from X X can obtain the large increment the small increment  ( X S )2  (  ( x)   ( x)3 )  0 . The later is the pseudo side effects issue, by Attaining Rule, which is just the food of the second physiological system of the steady multilateral system since that the economy is unhealthy, virtual and X intervened makes that the second physiological system will attain the Chi or energy (Yang energy) from the son X S of the intervened subsystem X . The attaining way is an By Definition 3.2, the relation disease between real X and real K X is rare since the relation disease cannot destroy the KX and X S will  ( X ) 2  (1   ( x)3 )  0 and the subsystem X S will get and (1  2 3 )  (2  13 )  (1  2 )  (1  2 )3 =(1  2 )(1  3 )  0. In other words, the diseases are transferred from real X to virtual X K against the killing relationship order transmission. X X increase their energies, i.e., changed by the increments  ( X )2  (1   ( x)3 )  0,  ( X S )2  (  ( x)   ( x)3 )  0, respectively. Since the RPI inflation rate x  a makes 0  1   ( x)  0 such that (  ( x)   ( x)3 )  (1   ( x)3 ) , The result is obtained from (1  2 3 )  ( 1  2 3 ) since order of the killing relationship from K X to X 1    0.  ( X S )14   ( X S )13   ( X S ) 2  ( 1   2 3 )  (  ( x)  c  ( x) 2 )  1  0, son X S of makes that the killing order from Despite of the positive way, the system will be still for the next round of disease transmission, until the disease rehabilitation. This completes the proof.# Proof of Theorem 4.1. Let a  0.8789%, b  5.2241%, t0  2.7047%. (1). If x  a , then from Theorem 2.1 and Corollary 2.1, there is that 0  1   ( x)  0 which means that the economy  [(1   2 3 )  ( 1  3 )  (  2  13 )]  [(1   2 )  3 ( 1   2 )  ( 1  3 )]  0, X 2 X indirect treating for an unhealthy economic subsystem X with a virtual disease. Thus the primary treatment should be to increase the energy of the subsystem X directly in order to avoid the side effects issue occurrence for an unhealthy economy. This is just one of the affording working principle of the second physiological system by Affording Rule. The idea means that “Virtual disease with an unhealthy economy is to fill itself”. to K X will be cured difficultly. Although rare refractory disease, but their disease transmission is natural since they are all virtual. By Definition 3.2, the relation disease between real K X and real X S , or between real X S and real S X , is also rare. Thus the 27 www.erpublication.org International Journal of Engineering and Technical Research (IJETR) ISSN: 2321-0869 (O) 2454-4698 (P) Volume-7, Issue-12, December 2017 Since a  x  t0 means that the RPI inflation rate is lower When the capability of self-protection is nearly to the worst state, i.e., 3  c ( x)  0 where c  0 , the first than the center t 0 , thus the subsystem X will encounter a virtual disease if the subsystem X falls ill. From Theorem 3.2 and Corollary 3.2 in [20], the subsystem X will be considered as virtual. First the case is studied that the capability of self-protection is in the best state, i.e., 3  c ( x)   ( x)  1  0 where c  1 . If physiological system will stop to work, or, the first transfer law will stop to run, while the second physiological system will begin to work, or, the second transfer law will begin to run. By Affording Rule and the second transfer law in Theorem 3.3, the purpose of the second physiological system working is to improve the physical ability of self-protection of the first physiological system, i.e., to make all of both 1  3   ( x)(1  c) and 2  13   ( x)2 (1  c) tending to be small, i.e., for fixed  ( x) , c tends to be large, at least, greater than zero, to drive the first physiological systems will begin to work. By the second transfer law in Theorem 3.3, for a virtual X , the more serious relation disease is the relation between virtual X S and real K X since virtual X S cannot kill real KX the energy of the subsystem S X is intervened to increase its energy, then its capabilities of intervention reaction and self-protection can make the subsystems K X , X K and X S restored at the same time, but the subsystems S X and  ( S X )2  (1   ( x)3 )  0,  ( X ) 2  (  ( x)   ( x)3 )  0, respectively. Since the RPI inflation rate a  x  t0 makes 1  1   ( x)  0 such that mainly ( ( x)   ( x)3 )  (1   ( x)3 ) , therefore the subsystem X can obtain the large increment  ( X )2  (  ( x)   ( x)3 )  0 and the subsystem S X will get disease continues to develop. Abiding by the TCE's idea of “Don’t have disease cure cure non-ill”, in order to avoid the more serious relation disease occurrence, it should be intervened when the intervened system was non-ill, but the incidence of second transfer law in Theorem 3.3 by this system will be to occur the more serious relation disease. According to the intervening principle of “Strong inhibition of the same time, support the weak” from Theorem 3.4 in [20], it can be gotten that the secondary treatment is to increase the energy of X S , and at the same time, to decrease the the small increment  (S X )2  (1   ( x)3 ) . The later is the pseudo side effects issue, by Attaining Rule, which is just the food of the second physiological system of the steady multilateral system since that the economy is healthy, virtual and S X intervened makes that the second physiological system will attain the Chi or energy (Yang energy) from the intervened subsystem S X directly for a healthy economy with a virtual disease. Thus the primary treatment should be gotten to increase the energy of the subsystem S X in order to avoid the side effects energy of K X . In general, although the economy is unhealthy and virtual, the capability of self-protection can be any state, i.e., 3  c ( x)  0 where 0  c  1 . The primary treatment is issue occurrence for a healthy economy. The idea means that “Virtual disease with a healthy economy is to fill its mother”. Since the economy is healthy, the worst state of the capability of self-protection will not be possible, i.e., 3  c ( x)  0 mainly for the normal state of the capability of self-protection, i.e., 0  3  c ( x)   ( x)  1, 0  1   ( x)  0 where 0  c  1 , the first physiological system will not stop to work, or, the first transfer law will not stop to run, while the second transfer law will not begin to run. Is the first physiological system working in order to improve its corresponding intervention ability, at the same time , to provide the food for the second physiological system. In other words, it makes 1  2 3   ( x)  c ( x)3 tending to be where 0  c  1 and ( 1  2 3 )  (1  2 3 ) . The secondary treatment is for the worst state of the capability of self-protection, i.e., 0  3  c ( x)   ( x)  1, 0  1   ( x)  0 where c  0 and ( 1  2 3 )  (1  2 3 ) . Comprehensive use large while 1  2 3  (1  c ( x)3 ) tending to be small, i.e.,  ( x) tends to large while c also tends to be large, the best, equal to 1, such that the non-existence of side effects, or, the non-existence of medical and drug resistance problem. The work mainly improves the loving relationship since the loving relationship is mainly used. By the first transfer law in Theorem 3.2 for a virtual X , the more serious relation disease is the relation between virtual X and real X K since virtual X cannot kill the real X K which of the two methods for the unhealthy economy with a virtual disease can deal with a general situation, i.e., 0  3  c ( x)   ( x)  1, 0  1   ( x)  0 where 0  c  1 and ( 1  2 3 )  (1  2 3 ) . # (2). If a  x  t0 , then from Theorem 2.1 and Corollary 1   ( x)  0 will increase their energies, i.e., changed by the increments which can destroy the killing order between X S and K X if the 2.1, there is 1  X which means that the economy is healthy where in general 1  c  1   ( x)  0 3 2  ( x) such that ( 1  2 3 )  (1  2 3 ) ; and 1  1   ( x)  c  0 such that ( 1  2 3 )  (1  2 3 ) , 2  ( x)3 i.e., | ( 1  2 3 )  (1  2 3 ) | 2 03  0.41024 . can destroy the killing order between X and X K if the disease continues to develop. Abiding by the TCE's idea of “Don’t have disease cure cure non-ill”, in order to avoid the more serious relation disease occurrence, it should be intervened when the intervened system was non-disease, but the incidence of the first transfer 28 www.erpublication.org RPI 1% to 5% – Mathematical Reasoning of Economic Intervening Principle Based on Yin Yang Wu Xing Theory in Traditional Chinese Economics (II) law in Theorem 3.2 by this system will be to occur the more serious relation disease. According to the intervening principle of “Strong inhibition of the same time, support the weak” from Theorem 3.4 in [20], the secondary treatment is gotten to increase the energy of X , and at the same time, to decrease the energy of X K . or energy (Yin energy) from the intervened subsystem X S directly for a healthy economy with a real disease. Thus the primary treatment should be gotten to decrease the energy of the subsystem X S in order to avoid the side effects issue occurrence for a healthy economy. The idea means that “Real disease with a healthy economy is to rush down its son”. Since the economy is healthy, the state of the capability of self-protection should be normal, i.e., 3  c ( x)  0 where 0  c  1 . In this case, the first physiological system will not stop to work, or, the first transfer law will not stop to run, while the second transfer law will not begin to run. Is the first physiological system working in order to improve its corresponding intervention ability, at the same time , to provide the food for the second physiological system. In other words, it makes 1  2 3   ( x)  c ( x)3 In general, since the economy is healthy and virtual, the capability of self-protection cannot be the worst state and should be normal, i.e., 3  c ( x)  0 where 0  c  1 . The primary treatment is for the best state of the capability of self-protection, i.e., 0  3  c ( x)   ( x)  1 , 0  1   ( x)  1 where c  1 and ( 1  2 3 )  (1  2 3 ) . The secondary treatment is for the normal state of the capability of self-protection, i.e., 0  3  c ( x)   ( x)  1 , 0  1   ( x)  1 where 0  c  1 and ( 1  2 3 )  (1  2 3 ) . Comprehensive tending to be large while 1  2 3  (1  c ( x)3 ) tending to be small. Equivalently, the way can make  ( x) tending to large and c also tending to be large, the best, equal to 1, such that the non-existence of side effects issue, or, the non-existence of medical and drug resistance problem. The work mainly improves the loving relationship since the loving relationship is mainly used. By the first transfer law in Theorem 3.2, the more serious relation disease is the relation between virtual K X and real X use of the two methods for the healthy economy with a virtual disease can deal with a general situation, i.e., 0  3  c ( x)   ( x)  1, 0  1   ( x)  1 where 0  c  1 and ( 1  2 3 )  (1  2 3 ) . # (3). If t0  x  b , then from Theorem 2.1 and Corollary 2.1, there is 1  1   ( x)  0 which means that the economy is healthy where in general 1  c  1   ( x)  0 such 3 2  ( x) since virtual K X cannot kill the real that ( 1  2 3 )  (1  2 3 ) ; and 1  1   ( x)  c  0 such that ( 1  2 3 )  (1  2 3 ) , 2  ( x)3 i.e., | ( 1  2 3 )  (1  2 3 ) | 2 03  0.41024 . killing order between K X and X will encounter a real disease if the subsystem X falls ill. From Theorem 3.2 and Corollary 3.2 in [20] , the subsystem X will be considered as real. First the case is studied that the capability of self-protection is in the best state, i.e., 3  c ( x)   ( x)  1 where c  1 . If the . In general, since the economy is healthy with an expected real disease, the capability of self-protection should be normal, i.e., 3  c ( x)  0 where 0  c  1 . The primary energy, then its capabilities of intervention reaction and self-protection can make the subsystems X K , K X and S X X if the disease continues to X energy of the subsystem X S is intervened to decrease its restored at the same time, but the subsystems which can destroy the develop. Abiding by the TCE's idea of “Don’t have disease cure cure non-ill”, in order to avoid the more serious relation disease occurrence, it should be intervened when the intervened system was non-disease, but the incidence of first transfer law in Theorem 3.2 by this system will be to occur the more serious relation disease. According to the intervening principle of “Strong inhibition of the same time, support the weak” from Theorem 3.4 in [20], the secondary treatment is gotten to increase the energy of K X , and at the same time, to decrease the energy of Since t0  x  b means that the RPI inflation rate is higher than or equal to the center t 0 , thus the subsystem X X treatment is for the best state of the capability of self-protection, i.e., and X S will 0  3  c ( x)   ( x)  1, 0  1   ( x)  1 where c  1 and ( 1  2 3 )  (1  2 3 ) . The secondary decrease their energies, i.e., changed by the increments  ( X )2  (  ( x)   ( x)3 )  0,  ( X S ) 2  (1   ( x)3 )  0, respectively. Since the RPI inflation rate t0  x  b makes 1  1   ( x)  0 such that mainly ( ( x)   ( x)3 )  (1   ( x)3 ) , therefore the subsystem X can obtain the substantial treatment is for the normal state of the capability of self-protection, i.e., 0  3  c ( x)   ( x)  1, 0  1   ( x)  1 where 0  c  1 and ( 1  2 3 )  (1  2 3 ) . Comprehensive use reduction  ( X )2  (  ( x)   ( x)3 )  0 and the subsystem The later is the pseudo side of the two methods for the healthy economy with a real disease can deal with a general situation, i.e., 0  3  c ( x)   ( x)  1, 0  1   ( x)  1 effects issue, by Attaining Rule, which is just the food of the second physiological system of the steady multilateral system since that the economy is healthy, real and X S intervened (4). If x  b , then from Corollary 2.1, there is 0  1   ( x)  0 which means that the economy is XS will get a  ( X S ) 2  (1   ( x)3 )  0 . modest reduction where 0  c  1 and ( 1  2 3 )  (1  2 3 ) .# unhealthy where 0  c  1 and ( 1  2 3 )  (1  2 3 ) . makes that the second physiological system will attain the Chi 29 www.erpublication.org International Journal of Engineering and Technical Research (IJETR) ISSN: 2321-0869 (O) 2454-4698 (P) Volume-7, Issue-12, December 2017 Since x  b means that the RPI inflation rate is too higher than the normal state, thus the subsystem X has encountered the real disease. From Theorem 3.2 and Corollary 3.2 in [20], the subsystem X was considered as real. When the capability of self-protection is in the best state, i.e., where , if the energy of c  1 3  c ( x)   ( x)  1 the subsystem X is intervened to decrease its energy directly, then its capabilities of intervention reaction and self-protection can make the subsystems X K , K X and X S restored at the same time, but the subsystems X law in Theorem 3.3 by this system will be to occur the more serious relation disease. According to the intervening principle of “Strong inhibition of the same time, support the weak” from Theorem 3.4 in [20], the secondary treatment is gotten to decrease the energy of S X , and at the same time, to increase the energy of X K . In general, although the economy is unhealthy with a real disease, the capability of self-protection can be any state, i.e., 3  c ( x)  0 where 0  c  1 . The primary treatment is mainly for the normal state of the capability of self-protection, i.e., 0  3  c ( x)   ( x)  1, 0  1   ( x)  2   ( x)2  0 where 0  c  1 and ( 1  2 3 )  (1  2 3 ) . The secondary and S X will  ( X )2  (1   ( x)3 )  0,  ( S X ) 2  (  ( x)   ( x)3 )  0, decrease their energies, i.e., changed by the increments respectively. Since the RPI inflation rate x  b makes 0  1   ( x)  0 such that ( ( x)   ( x)3 )  (1   ( x)3 ) , treatment is for the worst state of the capability of self-protection, i.e., 0  3  c ( x)   ( x)  1 , 0  1   ( x)  2   ( x)2  0 where c  0 and ( 1  2 3 )  (1  2 3 ) . Comprehensive use of the two methods for the unhealthy economy with a virtual disease can deal with a general situation, i.e., 0  3  c ( x)   ( x)  1 , 0  1   ( x)  2   ( x)2  0 where 0  c  1 and ( 1  2 3 )  (1  2 3 ) . This therefore the subsystem X can obtain the substantial and the reduction  ( X )2  (1   ( x)3 )  0 subsystem SX will get a modest reduction  (S X )  (  ( x)   ( x) )  0 . The later is the pseudo side effects, by Attaining Rule, which is just the food of the second physiological system of the steady multilateral system since that the economy is unhealthy, real and X intervened makes that the second physiological system will attain the Chi or energy (Yin energy) from the mother S X of the intervened 3 completes the proof. # REFERENCES [1]P.Levell.“Is the Carli index flawed?: assessing the case for the new retail price index RPIJ”. Journal of the Royal Statistical Society: Series A (Statistics in Society), 02/2015,Vol.178, No.2, pp: 303-336. DOI: 10.1111/rssa.12061 [2]T.M.Crone, N.I.Leonard and V.Richard,“Rents have been rising, not falling, in the postwar period”. 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[15]Y.S.Zhang, “Multilateral Matrix Theory”. Beijing:Chinese Statistics Press, 1993. [16]Y.S.Zhang,”Multilateral System Theor”. http://www.mlmatrix.com, 2007. [17]Y.S.Zhang,”Mathematical reasoning of treatment principle based on Yin Yang Wu Xing theory in traditional Chinese medicine”, Chinese Medicine, 2011, Vol.2, No.1, pp:6-15. doi:10.4236/cm.2011.21002 subsystem X . The attaining way is an indirect treating for an unhealthy economic subsystem X with a real disease. Thus the primary treatment should be gotten to decrease the energy of the subsystem X directly, in order to avoid the side effects issue occurrence for an unhealthy economy. This is just one of the affording working principle of the second physiological system by Affording Rule. The idea means that “Real disease with an unhealthy economy is to rush down itself”. When the capability of self-protection is at the worst state, i.e., 3  c ( x)  0 where c  0 , the first physiological system will stop to work, or, the first transfer law will stop to run, while the second physiological system will begin to work, or, the second transfer law will begin to run. By Affording Rule and the second transfer law in Theorem 3.3, the purpose of the second physiological system working is to improve the physical ability of self-protection of the first physiological system, i.e., to make all of both 1  3   ( x)(1  c) and 2  13   ( x)2 (1  c) tending to be small, i.e., for fixed  ( x) , c tends to be large, at least, greater than zero, to drive the first physiological systems will begin to work. The work mainly improves the killing relationship since the killing relationship is mainly used. By the second transfer law in Theorem 3.3, for a real X , the more serious relation disease is the relation between virtual X K and real S X since virtual X K cannot kill the real S X which can destroy the killing order between X K and S X if the disease continues to develop. Abiding the TCE's idea of “Don’t have disease cure cure non-ill”, in order to avoid the more serious relation disease occurrence, it should be intervened when the intervened system was non-disease, but the incidence of second transfer 30 www.erpublication.org RPI 1% to 5% – Mathematical Reasoning of Economic Intervening Principle Based on Yin Yang Wu Xing Theory in Traditional Chinese Economics (II) [18] Y.S.Zhang, “Mathematical reasoning of treatment principle based on Yin Yang Wu Xing theory in traditional Chinese medicine (II)”, Chinese Medicine, 2011, Vol.2, No.4, pp:158-170. doi:10.4236/cm.2011.24026 [19]Y.S.Zhang, “Mathematical reasoning of treatment principle based on the stable logic analysis model of complex systems”, Intelligent control and automation, 2012, Vol.3, No.1, pp:6-15. doi:10.4236/ica.2012.31001 [20]Y.S.Zhang and W.L.Shao, “Image mathematics-mathematical intervening principle based on Yin Yang Wu Xing theory in traditional Chinese mathematics (I)”, Applied Mathematics, 2012, Vol.3, No.2, pp:617-636. doi:10.4236/am.2012.36096 [21]Z.Q.Zhang and Y.S.Zhang, “Mathematical reasoning of economic intervening principle based on Yin Yang Wu Xing theory in traditional Chinese economics (I)”, Modern Economics, 2013, Vol.4, pp:130-144. doi:10.4236/me.2013.42016 [22]N.Q.Feng,Y.H.Qiu, F.Wang, Y.S..Zhang and S.Q.Yin, “A logic analysis model about complex system's stability: enlightenment from nature”. 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