The journal of Mathematical Researches (MR) aims to familiarize all Mathematical Scientists with recent advances in all fields of Mathematics published by Kharazmi University. It covers topics related to Mathematics in its broadest sense and publish applied, experimental and basic research works. The journal of Mathematical Researches (MR) was founded in 2015. The journal of Mathematical Researches (MR) is a peer-reviewed open access journal covering the full scope of Theoretical Mathematics, and Applied Mathematics. It is dedicated to publication of complete and important papers of original research in all areas of mathematics. Expository papers and research announcements of exceptional interest are also occasionally published. High standards are applied in evaluating submissions. https://mmr.khu.ac.ir/index.php?sid=1&slc_lang=en This account is managed by the Editor-in-Chief, Prof. Esmail Babolian. Phone: +98 2186072787 Address: Kharazmi University, No.43, South Mofatteh Ave., Tehran, Postal Code: 15719-14911, Iran. E-mail: mmr@khu.ac.ir, jscitmu@gmail.com
The judgment post stratification is a method of stratification of observation by using a key vari... more The judgment post stratification is a method of stratification of observation by using a key variable, such that stratification will be done after selecting the sample. In this paper, this method will use in two stage cluster sampling. In other words, instead of simple random sampling without replacement, we use the judgment post stratification method and the generalized judgment post stratification method in second stage of two stage cluster sampling, and obtain new estimators of the population mean. Finally, the proposed estimators are compared to usual two stage cluster simple random sampling estimator of the population mean by Monte Carlo simulation studies on a set of real data and generated data from symmetric and asymmetric distributions. The results of simulation study show that, in most cases, the proposed estimators have better performance than the mean of two stage cluster simple random sample.
In 2016, Prof. Shen et al. studied one of the most important warped structures of Finsler metrics... more In 2016, Prof. Shen et al. studied one of the most important warped structures of Finsler metrics and investigated Einstein type of the metrics. In this paper, we first compute the E-curvature of the metrics and characterize Finsler warped product metrics with isotropic E-curvature.
The natural and practical condition numbers for summation of complex numbers are introduced. Thes... more The natural and practical condition numbers for summation of complex numbers are introduced. These numbers measure the effect of loss of significant digits on the round-off error when computing a sum in floating point arithmetic. The relationship between the natural and practical condition numbers and their size are studied. It is shown that the practical condition number is equal to one when all the summands lie in one of the quadrants of the complex plane. Also, an upper bound for the natural condition number is obtained when the summands lie in a sector with an angle less than or equal to pi/2.
This manuscript deals with a Shannon wavelet regularization method to solve the inverse Cauchy pr... more This manuscript deals with a Shannon wavelet regularization method to solve the inverse Cauchy problem associated with the Helmholtz equation which uses to identify the radiation wave of an infinite “strip” domain. In view of Hadamard, the proposed problem extremely suffers from an intrinsic ill-posedness, i.e., the exact solution of this problem is computationally impossible to measure since any measurement or numerical computation is polluted by inevitable errors. To retrieve the solution, a regularization scheme based on Shannon wavelet is developed. The regularized solution is restored by Shannon wavelet projection on elements of Shannon multiresolution analysis. Furthermore, the concepts of convergence rate and stability of the proposed scheme are investigated and some new optimal stable estimates of the so-called Holder-Logarithmic type are rigorously derived by imposing an a priori information controlled by Sobolev scale. The computational performance of the proposed method effectively confirms the applicability and validity of our qualitative analysis.
In this paper, first by using the constructions of probabilistic b-metric Menger space and proba... more In this paper, first by using the constructions of probabilistic b-metric Menger space and probabilistic metric like Menger space, we introduce probabilistic b-metric like Menger space and present some examples of it. Then, we state and prove some fixed point theorems for teta-eta contraction multivalued mappings in these spaces. We show some fixed point results for generalized gamma-beta contraction type mappings on the probabilistic b-metric like Menger space. Finally, we present an example of usefulness and applicability of our results.
This paper, inspired by recent advances in the application of the multilevel Monte-Carlo (MLMC) a... more This paper, inspired by recent advances in the application of the multilevel Monte-Carlo (MLMC) approach to Lévy driven assets, is based on the valuation of financial derivatives. First, using the weak Euler method the numerical estimate of the underlying asset, which satisfies a multi-dimensional stochastic differential equation with Lévy noise, is calculated and then applying the weak multilevel Monte-Carlo method the expected price is obtained. In this paper, as an improvement of Belomestny’s work and with a new approach in the theory, we express and prove the convergence theorems in spacefor and not only 2. We also seek to implement the weak MLMC algorithm for nonlinear equations with dependent components and . In the end, we show numerical experiments when applied to different types of processes with call options.
Let and be nonempty subsets of metric space . In this paper, first we introduce two types ... more Let and be nonempty subsets of metric space . In this paper, first we introduce two types of non-cyclic contractions on Then we study the existence and uniqueness of an optimal pair of fixed points for such mappings by considering property UC, in metric spaces. Our main results are generalization of recent best proximity points theorems for the corresponding cyclic contractions due to Di Bari-Suzuki-Vetro and Felicit-Eldred.
Suppose is a finite measure space, E is a Banach lattice, and is the space of all Bochner int... more Suppose is a finite measure space, E is a Banach lattice, and is the space of all Bochner integrable E valued functions. In this note, we show that is a KB-space or has the sequential Fatou property if and only if so is E Among this, some results about Bochner integral convergence in using order structure of, have been proved, as well.
The cable equation is one the most fundamental mathematical models in the neuroscience, which des... more The cable equation is one the most fundamental mathematical models in the neuroscience, which describes the electro-diffusion of ions in denderits. New findings indicate that the standard cable equation is inadequate for describing the process of electro-diffusion of ions. So, recently, the cable model has been modified based on the theory of fractional calculus. In this paper, the two dimensional time fractional nonlinear cable equation as an improved mathematical model in neuronal dynamics, is investigated numerically. An efficient and powerful computational technique based on the combination of time integration scheme and local weak form meshfree method has been formulated and implemented to solve the underlying problem. An implicit difference scheme with second order accuracy is used to discretize the model in the temporal direction. Then a meshless method based on the local Petrov-Galerkin technique is employed to fully discretize the model. The proposed numerical technique is performed to approximate the solutions of three examples. Presented results through the Tables and figures confirm the high efficiency and accuracy of the method.
By using a new search direction, we propose an infeasible
interior-point method for monotone line... more By using a new search direction, we propose an infeasible interior-point method for monotone linear complementarity problem. The algorithm uses only one feasibility step in each iteration, and we prove that it suffices in order to obtain a polynomial-time method. The iteration bound coincides with the currently best iteration bound for linear complementarity problems. Moreover, the numerical results show that the new algorithm has a good performance.
In this paper, we present a generalization of well-posedness for a system of split multi-valued v... more In this paper, we present a generalization of well-posedness for a system of split multi-valued variational inequalities with set-valued maps and establish a metric characterization for them. Moreover, we show that the strong well-posedness is equivalent to the existence and uniqueness of solution for a split multi-valued variational inequality.
For given graphs G1 and G2 the Ramsey number R(G1;G2), is the smallest positive
integer n such th... more For given graphs G1 and G2 the Ramsey number R(G1;G2), is the smallest positive integer n such that each blue-red edge coloring of the complete graph Kn contains a blue copy of G1 or a red copy of G2. In 1983, Erd}os conjectured that there is an absolute constant c such that R(G) = R(G;G) 2c p m for any graph G with m edges and no isolated vertices. Recently this conjecture was proved by Sudakov. In this short note, we give an extention of this result. As a corollary of our result we have R(G1;G2) 2250 p m for graphs G1 and G2 with no isolated vertices and m1 and m2 edges, respectively, where m = fm1;m2g Keywords: Ramsey number, Erd}os' conjecrure.
Hilbert C∗-modules were firrst introduced in the work of I. Kaplansky.Hilbert C*-modules are the ... more Hilbert C∗-modules were firrst introduced in the work of I. Kaplansky.Hilbert C*-modules are the natural generalization that of Hilbert spaces arising by replacing of the field of scalars C by a C∗-algebra. Let us recall some basic facts about the Hilbert C∗-modules. Let A be a C∗-algebra. An right inner product A-module is a linear space X which is a right A-module (with compatible scalar multiplication: λ(x.a) =(λx).a = x.(λa) for x ∈ X, a ∈ A, λ ∈ C), together with a map (x, y)→ : X × X → A such that for all x, y, z ∈ X, a ∈ A, α, β ∈ C.
In This paper, we consider two boundary value problems for non homogenuous Cauchy- Riemann equat... more In This paper, we consider two boundary value problems for non homogenuous Cauchy- Riemann equation with local and non-local boundary conditions separatly.In the first problem boundary condition is local and for proving uniqueness of solution, we show that homogenuous boundary value problem has only non-trivial solution. In the second problem, the boundary condition is non-local. At first, the given problem changed to a second kind system of Fredholm integral equation. Then the singularities in the Kernels of integral equations are removed. Finaly, for the uniqueness of solution, we show that the regularized kernels satify in contraction mapping theorem.
In this paper, a numerical method based on the finite element method and the least square scheme ... more In this paper, a numerical method based on the finite element method and the least square scheme with the Tikhonov regularization method for nonlinear inverse diffusion problem is presented. For this propose, first finite element method and basis functions will be used to discretize the variational form of the problem; then the least square scheme and Tikhonov regularization method are proposed to correct diffusion. It is assumed that no prior information is available on the functional form of the unknown diffusion coefficient in the present study, and so, it is classified as the function estimation in inverse calculation. Numerical result shows that a good estimation on the unknown functions of the inverse problem can be obtained.
In this paper, we study and describe the higher derivatives on the lattices. We also provide exam... more In this paper, we study and describe the higher derivatives on the lattices. We also provide examples to clarify the content.
Survival analysis, and in particular survival distribution estimation, are important issues in th... more Survival analysis, and in particular survival distribution estimation, are important issues in the statistical sciences. Various parametric and nonparametric methods have been proposed to estimate the survival distribution. In this respect, the theoretical survival distributions are specified and their parameters are obtained by methods such as the maximum likelihood estimator and the Bayesian estimator and we can mention to nonparametric methods such as the Kaplan-Meier method, Cox regression and the life table. In addition, another important issue in survival analysis, especially in actuarial and biostatistics, is graduation of data for which smoothness and goodness of fit are two fundamental requirements.On the other hand, in the probability theory, there are two basic approaches to estimate probability distributions by using the concept of entropy: Maximum Entropy Principle (ME) and Minimum Kullback-Leibler Principle (MKL) or Minimum Cross Entropy Principle. In this paper, we examine the approach of the above two optimization models to estimate survival and probability distributions, especially for the classification of the data. In these studies, in addition to investigating parametric models, in order to achieve a compromise between the conditions of smoothness and goodness of fit, we apply a new entropy optimization model by defining an objective function combined from both of the two above principles and adjusting a coefficient that is used to ensure the degree of goodness of fitting and smoothing the estimates, as well as to show their priority in the classification of the data. We use this model to estimate the mortality probability distribution, particularly the column related to the mortality probability of a certain age ( qx) in life table. Finally, with the help of this method, we set the life table for Iranian women and men in 2011.
The judgment post stratification is a method of stratification of observation by using a key vari... more The judgment post stratification is a method of stratification of observation by using a key variable, such that stratification will be done after selecting the sample. In this paper, this method will use in two stage cluster sampling. In other words, instead of simple random sampling without replacement, we use the judgment post stratification method and the generalized judgment post stratification method in second stage of two stage cluster sampling, and obtain new estimators of the population mean. Finally, the proposed estimators are compared to usual two stage cluster simple random sampling estimator of the population mean by Monte Carlo simulation studies on a set of real data and generated data from symmetric and asymmetric distributions. The results of simulation study show that, in most cases, the proposed estimators have better performance than the mean of two stage cluster simple random sample.
In 2016, Prof. Shen et al. studied one of the most important warped structures of Finsler metrics... more In 2016, Prof. Shen et al. studied one of the most important warped structures of Finsler metrics and investigated Einstein type of the metrics. In this paper, we first compute the E-curvature of the metrics and characterize Finsler warped product metrics with isotropic E-curvature.
The natural and practical condition numbers for summation of complex numbers are introduced. Thes... more The natural and practical condition numbers for summation of complex numbers are introduced. These numbers measure the effect of loss of significant digits on the round-off error when computing a sum in floating point arithmetic. The relationship between the natural and practical condition numbers and their size are studied. It is shown that the practical condition number is equal to one when all the summands lie in one of the quadrants of the complex plane. Also, an upper bound for the natural condition number is obtained when the summands lie in a sector with an angle less than or equal to pi/2.
This manuscript deals with a Shannon wavelet regularization method to solve the inverse Cauchy pr... more This manuscript deals with a Shannon wavelet regularization method to solve the inverse Cauchy problem associated with the Helmholtz equation which uses to identify the radiation wave of an infinite “strip” domain. In view of Hadamard, the proposed problem extremely suffers from an intrinsic ill-posedness, i.e., the exact solution of this problem is computationally impossible to measure since any measurement or numerical computation is polluted by inevitable errors. To retrieve the solution, a regularization scheme based on Shannon wavelet is developed. The regularized solution is restored by Shannon wavelet projection on elements of Shannon multiresolution analysis. Furthermore, the concepts of convergence rate and stability of the proposed scheme are investigated and some new optimal stable estimates of the so-called Holder-Logarithmic type are rigorously derived by imposing an a priori information controlled by Sobolev scale. The computational performance of the proposed method effectively confirms the applicability and validity of our qualitative analysis.
In this paper, first by using the constructions of probabilistic b-metric Menger space and proba... more In this paper, first by using the constructions of probabilistic b-metric Menger space and probabilistic metric like Menger space, we introduce probabilistic b-metric like Menger space and present some examples of it. Then, we state and prove some fixed point theorems for teta-eta contraction multivalued mappings in these spaces. We show some fixed point results for generalized gamma-beta contraction type mappings on the probabilistic b-metric like Menger space. Finally, we present an example of usefulness and applicability of our results.
This paper, inspired by recent advances in the application of the multilevel Monte-Carlo (MLMC) a... more This paper, inspired by recent advances in the application of the multilevel Monte-Carlo (MLMC) approach to Lévy driven assets, is based on the valuation of financial derivatives. First, using the weak Euler method the numerical estimate of the underlying asset, which satisfies a multi-dimensional stochastic differential equation with Lévy noise, is calculated and then applying the weak multilevel Monte-Carlo method the expected price is obtained. In this paper, as an improvement of Belomestny’s work and with a new approach in the theory, we express and prove the convergence theorems in spacefor and not only 2. We also seek to implement the weak MLMC algorithm for nonlinear equations with dependent components and . In the end, we show numerical experiments when applied to different types of processes with call options.
Let and be nonempty subsets of metric space . In this paper, first we introduce two types ... more Let and be nonempty subsets of metric space . In this paper, first we introduce two types of non-cyclic contractions on Then we study the existence and uniqueness of an optimal pair of fixed points for such mappings by considering property UC, in metric spaces. Our main results are generalization of recent best proximity points theorems for the corresponding cyclic contractions due to Di Bari-Suzuki-Vetro and Felicit-Eldred.
Suppose is a finite measure space, E is a Banach lattice, and is the space of all Bochner int... more Suppose is a finite measure space, E is a Banach lattice, and is the space of all Bochner integrable E valued functions. In this note, we show that is a KB-space or has the sequential Fatou property if and only if so is E Among this, some results about Bochner integral convergence in using order structure of, have been proved, as well.
The cable equation is one the most fundamental mathematical models in the neuroscience, which des... more The cable equation is one the most fundamental mathematical models in the neuroscience, which describes the electro-diffusion of ions in denderits. New findings indicate that the standard cable equation is inadequate for describing the process of electro-diffusion of ions. So, recently, the cable model has been modified based on the theory of fractional calculus. In this paper, the two dimensional time fractional nonlinear cable equation as an improved mathematical model in neuronal dynamics, is investigated numerically. An efficient and powerful computational technique based on the combination of time integration scheme and local weak form meshfree method has been formulated and implemented to solve the underlying problem. An implicit difference scheme with second order accuracy is used to discretize the model in the temporal direction. Then a meshless method based on the local Petrov-Galerkin technique is employed to fully discretize the model. The proposed numerical technique is performed to approximate the solutions of three examples. Presented results through the Tables and figures confirm the high efficiency and accuracy of the method.
By using a new search direction, we propose an infeasible
interior-point method for monotone line... more By using a new search direction, we propose an infeasible interior-point method for monotone linear complementarity problem. The algorithm uses only one feasibility step in each iteration, and we prove that it suffices in order to obtain a polynomial-time method. The iteration bound coincides with the currently best iteration bound for linear complementarity problems. Moreover, the numerical results show that the new algorithm has a good performance.
In this paper, we present a generalization of well-posedness for a system of split multi-valued v... more In this paper, we present a generalization of well-posedness for a system of split multi-valued variational inequalities with set-valued maps and establish a metric characterization for them. Moreover, we show that the strong well-posedness is equivalent to the existence and uniqueness of solution for a split multi-valued variational inequality.
For given graphs G1 and G2 the Ramsey number R(G1;G2), is the smallest positive
integer n such th... more For given graphs G1 and G2 the Ramsey number R(G1;G2), is the smallest positive integer n such that each blue-red edge coloring of the complete graph Kn contains a blue copy of G1 or a red copy of G2. In 1983, Erd}os conjectured that there is an absolute constant c such that R(G) = R(G;G) 2c p m for any graph G with m edges and no isolated vertices. Recently this conjecture was proved by Sudakov. In this short note, we give an extention of this result. As a corollary of our result we have R(G1;G2) 2250 p m for graphs G1 and G2 with no isolated vertices and m1 and m2 edges, respectively, where m = fm1;m2g Keywords: Ramsey number, Erd}os' conjecrure.
Hilbert C∗-modules were firrst introduced in the work of I. Kaplansky.Hilbert C*-modules are the ... more Hilbert C∗-modules were firrst introduced in the work of I. Kaplansky.Hilbert C*-modules are the natural generalization that of Hilbert spaces arising by replacing of the field of scalars C by a C∗-algebra. Let us recall some basic facts about the Hilbert C∗-modules. Let A be a C∗-algebra. An right inner product A-module is a linear space X which is a right A-module (with compatible scalar multiplication: λ(x.a) =(λx).a = x.(λa) for x ∈ X, a ∈ A, λ ∈ C), together with a map (x, y)→ : X × X → A such that for all x, y, z ∈ X, a ∈ A, α, β ∈ C.
In This paper, we consider two boundary value problems for non homogenuous Cauchy- Riemann equat... more In This paper, we consider two boundary value problems for non homogenuous Cauchy- Riemann equation with local and non-local boundary conditions separatly.In the first problem boundary condition is local and for proving uniqueness of solution, we show that homogenuous boundary value problem has only non-trivial solution. In the second problem, the boundary condition is non-local. At first, the given problem changed to a second kind system of Fredholm integral equation. Then the singularities in the Kernels of integral equations are removed. Finaly, for the uniqueness of solution, we show that the regularized kernels satify in contraction mapping theorem.
In this paper, a numerical method based on the finite element method and the least square scheme ... more In this paper, a numerical method based on the finite element method and the least square scheme with the Tikhonov regularization method for nonlinear inverse diffusion problem is presented. For this propose, first finite element method and basis functions will be used to discretize the variational form of the problem; then the least square scheme and Tikhonov regularization method are proposed to correct diffusion. It is assumed that no prior information is available on the functional form of the unknown diffusion coefficient in the present study, and so, it is classified as the function estimation in inverse calculation. Numerical result shows that a good estimation on the unknown functions of the inverse problem can be obtained.
In this paper, we study and describe the higher derivatives on the lattices. We also provide exam... more In this paper, we study and describe the higher derivatives on the lattices. We also provide examples to clarify the content.
Survival analysis, and in particular survival distribution estimation, are important issues in th... more Survival analysis, and in particular survival distribution estimation, are important issues in the statistical sciences. Various parametric and nonparametric methods have been proposed to estimate the survival distribution. In this respect, the theoretical survival distributions are specified and their parameters are obtained by methods such as the maximum likelihood estimator and the Bayesian estimator and we can mention to nonparametric methods such as the Kaplan-Meier method, Cox regression and the life table. In addition, another important issue in survival analysis, especially in actuarial and biostatistics, is graduation of data for which smoothness and goodness of fit are two fundamental requirements.On the other hand, in the probability theory, there are two basic approaches to estimate probability distributions by using the concept of entropy: Maximum Entropy Principle (ME) and Minimum Kullback-Leibler Principle (MKL) or Minimum Cross Entropy Principle. In this paper, we examine the approach of the above two optimization models to estimate survival and probability distributions, especially for the classification of the data. In these studies, in addition to investigating parametric models, in order to achieve a compromise between the conditions of smoothness and goodness of fit, we apply a new entropy optimization model by defining an objective function combined from both of the two above principles and adjusting a coefficient that is used to ensure the degree of goodness of fitting and smoothing the estimates, as well as to show their priority in the classification of the data. We use this model to estimate the mortality probability distribution, particularly the column related to the mortality probability of a certain age ( qx) in life table. Finally, with the help of this method, we set the life table for Iranian women and men in 2011.
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Papers by Mathematical Researches
interior-point method for monotone linear complementarity problem. The
algorithm uses only one feasibility step in each iteration, and we prove that
it suffices in order to obtain a polynomial-time method. The iteration bound
coincides with the currently best iteration bound for linear complementarity
problems. Moreover, the numerical results show that the new algorithm has
a good performance.
integer n such that each blue-red edge coloring of the complete graph Kn contains a blue
copy of G1 or a red copy of G2. In 1983, Erd}os conjectured that there is an absolute constant
c such that R(G) = R(G;G) 2c
p
m for any graph G with m edges and no isolated vertices.
Recently this conjecture was proved by Sudakov. In this short note, we give an extention
of this result. As a corollary of our result we have R(G1;G2) 2250
p
m for graphs G1 and
G2 with no isolated vertices and m1 and m2 edges, respectively, where m = fm1;m2g
Keywords: Ramsey number, Erd}os' conjecrure.
Let A be a C∗-algebra. An right inner product A-module is a linear space X which is a right A-module (with compatible scalar multiplication: λ(x.a) =(λx).a = x.(λa) for x ∈ X, a ∈ A, λ ∈ C), together with a map (x, y)→ : X × X → A such that for all x, y, z ∈ X, a ∈ A, α, β ∈ C.
In this paper, we examine the approach of the above two optimization models to estimate survival and probability distributions, especially for the classification of the data. In these studies, in addition to investigating parametric models, in order to achieve a compromise between the conditions of smoothness and goodness of fit, we apply a new entropy optimization model by defining an objective function combined from both of the two above principles and adjusting a coefficient that is used to ensure the degree of goodness of fitting and smoothing the estimates, as well as to show their priority in the classification of the data. We use this model to estimate the mortality probability distribution, particularly the column related to the mortality probability of a certain age ( qx) in life table. Finally, with the help of this method, we set the life table for Iranian women and men in 2011.
interior-point method for monotone linear complementarity problem. The
algorithm uses only one feasibility step in each iteration, and we prove that
it suffices in order to obtain a polynomial-time method. The iteration bound
coincides with the currently best iteration bound for linear complementarity
problems. Moreover, the numerical results show that the new algorithm has
a good performance.
integer n such that each blue-red edge coloring of the complete graph Kn contains a blue
copy of G1 or a red copy of G2. In 1983, Erd}os conjectured that there is an absolute constant
c such that R(G) = R(G;G) 2c
p
m for any graph G with m edges and no isolated vertices.
Recently this conjecture was proved by Sudakov. In this short note, we give an extention
of this result. As a corollary of our result we have R(G1;G2) 2250
p
m for graphs G1 and
G2 with no isolated vertices and m1 and m2 edges, respectively, where m = fm1;m2g
Keywords: Ramsey number, Erd}os' conjecrure.
Let A be a C∗-algebra. An right inner product A-module is a linear space X which is a right A-module (with compatible scalar multiplication: λ(x.a) =(λx).a = x.(λa) for x ∈ X, a ∈ A, λ ∈ C), together with a map (x, y)→ : X × X → A such that for all x, y, z ∈ X, a ∈ A, α, β ∈ C.
In this paper, we examine the approach of the above two optimization models to estimate survival and probability distributions, especially for the classification of the data. In these studies, in addition to investigating parametric models, in order to achieve a compromise between the conditions of smoothness and goodness of fit, we apply a new entropy optimization model by defining an objective function combined from both of the two above principles and adjusting a coefficient that is used to ensure the degree of goodness of fitting and smoothing the estimates, as well as to show their priority in the classification of the data. We use this model to estimate the mortality probability distribution, particularly the column related to the mortality probability of a certain age ( qx) in life table. Finally, with the help of this method, we set the life table for Iranian women and men in 2011.