Shapes

All the fields of Mathematics-‘Algebra’, ‘Trigonometry’, ‘Geometry’, ‘Calculus’ and ‘Statistics’ are based on the Patterns, Shapes and Numbers and thus we can conclude that Mathematics is based on Pattern, Shapes and Numbers. Defining mathematics is always been keen concern of mathematicians as well as any introduction math class. One way of definition is defining it by “what it does in the era?” and that is the definition of mathematics for the era. So, in this era of analytical science where everyday people are dealing with lots and lots of data analysis in each and every field, the Pattern, Shapes and Numbers have become the limelight of Mathematics-Research and now mathematics has grown from just solving sums to an experimentation and observation, finding relation to the real world and thus it involves science which brings us to conclusion, “Mathematics is the Science of Patterns, Shapes and Numbers.” Thus, Mathematics can be defined as the science of “Pattern, Shapes and Numbers”.

In another time when kingdoms created their dynasty’s iconic buildings, the architect and artisans took their ques from the reigning monarch. In our modern pluralistic society the free reign of ideas and opinions as to contexts and their meanings are diverse. As the doctor takes the Hippocratic oath, the lawyer vows to defend all so there is one whose call is to capture the ethos (4.0 The Oxford English Dictionary, is defined as "the characteristic spirit, prevalent tone of sentiment, of a people or community” ) of his time into built metaphors, he is called architect. Not only is my childhood quest relevant but the essence of the responsibility of today’s architect who not only reasons the technical but individually reasons the conceptual. It is to the architect that society turns to be informed about the shape and form of the context in which life will be played. With this charge the need to know that we know and do by reasoning what science verifies by the scientific method to know that we know about the buildings, parks, and places we set into the environment. It is a public and private charge included in the contract for professional services but unspoken as professional life’s experience; to prove the relevant, meaningful and beneficial metaphors that edify encourage and equip society as well as provide for its’ health, safety and welfare. So it is critical to realize, control and accept as commonplace that the role of the architect is to do much more than build but build masterfully.

Dividing the discipline’s metaphors between technical and conceptual is a reality not fully explored, nor I believe never noticed. In addition to the multidisciplinary relevance and general use of metaphors, metaphoric axioms, arguments in favor of the stasis of why interior design is an art the two realities of the metaphor work separately and together in six  creative ways.  Many of my monographs included analyzing and explaining the syllogism:
• Art[I]  is the making of metaphors
• Interior design  is an art[I]
• Therefore interior design is the making of metaphors.
Art [I] is only when skill is applied with intent and advanced development of some skill.
Till now we did nothing to reason why art [I] is the making of metaphors, nor why interior is an art [I]. Since 1967 I proceeded to analyze the presumptions and find its many applications. This new information in Metaphor and Thought by Andrew Ortony first published in 1979, provides information to support inductive reasoning and to this end each axiom is its own warrant to the inferences of the above syllogism and the answer to questions of why metaphor is the stasis to any of the syllogism’s claims and implications.
The six priciples explain the stasis in terms of metaphor’s two technical and conceptual dimensions.  Both are valid separately and even more acceptable in combination.  But how do they two operate and how does knowing this benefit design, use and evaluation of built works?
The technical is that all art [I], including interior design, expresses one thing in terms of another by its inherent and distinct craft. On the one hand there is the designer who acts as the owsnere’s surrogate  and on the other the fountain of conceptual metaphors which expresses ideas as built conceptual metaphors other wise known as interior desings. Techne is actually a system of practical knowledge as a craft or art informed by knowledge of forms. 
For  example,  the craft of managing a firm ofinterior designers where even virtue is a kind of technê of management and design practice, one that is based on an understanding of the profession, business and market. In this case the technai are such activities as drafting, specifying, managing, negotiating, programming, planning, supervising, and inspection.  By association with these technai, we can include decorationg, funiture selection, color coordianation, writing, and painting.  So much so that the study and practice of design is devoid from the humanities and downplays theories of design;  developing rather the crafts, skill and understandings needed to plan, sketch, draw, delineate, specify, write, and design.
Contemporary interior design is replete with axioms, principles and theorems guiding the geometry, applications of science, use of engineering, and formal logic to produce technical metaphors and justly excluding a whole conversation about the conceptual part of the built metaphor.

Twenty eight dominant axioms and 54 sub-dominant axioms (total of 82) are evidence of the case that architecture is an art resolved that architecture was the making of metaphors because it (architecture) made metaphors, personified by metaphor stasis’ two technical and conceptual dimensions. Both are valid separately and even more usual in combination. But how do these two work, and, how does this knowledge benefit design, use and evaluation of built works? The axioms were derived by examining Andrew Ortony’s Metaphor and Thought’s evidence and works by Paul Weiss, William J.J. Gordon and the Yale lecture series titled architecture as the making of metaphors. . Prior monographs were steeped in deductive reasoning since there was no new information (evidence) pertaining to metaphors. Therefore the previous articles included analyzing and explaining the syllogism:
• Art [G] is the making of metaphors
• Architecture is an art [G]
• Therefore architecture is the making of metaphors.

The Augustan Period is of vital importance for the study of the history of glass production in the western provinces of the Imperium Romanum. The technique of glassblowing was introduced during the second quarter of the first century B.C. in the eastern Mediterranean and meant a genuine revolution of the glass vessels, both for the number of vessels produced and for the variety of their shapes. The innovation reached Italy some decades later and spread quickly over all of the western provinces. In these regions the first workshops for vessel glass arose at the end of the first century B.C. and the beginning of the first century A.D., probably mostly directed by immigrants from the East, e.g. the well-known Artas from Sidon, who worked in central and northern Italy.
Very important for this period is also the concept of skeuomorphism, the analogy of shape in different materials. By means of the new technique the production of glass vessels could be significantly increased. Therewith, a necessity of new shapes arose, the production of which was made possible just thanks to the technical innovations. The existence of a new wealthy clientele fostered the rise of the western production, which began to develop own innovations, affecting also the East, which was now losing its former hegemony.
Consequently many shapes of the glass vessels from this period can also be found in ceramics and precious metal. The specific study of these shapes reveals multilateral relations between the different materials and shows that the products of the glass workshops not only repeated shapes known from other materials, but started to influence the potters’ work.

A fin is a surface that extends from an object to increase the rate of heat transfer to or from the environment by increasing convection. Extensions on the finned surfaces is used to increases the surface area of the fin in contact with the fluid flowing around it. In the study of heat transfer, fins are surfaces that extend from an object to increase the rate of heat transfer to or from the environment by increasing convection. The amount of conduction, convection, or radiation of an object determines the amount of heat it transfers. Increasing the temperature gradient between the object and the environment, increasing the convection heat transfer coefficient, or increasing the surface area of the object increases the heat transfer. Sometimes it is not feasible or economical to change the first two options. Thus, adding a fin to an object, increases the surface area and can sometimes be an economical solution to heat transfer problems. There are two ways to increase the rate of heat transfer: 1) To increase the convection heat transfer coefficient h. 2) To increase the surface area As. It is noted that: Increasing h may require the installation of a pump or fan, or replacing the existing one with a large one. The alternative is to increase the surface area by attaching to the surface extended surfaces called fins made of highly conductive material such as aluminium.

In the present paper, a new approach for structural topology optimization based on dynamic implicit surface function (DISF) is proposed. DISF is used to describe the shape/topology of a structure, which is approximated in terms of the nodal values. Then, a relationship is established between the element stiffness and the values of the implicit surface function on its four nodes.

Twenty eight dominant axioms and 54 sub-dominant axioms (total of 82) are evidence of the case that architecture is an art resolved that architecture was the making of metaphors because it (architecture) made metaphors, personified by metaphor stasis’ two technical and conceptual dimensions. Both are valid separately and even more usual in combination. But how do these two work, and, how does this knowledge benefit design, use and evaluation of built works? The axioms were derived by examining Andrew Ortony’s Metaphor and Thought’s evidence and works by Paul Weiss, William J.J. Gordon and the Yale lecture series titled architecture as the making of metaphors. . Prior monographs were steeped in deductive reasoning since there was no new information (evidence) pertaining to metaphors. Therefore the previous articles included analyzing and explaining the syllogism:
• Art [G] is the making of metaphors
• Architecture is an art [G]
• Therefore architecture is the making of metaphors.

We describe a web application that takes advantage of new computer vision techniques to allow the user to make searches based on visual similarity of color and texture related to the object of interest. We use a supervised neural network strategy to segment different classes of objects. A strength of this solution is the high speed in generalization of the trained neural networks, in order to obtain an object segmentation in real time. Information about the segmented object, such as color and texture, are extracted and indexed as text descriptions. Our case study is the online commercial offers domain where each offer is composed by text and images. Many successful experiments were done on real datasets in the fashion field.

Early monographs were steeped in deductive reasoning since we could not find new information pertaining to metaphors. This included analyzing and explaining the syllogism:
• Art[I]  is the making of metaphors
• Architecture (design)  is an art [I]
• Therefore architecture (design) is the making of metaphors.
Till now we did nothing to reason why art [I] is the making of metaphors nor why architecture is an art. Since 1967 I proceeded to analyze the presumptions and find its many applications. This new information by Andrew Ortony first published in 1979, provides information to support inductive reasoning and to this end each axiom is its own warrant to the inferences of the above syllogism and the answer to why metaphor is the stasis to any of the syllogism’s claims and implications. The axioms are presented in labeled paragraph and subparagraphs format for easy reference and applications.
Keywords:
metaphor, architecture, thought, commonality, commonplace, dubbing, cognitive, knowing, stasis, art , [I]  linguistic analogy, equilibrium, equipoise, topoi, top-down, frame conflict, appreciate, conduit, parte, design system, modified culture, mapping, structure, domain, signs, apparatus, spaces, volumes, shapes, forms, metaphorical mappings, invariance principle, alive, dead, onomatopeics, surrogates, appetite, desire, mind, indirect use, direct use, vision, gestalt, formulae, grand design, psychological, processes, metaphor comprehension, memory, mnemonics, encoding, mapping, categorizing, inference, assimilation, accommodation, attribution, inferential import,  structured programming, stability, referential specificity, general acceptance of terms, vividness thesis, difference, identity, comparison sensible, communications.

We present a study of compression efficiency for binary objects or bi-level images for different chain-code schemes. Chain-code techniques are used for compression of bi-level images because they preserve information and allow a considerable data reduction. Furthermore, chain codes are the standard input format for numerous shape-analysis algorithms. In this work we apply chain codes to represent object with holes and we compare their compression efficiency for seven chain codes. We have also compared all these chain codes with the JBIG standard for bi-level images.

A new chain code for shapes composed of regular cells is defined. This boundary chain code is based on the numbers of cell vertices which are in touch with the bounding contour of the shape. This boundary chain code is termed vertex chain code (VCC). The VCC is invariant under translation and rotation. Also, it may be starting point normalized and invariant under mirroring transformation. Using this concept of chain code it is possible to relate the chain length to the contact perimeter, which corresponds to the sum of the boundaries of neighboring cells of the shape (Bribiesca, E., Comp. Math. Appl. 33(11) (1997) 1–9); also, to relate the chain nodes to the contact vertices, which correspond to the vertices of neighboring cells. So, in this way, these relations among the chain and the characteristics of interior of the shape allow us to obtain interesting properties. This work is motivated by the idea of obtaining various shape features computed directly from the VCC without going to Cartesian-coordinate representation. Finally, in order to illustrate the capabilities of the VCC: we present some results using real shapes.

The richness of natural images makes the quest for optimal representations in image processing and computer vision challenging. The latter observation has not prevented the design of image representations, which trade off between efficiency and complexity, while achieving accurate rendering of smooth regions as well as reproducing faithful contours and textures. The most recent ones, proposed in the past decade, share an hybrid heritage highlighting the multiscale and oriented nature of edges and patterns in images. This paper presents a panorama of the aforementioned literature on decompositions in multiscale, multi-orientation bases or dictionaries. They typically exhibit redundancy to improve sparsity in the transformed domain and sometimes its invariance with respect to simple geometric deformations (translation, rotation). Oriented multiscale dictionaries extend traditional wavelet processing and may offer rotation invariance. Highly redundant dictionaries require specific algorithms to simplify the search for an efficient (sparse) representation. We also discuss the extension of multiscale geometric decompositions to non-Euclidean domains such as the sphere or arbitrary meshed surfaces. The etymology of panorama suggests an overview, based on a choice of partially overlapping "pictures". We hope that this paper will contribute to the appreciation and apprehension of a stream of current research directions in image understanding.

In this study, the effect of coarse aggregate shape characteristics on the compactability and microstructural properties of asphalt mixtures was virtually investigated using a discreet element method (DEM). Results reveal there is a statistically significant correlation between coarse aggregate flatness, elongation, roundness, and sphericity as shape descriptors and initial asphalt mixture density, as a compaction parameter. Analyses indicate that among all particle shape descriptors, only roundness and regularity had a statistically significant relation with compaction slope, and as the amount of roundness and regularity increase, the compaction slope decreases. Additionally, flatness and elongation values greater than 0.75 result in lower average coordination number values compared to those values less than 0.75. Results also indicate that although the probability density function (PDF) of low contact force highly depends on flatness, elongation and sphericity of particles, the PDF of high and very high contact forces is independent of the particle shape.

Whewellite crystals are most commonly found in kidneys, ureter and urinary bladder causing urolithiasis. The purpose of the present in vitro study was to observe the possible growth patterns and morphology of whewellite crystals. The study was carried out in U-shaped test tubes. Bow shape, donuts and their aggregates, dumbbell, platy, prismatic, rosette, styloid, X-shape and tetragonal bipyramidal crystals were observed. Energy Dispersive X-ray, Fourier Transform Infra-Red spectroscopies and Scanning Electron Microscopy were used to characterize the crystals. This study will be helpful to determine the promotion, modulation and inhibition of the crystals evaluate risk factors and prophylactic management of urinary stones.

In this study, the shape of coarse aggregate particles has been related to the workability and compressive strength of cement concrete for rigid pavements. The shape characteristics such as elongation, flatness, shape factor, and sphericity were determined. Also,the slump and compressive strength of cement concrete were determined for various shapes of coarse aggregate. The test results indicated that there is a good correlation between some shape properties of aggregate, workability, and compressive strength.The highest compressive strength at different ages noted with concrete made from different shapes of coarse aggregates. Results indicate that the strength of concrete varies as a function of the shape of the coarse aggregate, which leads to the conclusion that the shape of aggregate shall be considered as an important parameter in deciding the suitability of coarse aggregate to prepare cement concrete for rigid pavements. I. INTRODUCTION To provide a stable and even surface for the traffic, the roadway is always provided with a suitably designed and constructed pavement structure. Thus, a pavement consisting of a few layers of pavement materials is constructed over a prepared layer of sub-grade to serve as a carriageway. Based on design consideration pavements can be classified as-Rigid pavements and Flexible pavement. Flexible pavements can be defined as the one consisting of a mixture of asphaltic or bituminous material and aggregates placed on a bed of compacted granular material of appropriate quality in layers over the subgrade. Rigid pavements are those, which possess noteworthy flexural strength or flexural rigid. The rigid pavement has the slab action and is capable of transmitting the wheel load stresses through a wider area below. Cement concrete is a composite material produced by the homogenous mixing of selected proportions of water, cement, and aggregates (fine and coarse). Strength is the most desired quality of a good concrete. It should be strong enough, at hardened state, to resist the various stresses to which it would be subjected. Aggregates are the most important constituents in cement concrete. For a long time aggregates were considered as inert materials, but after 1940 it was brought out that aggregates do show some reactivity. The mere fact that aggregates constitute 70-80% of the volume of concrete, their impact on various characteristics is undoubtedly considerable. Aggregates give the body to the concrete, reduce shrinkage, and affect the economy. Among all the characteristics of aggregates, the shape is most important because it affects the workability and compressive strength of cement concrete. Aggregates form the major portions of pavement structure and aggregates have to bear stresses occurring due to wheel loads on the pavement and on the surface-course they have to resist wear due to the abrasive action of traffic. Therefore, the properties of aggregates are of considerable significance to the highway engineers. Significant findings indicate that aggregate plays a more "active" role than was previously believed, and a better understanding will result from further research. Several authors have indicated the need for more research to determine the effect of aggregate particle shape on the properties of concrete at present there is only alimited amount of information concerning the effect of aggregate particle shape on concrete proportioning, workability, and strength. This lack of information is reflected in specifications that place conservative limits on allowable amounts of particles of certain shapes. The present study was undertaken to investigate the effect of different types of coarse aggregate effect on the fresh and hardened Portland cement concrete behavior by a means of aggregate shape indexes such as elongation, flatness, roundness, shape factor, and sphericity.

— With increase in the temperature due to global warming cold air is necessary for human being. Air conditioning system for air cooling is always better option but there is high level of power consumption and to overcome such difficulty vortex flow cooling is the better option. In vortex flow due to geometry more the turbulence in the flow and which dissipates more amount of heat and to enhance the rate of heat transfer cooling water will be circulated and this is nothing but aim of present work.

In  this  paper,  we  published  a  survey  and  analysis  on  a  variety  of  the  various  strategies  for  maximizing  gain  and bandwidth. Because of their low profile, light weight, lowcost, compactness etc., Microstrip Patch Antenna (MPA) is widely used in  various  antenna  systems.  Owing  to  its  versatility,  the  patch  antenna  is  often  used  with  the  Microwave  IC  and  Monolithic Microwave IC's. But MPA’s lower gain and bandwidth is one of the key disadvantages. The researchers used various methods to achieve  enrichment,  such  as  in  the  microstrip  antenna  array,  superstrate  structure,  change  of  dielectric  material  and  partialremoval of substrates.

This paper presents matching and similarity evaluation meth- ods between two NURBS surfaces, and their application to copyright protection of digital data representing solids or NURBS surfaces. Two methods are employed to match ob- jects: the moment and the curvature methods. The moment method uses integral properties, i.e. the volume, the princi- pal moments of inertia and directions, to find the rigid body transformation as well as the scaling factor. The curva- ture method is based on the Gaussian and the mean cur- vatures to establish correspondence between two objects. The matching algorithms are applied to problems of copy- right protection. A suspect model is aligned to an original model through the matching methods so that similarity be- tween two models can be assessed to determine if the suspect model contains part(s) of the original model, which may be stored in an independent repository. Three types of tests, the weak, intermediate and strong tests, are proposed for similarity assessment between two objects. The weak and intermediate tests are performed at node points obtained through shape intrinsic wireframing. The strong test relies on isolated umbilical points which can be used as finger- prints of an object for supporting an ownership claim to the original model. The three tests are organized in two decision algorithms such that they produce systematic and statistical measures for a similarity decision between two objects in a hierarchical manner. Based on the systematic and statistical evaluation of similarity, a decision can be reached whether the suspect model is an illegal copy of the original model.

A general parametric form of a dynamic finite-element model of a linear elastic structure with small deformations is presented, with the model consisting of a set of scalar parameters multiplying element kernel matrices. The parameters of the finite-element model can represent stiffness and inertia properties, as well as axial forces if linearized buckling is assumed. Optimization of an orthogonality-based objective