Now showing items 1-13 of 13
| Description: | Department of Mathematics, Cochin University of Science and Technology |
| URI: | http://dyuthi.cusat.ac.in/purl/2694 |
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| Dyuthi-T0746.pdf | (9.170Mb) |
| Abstract: | This thesis Entitled On Infinite graphs and related matrices.ln the last two decades (iraph theory has captured wide attraction as a Mathematical model for any system involving a binary relation. The theory is intimately related to many other branches of Mathematics including Matrix Theory Group theory. Probability. Topology and Combinatorics . and has applications in many other disciplines..Any sort of study on infinite graphs naturally involves an attempt to extend the well known results on the much familiar finite graphs. A graph is completely determined by either its adjacencies or its incidences. A matrix can convey this information completely. This makes a proper labelling of the vertices. edges and any other elements considered, an inevitable process. Many types of labelling of finite graphs as Cordial labelling, Egyptian labelling, Arithmetic labeling and Magical labelling are available in the literature. The number of matrices associated with a finite graph are too many For a study ofthis type to be exhaustive. A large number of theorems have been established by various authors for finite matrices. The extension of these results to infinite matrices associated with infinite graphs is neither obvious nor always possible due to convergence problems. In this thesis our attempt is to obtain theorems of a similar nature on infinite graphs and infinite matrices. We consider the three most commonly used matrices or operators, namely, the adjacency matrix |
| Description: | Department of mathematics, Cochin University of Science and Technology |
| URI: | http://dyuthi.cusat.ac.in/purl/3142 |
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| Dyuthi-T1116.pdf | (1.999Mb) |
| Abstract: | It is believed that every fuzzy generalization should be formulated in such a way that it contain the ordinary set theoretic notion as a special case. Therefore the definition of fuzzy topology in the line of C.L.CHANG E9] with an arbitrary complete and distributive lattice as the membership set is taken. Almost all the results proved and presented in this thesis can, in a sense, be called generalizations of corresponding results in ordinary set theory and set topology. However the tools and the methods have to be in many of the cases, new. Here an attempt is made to solve the problem of complementation in the lattice of fuzzy topologies on a set. It is proved that in general, the lattice of fuzzy topologies is not complemented. Complements of some fuzzy topologies are found out. It is observed that (L,X) is not uniquely complemented. However, a complete analysis of the problem of complementation in the lattice of fuzzy topologies is yet to be found out |
| Description: | Depantment of Mathematics and Statistics Cochin University of Scince and Technology |
| URI: | http://dyuthi.cusat.ac.in/purl/3440 |
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| Dyuthi-T1417.pdf | (1.609Mb) |
| Abstract: | This thesis is a study of abstract fuzzy convexity spaces and fuzzy topology fuzzy convexity spaces No attempt seems to have been made to develop a fuzzy convexity theoryin abstract situations. The purpose of this thesis is to introduce fuzzy convexity theory in abstract situations |
| Description: | Department of Mathematics and Statistics, Cochin University of Science and Technology |
| URI: | http://dyuthi.cusat.ac.in/purl/3728 |
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| Dyuthi-T1694.pdf | (1.237Mb) |
| Abstract: | In this thesis we investigate some problems in set theoretical topology related to the concepts of the group of homeomorphisms and order. Many problems considered are directly or indirectly related to the concept of the group of homeomorphisms of a topological space onto itself. Order theoretic methods are used extensively. Chapter-l deals with the group of homeomorphisms. This concept has been investigated by several authors for many years from different angles. It was observed that nonhomeomorphic topological spaces can have isomorphic groups of homeomorphisms. Many problems relating the topological properties of a space and the algebraic properties of its group of homeomorphisms were investigated. The group of isomorphisms of several algebraic, geometric, order theoretic and topological structures had also been investigated. A related concept of the semigroup of continuous functions of a topological space also received attention |
| Description: | Department of Mathematics and Statistics, Cochin University of Science and Technology |
| URI: | http://dyuthi.cusat.ac.in/purl/3324 |
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| Dyuthi-T1318.pdf | (2.631Mb) |
| Abstract: | This thesis is an attempt to initiate the development of a discrete geometry of the discrete plane H = {(qmxo,qnyo); m,n e Z - the set of integers}, where q s (0,1) is fixed and (xO,yO) is a fixed point in the first quadrant of the complex plane, xo,y0 ¢ 0. The discrete plane was first considered by Harman in 1972, to evolve a discrete analytic function theory for geometric difference functions. We shall mention briefly, through various sections, the principle of discretization, an outline of discrete a alytic function theory, the concept of geometry of space and also summary of work done in this thesis |
| Description: | Department of Mathematics and Statistics,Cochin University of Science & Technology |
| URI: | http://dyuthi.cusat.ac.in/purl/3347 |
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| Dyuthi-T1328.pdf | (3.633Mb) |
| URI: | http://dyuthi.cusat.ac.in/purl/1601 |
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| Dyuthi-T0022.pdf | (3.541Mb) |
| Abstract: | The doctoral thesis focuses on the Studies on fuzzy Matroids and related topics.Since the publication of the classical paper on fuzzy sets by L. A. Zadeh in 1965.the theory of fuzzy mathematics has gained more and more recognition from many researchers in a wide range of scientific fields. Among various branches of pure and applied mathematics, convexity was one of the areas where the notion of fuzzy set was applied. Many researchers have been involved in extending the notion of abstract convexity to the broader framework of fuzzy setting. As a result, a number of concepts have been formulated and explored. However. many concepts are yet to be fuzzified. The main objective of this thesis was to extend some basic concepts and results in convexity theory to the fuzzy setting. The concept like matroids, independent structures. classical convex invariants like Helly number, Caratheodoty number, Radon number and Exchange number form an important area of study in crisp convexity theory. In this thesis, we try to generalize some of these concepts to the fuzzy setting. Finally, we have defined different types of fuzzy matroids derived from vector spaces and discussed some of their properties. |
| Description: | Department of Mathematics, Cochin University of Science and Technology |
| URI: | http://dyuthi.cusat.ac.in/purl/3119 |
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| Dyuthi-T1093.pdf | (1.804Mb) |
| URI: | http://dyuthi.cusat.ac.in/purl/1600 |
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| Dyuthi-T0242.pdf | (1.945Mb) |
| Description: | Department of Mathematics, Cochin University of Science and Technology. |
| URI: | http://dyuthi.cusat.ac.in/purl/2989 |
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| Dyuthi-T0969.pdf | (2.186Mb) |
| Abstract: | In this study we combine the notions of fuzzy order and fuzzy topology of Chang and define fuzzy ordered fuzzy topological space. Its various properties are analysed. Product, quotient, union and intersection of fuzzy orders are introduced. Besides, fuzzy order preserving maps and various fuzzy completeness are investigated. Finally an attempt is made to study the notion of generalized fuzzy ordered fuzzy topological space by considering fuzzy order defined on a fuzzy subset. |
| URI: | http://dyuthi.cusat.ac.in/purl/1602 |
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| Dyuthi-T0282.pdf | (2.425Mb) |
| Abstract: | Mathematical models are often used to describe physical realities. However, the physical realities are imprecise while the mathematical concepts are required to be precise and perfect. The 1st chapter give a brief summary of the arithmetic of fuzzy real numbers and the fuzzy normed algebra M(I). Also we explain a few preliminary definitions and results required in the later chapters. Fuzzy real numbers are introduced by Hutton,B [HU] and Rodabaugh, S.E[ROD]. Our definition slightly differs from this with an additional minor restriction. The definition of Clementina Felbin [CL1] is entirely different. The notations of [HU]and [M;Y] are retained inspite of the slight difference in the concept.the 3rd chapter In this chapter using the completion M'(I) of M(I) we give a fuzzy extension of real Hahn-Banch theorem. Some consequences of this extension are obtained. The idea of real fuzzy linear functional on fuzzy normed linear space is introduced. Some of its properties are studied. In the complex case we get only a slightly weaker analogue for the Hahn-Banch theorem, than the one [B;N] in the crisp case |
| Description: | School of Mathematical Sciences , Cochin University of Science and Technology |
| URI: | http://dyuthi.cusat.ac.in/purl/3704 |
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| Dyuthi-T1684.pdf | (771.7Kb) |
| Abstract: | Mathematical models are often used to describe physical realities. However, the physical realities are imprecise while the mathematical concepts are required to be precise and perfect. Even mathematicians like H. Poincare worried about this. He observed that mathematical models are over idealizations, for instance, he said that only in Mathematics, equality is a transitive relation. A first attempt to save this situation was perhaps given by K. Menger in 1951 by introducing the concept of statistical metric space in which the distance between points is a probability distribution on the set of nonnegative real numbers rather than a mere nonnegative real number. Other attempts were made by M.J. Frank, U. Hbhle, B. Schweizer, A. Sklar and others. An aspect in common to all these approaches is that they model impreciseness in a probabilistic manner. They are not able to deal with situations in which impreciseness is not apparently of a probabilistic nature. This thesis is confined to introducing and developing a theory of fuzzy semi inner product spaces. |
| Description: | Department of mathematics, Cochin University of Science And Technology |
| URI: | http://dyuthi.cusat.ac.in/purl/3430 |
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| Dyuthi-T1398.pdf | (771.7Kb) |
Now showing items 1-13 of 13
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