Studies on some graph operators and related topics

Department of Mathematics, Cochin University of Science and Technology

Studies on Fuzzy Matroitls and Related Topics

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.

‘Studies on some topics in product graphs’

For routing problems in interconnection networks it is important to find the shortest containers between any two vertices, since the w-wide diameter gives the maximum communication delay when there are up to w−1 faulty nodes in a network modeled by a graph. The concept of ‘wide diameter’ was introduced by Hsu [41] to unify the concepts of diameter and The concept of ‘domination’ has attracted interest due to its wide applications in many real world situations [38]. A connected dominating set serves as a virtual backbone of a network and it is a set of vertices that helps in routing. In this thesis, we make an earnest attempt to study some of these notions in graph products. This include, the diameter variability, the diameter vulnerability, the component factors and the domination criticality.connectivity

A study on semigroup action on fuzzy subsets, inverse fuzzy automata and related topics

This thesis comprises five chapters including the introductory chapter. This includes a brief introduction and basic definitions of fuzzy set theory and its applications, semigroup action on sets, finite semigroup theory, its application in automata theory along with references which are used in this thesis. In the second chapter we defined an S-fuzzy subset of X with the extension of the notion of semigroup action of S on X to semigroup action of S on to a fuzzy subset of X using Zadeh's maximal extension principal and proved some results based on this. We also defined an S-fuzzy morphism between two S-fuzzy subsets of X and they together form a category S FSETX. Some general properties and special objects in this category are studied and finally proved that S SET and S FSET are categorically equivalent. Further we tried to generalize this concept to the action of a fuzzy semigroup on fuzzy subsets. As an application, using the above idea, we convert a _nite state automaton to a finite fuzzy state automaton. A classical automata determine whether a word is accepted by the automaton where as a _nite fuzzy state automaton determine the degree of acceptance of the word by the automaton. 1.5. Summary of the Thesis 17 In the third chapter we de_ne regular and inverse fuzzy automata, its construction, and prove that the corresponding transition monoids are regular and inverse monoids respectively. The languages accepted by an inverse fuzzy automata is an inverse fuzzy language and we give a characterization of an inverse fuzzy language. We study some of its algebraic properties and prove that the collection IFL on an alphabet does not form a variety since it is not closed under inverse homomorphic images. We also prove some results based on the fact that a semigroup is inverse if and only if idempotents commute and every L-class or R-class contains a unique idempotent. Fourth chapter includes a study of the structure of the automorphism group of a deterministic faithful inverse fuzzy automaton and prove that it is equal to a subgroup of the inverse monoid of all one-one partial fuzzy transformations on the state set. In the fifth chapter we define min-weighted and max-weighted power automata study some of its algebraic properties and prove that a fuzzy automaton and the fuzzy power automata associated with it have the same transition monoids. The thesis ends with a conclusion of the work done and the scope of further study.

Topics of divisibility

The set of integers forms a commutative ring whose elements admit a unique decomposition into primes. In this folder three lecture notes are bound, concerning topics, developed by dropping or replacing special properties of this most natural and most special ring. For short: investigated are groupoids w.r.t the interplay of multiplication - on the one hand - and divisibility, ideal decomposition and residuation, respectively, on the other hand.

SPSS Topics index - An animated guide

Need help with a given topic? Help to perform a test? Help understanding your results? Information and tutorials can be found using the Topics Index tab.

SPSS Topics Search - An animated guide

Need help on a given topic? Topics Search tab can help narrow down the search.

INFO 1010 CW3 Topics (2010)

List of topics for CW 3

Some Topics in Relation to José Celestino Mutis and Medicine

José Celestino Mutis showed different interest areas of study and worked in multiple knowledge fields: mathematics, mineralogy, astronomy, zoology and botanic, the one in which is best known. However, he was a medical doctor, whit profound an up to date knowledge. He studied at Sevilla University, and in the Royal College of Cadiz. He arrived to the “Nuevo Reino de Granada” as personal medical doctor of the the viceroy Pedro Messía de la Cerda and during 47 years, period of time he lived there, he always exercised his profession. We showed a special interest in the study of cinchona and the only work he published was El Arcano de la quina. He advised in public health many viceroys and he contributed in different fields but particularly in the prevention of smallpox by inoculation. He played a decisive role in the reopening of the medical school of the Colegio Mayor de Nuestra Señora del Rosario. Some of his achievements justifies the appellative “Father of the Medicine in Colombia”.

Selected topics in probiotics and prebiotics: meeting report for the 2004 international scientific association for probiotics and prebiotics

On August 2931, 2004, 84 academic and industry scientists from 16 countries gathered in Copper Mountain, Colorado USA to discuss certain issues at the forefront of the science of probiotics and prebiotics. The format for this invitation only meeting included six featured lectures: engineering human vaginal lactobacilli to express HIV inhibitory molecules (Peter Lee, Stanford University), programming the gut for health (Thaddeus Stappenbeck, Washington University School of Medicine), immune modulation by intestinal helminthes (Joel Weinstock, University of Iowa Hospitals and Clinics), hygiene as a cause of autoimmune disorders (G. A. Rook, University College London), prebiotics and bone health (Connie Weaver, Purdue University) and prebiotics and colorectal cancer risk (Ian Rowland, Northern Ireland Centre for Food and Health). In addition, all participants were included in one of eight discussion groups on the topics of engineered probiotics, host-commensal bacteria communication, 'omics' technologies, hygiene and immune regulation, biomarkers for healthy people, prebiotic and probiotic applications to companion animals, development of a probiotic dossier, and physiological relevance of prebiotic activity. Brief conclusions from these discussion groups are summarized in this paper.

PRESENTATION. Experimental and behavioral economics. Theory, tools and topics

This note presents the special issue on Experimental and Behavioral Economics. The volume includes some recent contributions from these correlated disciplines –empirical the former and theoretical the latter– and their potential contribution to the intersection of Economics with Psychology and Sociology. The project “El papel de la comparación social en las decisiones económicas bajo incertidumbre” (Junta de Andalucía, P07-SEJ-03155)” provided us with inspiration and financial support to publish this volume.

Secondary school teachers' perspectives on teaching about topics that bridge science and religion

The question of where to locate teaching about the relationships between science and religion has produced a long-running debate. Currently, Science and Religious Education (RE) are statutory subjects in England and are taught in secondary schools by different teachers. This paper reports on an interview study in which 16 teachers gave their perceptions of their roles and responsibilities when teaching topics that bridge science and religion and the extent to which they collaborated with teachers in the other subject area. We found that in this sample, teachers reported very little collaboration between the curriculum areas. Although the science curriculum makes no mention of religion, all the science teachers said that their approaches to such topics were affected by their recognition that some pupils hold religious beliefs. All the RE teachers reported struggling to ensure students know of a range of views about how science and religion relate. The paper concludes with a discussion about implications for curriculum design and teacher training.