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Full-Text Articles in Mathematics

Deformation Theory Of Dialgebras., Anita Majumdar Dr. Feb 2003

Deformation Theory Of Dialgebras., Anita Majumdar Dr.

Doctoral Theses

The main objective of this thesis is to develop an algebraic deformation theury for associative dialgebras, which are binary quadratic algebras discovered by J.-L. Loday in (16). (17), and subisequently, to derive a G-algebra siructure ou the dialgebra colhomology with cocfticients in itself.Deformation theory dates back at Ieast to Riemann's 1837 memoir on alelian fianetions in which he studied IHanifolds of complex dimension one and calculated the mumber of parameters (called moduli) upon which a deformation depends. The modern theory of deformations of structures on manifolds was developed extensively ly Frolicher-Kodaira-Nijenhnis-Nirenberg-Spencer (13], [14], [15). [25|, [26).The study of deformations of …


Certain Pattern Recognition Tasks For Data Mining Problems., Pabitra Mitra Dr. Feb 2003

Certain Pattern Recognition Tasks For Data Mining Problems., Pabitra Mitra Dr.

Doctoral Theses

Pattern recognition (PR) is an activity that we humans normally excel in. We do it almost all the time, and without conscious effort. We receive information via our various sensory organs, which is processed instantaneously by our brain so that, almost immediately, we are able to identify the source of the information, without having made any perceptible effort. What is even more impressive is the accuracy with which we can perform recognition tasks even under non-ideal conditions, for instance, when the information that needs to be processed is vague, imprecise or even incomplete. In fact, most of our day-to-day activities …


Essays In Financial Intermediation., Bappaditya Mukhopadhyay Dr. Feb 2003

Essays In Financial Intermediation., Bappaditya Mukhopadhyay Dr.

Doctoral Theses

No abstract provided.


Spectral Triples And Metric Aspects Of Geometry On Some Noncommutative Spaces., Partha Sarathi Chakraborty Dr. Feb 2003

Spectral Triples And Metric Aspects Of Geometry On Some Noncommutative Spaces., Partha Sarathi Chakraborty Dr.

Doctoral Theses

Quantization of mathematical theories is now more than half a century old idea in mathe- matics. It goes back to Gelfand-Naimarks seminal paper [37] in 1943. As the name suggests noncommutative geometry is the quantization" of differential geometry. It is the study of noncommutative algebras as if they were algebras of functions on spaces like the commuta- tive algebras associated to affine algebraic varieties, smooth manifolds, topological spaces. One can trace its roots in the Gelfand-Naimark theorems (1943, 37]). In modern terminol- ogy their theorem says there is an antiequivalence between the category of (locally) compact Hausdorff spaces and (proper, …


Theoretical Issues In The Economics Of International Trade And Environment., Meeta Keswani Mehra Dr. Nov 2002

Theoretical Issues In The Economics Of International Trade And Environment., Meeta Keswani Mehra Dr.

Doctoral Theses

In the wake of substantial trade liberalization in the world economy over the last two decades and growing environmental consciousness, the issues of the impacts of international goods trade and foreign direct investment (FDI) on local and global environment are becoming increasingly contentious. Whilst trade and FDI have been said to bring higher incomes and well-being for all, these are seen to act as "magnifiers" of environmental deterioration - especially in the developing countries. On the other hand, growing environmentalism is perceived to act as an impediment to freer trade and investment flows across countries. Hence, the central issues are …


Environmental Regulation In The Presence Of Environmentally Conscious Consumers., Sangeeta Bansal Dr. Oct 2002

Environmental Regulation In The Presence Of Environmentally Conscious Consumers., Sangeeta Bansal Dr.

Doctoral Theses

The Problem and Literature Review There is a growing concern for the environmental degradation caused by various economic activities. Clean environment, once regarded as a free good, has now become a scarce resource due to cumulative accumulation of pollution over the years. Being a public good, it may not be possible to assign clear property rights to environment. Hence, even though it has become a scarce resource, economic agents continue to regard it as a free good and tend to ignore the harmful effects of their activities on the environment. This causes a distortion between the market and socially optimal …


Slippage And Change Point Problem With Directional Data., Arnab Kumar Laha Dr. May 2002

Slippage And Change Point Problem With Directional Data., Arnab Kumar Laha Dr.

Doctoral Theses

In this thesis we develop statistical methods for dealing with two problems namely (1) THE SLIPPAGE PROBLEM and (2) THE CHANGE POINT PROB- LEM in the set-up of directional data. In this chapter, we provide an intro- duction to these problems and discuss the importance of the present work. The slippage problem is basically a problem to detect whether any unspecified observation in a given random sample comes from a distribution different from that for all the other remaining observations. This can also be viewed as a problem of outlier detection or that of spuriosity. This problem assumes great importance …


Essays In Indian Corporate Finance., K. V. S. Vinay Dr. Apr 2002

Essays In Indian Corporate Finance., K. V. S. Vinay Dr.

Doctoral Theses

This thesis comprises of three essays in corporate finance focusing on the Indian economy. The first essay contains a theoretical model while the second and the third essays are empirical exercises. In the subsequent paragraphs of this section, we examine the broader issues to which the contents of the thesis contribute.The past few years have seen rising interest in studies of financial insti- tutions and corporate financial policies in countries other than the United States. One of the reasons for such a shift in attention is the diversity in the size and structure of financial arrangements all over the world. …


Zero-Cycles And K-Theory On Normal Surfaces., Amalendu Krishna Dr. Mar 2002

Zero-Cycles And K-Theory On Normal Surfaces., Amalendu Krishna Dr.

Doctoral Theses

The main theme of this thesis is to study the theory of algebraic cycles on singular varieties over a field. This has been studied before extensively by Collins, Barbieri-Viale, Levine, Srinivas among several others. Our interest in this thesis is to address some well known problems in the theory of zero-cycles over nominal varieties. The use of K- theoretic techniques in our proofs illustrate the interplay between the study of algebraic cycles and algebraic K-theory.For a quasi-projective surface X over a field k, we define FA,(X) to be the subgroup of the Grothendieck group Ko(X) of vector bundies generated by …


Essay On Trade In Goods And Factor Movements Under Increasing Returns To Scale., Brati Sankar Chakraborty Dr. Feb 2002

Essay On Trade In Goods And Factor Movements Under Increasing Returns To Scale., Brati Sankar Chakraborty Dr.

Doctoral Theses

The central issues that have engaged trade theorists from its inception can broadly be classified under three leads. First, to identify, what countries trade with each other, or what has come to be known as the question of pattern of trade. Second, the consequent gains that trade allows for. And the third, which is an immediate appendage to the second is to identify the redistribution of income due to trade.The first and the third, as is immediately evident, are issues in positive trade theory. The second is a normative issue, which evidently brings in questions of welfare change of the …


Essays On Cooperative Behaviour And Collective Action., Anindya Bhattacharya Dr. Jan 2002

Essays On Cooperative Behaviour And Collective Action., Anindya Bhattacharya Dr.

Doctoral Theses

This dissertation explores some issues concerning the behaviour of coalitions of individuals in a game theoretic set-up and also studies one aspect of a society facing collective action of the masses. The common feature of the issues explored in the dissertation is that it investigates the properties of stable social states. Chapter 2 introduces a notion of a social state that is unlikely to be displaced by any coalition of agents endowed with a certain notion of rationality and a certain degree of farsightedness and explores the properties of such states. Chapter 3 is also concerned with coalitionally stable social …


On Some Optimal Tests In Finite Mixtures: Constructions And Applications., Chandranath Pal Dr. Nov 2001

On Some Optimal Tests In Finite Mixtures: Constructions And Applications., Chandranath Pal Dr.

Doctoral Theses

Mixtures of distributions are now-a-days playing very important roles in both theoretical and applied statistics. There is an abundance of real-life situations where mixture distributions are being extensively used for modelling data and drawing inference. Several books and monographs on mixtures have so far been published, e.g., Everitt and Hand (1981), Titterington et al. (1985), McLachlan and Basford (1988), McLachlan (1997) etc., which cover a wide area on different aspects of mixture distributions and their applications. The book by Titterington et al. (1985, pp. 16-21), in particular, contains a comprehensive list of references on direct applications of finite mixtures in …


Some Aspects Of Banks And Financial Markets In Emerging Economics., Gurbachan Singh Dr. May 2001

Some Aspects Of Banks And Financial Markets In Emerging Economics., Gurbachan Singh Dr.

Doctoral Theses

Liquidity and Bank RunsThe policy of deposit insurance in the banking sector has succeeded in pre- venting bank runs but it has encouraged moral haxard (Kane, 1985 and 1989). This has increased the cost of capital. So the government and/or the central bank need to regulate (Flannery, 1982). In chapter 2, we ask the question - Is there an alternative to deposit insurance? What is the role of equity capital in this context? Is full insurance optimal?The seminal paper on bank runs by Diamond and Dybvig (1983) argues that a lack of deposit insurance leads to muitiple Nash equilibria, including …


Some Problem In Homogenization., M. Rajesh Dr. Apr 2001

Some Problem In Homogenization., M. Rajesh Dr.

Doctoral Theses

No abstract provided.


Engineering Production Function And Choice Of Technique., N. S. S. Narayana Dr. Apr 2001

Engineering Production Function And Choice Of Technique., N. S. S. Narayana Dr.

Doctoral Theses

This study deala wi th the selection of technological al ternaid ves of production, a problom referred to as choice of techninues" in ecommie theory. Selection of an appropriate technique (or a technolo gical al ternative) haa to be Bede with ro spe et to speci fied objectives and avail phle reDurces. Selection of proper techniques from smong many avall ablo el ternatives ha boen one of the min tasks whilu planni ng for econonio development. Generally develooping co untries like India are handi capped by problema of BCerci ty of on-lebour reaources, abundant labour force, lini ted foreign-aid, 1inited …


Stochastic Comparision And Dependence Among Order Statistics,Spacing And Concomitants Of Order Statistics., Baha-Eldin Khaledi Dr. Mar 2001

Stochastic Comparision And Dependence Among Order Statistics,Spacing And Concomitants Of Order Statistics., Baha-Eldin Khaledi Dr.

Doctoral Theses

The simplest and the most common way of comparing two random variables is through their means and variances. It may happen that in some cases the median of X is larger than the median of Y, while the mean of X is smaller than the mean of Y. However, this confusion will not arise if the random variables are stochastically ordered. Similarly, the same may happen if one would like to compare the variability of X with that of Y based only on numerical measures of variability. Besides, these characteristics of distributions might not exist in some cases. In most …


Mapping Quantitative Trait Loci In Humans: Some Statistical Contributions., Saurabh Ghosh Dr. Feb 2001

Mapping Quantitative Trait Loci In Humans: Some Statistical Contributions., Saurabh Ghosh Dr.

Doctoral Theses

Maty qualitative tralts - such an, milk yield la cows, blood pressure in lumans --are known to be determined primarly, though zot exclusively, by inherited genetic luctora. It ls the of coasklerable impartance to identify chromosontal locations of tho genes that control a quantitative character. Linkage analysis (Ou 1990), which deals with the deduction of linkagn and estimation of recombination fractions among the loci controlling a qualitative/quantitative character and major loci wkoo poertions are knows aprfori, is widely used for localisation of gens. Although statistical methodologies for magplag gemen determining dichotomos qualitative charactes in humans aro well-developed, the demicrant of …


Boolean Functions With Important Cryptographic Properties., Subhamoy Maitra Dr. Feb 2001

Boolean Functions With Important Cryptographic Properties., Subhamoy Maitra Dr.

Doctoral Theses

In this thesis we concentrate on properties of cryptographically significant Boolean functions.The techniques are mainly combinstorial and provide new resulta on enumeration and construction of such functions. Initially we concentrate on a partieular subset of Boolean functions called the symmetric Boolean functions. A closed form expression for the Walsh transform of an arbitrary symmetric Boolean function is presented. We completely characterize the symmetric functions with maximum nonlinearity and show that the maximum nonlinearity of n-variable symmetrie function can be 2n-1-2[n-1l2], Moreover, new classes of symmetric balanced and symmetric correlation immune functions are considered.We provide a randomised heuristic to construct balanced …


Contributions To Random Interactions And Dynamical Systems., Santanu Chakraborty Dr. Feb 2001

Contributions To Random Interactions And Dynamical Systems., Santanu Chakraborty Dr.

Doctoral Theses

In recent years random iterations of maps on Polish spaces has gained prominence. They are. nice examples of Markov processes whose invariant measures can be used in Computer imaging (see Berger ( 1). They also arise as random perturabations of deterministic dynamical systems.Let S be a Polish space with its Borel a-field. Let r be a collection of Borel maps from S to S. Let P be a probability on r. Then starting with a point z in S, we choose a map yn er according to the law P and move to ya(x). Then we choose 2 € r …


Topological Conjugacy And Rigidity Of Affine Actions., Siddhartha Bhattacharya Dr. Jan 2001

Topological Conjugacy And Rigidity Of Affine Actions., Siddhartha Bhattacharya Dr.

Doctoral Theses

The main theme of this thesis is topological classiication of aline Hows on homogeneous spaces and rigidity of equivariant continuous maps between such dows. Both these aspects have been extensively studied in the literature for subgroup actions (cf. [Be), [B-Dj and [Wi) and for automorphism flows of the cyclic group (cf. [Ar]. [K-R] and [C-S). We will consider similar questions in more general situations. A detailed outline is given below. For a topological group T, by a r-flow we mean pair (X,p), where X is a opological space and p is a continuous action of I on X. For any …


Routing Algorithms For Channels, Switchboxes And Mcm's In Vlsi Layout Design., Sandip Das Dr. Jan 2001

Routing Algorithms For Channels, Switchboxes And Mcm's In Vlsi Layout Design., Sandip Das Dr.

Doctoral Theses

The term Very Large Scale Integration (VLSI) reflects the capability of semi- conductor industry to fabricate a complex electronic circuit consisting of millions of components on a single silicon substrate. The growth of semiconductor technol- ogy in recent years has been described by "Moore's law", enunciated in the late 1960s, which projected quadrupling of components in a chip in every three to four years. Several factors contributed to this tremendous growth : (i) reduction of line width of the basic device and interconnection wires due to the development of high- resolution lithographic techniques and improved processing capabilities, (ii) increase in …


Stability And Largeness Of The Core Of Cooperative Games., Amit K. Biswas Dr. Nov 2000

Stability And Largeness Of The Core Of Cooperative Games., Amit K. Biswas Dr.

Doctoral Theses

This monograph deals with the area from game theory known as co operativo games. Except the last chapter on NTU games, it deals with transferable utility games. llere we will introiduce and diseus the involved game theuretie notions and set a mathematical hase for the chapters to come.In 1944 von Neamann and Morgenstern(15) introduced a theory of solutions for n-person games in characteristic function form in which cooperation and coalition formation is a crucial aspect. The primary mathematical concern regarding this model is the existence of solutions or stable set. In 1968 Lucas|19 described a tem person game which has …


On Logistic And Some New Discrimination Rules:Charecterizations,Inference And Application., Supratik Roy Dr. Sep 2000

On Logistic And Some New Discrimination Rules:Charecterizations,Inference And Application., Supratik Roy Dr.

Doctoral Theses

Introduction and Summary Consider the problem of classification of an observation into one of two specified populations. Fisher's classification rale, just as several other rules commonly used in practice, depends only on the ratio of the individual densities fi(x), i = 1,2. This led Cox (1966),/27) to model the "posterior odds" by a simple function. Specifically,Cox's logistic discrimination (LGD) rule is then based on the statistic a + 'ßx. This has the advantage that individual densities f.(x) need not be known and we only need to estimate the parameters a and B.Another advantage, which is claimed , is that the …


On Some Self-Organizing Models And Their Applications., Amitava Dutta Dr. Aug 2000

On Some Self-Organizing Models And Their Applications., Amitava Dutta Dr.

Doctoral Theses

Abstract: Self-organizing neural network models constitute the main theme of this thesis. Some well-known self-organizing models are surveyed and their properties are discussed. The application areas on which the thesis focuses are briefly described.This thesis deals with Artificial Neural Network models, in particular, Self- organizing (unsupervisnd) models. We develop here a few self-organizing neural net- work models to solve certain problems which are well studied in the areas of Image Processing and Computationel Geometry and have wide applications in shape eztrac- tion and optimization.1.1 Artificial neural networkThe study of Biological Neural Networks originally comes under biological sciences. They deal with …


Feature Evaluation, Classification And Rule Generation Using Fuzzy Sets And Neural Networks., Rajat Kumar De Dr. Mar 2000

Feature Evaluation, Classification And Rule Generation Using Fuzzy Sets And Neural Networks., Rajat Kumar De Dr.

Doctoral Theses

Pattern recognition and machine learning form a major area of research and develop- ment activity that encompasses the processing of pictorial and other non-numerical information obtained from the interaction between science, technology and society. A motivation for the spurt of activity in this field is the need for people to com- municate with the computing machines in their natural mode of communication. Another important motivation is that the scientists are also concerned with the idea of designing and making intelligent machines that can carry out certain tasks that we human beings do. The most salient outcome of these is the …


Essays On First Best Implementable Incentive Problem., Manipushpak Mitra Dr. Mar 2000

Essays On First Best Implementable Incentive Problem., Manipushpak Mitra Dr.

Doctoral Theses

The theory of mechanism design originated in the mid 1930s with the work of Lange[27], Lerner (28] and Hayek [20] on market socialism'. Further regular was added to their ideas by Arrow and Hurwicz (1). Hurwicz extended them to the general problem of mechanism design. An important aspect of mechanism design is asymmetric information. Information asymmetry typically imposes constraints on the goals which can be attained. For example. in the classic pure public goods problem, mechanisms that achieve truthful revelation of private information are Pareto sub-optimal i.e. these mechanisms lead to a welfare loss (see Hurwicz [24]). When can mechanism …


On Fractal Based Representation Of Image With Application To Image Processing., Suman Kumar Mitra Dr. Feb 2000

On Fractal Based Representation Of Image With Application To Image Processing., Suman Kumar Mitra Dr.

Doctoral Theses

The language of an image is universal. Images were the means of communicating infor- mation in ancient days. Even today, although people from different parts of the world speak in different languages, an image conveys almost the same universal meaning to all. With the rapid development of modern computer technologies and with the increasing attempt in getting information at ones finger tips, the importance of communication of information using images can not be ignored.Images are stored in computers in the form of a collection of bits representing pixels (picture elements). Pictures are to be digitized to store them in computers. …


Similarity Based Approximate Reasoning., Swapan Raha Dr. Feb 2000

Similarity Based Approximate Reasoning., Swapan Raha Dr.

Doctoral Theses

Many years of research in Artificial Intelligence, Cognitive Science and allied area reveal that the cognitive process of human reasoning deals with imprecise premises. As cognitive process of human reasoning is mainly concerned with the individual's perception, it is liable to be imprecise in nature. Precise traditional two-valued logic and/or multi-valued logics are not effective in handling such reasoning processes. This motivated Zadeh (109) to investigate how these impreciseness in human rea- soning could be modeled through some computable entities. In this regard, Zadeh has shown how such imprecise linguistic terms could be expressed through fuzzy sets over universes of …


Some Contribution To Reliability Analysis Of A Consecutive-K-Out-Of N: F System., Mohammad Khanjari Sadegh Dr. Feb 2000

Some Contribution To Reliability Analysis Of A Consecutive-K-Out-Of N: F System., Mohammad Khanjari Sadegh Dr.

Doctoral Theses

Present day technology has been characterized by development of complex systems or equipments containing a large number of subaystems and com- ponents. Reliability, as a buman attribute, has been praised for a very long time. For technical systems, however, the reliability concept has not been applied for more than about 50 years. Reliability is the concern of all scien- tists and engineers engaged in developing a system, from design, through the manufacturing, to its ultimate use. Reliability technology has a potentially wide range of application areas like safety or risk analysis, environmental protection, quality, optimization, maintenance, engineering design, etc.For a …


Quantum Stochastic Dilation Of Completely Positive Semigroups And Flows., Debashish Goswami Dr. Feb 2000

Quantum Stochastic Dilation Of Completely Positive Semigroups And Flows., Debashish Goswami Dr.

Doctoral Theses

The central theme of the present thesia is quantum stochastic dilation af semigroupe of completely panitive mapa on operator algebran. It is the sim of all mathemati- cal, or even all scientific theorics, to understand a given class of objects through a tanonical and simpler subclass of it. For example, abstract C"-algebras are studied through their conerete realisation as elgebra of operators, contractions on a Hilbert space by unitaries. Hilbert modules by the factorissble ones, to mention anly a few. In most af these caes, a general object of the relavant class is sociated with a canonical candidate of the …