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Full-Text Articles in Mathematics

Walrasian Theory Without On Auctioneer: A Study Of Monetary Exchange Through Trading Posts And A Diagrammatic View Of Disequilibria., Meenakshi Rajeev Dr. Feb 1994

Walrasian Theory Without On Auctioneer: A Study Of Monetary Exchange Through Trading Posts And A Diagrammatic View Of Disequilibria., Meenakshi Rajeev Dr.

Doctoral Theses

The theory of Walrasian equilibrium yields a set of prices at which the aggregate competitive demand for each commodity equals its aggregate competitive supply. Two important issues arise in this context. The first is concerned with discovering laws which guide the behaviour of the many economic variables, especially prices, when the analyst m is out of equilibrium. Walras (1900) tackled this problem by providing an algorithm (or the stÃ¥tenement scheme") which can be viewed as an auctioneer quoting different peices for the various goods an. adjusting them according t the sigus of the resulting aggregate excess demands. This is the …


Study Of Moduli Of Bundles., Indranil Biswas Dr. Feb 1994

Study Of Moduli Of Bundles., Indranil Biswas Dr.

Doctoral Theses

Hitchin (Hi2) realized the importance of studying pairs (E,∅) where E is a vector bundle and ∅ is a homomorphism of E into EOL for a fixed line bundle L. When C is a smooth pro jective algebraic curve this has since been studied quite extensively. One can construct a covering of C in this situation and the given data can be completely recovered by this covering map and a line bundle on the covering curve (see Beauville, Narasimhan and Ramanan (BNR]). When L is the canonical bundle this procedure gives a completely integrable system on the cotangent bundle of …


Parametric Homotopy Principle Of Some Practical Differential Relations., Mahuya Datta Dr. Feb 1994

Parametric Homotopy Principle Of Some Practical Differential Relations., Mahuya Datta Dr.

Doctoral Theses

A system uf r-th order partial differential inequalities is a subspace in the space of r-jets of CT" maps between manifolds. The problem of homotopy classification of C solutions of such systems is stauliel in this thesis. The text roughly divides into two parts. In the first part, the problem is considered in an equivariant setting when the system is open and invariant under the action of a compact L.ie group, but may not be invariant under the action of the pseudogroup of equivariant local diffeomorphisms. The second part concerns a non-equivariant set-up without the openness condition on the systern. …


Interaction Of Price And Technology In The Presence Of Structural Specificities:An Analysis Of Crop Production In Kerala., Delampady Narayana Dr. Nov 1993

Interaction Of Price And Technology In The Presence Of Structural Specificities:An Analysis Of Crop Production In Kerala., Delampady Narayana Dr.

Doctoral Theses

The present study attempts to understand the agricultural economy of Kerala in terms of the structural characteristics specific to the state. This approach requires such aspects to be incorporated in the analysis, and also entails a shift from certain accepted modes of thinking and statistical treatment used in the analysis of field crops.The specificities arise from certain distinctive features on the demand and supply sides'. On the demand side, there is substi tution between rice and tapioca, and the two crops constitute the food group. The rest of the crops form the non-food group, and there is no substitution among …


On Image Segmentation Using Neural Networks And Fuzzy Sets., Ashish Ghosh Dr. Nov 1993

On Image Segmentation Using Neural Networks And Fuzzy Sets., Ashish Ghosh Dr.

Doctoral Theses

During the last five decades or even more a large number of researchers are trying to design intelligent systems to perform tasks at which human beings are more efficient at present. One of the most important behavioral tasks in which human beings show their expertise is image analysis or recognition; where a large amount of pictorial data is processed in a very small amount of time (called real time). Widespread attempts have been made to develop intelligent systems (under different names, like pattern recognition system, image under- standing system, computer vision system etc.) for pictorial pattern analysis and recognition. The …


On Markov Processes Charecterised Via Martingale Problem., Abhay G. Bhatt Dr. Oct 1993

On Markov Processes Charecterised Via Martingale Problem., Abhay G. Bhatt Dr.

Doctoral Theses

Martingale approach to the study of finite dimensional diffusions was initiated by Stroock-Varadhan, who coined the term martingale problem. Their success led to a similar approach being used to study Markov processes occuring in other areas such as infinite particle systems, branching processes, genetic models, density dependent population processes, random evolutions etc.Suppose X is a Markov process corresponding to a semigroup (T)e20 with generator L. Then all the information about X is contained in L. We also have thatMf(t) := f(X(t)) – ∫t0 Lf(X(s))dsis a martingale for every f ∈ D(L). i.e. X is a solution to the martingale problem …


Joint Venture And Bargaining., Prabal Ray Chaudhuri Dr. Sep 1993

Joint Venture And Bargaining., Prabal Ray Chaudhuri Dr.

Doctoral Theses

My dissertation deals with some problems in theoretical economics. The five essays in this thesis can be classified under the broad categories of industrial organization and game theory.Part I of the thesis comprises three chapters. These deal with some issues in the area of joint ventures and technology transfer. Chapter 2 investigates the relationship between technological dissimilarity and joint venture success. The third chapter explores some policy issues related to joint product development. Chapter 4 examines the relative efficacy of centralized and decentralized bargaining schemes in technology transfer.In part II I examine some issues in bargaining theory. The fifth chapter …


Coxeter Groups And Positive Matrices., Arbind Kumar Lal Dr. Aug 1993

Coxeter Groups And Positive Matrices., Arbind Kumar Lal Dr.

Doctoral Theses

In this thesis, we study positive matrices (matrices whose entries are nonnegative as well as matrices which are positive semidefinite) with Coxeter groups as the underlying theme. For an exposition on Coxeter groups see Humphreys (1990).A Cozeter system consists of a pair (W, s); where W is a group and S is a set which consists of the generators of the group W. The elements of the set S have only the relations of the form (ss')m(s.) 1; where m(s, s) 1, m(s, s') = m(s,s) 2 2 for s s in S. In case no relation occurs for a …


Agricultural Tenancy In Palanpur., Naresh Kumar Sharma Dr. Feb 1993

Agricultural Tenancy In Palanpur., Naresh Kumar Sharma Dr.

Doctoral Theses

Institutions and arrangements governing the property and use of land are crucial to the development of productive forces. This is true, in particular, of triennial arrangements. The system of land tenures that prevailed during the colonial period was widely considered the main cause of economic stagnation at the time of India's independence (1947). It was also perceived as highly exploitative of the tenants. Thus, land reforms were accorded the highest priority by the new Indian Government. Soon all the State Legislatures started enacting land reform laws - starting with the Legislative Assembly of Bihar immediately after 1947 and the Legislative …


Survival Function Estimation Under Random Censoring., Debajyoti Dhar Dr. Feb 1993

Survival Function Estimation Under Random Censoring., Debajyoti Dhar Dr.

Doctoral Theses

Statistical methods for life data analysis are used to measure, compare and predict characteristics of the distribution of the time to some particular event of interest, often called failure after a length of time, called life time. Failure can occur at most once for an individual. Examples of failure time include the lifetimes of machine components in industrial reliability, the duration of strikes or periods of unemployment in economic studies, the time taken by subjects to complete specified tasks in psychological experiments, the lengths of tracks photographic plates in particle physics and the on survival time of patients in clinical …


Optimal Short Run Electricity Supply India:Rationing And Pricing Optionsa., Uma Vishvanathan Dr. Feb 1993

Optimal Short Run Electricity Supply India:Rationing And Pricing Optionsa., Uma Vishvanathan Dr.

Doctoral Theses

The supply of electricity to consumers in India is governed by the Electricity Supply Act (1948). Under the Act, electricity can be supplied from two sources: (i) licensees - that is, a person or body licensed under the Indian Electricity Act 1910 to supply energy, or a person who has obtained sanction under Section 28 of that Act to engage in the business of supplying energy. (ii) The State Electricity Boards constituted under various State Governments and charged with the general duty of promoting the coordinated development of the generation, supply and distribution of electricity within the State in the …


Generalised Inverses Of Matrices Over Rings., K. Manjunatha Prasad Dr. Feb 1993

Generalised Inverses Of Matrices Over Rings., K. Manjunatha Prasad Dr.

Doctoral Theses

For a complex or a real matrix A, a matrix G is called a generalized inverse ( or g-inverse) of A if(1) AGA = AThe theory of generalized inverses over the field of complex numbers is well- studied in the literature (see (2), (11), (33), and (62) for an extensive bibliography). Even for matrices over a general field the above equation carries over. In fact, even for matrices over a general ring, equation (1) makes sense. Hence one can talk of g-inverses of matrices over general rings. Some work on g-inverses of matrices over fields also can be found in …


On Some Measurement Problem In Economics., Nachiketa Chattopadhyay Dr. Feb 1993

On Some Measurement Problem In Economics., Nachiketa Chattopadhyay Dr.

Doctoral Theses

In many branches of economie theory, quantitative relationships play a major role. Translating actions of individuals or groups of individuals, in the various soci- etal processes of production, distribution or consumption, into measurable or quan- tifiable notions has been one of the most important problems. When we take the society as a whole, diverse economic activities of ita memhers need to be collectively presented and it has given rise to interesting aggregation problems. Economists have tried to solve these problems by constructing social index numbers. Simi- larly, quantifying actions of individual units (for example, a firm /a consumer) has brought …


Rural Labour Markets And Seasonality: A Theoretical And Empirical Analysis., Anindita Mukherjee Dr. Nov 1992

Rural Labour Markets And Seasonality: A Theoretical And Empirical Analysis., Anindita Mukherjee Dr.

Doctoral Theses

A large proportion of the labour force in India (that is, 66.56% of the main workers according to the Census of India, 1981) is engaged in agriculture. Just this simple fact would make a study of the functioning of agricultural labour markets highly important. But quite apart from this observation, there are several reasons for a detailed study of rural labour markets, particularly in the context of the problem of economic development.A major issue facing developing economies is industrial growth. The agricultural sector can foster growth by creating demand for industrial products, by providing a supply of certain primary inputs, …


Planning For Basic Needs In India: A Supplement., Monoj Kumar Panda Dr. May 1992

Planning For Basic Needs In India: A Supplement., Monoj Kumar Panda Dr.

Doctoral Theses

Problems of economic development have received a great deal of attention in the last four decades. This has led to the evolution of several development goals like growth, redistribution, poverty alleviation and basic needs satiafac- tion. Initially, development atrategies e eared to were achieve maximum feasible growth rates. It was generally felt that the benefits of growth would spread widely to different sections of the population and in particular would percolate to the lower income groups. Judged by growth in national income, the development efforts have been successful, though to varying ext ent in different countries. But the percola- tion …


Some Aspects Of Multi Source Satellite Image Processing., L. Lalitha Dr. Feb 1992

Some Aspects Of Multi Source Satellite Image Processing., L. Lalitha Dr.

Doctoral Theses

The observation of a target by a device plaoed at some distance from it is cal.led remote sensing as ngainst in situ sensing where the sensor is kept in contact with the target. Usually physical emanations such as the electr omagnetic radiation from the target s observed by the sensing device. Sensors mounted on aircraft or satallite platforms measure the amount of energy reflected from or emitted by the earth's surface. Sensors scan the ground below a nd to either side of the satellite platform and as the platform noves forward, an image of the earths surface is formed.A satellite …


Diagnostic Regional Analysis On The Shortfalls In Development And Utilization Of Human Resource In India: A Statistical Study On The Spatial Variations By Districts Of India., Prasanta Pathak Dr. Feb 1992

Diagnostic Regional Analysis On The Shortfalls In Development And Utilization Of Human Resource In India: A Statistical Study On The Spatial Variations By Districts Of India., Prasanta Pathak Dr.

Doctoral Theses

The main objective of this study has been estimation of model formulations, empirical evaluations and statistical analyses for identifying the existing regional patterns and structures of human resource development in the formative phase of human life-span through education, and the utilisation, or other- wise non-utilisation, during the activity phase of life-span in existing productive and related activities of our labour-abundant developing economy of India. Despite some awareness to the problems of development and balanced-utilisations of human resources into activities and also despite the various follow- up planning efforts undertaken, or stated to be undertaken, as reported in different Five-Year Plan …


Equivariant Cohomology With Local Coefficients., Goutam Mukherjee Dr. Feb 1992

Equivariant Cohomology With Local Coefficients., Goutam Mukherjee Dr.

Doctoral Theses

In this thesis we shall present an equivariant analogue of the steenrod cohomology with local coefficients, and use this to develop an obstruction therory for equivariant fibrations. The work is inspired by a remark of tom dieck [2] which says that a sensible translation of the classical obstruction theory to equivariant fibrations uses (meaning 'should use') equivariant cohomology with local coefficients.The equivariant singular cohomology of illman (9] is unsuitable for obstruction theory for equivariant sections of an equivariant fibration. The difficulty lies in connecting the obstruction cochains which arise from different fixed point sets, and the situation becomes no better …


Contributions To The Neyman-Scott And Mixture Problem., Joydeep Bhanja Dr. Feb 1992

Contributions To The Neyman-Scott And Mixture Problem., Joydeep Bhanja Dr.

Doctoral Theses

Neyman and Scott (1948) were the first to point out that the method of maximum likelihood fails to provide elfficient estimates when the number of parameters grows with the sample size n. Consider the following examples introduced by them:Ezample 1.1 Let { Xi } be a sequence of independent random vectors in I", components Xij of Xi being independent normal with mean u, and variance o2 Ilere o2 is the parameter of interest. It is casy to sce that the maxinum likelihood estimate for o2 is not even consistent. It is also known (see Lindsay (1980), Pfanzagl (1982), van der …


The Mazur Intersection Property In Banach Spaces And Related Topics., Pradipta Bandyopadhyaya Dr. Feb 1992

The Mazur Intersection Property In Banach Spaces And Related Topics., Pradipta Bandyopadhyaya Dr.

Doctoral Theses

In the first part of this chapter we explain in general terms the main theme of this thesis and provide a chapter wise summary of its principal results. The second part recapitulates some of the known notions and results used in the subsequent chapters. The numbers given in parentheses correspond to those in the list of references on page 70.S. Mazur (40] was the first to consider the following smoothness property in normed linear spaces, called the Mazur Intersection Property (MIP), or, more briefly, the Property (1):Every closed bounded convex set is the intersection of closed balls containing it.He showed …


On Some Problems In Analysis Of Covariance Structure., Sadhan Samar Maiti Dr. Jul 1991

On Some Problems In Analysis Of Covariance Structure., Sadhan Samar Maiti Dr.

Doctoral Theses

In recent years, the teahniques of struotural analynie of covarianoe and correlation matrioes have frequently be en employed espeed ally in the s ooial and behavioural soieno es for analysing multivariate data. Analysis of covarlance structures (ACOVS) lea; generie tem describing a variety of statistioal procedures for testing and measuring the goodnese-of-fit of certain types of struotures postulated a priori for the cova- riance matrix by plaoing al temative restriotione on the para- neter natrioes of the general model" [Mukherjee, 1976, p. 132].The aoronyn AOOVS' standa for; analyeis of covarianoe atructurea; and waa firat proposed by Book (1960) as a …


Planning And Resource Mobilization In A Developing Economy., Dilip Ratha Dr. Feb 1991

Planning And Resource Mobilization In A Developing Economy., Dilip Ratha Dr.

Doctoral Theses

In developing economies, the per capita availability of essential goods and services is quite low. Hence a large section of the society cannot afford even the mininum necessities of 1ite. While human and natural resources are plenty, produced means of produetion like plant and equipment and construction materiais are soaroe. Hence the human resources are not fully utilized. Since the distribution of income and assets is highly skewed, even the snall quantity of essential goods and services is not equitably distributed. When resources 11ke land and capital are privately owned and goods and services are distributed through the narket mechanism, …


Component Importance In A Consecutive K-Out Of N:F System., Arvind Seth Dr. Feb 1991

Component Importance In A Consecutive K-Out Of N:F System., Arvind Seth Dr.

Doctoral Theses

Reliability theory has nequired a special significance during the last few decades. It is mainly because of rapid advancement in technology which has given rise to complex and sophisticated systems. These systema suf- fer from derign flawe and wenknesses and their failures not only result in monetary lom but also pose a serious threat to human life and national se curity. Hence product reliability and safety is of paramount importance to us. Since system effectiveness can be optimised during design and develop- ment phases, it therefore calls for a detailed reliability engineering program during initial stanges. Often we find that …


On Image Information Measures And Object Extraction., Nikhil Ranjan Pal Dr. Feb 1991

On Image Information Measures And Object Extraction., Nikhil Ranjan Pal Dr.

Doctoral Theses

The field of image processing deals with the manipulation of data which are inherently two-dimensional in nature. techniques of image processing sten from two principal application The areas, namely, Improvement of pictorial information for human interpretation and processing of scene data for automatic machine perception. These areas together have experienced a vigorous growth in recent years because they have offered a number of important applications in solving scientific and engineering problems. In biological and medical sciences, we are interested in automatie analysis and interpretation of radiographs, cell images micrographs. In netallurgical, geological and and tissue environmental sciences, we are concerned …


Search Designs And Other Topic In Fractional Replication., Kashinath Chatterjee Dr. Dec 1990

Search Designs And Other Topic In Fractional Replication., Kashinath Chatterjee Dr.

Doctoral Theses

This thesis primarily deals with search designs (see Srivastava (1975)) of various types for general symmetric and asymmetric factorials. The thesis also considers some other types on fractional factorials. We have made use of Kronecker products and various other results from matrix theory.In the first four chapters, different types of search designs have been studied. Chapter 5A considers the construction of orthogonal main-effect plans for general factorial experiments under the presence of a linear time trend. Chapter 5B extends the calculus for factorial arrangements to a fractional factorial set-up and examines critically the proportional frequency plans from the point of …


Some Contributions To Generalized Inverse And The Linear Complementarity Problem., N. Eagambaram Dr. May 1990

Some Contributions To Generalized Inverse And The Linear Complementarity Problem., N. Eagambaram Dr.

Doctoral Theses

A generalized inverse (g-inverse) of a matrix A is a solution x to the matrix equationA XA = A(1.1.1)A g-inverse of A can be defined alternatively as a matrix x such that x = Xb is a solution to the linear equation Ax -b for any b that makes - b consistent. There is a vast literature on g-inverse. For a number of results on g-inverses and their applications one may refer to the well known books in the literature by Rao and Mitra (1971); and by Ben Israel and Greville (1974).Another inverse that lies hidden in the definition of …


Studies On Level Of Living And Poverty In Rural India., Padmaja Pal Dr. Feb 1990

Studies On Level Of Living And Poverty In Rural India., Padmaja Pal Dr.

Doctoral Theses

The present dissertation consists of several studies on disparities in level of living and poverty in rural India. These studies are based on a special tabulation of disaggregated household budget data, from the Central Sample of the Indian National Sample Survey (NSS) 28th round (october 1973- June 1974). This was based on a copy of the updated Honey- well tape provided by the authorities of the NSS Organisation, Government of India. Two of the main aims of this dissertation are to study disparities in level of living and incidence of poverty across (1) Social groups, such as Scheduled Castes, Scheduled …


Curvatures Of Left Invariant Metrics On Lie Group And Parametric Homotopy Principles For A Class Of Partial Differential Relations On Closed Manifolds., Amitabh Tiwari Dr. Feb 1990

Curvatures Of Left Invariant Metrics On Lie Group And Parametric Homotopy Principles For A Class Of Partial Differential Relations On Closed Manifolds., Amitabh Tiwari Dr.

Doctoral Theses

The title of this thesis refers to two problems of different nature having no connection between them. These problems ere presented in two parts. In Pert I we have settled two conjectures of Milnor, on Lie groups with left-invariant metrics, in the affirmative and in Part II we have obtained a now Smale - Hirsch - Gromov - type theorem on the homotopy classification of a close of portial differential relations on closed manifolds. More detailed introduotions to these parts are given at the beginning of each part, It has bean our attempt to make the presentations as self-contained as …


Disparities In Development: A Case Study Of Karnataka State (India)., Jayalaxmi Jayaram Dr. Feb 1990

Disparities In Development: A Case Study Of Karnataka State (India)., Jayalaxmi Jayaram Dr.

Doctoral Theses

The Five Year Plans have recognised the need to bridge the developmental disparities across the regions and have formulated strategies for accelerated development of backward are as. However, the widening disparities between a few highly developed centres and vast areas of under development only bring out the inadequacies of the plans which are yet to integrate the resources of a region to its people. This study is an attempt to understand the spatial processes and patterns of development which offer an explanation to the intra/inter-regional contrasts in development. The study while high-lighting the importance of the Spatial approach has, in …


Semi-Martiangales Associated With Crossing, B. Rajeev Dr. Feb 1990

Semi-Martiangales Associated With Crossing, B. Rajeev Dr.

Doctoral Theses

In thia theoia ve study the locel behaviour or semi mertingalea. Civen e cant!nuoue sent rartineale and an i-tetval (n,t), ve define a new pracees which airrara the bereufour of the originel procese in the interval (a, b). Thie neu procees tur ns cut to he a semi-nartingale uhose junpa during [J,t: ere closely reinted to the number of croosinge of (o,t) during [0,t ].Jur sterting point is indned P, Levy's rortingale cherocterizotion of around an motion : If (xt) and (x2t - t) ore cantinuOun lacol nar- tingales then (xt) must be a Srownion mation. Let now Hn(x,t) denote …