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Evaluating In Dual Economy Framework The Indian Industrial Performance During 1951-52 To 1989-90., R. Kavita Rao Dr. Feb 1994

Evaluating In Dual Economy Framework The Indian Industrial Performance During 1951-52 To 1989-90., R. Kavita Rao Dr.

Doctoral Theses

The primary goal of economic development is to achieve high rates of growth of outputs and incomes so to ensure high per as capita income and levels of living in the economy. In India, this was sought to be achleved, to a large extent, through a rapid expansion and growth of the industrial sector, as is evident in the emphasis placed on the industrialisation programmes in her various Five Year Plans. However, the growth of this sector has exhibited considerable ups and downs over the years, belying expectations. Quite expectedly, this has evoked substantial debate on the factors influencing and/or …

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Hypergroup Graphs And Subfactors., A. K. Vijayarajan Dr. Feb 1994

Hypergroup Graphs And Subfactors., A. K. Vijayarajan Dr.

Doctoral Theses

The main theme of this t hesis is hypergroups. In this thesis the the- ory of hypergroups is applied to study the relation between certain graphs and subfactors of II, factors in the context of principal graphs associated with the inclusions of II, factors. More general classes of hypergroups are iutroduced, new examples of hypergroups associated to certain graphs are coustructed and classification of small order hypergroups is discussed.The text of the thesis is arranged in four chapters. The first chapter is on preliminaries of the theory of hypergroups, the second on the appli- cation of the theory of hyjrrgroups …

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Some Limit Theorem On Conditional U-Statistics And Censored Data Non Parametric Regression., Arusharka Sen Dr. Feb 1994

Some Limit Theorem On Conditional U-Statistics And Censored Data Non Parametric Regression., Arusharka Sen Dr.

Doctoral Theses

In Statistics, a classical problem is that of estimating the regression function which is defined as m{t) := E(Y|X = ), te R, for two random variables X and Y such that EY < 0o. The estimators are constructed iased on a sample {(Xi, Yi.)}, 1sis n,n 2 1, from the distribution of (X, Y). Throughout this thesis, we assume X and Y to be real-valued for the sake of convenience. The classical approach to this problem is to assume a parametrized, polynomial form for nt-), i.e., m(t) := Bo + E-1 P,ti, p 21, and obtain estimates of the unknown paraineters Bo, Bj,, 1sjsp. Later, with the development of techıniques for non-parametrie density estimation, it was sought to extend these techniques to regression estimation. Heuristically, the two problems can be seen to be related as follows : let fi(-) be the marginal density of X and note that E1(X S x) = h(t)dt, z € R, whereas EY 1(X Sx) = m(t)fi(t)dt, x E MR. (1.0.2) In other wordds, (1.0.1) can be looked upon as a special case of (1.0.2), with Y = 1. + similarity, as we shall see later on, has been the underlying theme in Chapters 2 and 4 of the present work.) The following non-parametric regression estimator was proposed independently by Nadaraya (1964) and Watson (1964): "(): := m.(Y,)/m.(1, ), te R, (1.0.3) where m,(Y, t) = (nan)- E-, Y;K((t - X:)/an). (1.0.4) m,(1,1) (na,)-E, K((I - X)/a,). Here K(), the so-called kernel function, is chosen to satiafy various analytical conditions (typically, K(-) is taken to be a density function), and a, 1 0 are the bandwidths which go to zero sufficiently slowly (e.g., na,0o as n00) in order to ensure consistency of the estimator mW (). The intuition behind such an estimator is that m,(Y,) is an estimator of mt-)fi() while m,(1,) cstimates the density fa(-). See Prakasa Rao (1983), Chapters 1-4. for an introduction to non-parametric density and regression estimation. Now, m(t) is a functional of the conditional distribution of Y, given X = t. A natu- ral generalisation of the regression estimation problem seems to be the estimation of the following functionals: mh(t1,....tk) := E{h(Y1,.....Yk) | X1, = t1.,Xk. = tk), (t....) € R*, k 2 1, (1.0.5) where h: R*- R is such that Elh(Y...., Y) < 0. A similar generalisation led Hoelfding (1948) from the sample mcan to the theory of so-called U-statistics, in the uncondilional set-up. The estimation of (1.0.5) were considerexl, for the first time in published form, in Stute (1991) where the following conditional U-statistics were proposed as estimators;where Fn(-) := n-1E, 1(Xi; < ) denotes the empirical distribution function (c.d.f Bochynek discussed the asymptotic normality of conditional U- and V-statistics and pei formed simulation studies on them. Stute (1991) established weak and strong pointwis consistency and asymptotic normality of U(t). Liero (1991) studied uniform strong con sistency of conditional U-statistics and established asymptotic normality of the integrate squared error (ISE) statistic:for suitable A c R* and weight function w(-). We quote the following examples to illustrate the possible use of conditional U-statistics See Stute (1991) and Bochynek (1987) for other examples. Throughout this thesis, our set up will be as foliows: {(Xn, Yn)}n>ı is a bi-variate i.i.d sequence, with (X1, Y1) having join density f(,-) and X, having marginal density fi(-). Consequently,

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Multivalued Approach For Uncertainty Management., Deba Prasad Mandal Dr. Feb 1994

Multivalued Approach For Uncertainty Management., Deba Prasad Mandal Dr.

Doctoral Theses

Real life problems are rarely free from uncertainty which usually emerges from the deficiencies of information available from a situation. The defi- ciencies may result from incomplete, imprecise, not fully reliable, vague or contradictory information depending on the problem. Management of uncer- tainty in a decision making system has been an important research problem for many years.Until the inception of the concept of fuzzy set theory in 1965 (1), the theory of probability and statistics was the primary mathematical tool for modeling uncertainty in a system/situation. Fuzzy set theory has shown enormous proinise in handling uncertaintics to a reasonable extent …

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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 …

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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 …

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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. …

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Conjugating Polynomials On Finite Rings, M. Insall, L. Mullin, R. Wilkerson Feb 1994

Conjugating Polynomials On Finite Rings, M. Insall, L. Mullin, R. Wilkerson

Computer Science Technical Reports

No abstract provided.

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Square Roots Of Finite Groups, Kashi Abhyankar, Daniel Grossman Feb 1994

Square Roots Of Finite Groups, Kashi Abhyankar, Daniel Grossman

Mathematical Sciences Technical Reports (MSTR)

Let G be a finite group of order n2. A perfect square root of G is a subset X of G such that |X| = n and X2 = G. Neither generalized dihedral groups nor groups of nilpotency class two have perfect square roots.

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Letter From The Editor, Issue 9, 1994, Alvin White Feb 1994

Letter From The Editor, Issue 9, 1994, Alvin White

Humanistic Mathematics Network Journal

No abstract provided.

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Mathematics And The Arts: Taking Their Resemblances Seriously, Frederick Reiner Feb 1994

Mathematics And The Arts: Taking Their Resemblances Seriously, Frederick Reiner

Humanistic Mathematics Network Journal

No abstract provided.

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Students' Understanding Of Functions In Calculus Courses, G. S. Monk Feb 1994

Students' Understanding Of Functions In Calculus Courses, G. S. Monk

Humanistic Mathematics Network Journal

No abstract provided.

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Poems, Lee Goldstein Feb 1994

Poems, Lee Goldstein

Humanistic Mathematics Network Journal

No abstract provided.

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Complete Issue 9, 1994 Feb 1994

Complete Issue 9, 1994

Humanistic Mathematics Network Journal

No abstract provided.

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Letter To The Editor, Ken Ross Feb 1994

Letter To The Editor, Ken Ross

Humanistic Mathematics Network Journal

No abstract provided.

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The Language Of Mathematics: A Quantitative Course For A General Audience, Stephanie F. Singer Feb 1994

The Language Of Mathematics: A Quantitative Course For A General Audience, Stephanie F. Singer

Humanistic Mathematics Network Journal

No abstract provided.

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Writing Mathematics, E. G. Bernard Feb 1994

Writing Mathematics, E. G. Bernard

Humanistic Mathematics Network Journal

No abstract provided.

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Mathematics For Math Majors: Loss Of Self-Esteem, Chun-Ip Fung, Man-Keung Siu Feb 1994

Mathematics For Math Majors: Loss Of Self-Esteem, Chun-Ip Fung, Man-Keung Siu

Humanistic Mathematics Network Journal

No abstract provided.

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Philosophy Of Mathematics, Mathematics Education, And Philosophy Of Mathematics Education, Yuxin Zheng Feb 1994

Philosophy Of Mathematics, Mathematics Education, And Philosophy Of Mathematics Education, Yuxin Zheng

Humanistic Mathematics Network Journal

No abstract provided.

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Space Venture, Edward E. Chipman Feb 1994

Space Venture, Edward E. Chipman

Humanistic Mathematics Network Journal

No abstract provided.

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Back Matter, Issue 9, 1994 Feb 1994

Back Matter, Issue 9, 1994

Humanistic Mathematics Network Journal

No abstract provided.

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Composite Knots In The Figure-8 Knot Complement Can Have Any Number Of Prime Factors, Michael C. Sullivan Feb 1994

Composite Knots In The Figure-8 Knot Complement Can Have Any Number Of Prime Factors, Michael C. Sullivan

Articles and Preprints

We study an Anosov flow Фt in S3 – {figure-8 knots}. Birman and Williams conjectured that the knot types of the periodic orbits of this flow could have at most two prime factors. Below, we give a geometric method for constructing knots in this flow with any number of prime factors.

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Uniqueness Of Stable And Unstable Positive Solutions For Semipositone Problems, Alfonso Castro, Sudhasree Gadam Feb 1994

Uniqueness Of Stable And Unstable Positive Solutions For Semipositone Problems, Alfonso Castro, Sudhasree Gadam

All HMC Faculty Publications and Research

Abstract not included in this article.

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Optical Hamiltonians And Symplectic Twist Maps, Christophe Golé Feb 1994

Optical Hamiltonians And Symplectic Twist Maps, Christophe Golé

Mathematics Sciences: Faculty Publications

This paper concentrates on optical Hamiltonian systems of T*Tn, i.e., those for which Hpp is a positive definite matrix, and their relationship with symplectic twist maps. We present theorems of decomposition by symplectic twist maps and existence of periodic orbits for these systems. The novelty of these results resides in the fact that no explicit asymptotic condition is imposed on the system.

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An Involutive System And Integrable C. Neumann System Associated With The Modified Korteweg-De Vries Hierarchy, Zhijun Qiao Feb 1994

An Involutive System And Integrable C. Neumann System Associated With The Modified Korteweg-De Vries Hierarchy, Zhijun Qiao

School of Mathematical & Statistical Sciences Faculty Publications

In this article, a system of finite-dimensional involutive functions is presented and proven to be integrable in the Liouville sense. By using the nonlinearization method, the C. Neumann system associated with the modified Korteweg-de Vries (mKdV) hierarchy is obtained. Thus, the C. Neumann system is shown to be completely integrable via a gauge transformation between it and an integrable Hamiltonian system. Finally, the solution of a stationary mKdV equation and the involutive solutions of the mKdV hierarchy are secured. As two examples, the involutive solutions are given for the mKdV equation: u,+ ;uXXX- $u2u,=0 and the 5th mKdV equation v,- …

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Gravity And Electromagnetism In Noncommutative Geometry, Giovanni Landi, Nguyen Ai Viet, Kameshwar C. Wali Jan 1994

Gravity And Electromagnetism In Noncommutative Geometry, Giovanni Landi, Nguyen Ai Viet, Kameshwar C. Wali

Physics - All Scholarship

We present a unified description of gravity and electromagnetism in the framework of a Z 2 non-commutative differential calculus. It can be considered as a “discrete version” of Kaluza-Klein theory, where the fifth continuous dimension is replaced by two discrete points. We derive an action which coincides with the dimensionally reduced one of the ordinary Kaluza-Klein theory.

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Injective Endomorphisms Of 풢X-Normal Semigroups: Finite Defects., Inessa Levi Jan 1994

Injective Endomorphisms Of 풢X-Normal Semigroups: Finite Defects., Inessa Levi

Faculty Bibliography

A semigroup of transfonnations of an infinite set X is called ^'x-normal if S is invariant under conjugations by permutations of X. In this paper we describe injective endomorphisms of & x -normal semigroups of total one-to-one transformations / such that the range of / has a finite non-empty complement in X.

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Projective Plane Embeddings Of Polyhedral Pinched Maps, Adrian Riskin Jan 1994

Projective Plane Embeddings Of Polyhedral Pinched Maps, Adrian Riskin

Mathematics

We give various conditions on pinched-torus polyhedral maps which are necessary for their graphs to be embeddable in the projective plane. Our other main result is that even if the graph of a polyhedral map in the pinched torus is embeddable in a projective plane, the map induced by the embedding cannot be polyhedral, but must have all faces bounded by cycles. Finally, we give a class of examples of graphs which have polyhedral embeddings on the pinched torus and also on orientable surfaces of arbitrary high genus.

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Finite Groups Can Be Arbitrarily Hamiltonian, Stephen Ahearn, Mark Huber Jan 1994

Finite Groups Can Be Arbitrarily Hamiltonian, Stephen Ahearn, Mark Huber

Mathematical Sciences Technical Reports (MSTR)

Let r be a rational in (0,1]. There exists a finite group G which is the direct product of at most four metacyclic groups and whose proportion of normal subgroups is r. An analogous result holds for three other measures of "Hamiltonianess".

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Elimination Of Supply Harmonics: An Evolution Of Current Compensation And Active Filtering Methods, Stephen L. Clark, P. Famouri, W. L. Cooley Jan 1994

Elimination Of Supply Harmonics: An Evolution Of Current Compensation And Active Filtering Methods, Stephen L. Clark, P. Famouri, W. L. Cooley

Mathematics and Statistics Faculty Research & Creative Works

The price of the extensive use of power electronic devices is becoming clear: increasing harmonic "pollution." This survey takes a brief look at background information related to harmonics, including their sources, effects, and characteristics. Then, the evolution of the harmonics elimination approaches of current compensation and active filtering, which are becoming more feasible due to research and technological improvements, are discussed in order to give some insight into the directions that research is taking.

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