Physical Sciences and Mathematics Commons^™

The Sharp Sobolev Inequality And The Banchoff-Pohl Inequality On Surfaces, Ralph Howard

Faculty Publications

No abstract provided.

Asymptotic Norming Properties And Related Themes., Sudeshna Basu Dr.

Doctoral Theses

In the first part of this chapter, we explain the main theme of this thesis. The second part consists of some of the notions and results used in subsequent discussions.It is a very familiar fact that a point outside a (bounded) closed convex set in a Banach space can be separated from the latter by a hyperplane. One can ask whether the separation can be effected by disjoint balls. This is a typical example of a ball separation property, study of which has become important in Banach space theory. In this thesis, we study several such properties along with some …

On The Developement Of An Optical Character Recognition(Ocr) System For Printed Bangla Script., Umapada Pal Dr.

Doctoral Theses

This thesis concerns OCR development of machine printed text in an Indian lan- guage, Bangla (Bengali) which is the fourthmost popular language in the world and the secondmost popular language in India.1.1 Optical Character Recognition Optical Character Recognition (OCR) is a process of automatic computer recog- nition of characters in optically scanned and digitized pages of text. OCR is ene of the most fascinating and challenging areas of pattern recognition with various practical applications. It can contribute tremendously to the advancement of an automation process and can improve the interface between man and machine in many applications, including office automation …

Σary, Moorhead State University, Mathematics Department

Math Department Newsletters

No abstract provided.

Neuro Fuzzy Reasoning For Pattern Classification And Object Recognition., Jayati Ghosh Dr.

Doctoral Theses

In real world, pattern classification and object recognition problems are faced with fuzzi- ness that is connected with diverse facets of cognitive activity of the human being. An origin of sources of fuzziness is related to labels expressed in feature space as well as to labels of classes taken into account in classification and /or recognition procedures. Though a lot of scientific efforts have already been dedicated to pattern recognition problems, especially to classification procedures, still pattern recognition is confronted with a continuous challenge coming from a human being who can perform lot of ex- tremely complex classification tasks by …

Wiener Tauberian Theorems On Semisimple Lie Group., Rudra Pada Sarkar Dr.

Doctoral Theses

In their celebrated study of Harmonic analysis on semi-simple Lie groups Ehrenpreis and Mautner [E-M] noticed that the analogue of the claasical Wiener Tauberian theorem resting on the unitary dual does not hold for semisimple Lle groups. A simple proof of this fact due to M. Duflo appears in (H). Ehrenpreis and Mautner went on in (E-M] to formulate the problem on the commutative Banach algebra of the SO2(R)-biinvariant functions in L1(SL2(R))1, and obtained two different versions of the theorem involving, this time, the dual of the Banach algebra which includes, beside the unitary dual of G, a part of …

Static Interconnection Networks And Parallel Algorithms For Efficient Problem Solving., T. Krishnan Dr.

Doctoral Theses

There is nothing more difficult to take in hand, more perilous to conduct, or more uncertain in its success, than to take the lead in the introduction of a new order of things.

On The Geometrisability Of Some Strongly Regular Graphs Related To Polar Spaces., Pratima Panigraphi Dr.

Doctoral Theses

GraphsA graph G = (VE) consists of a finite set V and a subset E of ). (Here () denotes the set of all 2-subsets of V.) Elements of Vare called the vertices and the elements of E are called the edges of the graph. So Vis the vertex set and E is the edge set of the graph G. Two vertices a, y are said to be adjacent if the pair {a, y} is an edge; otherwise they are non-adjacent. If two vertices are adjacent then each is called a neighbour of the other vertex.Sometimes the edges of a …

The Set Of Hemispheres Containing A Closed Curve On The Sphere, Mary Kate Boggiano, Mark Desantis

Department of Math & Statistics Technical Report Series

Suppose you get in your car and take a drive on the sphere of radius R, so that when you return to your starting point the odometer indicates you've traveled less than 2πR. Does your path, γ, have to lie in some hemisphere?

This question was presented to us by Dr. Robert Foote of Wabash College. Previous authors chose two points, A and B, on γ such that these points divided γ into two arcs of equal length. Then they took the midpoint of the great circle arc joining A and B to be the North Pole and showed that …

Characterisations Of Slender Groups, Thomas Kelly

Masters

Chapter 1 summarises some necessary results concerning free, divisible, algebraically compact and cotorsion groups. A detailed proof of the well-known result that the Specker group P is ℵ1 free but not free is included and the structure of the quotient group P/S is determined. The basic properties of slender groups are examined and cotorsion groups of cardinality less than or equal to that of the continuum are shown to be epimorphic images of P. Chapter II presents Nunke’s characterisation of slender groups. This approach establishes that homomorphic images of the Specker group P are the direct sum of a cotorsion …

New Topologies And Parallel Algorithms For Static Interconnection Networks., Srabani Sen Gupta Dr.

Doctoral Theses

Many real-life applications in the areas of signal processing, image processing, etc., require a large amount of fast computations to be performed. Although high speed powerful processors are currently available due to the phenomenal advances in VLSI technology, the increasing demand for massive real-time computations can not be met just by a uniprocessor system. One way of achieving the goal of fast computation is through parallel processing. In parallel processing, a problem is broken into several subproblems, which are distributed among different processors so that each of the processors can perform its task simultaneously. Main areas of recent research in …

Some Problems In Estimating Finite Population Total And Variance In Survey Sampling., Saswati Bhattacharya Dr.

Doctoral Theses

The problem of drawing inference concerning the parameters of a finite population of identifiable units has been increasingly engaging the attention of statisticians. The central problem here is to devise a suitable method of selecting a sample from the population and to employ an appropriate estimator to estimate the finite population total or mean. A consider- able progress in this field of study has been made and many authors have contributed towards the development of the theory in this aspect of the problem of statistical inferenceNumerous papers have been written covering the first aspect of the problem, namely, method of …

Pompeiu Problem And Analogues Of The Weiner-Tauberian Theorem For Certain Homogeneous Spaces., Rama Rawat Dr.

Doctoral Theses

Let G be a connected locally compact unimodular group acting transitively on a locally compact space X. For a function f on X and g € G, define of by 9f(x) = fA 9.a), a € X. One of the recurring themes in analysis is the question of when a function f in a given function space F(X) will have property that Span{gf : g € G} is dense in F(X). If X = R and G = R, the celebrated Wiener-Tauberian theorem answers this question completely for the space L1(R): The span of the translates of fE L1(R) is …

Using The Simplex Code To Construct Relative Difference Sets In 2-Groups, James A. Davis, Surinder K. Sehgal

Department of Math & Statistics Faculty Publications

Relative Difference Sets with the parameters (2^a, 2^b, 2^a, 2^a-b) have been constructed many ways (see [2], [3], [5], [6], and [7] for examples). This paper modifies an example found in [1] to construct a family of relative difference sets in 2-groups that gives examples for b = 2 and b = 3 that have a lower rank than previous examples. The Simplex code is used in the construction.

Σary, Moorhead State University, Mathematics Department

Math Department Newsletters

No abstract provided.

On Some Problems Related To Hermite And Laguerre Expansions., P. K. Ratnakumar Dr.

Doctoral Theses

The first three chapters of this thesis are concerned with the spherical means associated to the Hermite and Laguerre expansions. The study of spherical means has a very long history. The classic work of F. John deals with various applications of the spherical means to the theory of partial differential equations. They entered Fourier analysis with the celebrated theorem of E. Stein on spherical analogue of the Lebesgue differentiation theorem. Ever since they have appcared again and again in several areas of analysis like integral geometry, inversion of Fourier transforms and related arcas.

The Fixed Point Index As A Local Lefschetz Number., Neeta Pandey Dr.

Doctoral Theses

In this thesis we defitne a class of self maps of connected compact polyhodza - those which prmserve erpanding directions - and define the fixed point indices of such maps at an isolated set of fixed points of the map as a local Lefschets rumber. Our definition uses simplicial approximations of the given map in the spirit of O Nell (I19| and Fournier (71) and is intrinsic so that it is computable.Let X be a connected compact polyhedron and f:X→ X be a map an X. The Lefscheta number L() of / is then defined to be ([13]),L) -E(-1)jTrace {, …

On Cvt Minimization In Single Machine Scheduling., D. K. Manna Dr.

Doctoral Theses

Scheduling problens are quite common in real life. They arise whenever there is a need to plan execution of various tasks over time and therefore they play very important roles in commercial set-ups concerning manufacturing or service in the optimal use of resources and/or customers satisfaction. The theory of scheduling deals with the construction of suitable models and their analyses. Researchersattention was drawn to the study of scheduling problems using mathematical modeling, probably for the first time when Johnson (1954] published his famous work on flowshop problem. Since then, the study of scheduling problem and its context has gradually attracted …

Fourier Transforms Of Very Rapidly Decreasing Functions On Certain Lie Groups., M. Sundari Dr.

Doctoral Theses

Recall that for a function f ϵ L1(Rn ), its Fourier transform fÌ‚ is definedby: fÌ‚ (ƹ) = ʃ Rnf(x)ei(ƹ,x)dx ( 0.1.1)where (.,.) denotes the standard inner product on Rn and dr the Lebesgue measure on Rn. A celebrated theorem of L. Schwartz asserts that a function f on Rn is rapidly decreasing (or in the Schwartz class ) if and only if its Fourier transform is rapidly decreasing . In sharp contrast to Schwartz s theorem, is a result due to Hardy ([18) which says that ʃ and fÌ‚ cannot both be very rapidly decreasing . More precisely, if …

Recurrence And Transience Of Reflecting Diffusions., S. Balaji Dr.

Doctoral Theses

An attempt to obtain conditions for certain stability properties of reflecting diffusions in unbounded domains with boundary has been made in this thesis. For diffusions in R', such stability properties like recurrence, transience and positive recurrence have been studied extensively; see Bhattacharya (1978), Kliemann (1987), Pinsky (1987). One might see Pinsky (1995) for an up-to-date review of kuown methods and results in this all case. (For corresponding recurrence classification results on Markov chains using martin- gale ideas based on stoxchastic analogues of Lyapunov functions, see Meyn and Tweedie (1993a), (1993b) and the references given therein). The main concern in this …

The Duals Of Warfield Groups, Peter Loth

Mathematics Faculty Publications

A Warfield group is a direct summand of a simply presented abelian group. In this paper, we describe the Pontrjagin dual groups of Warfield groups, both for the p-local and the general case. A variety of characterizations of these dual groups is obtained. In addition, numerical invariants are given that distinguish between two such groups which are not topologically isomorphic.

The Laws Of Complexity & The Complexity Of Laws: The Implications Of Computational Complexity Theory For The Law, Eric Kades

Faculty Publications

No abstract provided.

Arboreal Adventure: A Cross Curricular Unit On Trees, Anne Elizabeth Boshoven

Theses Digitization Project

No abstract provided.

Collected Papers, Vol. 2, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Some Problems Of Continuum Percolation., Anish Sarkar Dr.

Doctoral Theses

The model of continuum percolation can be described as follows. We start with a homogeneous Poisson point process X. At each point of X we centre a ball with a random radius such that the radii corresponding to different points are independent of each other and also independent of the Poisson process X. In this way, the space is divided into two regiorns, the covered region or the occupied region consisting of the region which is covered by at least one ball, and the uncovered region or the vacant region which is complement of the covered region. In this dissertation …

Design,Analysis And Routing In Static Interconnection Networks., Rajib Kumar Das Dr.

Doctoral Theses

Many real-life applications such as image processing, weather forecasting, digital signal processing, etc., require large amount of computations. By distributing the task among several processors, one can appreciably reduce the computation time. To solve complex problems, several computer architectures using multiple processors have been introduced. Recent developments in IC technology have made it economically feasible to construct multiple processor systems consisting of hundreds or thousands of processors.There are two types of multiprocessor systems (PS87). One is tightly coupled, where the processors share a common clock and/or memory. The other is loosely coupled, where each processor runs independently with a local …

Σary, Moorhead State University, Mathematics Department

Math Department Newsletters

No abstract provided.

Some Problems In Joint Spectral Theory., Tirthankar Bhattacharya Dr.

Doctoral Theses

No abstract provided.

A Note On Generators Of Least Degree In Gorenstein Ideals, Matthew Miller, Rafael H. Villarreal

Faculty Publications

No abstract provided.

Paracompact Subspaces In The Box Product Topology, Peter Nyikos, Leszek Piatkiwicz

Faculty Publications

No abstract provided.