Physical Sciences and Mathematics Commons^™

Perturbed Laplacian Matrix And The Structure Of A Graph., Sukanta Pati Dr.

Doctoral Theses

Laplacian matrices Let G be a connected simple graph with vertex set V = {1,2,.,n), edge set E and let each edge be associated with a positive number, the weight of the edge. The above graph is called a weighted graph. An unweighted graph is just a weighted graph with each of the edges bearing weight 1. All the graphs considered are weighted and simple, unless specified otherwise; all the matrices considered are real. The adjacency matrix A(G) related to this graph is defined as A(G) = (aij), whereaij, if (i, j] € E and the weight of the edge …

[Introduction To] Mathematics Calculus Bc, John R. Hubbard, David R. Arterburn, Michael A. Perl

Bookshelf

This book gives you the tools to prepare effectively for the Advanced Placement Examination in Mathematics: Calculus BC. These tools include a concise topical review and six full-length practice tests. Our review succinctly covers areas considered most relevant to this exam. Following each of our tests is an answer key complete with detailed explanations designed to clarify the material for you.

Collected Papers Vol. Iii, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Algebra În Exercijii Şi Probleme Pentru Liceu, Florentin Smarandache, Ion Goian, Raisa Grigor, Vasila Marin

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

On Measuring The Cost Of Children:The Case Of Rural Maharashtra., Manisha Chakrabarty Dr.

Doctoral Theses

In this dissertation we have attempted to measure the cost of children, which plays a crucial role in matters relating to welfare and public policy like child benefits and compensation policies of the government. The cost is measured based on the single equation as well as the systems approach using the 38th round National Sample Survey (NSS) data on household consumer expenditure for rural Maharashtra (relating to the period of January to December, 1983).The first chapter provides a brief account of the basic literature on empirical demand analysis which is relevant for welfare comparison between households. To be specific in …

Intersecting Chains In Finite Vector Spaces, Eva Czabarka

Faculty Publications

We prove an Erdős–Ko–Rado-type theorem for intersecting k-chains of subspaces of a finite vector space. This is the q-generalization of earlier results of Erdős, Seress and Székely for intersecting k-chains of subsets of an underlying set. The proof hinges on the author's proper generalization of the shift technique from extremal set theory to finite vector spaces, which uses a linear map to define the generalized shift operation. The theorem is the following.

For c = 0, 1, consider k-chains of subspaces of an n-dimensional vector space over GF(q), such that the smallest subspace in any chain has dimension at least …

An Ellam Scheme For Advection-Diffusion Equations In Two Dimensions, Hong Wang, Helge K. Dahle, Richard E. Ewing, Magne S. Espedal, Robert Sharpley, Shushuang Man

Faculty Publications

We develop an Eulerian--Lagrangian localized adjoint method (ELLAM) to solve two-dimensional advection-diffusion equations with all combinations of inflow and outflow Dirichlet, Neumann, and flux boundary conditions. The ELLAM formalism provides a systematic framework for implementation of general boundary conditions, leading to mass-conservative numerical schemes. The computational advantages of the ELLAM approximation have been demonstrated for a number of one-dimensional transport systems; practical implementations of ELLAM schemes in multiple spatial dimensions that require careful algorithm development are discussed in detail in this paper. Extensive numerical results are presented to compare the ELLAM scheme with many widely used numerical methods and to …

Σary, Moorhead State University, Mathematics Department

Math Department Newsletters

No abstract provided.

The Best Way To Knock 'M Down, Arthur T. Benjamin, Matthew T. Fluet '99

All HMC Faculty Publications and Research

"Knock 'm Down" is a game of dice that is so easy to learn that it is being played in classrooms around the world. Although this game has been effective at developing students' intuition about probability [Fendel et al. 1997; Hunt 1998], we will show that lurking underneath this deceptively simple game are many surprising and highly unintuitive results.

Time-Space Harmonic Polynomials For Stochastic Processes., Arindam Sengupta Dr.

Doctoral Theses

The sequence of polynomials of a single variable known as the Hermite polynomialshala) = ), k21, (-1)* ha(z) =has many close links with the Normal distribution. Their association goes very doep, and extends to several connections bet ween the two-variable Hermite polynomialsHll, 2) = the(z/t), . k21.and the prime example of Gaussian processes, that is Brownian motion, as well. Much of this connection stems from what we term the time-space harmonic property of these polynomials for the Brownian motion process. An exact definition of this property follows later. A natural question that arises is, for stochastic processes in general, when …

Pattern Classification Using Genetic Algorithms., Sanghamitra Bandyopadhyay 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 …

Muyltivariate And Regression Analysis Based On The Geometry Of Data Clouds., Biman Chakraborty Dr.

Doctoral Theses

Median is a natural estimate of location of a data set, and there are several versions of inultivariate median studied in the literature, each of which is an interesting descriptive statistic for multivariate data and provides some nice geometric insights into the data cloud. One would expect that multidimensional median will be a natural estimate for the center of symmetry of a multivariate distribution. However, there is no unique concept of symmetry in multivariate problems. The center of symmetry can be defined in several ways there. For example, the d-dimensional random variable X is spherically symmetric about e €Rd if …

The Deconstruction Of Mathematics: A Criticism Of Reuben Hersh's What Is Mathematics, Really? And The Humanist Philosophy Of Mathematics, David J. Stucki

Mathematics Faculty Scholarship

Mathematics, as an academic discipline, has stood for many years as the last bastion against a growing tide of intellectual relativism that has become all but ubiquitous. More recently, however, efforts have been made to "humanize" mathematics by advocating a social-constructivist approach to the philosophy of mathematics, both in practice and education. This paper is intended to serve as a critical response to one advocate of this approach, Reuben Hersh (What Is Mathematics, Really?, 1997), and in the process a defense of Platonism.

Bounds On A Bug, Arthur T. Benjamin, Matthew T. Fluet '99

All HMC Faculty Publications and Research

In the game of Cootie, players race to construct a "cootie bug" by rolling a die to collect component parts. Each cootie bug is composed of a body, a head, two eyes, one nose, two antennae, and six legs. Players must first acquire the body of the bug by rolling a 1. Next, they must roll a 2 to add the head to the body. Once the body and head are both in place, the remaining body parts can be obtained in any order by rolling two 3s for the eyes, one 4 for the nose, two 5s for the …

Asupra Unor Noi Functii În Teoria Numerelor, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Performantele matematicii actuale,ca si descoperirile din viitor isi au,desigur, inceputul in cea mai veche si mai aproape de filozofie ramura a matematicii, in teoria numerelor. Matematicienii din toate timpurile au fost, sunt si vor fi atrasi de frumusetea si varietatea problemelor specifice acestei ramuri a matematicii. Regina a matematicii, care la randul ei este regina a stiintelor, dupa cum spunea Gauss, teoria numerelor straluceste cu lumina si atractiile ei, fascinandu-ne si usurandu-ne drumul cunoasterii legitatilor ce guverneaza macrocosmosul si microcosmosul. De la etapa antichitatii, cand teoria numerelor era cuprinsa in aritmetica, la etapa aritmeticii superioare din perioada Renasterii, cand teoria …

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 …

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 …

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.

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 …

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.