Physical Sciences and Mathematics Commons^™

Triangle Trek, Thomas E. Moore

Bridgewater Review

No abstract provided.

Graph Theory Based Routing Algorithms, Bo Wu

Masters Theses

In this thesis, we study two VLSI layout problems.

We investigate the Minimum-Bend Single Row Routing Problem in which the objective function is to minimize the number of doglegs (or blends) per net. Our approach uses a graph theoretic representation in which an instance of the Single Row Routing Problem is represented by three graphs, an overlap graph, a containment graph and an interval graph. Using this graph representation, we develop three algorithms for minimum-bend single row routing problem.

We present a three-layer over-the-cell router (ICR-3) for the standard cell design style based on a new cell model which assumes …

Optimization In Chemical Kinetics, Arthur T. Benjamin, Gordon J. Hogenson '92

All HMC Faculty Publications and Research

No abstract provided in this article.

Some Solutions To A Lens Model With Applications To Warm-Core Eddies, Juping Liu

OES Theses and Dissertations

A model of lens-shaped anticyclonic eddies based on nonlinear shallow water equations is developed. The model is a three-layer fluid and allows for one asymmetric mode as well as specified environmental flows. The solution scheme is a polynomial expansion of the field variables. When inserted into the hydrographic equations, the expansion yields eight first-order differential equations for the time dependent amplitudes. This system of ordinary differential equations is numerically tractable. As long as the initial values meet the requirement of elliptical structure and the prescribed external force is tolerable for the initial values, the numerical solutions are stable. Numerical solutions …

On Electron Attraction & Newtonian Methodology For Approximating Quantum Mechanical Phenomena, Donald Greenspan

Mathematics Technical Papers

Classical dynamical computations for ground state [see pdf for notation], and [see pdf for notation] have been shown to yield correct vibrational frequencies and molecular diameters under an assumption of electron attraction for bonding electrons. In this paper, it is shown that such a mechanism also extends to [see pdf for notation] and to the nonhomogeneous molecules [see pdf for notation] and [see pdf for notation]. The vibrational motions are, apparently, quasi-periodic rather than periodic.

Pointwise Kernels Of Schwartz Distributions, Todor D. Todorov

Mathematics

We show that Schwartz distributions have kernels in the class of the pointwise nonstandard functions.

A4 Rewriteability, Eric Wepsic, Kevin O'Bryant, Lawren Smithline

Mathematical Sciences Technical Reports (MSTR)

The concept of 4-rewriteability with permutation coming form the alternating group A₄ is explored.

A Generalization Of Kraemer's Result On Difference Sets, James A. Davis

Department of Math & Statistics Faculty Publications

Kraemer has shown that every abelian group of order 2^{2d+ 2} with exponent less than 2^{2d+ 3} has a difference set. Generalizing this result, we show that any nonabelian group with a central subgroup of size 2^{d+ 1} together with an exponent-like condition will have a difference set.

Multiweighted Shapley Values And Random Order Values, Irinel C. Dragan

Mathematics Technical Papers

Recently, R. J. Weber introduced axiomatically in [14] the concept of random order value, an operator from [see pdf for notation], the space of TU games, to [see pdf for notation], satisfying linearity, dummy, efficiency and monotonicity axioms. In the present paper, we consider the concept of multiweighted Shapley value (MWSV), an operator from [see pdf for notation], satisfying linearity and carrier axioms. In the first section, we show that a MWSV is defined by its matrix representation relative to the unanimity basis for [see pdf for notation] and the standard basis for [see pdf for notation], if and only …

Some Lesson About The Law From Self-Referential Problems In Mathematics, John M. Rogers, Robert E. Molzon

Michigan Law Review

We first describe briefly mathematician Kurt Gödel's brilliant Incompleteness Theorem of 1931, and explore some of its general implications. We then attempt to draw a parallel between axiomatic systems of number theory (or of logic in general) and systems of law, and defend the analogy against anticipated objections. Finally, we reach two types of conclusions. First, failure to distinguish between language and metalanguage in mathematical self-referential problems leads to fallacies that are highly analogous to certain legal fallacies. Second, and perhaps more significantly, Gödel's theorem strongly suggests that it is impossible to create a legal system that is "complete" in …

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.

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.

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.

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.

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 …

Rewriteability, Commutators, And Fundamental N-Rewritings, Lawren Smithline

Mathematical Sciences Technical Reports (MSTR)

We consider the relationship between commutators and rewriteability.

Boundedness And Periodic Solutions In Infinite Delay Systems, Roger H. Hering

Mathematics and Statistics Faculty Research & Creative Works

Liapunov methods are used to give conditions ensuring that solutions of infinite delay equations are uniformly bounded and uniformly ultimately bounded with respect to unbounded (Cg) initial function spaces; and the connection to proving existence of periodic solutions is examined. Several examples illustrate the application of these results, especially to integrodifferential equations. © 1992.

Fixed Point Theorems For D-Complete Topological Spaces I, Troy L. Hicks

Mathematics and Statistics Faculty Research & Creative Works

Generalizations of Banach's fixed point theorem are proved for a large class of non-metric spaces. These include d-complete symmetric (semi-metric) spaces and complete quasi-metric spaces. The distance function used need not be symmetric and need not satisfy the triangular inequality. © 1992, Hindawi Publishing Corporation. All rights reserved.

Prediction Intervals, Based On Ranges And Waiting Times, For An Exponential Distribution, Laura Colangelo, Jagdish K. Patel

Mathematics and Statistics Faculty Research & Creative Works

This article contains two prediction intervals applicable to a 2-parameter as well as a 1-parameter exponential distribution. One can be used to predict a future sample range on the basis of an observed sample range. Appropriate prediction factors are tabulated. The other can be used to predict a waiting time between two future successive failures on the basis of an observed waiting time between two previous successive failures. © 1992 IEEE

A P-Adic Cohomological Method For The Weierstrass Family And Its Zeta Invariants, Goro Kato

Mathematics

After a survey of the Weierstrass family and cohomology, we compute the lifted homology of the Weierstrass family with compact supports so that explicit formulae for the zeta function of each fibre of the Weierstrass family may be obtained. The (co-)homology theory that we use is found in [L₁], [L₂] and [L₃]. Therefore, this article can be regarded as an application of Lubkin's p-adic theory of cohomologies to an algebraic family called the Weierstrass scheme over the ring (Z/pZ)[g₂,g₃). The cohomological background for the computation will be rather carefully exploited.

A Binary Tree Decomposition Space Of Permutation Statistics, Don Rawlings

Mathematics

Based on the binary tree decomposition of a permutation, a natural vector space of permutation statistics is defined. Besides containing many well known permutation statistics, this space provides the general context for an archetypal recurrence relationship that contains most of the classic combinatorial sequences and some of their known generalizations.

Riemannian Geometry Of Orbifolds, Joseph Ernest Borzellino

Mathematics

We investigate generalizations of many theorems of Riemannian geometry to Riemannian orbifolds. Basic definitions and many examples are given. It is shown that Riemannian orbifolds inherit a natural stratified length space structure. A version of Toponogov's triangle comparison theorem for Riemannian orbifolds is proven. A structure theorem for minimizing curves shows that such curves cannot pass through the singular set. A generalization of the Bishop relative volume comparison theorem is presented. The maximal diameter theorem of Cheng is generalized. A finiteness result and convergence result is proven for good Riemannian orbifolds, and the existence of a closed geodesic is shown …

One-Sided Refinements Of The Strong Law Of Large Numbers And The Glivenko-Cantelli Theorem, David Gilat, Theodore P. Hill

Research Scholars in Residence

A one-sided refinement of the strong law of large numbers is found for which the partial weighted sums not only converge almost surely to the expected value, but also the convergence is such that eventually the partial sums all exceed the expected value. The new weights are distribution-free, depending only on the relative ranks of the observations. A similar refinement of the Glivenko-Cantelli theorem is obtained, in which a new empirical distribution function not only has the usual uniformly almost-sure convergence property of the classical empirical distribution function, but also has the property that all its quantiles converge almost surely. …

A Survey Of Prophet Inequalities In Optimal Stopping Theory, Theodore P. Hill, Robert P. Kertz

Research Scholars in Residence

This paper surveys the origin and development of what has come to be known as "prophet inequalities" in optimal stopping theory. Included is a review of all published work to date on these problems, including extensions and variations, descriptions and examples of the main proof techniques, and a list of a number of basic open problems.

Splitting Of The Identity Component In Locally Compact Abelian Groups, Peter Loth

Mathematics Faculty Publications

In this paper we are concerned with the splitting of the identity component G₀ in an LCA group G. As Pontrjagin duality shows, this splitting is to the splitting of the torsion part tA in a discrete abelian group A, if G is assumed to be compact.

A Note On The Connectedness Problem For Nest Algebras, David R. Pitts

Department of Mathematics: Faculty Publications

It has been conjectured that a certain operator T belonging to the group ff of invertible elements of the algebra Alg Z of doubly infinite uppertriangular bounded matrices lies outside the connected component of the identity in W. In this note we show that T actually lies inside the connected component of the identity of & .

The Statistics Of Lotteries, Matthew Thomas Bremer

Honors Theses, 1963-2015

This project begins with the analysis of several existing lotteries in the state of Minnesota. The raw data of these lotteries are used to calculate the expected values of certain random variables in an effort to describe and compare the lotteries mathematically. Next, the different criteria that contribute to a successful lottery are described and brought together. Finally, via mathematical modeling and computer simulation, a new lottery proposal is presented with the claim that it is superior to existing lotteries from an administrative standpoint.

On The Asymptotic Behavior And Radial Symmetry Of Positive Solutions Of Semilinear Elliptic Equations In R N Ii. Radial Symmetry, Yi Li, Wei-Ming Ni

Yi Li

The main purpose of this paper is to prove Theorems 1 and 2 of the preceding paper, Part I, together with their extensions and related symmetry results. To make this part essentially self-contained, we shall apply the method developed in Section 2 to equations with radial symmetry. Combining the asymptotic behavior and the "moving plane" technique, we are then able to obtain the desired results.

On The Asymptotic Behavior And Radial Symmetry Of Positive Solutions Of Semilinear Elliptic Equations In Rn. I. Asymptotic Behavior, Yi Li, Wei-Ming Ni

Yi Li

No abstract provided.

A Queueing System With A Fixed Accumulation Level, Random Server Capacity And Capacity Dependent Service Time, Jewgeni H. Dshalalow, Lotfi Tadj

Mathematics and System Engineering Faculty Publications

This paper introduces a bulk queueing system with a single server processing groups of customers of a variable size. If upon completion of service the queueing level is at least r the server takes a batch of size r and processes it a random time arbitrarily distributed. If the queueing level is less than r the server idles until the queue accumulates r customers in total. Then the server capacity is generated by a random number equals the batch size taken for service which lasts an arbitrarily distributed time dependent on the batch size. The objective of the paper is …