Physical Sciences and Mathematics Commons^™

Hopf Bifurcation In A Parabolic Free Boundary Problem, Yoon-Mee Lee

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

We deal with a free boundary problem for a nonlinear parabolic equation, which includes a parameter in the free boundary condition. This type of system has been used in models of ecological systems, in chemical reactor theory and other kinds of propagation phenomena involving reactions and diffusion.

The main purpose of this dissertation is to show the global existence, uniqueness of solutions and that a Hopf bifurcation occurs at a critical value of the parameter r. The existence and uniqueness of the solution for this problem are shown by finding an equivalent regular free boundary problem to which existence …

Mielnik Probability Spaces And Functional Equations, J. J. Mitchell

Opportunities for Undergraduate Research Experience Program (OURE)

The invariance properties of the solutions of those functional equations naturally occurring in the construction of Mielnik probability spaces are studied, and in turn are related to one another. In particular, the possibilities for fixed points of these solutions are found, and the relationships between these results are discussed. The two functional equations studied include a representation of the generalized parallelogram law and an equation used in the modeling of polarization phenomena. The main result of the paper lies in the extention of previous research on Mielnik probability spaces to a higher dimension, as well as a discussion of their …

Shooting Method Solutions Of Eigenvalue Problems, Xi Chen

Opportunities for Undergraduate Research Experience Program (OURE)

A shooting method was developed to study eigenvalue problems derived from Schrodinger equation. The challenging problem, the two-dimensional hydrogen system with the logarithmic potential function, was successfully solved by the shooting method. But no complete proof was given for its rationale and correctness. This paper not only gives the complete proof for the shooting method, but also generalizes it to solve a large class of eigenvalue problems. In a certain sense, the shooting method proves more effective numerically and more powerful theoretically than the classical functional analysis approach.

Some Facts About Cycels And Tidy Groups, Kevin O'Bryant, D. Patrick, Lawren Smithline, Eric Wepsic

Mathematical Sciences Technical Reports (MSTR)

No abstract provided.

From The Editor, Issue 7, 1992, Alvin White

Humanistic Mathematics Network Journal

No abstract provided.

Three Comments On Ethics, Saunders Maclane

Humanistic Mathematics Network Journal

No abstract provided.

Toward A Definition Of 'Humanistic Mathematics', Sherman K. Stein

Humanistic Mathematics Network Journal

No abstract provided.

Letter To Professor Joanne S. Growney, John S. Lew

Humanistic Mathematics Network Journal

No abstract provided.

Poems Taken From "An Evening Of Mathematical Poetry"

Humanistic Mathematics Network Journal

No abstract provided.

Mathematics As A Humanistic Discipline, Elena Anne Corie Marchisotto

Humanistic Mathematics Network Journal

No abstract provided.

Mathematical References In Literature, John S. Lew

Humanistic Mathematics Network Journal

No abstract provided.

Epistemological Pluralism: Styles And Voices Within The Computer Culture, Sherry Turkle, Seymour Papert

Humanistic Mathematics Network Journal

No abstract provided.

What Is Mathematics And Why Don't They Know That?, Harald M. Ness

Humanistic Mathematics Network Journal

No abstract provided.

Writing Humanistic Mathematics, Ruth Hubbard

Humanistic Mathematics Network Journal

No abstract provided.

Mathematics From An English Major's Point Of View, Elizabeth Miller, Kathleen M. Shannon

Humanistic Mathematics Network Journal

No abstract provided.

The Profit Motive: The Bane Of Mathematics Education, Neal Koblitz

Humanistic Mathematics Network Journal

No abstract provided.

Triangle Trek, Thomas E. Moore

Bridgewater Review

No abstract provided.

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

All HMC Faculty Publications and Research

No abstract provided in this article.

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.

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 …

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 …

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 …

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 …

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 …

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 …