Physical Sciences and Mathematics Commons^™

Scs 92: Products Of Continuous Partially Ordered Sets, Marcel Erné

Seminar on Continuity in Semilattices

No abstract provided.

Scs 91: Compactly Generated And Continuous Closure Systems, Marcel Erné

Seminar on Continuity in Semilattices

No abstract provided.

Scs 90: About Polytopes Of Valuations On Finite Distributive Lattices, Hans Dobbertin

Seminar on Continuity in Semilattices

No abstract provided.

Scs 89: Continuity Concepts For Partially Ordered Sets, Marcel Erné

Seminar on Continuity in Semilattices

No abstract provided.

Particle Simulation Of Compression Waves, Donald Greenspan

Mathematics Technical Papers

Compression waves are studied using a quasi-molecular, particle approach. Explosive type disturbances are simulated to generate such waves, which propagate by the interaction of each particle with its immediate neighbors. Obstacles to wave motions are studied by the introduction of variable densities. Computer examples are described and discussed.

Scs 88: A Proof Of A Theorem Of B. B., Klaus Keimel

Seminar on Continuity in Semilattices

Source: University archive of the Technische Universität Darmstadt.

The Chromatic And Cochromatic Number Of A Graph, John Gordon Gimbel

Dissertations

Clearly, there are many ways that one can partition the vertex sets of graphs. In the first chapter of this work I examine the problem of determining, for a given graph, the minimum order of a vertex partition having specified properties. In the remaining chapters I concentrate on partitions of two types--those in which each subset induces an empty graph and those in which each subset induces an empty or a complete graph.

The chromatic number of a graph G is the minimum number of subsets into which V(G) can be partitioned so that each subset induces an empty graph. …

Block Transform Coding Of Presample Filtered Data, Thomas A. Shull

Electrical & Computer Engineering Theses & Dissertations

This dissertation addresses the application of non-adaptive transform coding for bit rate reduction of presampled filtered data. Transform coding is examined as an alternative to conventional pulse code modulation (PCM) for multi-source, fixed rate data acquisition systems. Typical bandlimiting presample filters introduce redundancy into the sequence of data samples. Linear transformation of successive N-length blocks of the data sequence and subsequent binary coding of the resulting components is shown to lead to reduced average bit rate for the same less distortion as PCM.

Four Butterworth filters, two corresponding to eight bit PCM systems, and two corresponding to ten bit PCM …

Error-Bounds For Gaussian Quadrature And Weighted-L1 Polynomial Approximation, Ronald A. Devore, L R. Scott

Faculty Publications

Error bounds for Gaussian quadrature are given in terms of the number of quadrature points and smoothness properties of the function whose integral is being approximated. An intermediate step involves a weighted-L' polynomial approximation problem which is treated in a more general context than that specifically required to bound the Gaussian quadrature error.

Cultural Commentary: What Hath Rubik Wrought?, Thomas E. Moore

Bridgewater Review

In May, 1980 the Ideal Toy Company launched its newest offering, Rubik’s Cube, at a party in Hollywood, hosted by Zsa-Zsa Gabor and Solomon W. Golomb. Of course Gabor, like the cube, is a Hungarian product but who is Golomb? Well, he is a mathematician at the University of Southern California and an expert in number theory, combinatorics, abstract algebra and coding theory. Rubik invented the cube as an aid in teaching his students three-dimensional thinking. The cube has become the darling of algebraists, who use it to teach group theory to their students.

Space Charge Limit Instabilities In Electron Beams, Evangelos A. Coutsias, D.J. Sullivan

Branch Mathematics and Statistics Faculty and Staff Publications

The method of characteristics and multiple-scaling perturbation techniques are used to study the space-charge instability of electron beams. It is found that the stable oscillating state (virtual cathode) created when the space-charge limit is exceeded is similar to a collisionless shock wave. The oscillatory solution originates at the bifurcation point of two unstable steady states. Complementary behavior (virtual anode) results when an ion beam exceeds its space-charge limit. The virtual cathode can also exist in the presence of a neutralizing heavy-ion background. The Pierce instability, where the electron and ion charge densities are equal, is a special case of this …

Bargaining Sets With Thresholds, Irinel C. Dragan

Mathematics Technical Papers

A concept of bargaining set for cooperative n person games with side payments has been defined by assuming that a player could be attracted in a new coalition only if his supplementary gain exceeds a fixed threshold and could reject a new coalition only if his loss exceeds another fixed threshold. Necessary and sufficient conditions for the existence of the objections with thresholds and for the existence of the counter objections with thresholds associated to couples consisting of a group of players and a coalition structure subjected to some conditions have been proved. These results enabled us to state a …

Computer Studies In Particle Modeling Of Fluid Phenomena, Donald Greenspan

Mathematics Technical Papers

A new, numerical approach is developed for modeling fluid phenomena. Unlike the continuum and statistical mechanics approaches, it uses relatively small sets of quasi-molecular particles which interact in accordance with classical, molecular-type formulas. Computer examples are described and discussed, as is the potential for modeling turbulent behavior.

Scs 85: The Space Of Compact Convex Subsets Of A Locally Convex Topological Vector Space, Klaus Keimel

Seminar on Continuity in Semilattices

Source: University archive of the Technische Universität Darmstadt.

An Artin Relation (Mod 2) For Finite Group Actions On Spheres, Ronald M. Dotzel

Ronald Dotzel

Enumeration Of Permutations By Descents, Idescents, Imajor Index, And Basic Components, Don Rawlings

Mathematics

Multivariable extensions of classic permutation cycle structure results are obtained by counting permutations by descents, idescents, imajor index, and basic components.

Math 752 Algebraic Topology Ii - Winter '84, David Handel

Mathematics Faculty Research Publications

A collection of notes for the course MAT 752, Algebraic Topology II, prepared by Professor David Handel of the Wayne State University Mathematics Department. This course builds on MAT 751, Algebraic Topology I, and the notes include examples, exercises, and suggestions for further reading.

Asymptotic Integration Of Linear Differential Equations Subject To Mild Integral Conditions, William Trench

William F. Trench

No abstract provided.

Spectral Properties Of Selfadjoint Ordinary Differential Operators With An Indefinite Weight Function, Branko Ćurgus, H. Langer

Mathematics Faculty Publications

Spectral properties of the equation l (f ) - λrf = 0 with an indefinite weight func­tion r are studied in L_I²rl . The main tool is the theory of definitizable operators in Krein spaces. Under special assumptions on the weight function, for the operator associated with the problem, the regularity of the critical point infinity is proved. Some relations to full- and half-range expansions are indicated.

2-Sphere Bundles Over Compact Surfaces, Paul Melvin

Mathematics Faculty Research and Scholarship

Closed 4-manifolds which fiber over a compact surface with fiber a sphere are classified, and the fiberation is shown to be unique (up to diffeomorphism).

A Note On Irreducibility And Weak Covering Properties, Joe Mashburn

Mathematics Faculty Publications

A space X is irreducible if every open cover of X has a minimal open refinement. Interest in irreducibility began when Arens and Dugendji used this property to show that metacompact countably compact spaces are compact. It was natural, then, to find out what other types of spaces would be irreducible and therefore compact in the presence of countable compactness or Lindelof in the presence of N₁-compactness. …

It is shown in this paper that T₁ δθ -refinable spaces and T1 weakly δθ-refinable spaces are irreducible. Since examples of Lindelof spaces that are neither T₁ nor …

Perturbation Of Periodic Boundary-Conditions, Larry Turyn

Mathematics and Statistics Faculty Publications

We consider perturbations of the problem (*) - x'' + bx = lambda ax, x(0) - x(1) = 0 = x'(0) - x'(1) both by changes of the boundary conditions and by addition of nonlinear terms. We assume that at lambda = lambda 0 there are two linearly independent solutions of the unperturbed problem (*) and that a(dot) is bounded away from zero. When only the boundary conditions are perturbed either the Hill’s discriminant or the method of Lyapunov–Schmidt reduces the problem to 0 = det ((lambda - lambda 0)A - epsilon …

An Essentially Semi-Rigid Class Of Modules, Brendan Goldsmith

Articles

No abstract available

Uniqueness Of Positive Solutions For A Class Of Elliptic Boundary Value Problems, Alfonso Castro, Ratnasingham Shivaji

All HMC Faculty Publications and Research

Uniqueness of non-negative solutions conjectured in an earlier paper by Shivaji is proved. Our methods are independent of those of that paper, where the problem was considered only in a ball. Further, our results apply to a wider class of nonlinearities.

On Monotone Formulae With Restricted Depth, Maria M. Klawe, Wolfgang J. Paul, Nicholas J. Pippenger, Mihalis Yannakakis

All HMC Faculty Publications and Research

We prove a hierarchy theorem for the representation of monotone Boolean functions by monotone Boolean functions by monotone formulae with restricted depth. Specifically, we show that there are functions with Π_k-formulae of size n for which every Σ_k-formula has size exp Ω(n^1/(k-1)). A similar lower bound applies to concrete functions such as transitive closure and clique. We also show that any function with a formula of size n (and any depth) has a Σ_k-formula of size exp O(n^1/(k-1)). Thus our hierarchy theorem is the best possible.

The Relationship Of Self-Concept, Sex, Age, Major, Anxiety, Mathematics Background, And Mathematics Ability To The Level Of Mathematics And Statistical Anxiety Among College Juniors, David John Maysick

Dissertations

Problem. One's choice of career has significant effect upon one's future life in terms of earning potential and social interaction. Mathematics/statistical anxiety and the mathematics avoidance often accompanying such anxiety, can influence career choice, causing otherwise talented people to limit their future. The purpose of this study was to determine from selected variables--particularly self-concept--which, if any, were related to the problem of mathematics and/or statistical anxiety.

Method. The statistical sample used was 350 juniors. Stratification was by degree of mathematics content in subject's major field of study. For the study, subjects had to be in the same major category as …

Chartering Recreational Boats In The United States: A Compilation And Analysis Of Applicable Federal Maritime Law, Mary Nathalie Peter

Marine Affairs Theses and Major Papers

No single primary source exists to provide current and would-be participants in recreational charter boat operations in the United States with a basic legal understanding of their rights and obligations. The relevant federal maritime standards, laws, regulations, and judicial interpretations are scattered in isolated codebooks, reporters, and bulletins. Moreover, the governing body of law for boat chartering is admiralty law, which has been shaped throughout the centuries primarily by the traditions and dictates of the commercial shipping and shipbuilding industries. As a result, the logic behind the admiralty framework tends to be obscure when viewed in the context of a …

Effects Of Thermal Spread On The Space Charge Limit Of An Electron Beam, Evangelos A. Coutsias

Branch Mathematics and Statistics Faculty and Staff Publications

An asymptotic analysis is carried out to calculate the effects of a small thermal spread in the injection energy of an electron beam on its space charge limit. It is found that the space charge limit is lowered proportionally to the beam temperature T near T = O.

Neural Population Modeling And Psychology: A Review, Daniel S. Levine

Mathematics Technical Papers

The development of neural population modeling as it relates to psychology is traced from the early 1940s to the present. The evolution of the field has been from descriptions of randomly connected neurons transmitting all-or-none signals to analyses of structured multi-level net-works whose dynamics involve several different spatial and temporal scales. The cybernetic revolution of the 1940s led to the incorporation into digital neural models of such concepts as linear threshold logic, redundant computation. and information. Each of these concepts has more recently been synthesized with learning to generate a set of adaptive neural models. Concurrently, a variety of data …

Natural Variational Principles On Riemannian Structures, Ian M. Anderson

Ian M. Anderson

No abstract provided.