Digital Commons Network^™

Triple Trigonometric Series And Their Application To Mixed Boundary Value Problems, Gordon Melrose

Mathematics & Statistics Theses & Dissertations

In this dissertation the author investigates some triple trigonometric series which occur in the solution of mixed boundary value problems in elasticity and potential theory. By choosing a suitable integral representation for the sequence of unknown constants, the problem is reduced to solving a singular integral equation of the first kind. Twenty four cases in which the integral equation can be solved in closed form are discussed in detail.

In later chapters, the application of triple trigonometric series to problems in physics and engineering is demonstrated and closed form solutions for the physical parameters of interest are obtained.

Expressive Power In First Order Topology, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

A first order representation (f.o.r.) in topology is an assignment of finitary relational structures of the same type to topological spaces in such a way that homeomorphic spaces get sent to isomorphic structures. We first define the notions "one f.o.r. is at least as expressive as another relative to a class of spaces" and "one class of spaces is definable in another relative to an f.o.r.", and prove some general statements. Following this we compare some well-known classes of spaces and first order representations. A principal result is that if X and Y are two Tichonov spaces whose posets of …

On The Differentiability Of Functions In Rn, Ronald A. Devore, Robert C. Sharpley

Faculty Publications

No abstract provided.

Scs 93: Refinement Monoids, Hans Dobbertin

Seminar on Continuity in Semilattices

Source: University archive of the Technische Universität Darmstadt.

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 - Archive

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.

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.

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 …

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 …

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.

Bargaining Sets With Thresholds, Irinel C. Dragan

Mathematics Technical Papers - Archive

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 - Archive

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.

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 …

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).

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.

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.

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 …

Representations Of Algebras Over A Complete Discrete Valuation Ring, Brendan Goldsmith, Manfred Dugas, Rudiger Gobel

Articles

No abstract available

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.

On A Class Of Strongly Nonlinear Dirichlet Boundary-Value Problems: Beyond Pohozaev's Results, Pierre A. Vuillermot

Mathematics Technical Papers - Archive

Let [see pdf for notation] be an open bounded domain with closure [see pdf for notation] and smooth boundary [see pdf for notation]. Consider the class of nonlinear boundary-value problems defined by [see pdf for notation] with [see pdf for notation] regular enough,[see pdf for notation] and where [see pdf for notation] denotes Laplacian. If n = 2, it is known that the boundary-value problem (1.1) possesses nontrivial, classical eigensolutions (with appropriate eigenvalues ^) even if ø grows exponentially fasts if n ≥ 3, it is also known that problem (1.1) has, with ^ starshaped, no nontrivial, classical solutions as …

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.

A Discrete Model For The Recovery Of Oil From A Reservoir, Cristobal Vargas-Jarillo

Mathematics Technical Papers - Archive

In this work we simulate oil recovery by means of a molecular type approach. This means that we consider the solid and liquid materials to be composed of a finite number of particles, which are approximants for molecules. Porous flow is studied qualitatively under the assumption that particles of rock, oil and the flooding flow interact with each other locally by means of a compensating LennardJones type potential and are also under the influence of gravity. Extensive computations are described and discussed in which initial data and parameters are varied. A comparison is made with actual physical experiments.

A Class Of Elliptic Partial Differential Equations With Exponential Nonlineraities, Pierre A. Vuillermot

Mathematics Technical Papers - Archive

This is the second of a series of papers devoted to systems of ordinary and partial differential equations with exponential nonlinearities [20], in which we prove the existence of at least a countable infinity of one- parameter families of nontrivial, Hölder continuous solutions for a class of second-order, strongly nonlinear Dirichlet boundary-value problems in two and more dimensions. Let Y be a C(2)-Young function, namely a twice continuously differentiable, even convex lR—valued function on IR such that[see pdf for notation] and[see pdf for notation]. By C(2)-function, we shall mean a function which is twice continuously differentiable everywhere except possibly at …

Particle Modeling Of Unstable Mode Configurations And Elastic Bending Of Deformable Shells, Vincenzo Casulli, Donald Greenspan

Mathematics Technical Papers - Archive

A new particle-type of modeling is developed for the simulation of phenomena related to the bending of elastic shells. Application is made to the determination of unstable equilibrium modes and to the simulation of snap-through inversion. Computer examples are described and discussed.