Physical Sciences and Mathematics Commons^™

On Finite Element Methods For The Euler-Poisson-Darboux Equation, Anatoly M. Genis

Mathematics and System Engineering Faculty Publications

We deal primarily with the derivation of various convergence estimates for some semidiscrete and fully discrete procedures which might be used in the approximation of exact solutions of initial-boundary value problems with homogeneous Dirichlet boundary conditions for the Euler-Poisson-Darboux equation. Although the equation is of hyperbolic type, the results are somewhat analogous to those known for parabolic equations, due to the presence of a limited 'smoothing' property. This paper contain L//2 estimates, maximum norm estimates, negative norm estimates, interior estimates of difference quotients and superconvergence estimates of the error.

The Energy States Of Helium Via Bohr-Einstein Determinism, Donald Greenspan

Mathematics Technical Papers

Correct ground, ionization, singly excited and doubly (excited energy states are deduced deterministically by a direct extension of Bohr's method for hydrogen. The theory incorporates a classical interpretation of electron pairing and requires computer methodology to solve the resulting mathematical equations.

Life Table Construction From Population Age Distributions Suffering From Response Biases In Age-Reporting:A New Technique(Not Requiring Age Smoothing)With Application To Indian Census Age-Returns., Subrata Lahiri Dr.

Doctoral Theses

Preliminary concepts of life tables, its role in demographic analysis, a brief chronological review of various literature on the construction of life table starting from John Grants investigation on mortality, along with an introduction to the basic problem and objectives of the present study.Chapter II describes the concept and utility of cumulative census survival ratios, first introduced by Professors Ansley J. Coale and Paul Demeny (1967) as the ratio of the number of persons aged x+10 end above enumerated at time t+10 to the number of persons aged x and above enumerated at time t. These are compared to the …

U.S. Input-Output Data: A 1984 Update, Ronald E. Miller

Accounts and Data

This paper calls attention to the U.S. national input-output data for 1977 and the U.S. multiregional input-output data for the same year; both of these data sets became available during 1984. In particular, the commodity-by- industry accounting scheme which underpins both the 1972 and 1977 U.S. national models (as well as the U.S. 1977 multiregional model), is contrasted with the industry-by-industry approach of the original Leontief framework, which was the basis of the pre-1972 U.S. national tables.

Review Of "The Future Of College Mathematics" Edited By A. Ralston And G. S. Young, Stephen B. Maurer , '67

Mathematics & Statistics Faculty Works

No abstract provided.

Sample Solutions Of Stochastic Ordinary Differential Equations, K. Waling

Mathematics Technical Papers

Motivated by the stochastic differential equation[see pdf for notation] in [see pdf for notation] we prove a measurable dependence on parameters theorem for ODEs in case f is only continuous in [see pdf for notation] is done by means of a known result about measurable selections of multivalued maps. Afterwards we discuss consequences for stochastic ODEs.

An Elementary Algebraic Method For Approximating Average Radii Of First And Secong Ring Electrons, Donald Greenspan

Mathematics Technical Papers

In this paper, experimental ionization energies are used to determine algebraic equations whose solutions approximate relativistic quantum mechanical estimates of average atomic radii. These algebraic equations are nonlinear and are solved on a digital computer by Newton's method. Pairing is an essential element in the formulation.

Sample Solutions Of Stochastic Boundary Value Problems, V. Lakshmikantham, G. S. Ladde, K. Deimling

Mathematics Technical Papers

We prove existence theorems for nonlinear stochastic Sturmiouville problems which improve results from [4]. In the simplest case this is done by means of a known result about measurable selections of multivalued maps and a new fixed point theorem for stochastic nonlinear operators which is more realistic than existing ones.

Existence And Regularity Theory For Isoperimetric Variational Problems On Orlicz-Sobolev Spaces: A Review, Pierre A. Vuillermot

Mathematics Technical Papers

In this review article, we outline and discuss our most recent results regarding the existence and the regularity theory for a class of strongly nonlinear eigenvalue problems on Orlicz-Sobolev spaces, with a glance at other contemporary attempts to understand the structure of some strongly nonlinear variational boundary-value problems defined on certain nonreflexive Banach spaces. The class of eigenvalue problems recently investigated can best be defined as follows. With [see pdf for notation] be an open bounded domain with closure -6 and smooth [see pdf for notation] boundary asp; let [see pdf for notation] be a family of [see pdf for …

Interval Estimation Of The Noncentrality Parameter Of A Gamma Distribution, Chien-Pai Han, Paul Chiou

Mathematics Technical Papers

Asymptotic confidence interval for the noncentrality parameter of a Gamma distribution (or Chi-squared distribution) is derived. An algorithm for computing the maximum likelihood estimator of the non-centrality parameter is developed. A formula for the asymptotic variance of the maximum likelihood estimator is given. From the properties of the maximum likelihood estimator an asymptotic confidence interval is obtained.

On The Choice Of Shadow Prices For Project Evaluation., Jean Dreze Dr.

Doctoral Theses

Manohar athanna is one of the remotest parts of Jhalawar District (Rajasthan, India). In the month of June it offers a striking contrast of scenic beauty and economic destitution. Agricultural activity is at a virtual standstill. The soil is very arid, irrigation practically non-existent, and by then the villagers (many of them tribals) have resolved to wait upon the good will of the rain gods.. Hence they have very little to do, or at least so they believe. Some gather wood to sell it in Manohar, walking miles under the scorching sun for a meagre reward, and adding slowly but …

On The Genus Of A Block Design, Joan Marie Rahn

Dissertations

The genus of a design (BIBD or PBIBD) is defined to be the genus of its corresponding hypergraph (objects as vertices, blocks as edges); that is, the genus of the bipartite graph associated with the hypergraph in a natural way. The Euler formula is used to establish a lower bound (gamma) for the genus of a block design. An imbedding of the design of the surface of genus (gamma) is then described by a voltage hypergraph or voltage graph. Use of the lower bound formula leads to a characterization of planar BIBDs. A connection between a block design derived from …

[See Pdf For Notation]-Reularity For The Solution Of Strongly Nonlinear Eigenvalue Problems On Orlicz-Sobolev Spaces, Pierre A. Vuillermot

Mathematics Technical Papers

We present a new method to prove the [see pdf for notation]-regularity of the eigenfunctions for Dirichlet problems with strictly convex Young functionnonlinearities in their principal part. The basic idea is threefold: we first invoke the topological methods of [12] to infer the existence of a countable infinity of [see pdf for notation]-eigensolutions; we then use Schauder's inversion technique to associate with each one of these eigensolutions a unique [see pdf for notation]-solution of an auxiliary Dirichlet problem; we finally prove the [see pdf for notation]-regularity of the original elgensolutions from the [see pdf for notation]-regularity of the auxiliary solutions, …

Deformation And Linkage Of Gorenstein Algebras, Andrew R. Kustin, Matthew Miller

Faculty Publications

General double linkage of Gorenstein algebras is defined. Rigidity, genericity, and regularity up to codimension six all pass across general double linkage. Rigid strongly unobstructed codimension four Gorenstein algebras which lie in different Herzog classes are produced.

Difference Equations, Isoperimetric Inequality And Transience Of Certain Random Walks, Jozef Dodziuk

Publications and Research

No abstract provided.

Scs 94: Algebraic Theories For Proper Filter Monads, Oswald Wyler

Seminar on Continuity in Semilattices

No abstract provided.

On Maximizing The Average Time At A Goal, S. Demko, Theodore P. Hill

Research Scholars in Residence

In a decision process (gambling or dynamic programming problem) with finite state space and arbitrary decision sets (gambles or actions), there is always available a Markov strategy which uniformly (nearly) maximizes the average time spent at a goal. If the decision sets are closed, there is even a stationary strategy with the same property.Examples are given to show that approximations by discounted or finite horizon payoffs are not useful for the general average reward problem.

The Expectation Of Success Using A Monte Carlo Factoring Method – Some Statistics On Quadratic Class Numbers, Duncan A. Buell

Faculty Publications

A method has been proposed for factoring an integer N by using the structure of the class groups of quadratic fields of radicand – kN for various small multipliers k. We discuss the method and an implementation of the method, and various theoretical questions which have an impact on the practical use of the method in factoring. Some of the theoretical questions relate to the nature of class numbers and class groups; we present extensive statistical results on the class numbers and class groups of imaginary quadratic fields.

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.

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

Faculty Publications

No abstract provided.

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 …

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

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. …

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.