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Articles 7801 - 7830 of 7987
Full-Text Articles in Physical Sciences and Mathematics
Dissertation: The Least Fixed Point Property For Ω-Chain Continuous Functions, Joe Mashburn
Dissertation: The Least Fixed Point Property For Ω-Chain Continuous Functions, Joe Mashburn
Mathematics Faculty Publications
The basic definitions are given in the first section, including those for ω-chain continuity, ω-chain completeness, and the least fixed point property for ω-chain continuous functions. Some of the relations between completeness and fixed point properties in partially ordered sets are stated and it is briefly shown how the question basic to the dissertation arises.
In the second section, two examples are given showing that a partially ordered set need not be ω-chain complete to have the least fixed point property for ω-chain continuous functions.
Retracts are discussed in section 3, where it is seen that they are not sufficient …
Complement Theorems Beyond The Trivial Range1, I. Ivanšić, R. B. Sher, Gerard A. Venema
Complement Theorems Beyond The Trivial Range1, I. Ivanšić, R. B. Sher, Gerard A. Venema
University Faculty Publications and Creative Works
No abstract provided.
Three Counterexamples Concerning Ω-Chain Continuous Functions And Fixed-Point Properties, Joe Mashburn
Three Counterexamples Concerning Ω-Chain Continuous Functions And Fixed-Point Properties, Joe Mashburn
Mathematics Faculty Publications
A partially ordered set is ω-chain complete if, for every countable chain, or ω-chain, in P, the least upper bound of C, denoted by sup C, exists. Notice that C could be empty, so an ω-chain complete partially ordered set has a least element, denoted by 0.
Bounds On The Performance Of Protocols For A Multiple-Access Broadcast Channel, Nicholas Pippenger
Bounds On The Performance Of Protocols For A Multiple-Access Broadcast Channel, Nicholas Pippenger
All HMC Faculty Publications and Research
A general model is presented for synchronous protocols that resolve conflicts among message transmissions to a multiple-access broadcast channel. An information-theoretic method is used now to show that if only finitely many types of conflicts can be distinguished by the protocol, utilization of the channel at rates approaching capacity is impossible. A random-coding argument is used to show that if the number of conflicting transmissions can be determined (which requires distinguishing infinitely many types of conflicts) then utilization of the channel at rates arbitrarily close to capacity can be achieved.
On The Optimal Stopping Time Problem For Degenerate Diffusions, J. L. Menaldi
On The Optimal Stopping Time Problem For Degenerate Diffusions, J. L. Menaldi
Mathematics Faculty Research Publications
In this paper we give a characterization of the optimal cost of a stopping time problem as the maximum solution of a variational inequality without coercivity. Some properties of continuity for the optimal cost are also given.
On The Optimal Impulse Control Problem For Degenerate Diffusions, J. L. Menaldi
On The Optimal Impulse Control Problem For Degenerate Diffusions, J. L. Menaldi
Mathematics Faculty Research Publications
In this paper, we give a characterization of the optimal cost of an impulse control problem as the maximum solution of a quasi-variational inequality without assuming nondegeneracy. An estimate of the velocity of uniform convergence of the sequence of stopping time problems associated with the impulse control problem is given.
Existence And Uniqueness For A Variational Hyperbolic System Without Resonance, Peter W. Bates, Alfonso Castro
Existence And Uniqueness For A Variational Hyperbolic System Without Resonance, Peter W. Bates, Alfonso Castro
All HMC Faculty Publications and Research
In this paper, we study the existence of weak solutions of the problem
□u + ∇G(u) = f(t,x) ; (t,x) є Ω ≡ (0,π)x(0,π)
u(t,x) = 0 ; (t,x) є ∂Ω
where □ is the wave operator ∂2/∂t2 - ∂2/∂x2, G: Rn→R is a function of class C2 such that ∇G(0) = 0 and f:Ώ→R^n is a continuous function having first derivative with respect to t in (L2,(Ω))n and satisfying
f(0,x) = f(π,x) = 0
for all x є [0,π].
The Effects On Grain-Boundary Processes Of The Steps In The Boundary Plane Associated With The Cores Of Grain-Boundary Dislocations, Alexander H. King, D. A. Smith
The Effects On Grain-Boundary Processes Of The Steps In The Boundary Plane Associated With The Cores Of Grain-Boundary Dislocations, Alexander H. King, D. A. Smith
Alexander H. King
The contribution of the associated steps to the properties of grain-boundary dislocations are investigated. Two methods of step-height determination are given and it is shown that the step height, like the Burgers vector, must be conserved during the reactions of grain-boundary dislocations: this is not always automatic and additional coherent steps must take part in some reactions. The energies associated with steps have been estimated and compared with the elastic energies of grain-boundary dislocations; these comparisons suggest that (a) the reduction of elastic energy alone may not be a sufficient criterion for the progress of a reaction and (b) that …
A New Lower Bound For The Number Of Switches In Rearrangeable Networks, Nicholas Pippenger
A New Lower Bound For The Number Of Switches In Rearrangeable Networks, Nicholas Pippenger
All HMC Faculty Publications and Research
For the commonest model of rearrangeable networks with $n$ inputs and $n$ outputs, it is shown that such a network must contain at least $6n \log _6 n + O( n )$ switches. Similar lower bounds for other models are also presented.
An Algorithm For The Electromagnetic Scattering Due To An Axially Symmetric Body With An Impedance Boundary Condition, F. Stenger, M. Hagmann, J. Scheing
An Algorithm For The Electromagnetic Scattering Due To An Axially Symmetric Body With An Impedance Boundary Condition, F. Stenger, M. Hagmann, J. Scheing
Computer Science Faculty Publications
Let B be a body in R3, and let S denote the boundary of B. The surface S is described by S = {(x, y, z): (x2 + Y2)½= ƒ(z), -1≤ z ≤ I}, where ƒ analytic function that is real and positive on (-1, 1) and ƒ(±1) = 0. An algorithm is described for computing the scattered field due to a plane wave incident field, under Leontovich boundary conditions. The Galerkin method of solution used here leads to a block diagonal matrix involving 2M …
A Numerical Method For The Solution Of The Schrödinger Equation By A Trial Wavefunction Improvement Formula, Chun-Sheng Ko
A Numerical Method For The Solution Of The Schrödinger Equation By A Trial Wavefunction Improvement Formula, Chun-Sheng Ko
Masters Theses
A numerical method and corresponding computer algorithm for solving the one-dimensional radial Schrödinger equation to any desired accuracy is developed. The method uses a finite difference scheme in which an initial trial wavefunction is digitalized over a lattice covering the region of integration. The values of a rough solution are then altered at each lattice point by a simple improvement formula decreasing the value of the variational energy until the desired minimum is reached. The accuracy of these solutions depends only on the grid size. This method is characterized and tested with a harmonic oscillator potential. Practical evaluations and applications …
Critical Point Theory And The Number Of Solutions Of A Nonlinear Dirichlet Problem, Alfonso Castro, A. C. Lazer
Critical Point Theory And The Number Of Solutions Of A Nonlinear Dirichlet Problem, Alfonso Castro, A. C. Lazer
All HMC Faculty Publications and Research
No abstract provided.
Making Curriculum Decisions And The Nature Of Mathematics, Paul Zwier
Making Curriculum Decisions And The Nature Of Mathematics, Paul Zwier
ACMS Conference Proceedings 1979
This paper explores the pedagogical decisions made by those teaching mathematics by discussing the various values and priorities of a mathematics course.
Mathematics In The Christian Philosophy Of Life, C. Ralph Verno
Mathematics In The Christian Philosophy Of Life, C. Ralph Verno
ACMS Conference Proceedings 1979
It is universally agreed that mathematics is important, that it is indeed very significant in life. This would be admitted even by those who are ignorant of or who dislike mathematics. There would be much less agreement, however, about why mathematics is important or significant. Such disagreement exists even more among mathematicians and mathematics educators. Unhappily many of the Christians who think about such things (and there are not very many who think about them at all) basically share the utilitarian view of many non-Christian thinkers, although endeavoring to place it within a Christian context. They think it is wonderful …
Brief Position Paper For Panel Discussion On Relation Of Mathematics And Christianity, C. Ralph Verno
Brief Position Paper For Panel Discussion On Relation Of Mathematics And Christianity, C. Ralph Verno
ACMS Conference Proceedings 1979
Some people view a conjoining of Christianity and Mathematics as improper. They miss the point of the relationship. The content of mathematics is not affected by Christianity. The relationship does not concern what, or how (the Christian doesn’t solve equations or differentiate differently), but it concerns why. It concerns such things as the interpretation and appreciation of the beauty, the symmetries, the coincidences, the remarkable properties, man’s creative role, etc. This paper explores the relationship between Christianity and mathematics as part of a panel discussion on the topic.
On Kuyk’S Complementarity In Mathematics, Gene B. Chase
On Kuyk’S Complementarity In Mathematics, Gene B. Chase
ACMS Conference Proceedings 1979
This paper examines Willem Kuyk’s book, Complementarity in Mathematics, and the interplay between the subjects of mathematics.
Are Mathematical Objects Ontologically Real? Ideas And Suggestions, Frank R. Bernhart
Are Mathematical Objects Ontologically Real? Ideas And Suggestions, Frank R. Bernhart
ACMS Conference Proceedings 1979
This essay will consider a few ways that realism in the modern philosophy of mathematics might be understood and defined.
Intuitionism, Terence H. Perciante
Intuitionism, Terence H. Perciante
ACMS Conference Proceedings 1979
Intuitionism derives philosophically from Kant's Conceptualism -- the object of the mathematical knowledge only have reality within the mind, they do not have reality apart from our thinking. This paper examines the nature of intuitionism and its strengths.
Non-Standard Calculus, Ron Friewald
Non-Standard Calculus, Ron Friewald
ACMS Conference Proceedings 1979
This paper is intended to provide a very cursory introduction to how “nonstandard calculus” works, giving a sketch of how elementary calculus can be presented using hyperreal numbers.
Axiomatic Structure And The Method Of Analysis: Shifting Styles In The History Of Mathematics, Calvin Jongsma
Axiomatic Structure And The Method Of Analysis: Shifting Styles In The History Of Mathematics, Calvin Jongsma
ACMS Conference Proceedings 1979
This article surveys the different views of mathematical methodology that occurred from ancient Greek times through the early modern period up until its codification around 1900. After summarizing the axiomatic approach advocated by Aristotle and implemented in mathematics by Euclid, the talk explores the character of analysis in ancient Greek times, its development into a symbolic algebra by Viete and Descartes, and its expansion into a calculus of fluxions and differentials by Newton and Leibniz. The article concludes by touching on the recovery and transformation of the deductive ideal for mathematics by Pasch, Peano, and Hilbert during the late nineteenth …
Two Philosophical Problems About Mathematics, Stephen Barker
Two Philosophical Problems About Mathematics, Stephen Barker
ACMS Conference Proceedings 1979
Mathematics is a flourishing field of human endeavor, a field that is accorded great respect and high standing. For 2500 years or more, many of the best minds available have worked in this field; and the results produced have indirectly been of enormous value to other fields, such as physics, engineering, architecture, economics, and so on. But with is mathematics about? Physics studies moving bodies; engineering studies bridges; architecture studies buildings; economics studies commercial behavior: here there are phenomena we can point to that constitute the subject matter. But what does mathematics study? If you answer “Numbers”, or “Abstract types …
Introduction (1979), Robert Brabenec
Introduction (1979), Robert Brabenec
ACMS Conference Proceedings 1979
No abstract provided.
Table Of Contents (1979), Association Of Christians In The Mathematical Sciences
Table Of Contents (1979), Association Of Christians In The Mathematical Sciences
ACMS Conference Proceedings 1979
A Second Conference on the Foundations of Mathematics
Markovian Multiserver Queueing Systems With Servers In Series, Nancy Jean Boynton
Markovian Multiserver Queueing Systems With Servers In Series, Nancy Jean Boynton
Dissertations
No abstract provided.
Secrets Of A Mississippi Riverboat Gambler, Harlan D. Mills
Secrets Of A Mississippi Riverboat Gambler, Harlan D. Mills
The Harlan D. Mills Collection
No abstract provided.
A Semilinear Dirichlet Problem, Alfonso Castro
A Semilinear Dirichlet Problem, Alfonso Castro
All HMC Faculty Publications and Research
Let Ω be a bounded region in R^n. In this note we discuss the existence of weak solutions (see [4, Section 2]) of the Dirichlet problem:
Δu(x) + g(x, u(x)) + f(x, u(x), ∇u(x)) = 0 ; x є Ω
u(x) = 0 ; x є ∂Ω
where Δ is the Laplacian operator, g : Ω x R → R and f : Ω x Rn+1 → R are functions satisfying the Caratheodory condition (see [2, Section 3]), and ∇ is the gradient operator.
Evaluation And Improvement Of The Wu-Koh Model For The Prediction Of Multiple-Cell Cooling Tower Plumes, Michael Joseph Wastag
Evaluation And Improvement Of The Wu-Koh Model For The Prediction Of Multiple-Cell Cooling Tower Plumes, Michael Joseph Wastag
Masters Theses
This paper evaluates and improves the performance of the Wu-Koh mathematical model for the prediction of plume dispersion from multiple natural-draft (NDCT) and mechanical-draft (MDCT) cooling towers. The Wu-Koh multiple-tower model was chosen for study due to its advanced treatment of plume merging.
Our evaluation of the Wu-Koh model was carried out by comparing model predictions of field and laboratory data. Comparisons of model predictions of visible plume outlines were made to single- and multiple-tower visible plume data. The sites of the single-tower data were Lunen (300 MWe), Chalk Point (630 MWe) and Paradise (1100 MW …
Stochastic Dominance And Information Value, Young Koan Kwon, John C. Fellingham, D. Paul Newman
Stochastic Dominance And Information Value, Young Koan Kwon, John C. Fellingham, D. Paul Newman
Research Collection School Of Accountancy
Incentives for producing and disseminating information have been analysed in many different contexts. Kihlstrom [6], for example, develops a Bayesian framework to analyze the properties of demand functions for information about product quality. From an entirely different perspective, Spence [8, 91 demonstrates the private value of “signalling” information. Similarly, Wilson [lo] considers the value to the firm of producing technological information and the effect of such production on equilibrium theory.
Sufficiency Of A Numerical Downstream Continuation, Charlie H. Cooke
Sufficiency Of A Numerical Downstream Continuation, Charlie H. Cooke
Mathematics & Statistics Faculty Publications
(First paragraph) Customarily one does not impose n-th order boundary conditions on the solution of initial/boundary value problems whose characterizing partial differential equations are also n-th order. However, conjecture that such problems are not well-posed, or that a solution might not exist, is not always justified [l]. Perhaps a physically more natural example is provided by problems of computational fluid dynamics. Here boundary conditions which correctly should be applied at an infinite distance downstream from the region of interest are for computational convenience often applied at a finite location [2]. Results of numerical experimentation on viscous flows governed by …
An Illustrative Model Describing The Refraction Of Long Water Waves By A Circular Island, Gregory A. Kriegsmann
An Illustrative Model Describing The Refraction Of Long Water Waves By A Circular Island, Gregory A. Kriegsmann
Department of Mathematics: Faculty Publications
The refraction of small shallow water waves by an idealized island is studied in this paper. The island's shoal is modeled by a quartic polynomial in the radial variable. This particular model allows the explicit construction of the rays (wave orthogonals) and the determination of several important features of the wave motion. The various shortcomings of the particular profile are discussed.