Applied Mathematics Commons^™

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 …

Optimal Stochastic Scheduling Of Power Generation Systems With Scheduling Delays And Large Cost Differentials, G. L. Blankenship, J.-L. Menaldi

Mathematics Faculty Research Publications

The optimal scheduling or unit commitment of power generation systems to meet a random demand involves the solution of a class of dynamic programming inequalities for the optimal cost and control law. We study the behavior of this optimality system in terms of two parameters: (i) a scheduling delay, e.g., the startup time of a generation unit; and (ii) the relative magnitudes of the costs (operating or starting) of different units. In the first case we show that under reasonable assumptions the optimality system has a solution for all values of the delay, and, as the delay approaches zero, that …

Generalisations Et Generalites, Florentin Smarandache, Eleonora Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

"Généralisations et Généralités" , pourquoi ce titre? Parce Que l'auteur a voulu rassembler ici Quelques-unes de ses recherches originales C Qui sont donc des "s~n:§rali tés") , df'2ls diverses branches des mathématiques (algèl)re, thôorie des nombres, Gométrie, analyse, linguistique, mathématiQues distrayantes) , mêlne si les articles qui composent ce recueil n'ont pas toujours de liaison entre eux.

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 …

Stochastic Estimation Applied To The Land Speed Of Sound Record Attempt By A Rocket Car, David A. Reinholz

Theses and Dissertations

Optimal linear smoothing theory is applied to the data from the Speed of Sound record attempt of a three-wheeled rocket car on 17 December 1979. A forward-backward estimation method is used which employs a seven state forward-running extended Kalman filter and a Meditch-form backward recursive 'fixed-interval' smoothing algorithm. Data for this analysis is supplied by a longitudinal accelerometer mounted on the vehicle and tracking radar measurements of range, azimuth, and elevation. States of interest include two components of vehicle position and velocity, accelerometer time-correlated error, and radar range and azimuth bias errors. Two iterations of the forward-backward smoothing algorithm provide …

Mathematical Evaluation Of Steady, Laminar Flow By The Use Of Continuous-Wave (Cw) Doppler And Pitot Tube System, Malek Mansoor Sharif

Loma Linda University Electronic Theses, Dissertations & Projects

Investigation, as to the usefulness of spectral analysis of the acoustical signal from the Doppler ultrasonic flowmeter, is being conducted. The purpose was to determine some of the hemodynamic influences on the spectrum. The hypothesis was that both hematocrit and pressure head influence the amplitude of the spectrum. Experiments were designed to: a) evaluate their roles on amplitude; b) derive the associated functional relationship.

Preliminary experiments revealed that: a) the accuracy of our Doppler flowmeter was satisfactory, since a very good linear relation was found between electromagnetically and Doppler derived flow; b) the relative weight of the hematocrit parameter on …

Using Mathematical Concepts To Illustrate Scriptural And Spiritual Ideas, Robert Brabenec

ACMS Conference Proceedings 1983

Christian mathematics faculty and students respond in differing ways to this idea of applying mathematics to Scripture, and vice-versa. Mathematics is man-made, while Scripture is inspired by God, so they should be disjoint entities. However, it is well known that the Scripture used analogies of familiar human objects and ideas in order to explain spiritual ideas. This paper discusses various mathematical concepts and how they illustrate Scriptural and spiritual ideas.

The Activitiy And Application Of Mathematics, R. S. D. Thomas

ACMS Conference Proceedings 1983

There are four so-called philosophies of mathematics that I regard as totally discredited, formalism, intuitionism, logicism, and Platonism. It is a common feature of the ism philosophies of mathematics that they do not take the application of mathematics very seriously. This paper examines a view of mathematics that takes applications seriously.

Arrogance And Humility In The Philosophy Of Mathematics, James Murdock

ACMS Conference Proceedings 1983

This paper explores the philosophical, sociological, and theological questions related to the field of mathematics and whether or not it is ethical to pursue when its discoveries are used for evil.

An Outline Of A Complementarist Philosophy Of The Sciences, With A Special Reference To Mathematics, Willem Kuyk

ACMS Conference Proceedings 1983

No abstract provided.

A Neuropsychodynamical Theory Of Mathematics Learning, Willem Kuyk

ACMS Conference Proceedings 1983

No abstract provided.

One Possible Outline For A First Undergraduate Course In Philosophy Of Mathematics, Harold Heie

ACMS Conference Proceedings 1983

No abstract provided.

The Role Of Creativity In Mathematics, John M. Dubbey

ACMS Conference Proceedings 1983

No abstract provided.

Mathematics: The Loss Of Certainty, Calvin Jongsma

ACMS Conference Proceedings 1983

Morris Kline was a contentious mathematician and author, documenting (as he saw it) both the deficiencies of mid-twentieth-century reformist trends in mathematics education and formalist views of the foundations (and practice) of mathematics. This brief introduction to a discussion of Kline's 1980 book and its mixed reception by the mathematics community provides a context for assessing his ideas as part of his overall views on the nature of mathematics.

A Comparative Study Of Christian Mathematical Realism And Its Humanistic Alternatives, Paul Zwier

ACMS Conference Proceedings 1983

This paper explores what sort of stance a Christian should have on important mathematical questions such as realism.

Introduction (1983), Robert Brabenec

ACMS Conference Proceedings 1983

No abstract provided.

Table Of Contents (1983), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 1983

A Fourth Conference on Mathematics from a Christian Perspective

Edited by Robert L. Brabenec, Wheaton College

An Interval Newton Method, E R. Hansen, R I. Greenberg

Computer Science: Faculty Publications and Other Works

We introduce an interval Newton method for bounding solutions of systems of nonlinear equations. It entails three subalgorithms. The first is a Gauss-Seidel-type step. The second is a real (noninterval) Newton iteration. The third solves the linearized equations by elimination. We explain why each subalgorithm is desirable and how they fit together to provide solutions in as little as one-third or one-quarter the time required by Krawczyk's method [7] in our implementations.

Viscous Modeling And Computation Of Leading-And Trailing-Edge Vortex Cores Of Delta Wings, Balakrishnan Lakshmanan

Mechanical & Aerospace Engineering Theses & Dissertations

A Finite-Difference method is presented for calculating steady quasi-axisymmetric flow of an incompressible fluid at large Reynolds number. Approximations of the boundary-layer type are employed to reduce the Navier-Stokes equations to a pair of non-linear parabolic equations. Along with the governing equations, initial conditions are specified at some upstream cross section and boundary conditions are specified at the axis of symmetry and on the outer bounding surface.

The governing equations are replaced by a set of quasilinear finite-difference equations. The solution is obtained by a marching technique, which proceeds step-by-step in the axial direction. At each axial station, an iterative …

Bending Vibrations Of A Cantilever Beam On An Eccentric Rotating Disc, Yousry S. Aboelnaga

Theses

The differential equation of motion for the C.G. line of a vibrating cantilever beam which is mounted on an eccentric rotating disc is derived. Exact solutions in terms of hypergeometric functions of this fourth order differential equation with variable coefficients are obtained by making several mild assumptions. These solutions include a large class of vibrational modes.

The primary idea leading to the exact solutions is the factorization of the fourth order differential operator into a pair of commuting second order operators.

A Comparative Study Of Christian Mathematical Realism And Its Humanistic Alternatives, Paul Zwier

ACMS Journal 2004

This paper addresses the growing popularity of views of mathematics that see it primarily as a social entity and that reject Platonism. It contrasts two Christian realist philosophies - those of Alvin Plantinga and Vernon Poythress - with the secular perspective of Philip Davis and Reuben Hersch. It affirms the insight of Davis and Hersch that mathematics is indeed a social entity. However, it argues that belief in God enables a fuller understanding of mathematics - one that accounts for the apparent transcendence of mathematics and its power to explain concepts in the physical world.

The Least Fixed Point Property For Ω-Chain Continuous Functions, Joe Mashburn

Mathematics Faculty Publications

A partially ordered set P is ω-chain complete if every countable chain (including the empty set) in P has a supremum. … Notice that an ω-chain continuous function must preserve order. P has the (least) fixed point property for ω-chain continuous functions if every ω-chain continuous function from P to itself has (least) fixed point.

It has been shown that a partially ordered set does not have to be ω-chain complete to have the least fixed point property for ω-chain continuous functions. This answers a question posed by G. Plotkin in 1978. I.I. Kolodner has shown that an ω-chain complete …

An Interval Arithmetic Newton Method For Solving Systems Of Nonlinear Equations, Ronald I. Greenberg, Eldon R. Hansen

Computer Science: Faculty Publications and Other Works

We introduce an interval Newton method for bounding solutions of systems of nonlinear equations. It entails three sub-algorithms. The first is a Gauss-Seidel type step. The second is a real (non-interval) Newton iteration. The third solves the linearized equations by elimination. We explain why each sub-algorithm is desirable and how they fit together to provide solutions in as little as 1/3 to 1/4 the time required by a commonly used method due to Krawczyk.

Rapid Method Of Estimating The Phosphorous Sorption Capacity Of Soils, A, G.F. Griffin

Storrs Agricultural Experiment Station

No abstract provided.

Evidence Of Intrinsic Double Acceptor In Gaas, Phil Won Yu, W. C. Mithel, M. G. Mier, S. S. Li, Weizhen Wang

Mathematics and Statistics Faculty Publications

Acceptors present in undoped p‐type conducting GaAs have been studied with photoluminescence, temperature‐dependent Hall measurements, deep level transient spectroscopy, and spark source mass spectrometry. It is shown that p‐type conduction is due to presence of the shallow acceptor C_As and the cation antisite double acceptor Ga_As. The first and second ionization energies determined for Ga_As are 77 and 230 meV from the valence‐band edge.

Optimal Control Of Stochastic Integrals And Hamilton-Jacobi-Bellman Equations, Ii, Pierre-Louis Lions, José-Luis Menaldi

Mathematics Faculty Research Publications

We consider the solution of a stochastic integral control problem, and we study its regularity. In particular, we characterize the optimal cost as the maximum solution of ∀v ∈ V, A(v)u ≤ ƒ(v) in D'(Ο), u = 0 on ∂Ο, u ∈ W^1,∞(Ο),

where A(v) is a uniformly elliptic second order operator and V is the set of the values of the control.

Optimal Control Of Stochastic Integrals And Hamilton-Jacobi-Bellman Equations, I, Pierre-Louis Lions, José-Luis Menaldi

Mathematics Faculty Research Publications

We consider the solution of a stochastic integral control problem and we study its regularity. In particular, we characterize the optimal cost as the maximum solution of ∀v ∈ V, A(v)u ≤ ƒ(v) in D'(Ο), u = 0 on ∂Ο, u ∈ W^1,∞(Ο),

where A(v) is a uniformly elliptic second order operator and V is the set of the values of the control.

Entropy Measures In Input-Output Analysis, Martin Zwick, Abbas Heiat

Complex Systems Faculty Publications and Presentations

Applications of Shannon's entropy measure to the matrices of technical and interdependence coefficients, to the final demand vector, and to other aspects of input- output tables are proposed. These entropy measures serve as indices of different types of economic diversity. The relevance of such indices for economic planning and for analyses of economic structural complexity and development is discussed.

Reality And Imagination In Mathematics And Religion, Dave Neuhouser

ACMS Conference Proceedings 1981

What does either reality or imagination have to do with mathematics? What does either reality or imagination have to do with religion? The thesis of this paper is that mathematics and religion, both, should be closely related to reality and that imagination is essential in both areas. In fact, imagination is essential in our attempts to understand reality.