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Articles 1 - 30 of 35
Full-Text Articles in Mathematics
Averaged Motion Of Charged Particles In A Curved Strip, Avner Friedman, Chaocheng Huang
Averaged Motion Of Charged Particles In A Curved Strip, Avner Friedman, Chaocheng Huang
Mathematics and Statistics Faculty Publications
This paper is concerned with the motion of electrically charged particles in a "curved" infinite strip.
On Multiple Solutions Of A Nonlinear Dirichlet Problem, Alfonso Castro, Jorge Cossio, John M. Neuberger
On Multiple Solutions Of A Nonlinear Dirichlet Problem, Alfonso Castro, Jorge Cossio, John M. Neuberger
All HMC Faculty Publications and Research
We prove that a semilinear elliptic boundary value problem has five solutions when the range of the derivative of the nonlinearity includes at least the first two eigenvalues. We also prove that if the region is a ball the semilinear elliptic problem has two solutions that change sign and are nonradial.
On The Product Of Two Generalized Derivations, Mohamed Barraa, Steen Pedersen
On The Product Of Two Generalized Derivations, Mohamed Barraa, Steen Pedersen
Mathematics and Statistics Faculty Publications
Two elements A and B in a ring R determine a generalized derivation deltaA,B on R by setting δA,B(X) = AX - XA for any X in R. We characterize when the product δC,DδA,B is a generalized derivation in the cases when the ring R is the algebra of all bounded operators on a Banach space epsilon, and when R is a C*-algebra U. We use the se characterizations to compute the commutant of the range of δA,B.
Invariant Subspaces And Hyper-Reflexivity For Free Semigroup Algebras, Kenneth R. Davidson, David R. Pitts
Invariant Subspaces And Hyper-Reflexivity For Free Semigroup Algebras, Kenneth R. Davidson, David R. Pitts
Department of Mathematics: Faculty Publications
In this paper, we obtain a complete description of the invariant subspace structure of an interesting new class of algebras which we call free semigroup algebras. This enables us to prove that they are reflexive, and moreover to obtain a quantitative measure of the distance to these algebras in terms of the invariant subspaces. Such algebras are called hyper-reflexive. This property is very strong, but it has been established in only a very few cases. Moreover the prototypes of this class of algebras are the natural candidate for a non-commutative analytic Toeplitz algebra on n variables. The case we make …
Hypersurfaces In R-D And The Variance Of Exit Times For Brownian Motion, Kimberly Kinateder, Patrick Mcdonald
Hypersurfaces In R-D And The Variance Of Exit Times For Brownian Motion, Kimberly Kinateder, Patrick Mcdonald
Mathematics and Statistics Faculty Publications
Using the first exit time for Brownian motion from a smoothly bounded domain in Euclidean space, we define two natural functionals on the space of embedded, compact, oriented, unparametrized hypersurfaces in Euclidean space. We develop explicit formulas for the first variation of each of the functionals and characterize the critical points.
Quasi-Steady Monopole And Tripole Attractors In Relaxing Vortices, Louis F. Rossi, Joseph F. Lingevitch, Andrew J. Bernoff
Quasi-Steady Monopole And Tripole Attractors In Relaxing Vortices, Louis F. Rossi, Joseph F. Lingevitch, Andrew J. Bernoff
All HMC Faculty Publications and Research
Using fully nonlinear simulations of the two-dimensional Navier–Stokes equations at large Reynolds number (Re), we bracket a threshold amplitude above which a perturbed Gaussian monopole will relax to a quasi-steady, rotating tripole, and below which will relax to an axisymmetric monopole. The resulting quasi-steady structures are robust to small perturbations. We propose a means of measuring the decay rate of disturbances to asymptotic vortical structures wherein streamlines and lines of constant vorticity correspond in some rotating or translating frame. These experiments support the hypothesis that small or moderate deviations from asymptotic structures decay through inviscid and viscous mixing.
The Role Of Mathematics In Culture, W. James Bradley
The Role Of Mathematics In Culture, W. James Bradley
ACMS Conference Proceedings 1997
This paper examines theories of the role of mathematics in culture and seeks to understand how a Christian should view the role of mathematics.
Solomon's Sea And The Biblical Π, Andrew Simoson
Solomon's Sea And The Biblical Π, Andrew Simoson
ACMS Conference Proceedings 1997
From I Kings 7:23, the apparent diameter and circumference of a circular ring are given as 10 and 30 cubits which suggests that the Biblical value of π is 3 rather a number closer to π. However we recount seven different somewhat whimsical explanations as to why this conclusion is overly-hasty.
Mathematics And Values: Can Philosophy Guide Projects?, Michael H. Veatch
Mathematics And Values: Can Philosophy Guide Projects?, Michael H. Veatch
ACMS Conference Proceedings 1997
The philosophy of mathematics has provided insight on questions of foundations and mathematical truth; however, it has not been very fruitful in guiding the practice of mathematics. This paper attempts to find points of contact between a Christian worldview and the choice of mathematical projects and methods. Three areas are considered: (i) dubitability in current research, (ii) the intrinsic value of contemporary mathematics to contemporary society, and (iii) the affirmation of human value in the use of mathematics. Finally, a framework for valuing mathematics is proposed as an encouragement to think more deeply about how a Christian might choose a …
The Mathematical Sciences And The Mediator Of Creation, W. David Laverell
The Mathematical Sciences And The Mediator Of Creation, W. David Laverell
ACMS Conference Proceedings 1997
This article stems from a conviction that while the development of a theistic view of the mathematical sciences is a laudable goal and much to be encouraged, it is incumbent upon us to explore every avenue that might lead to a distinctively Christian perspective. This leads naturally to a consideration of the unique role played by Christ in Creation, and a convenient framework is provided by seeing Christ as Mediator of Creation. We shall discuss the term itself, examine the biblical passages that seem to present the concept, consider the ways these passages have been understood by theologians, and …
Digital Filtering And Smoothing: A Student Simulation Project, Eric Gossett
Digital Filtering And Smoothing: A Student Simulation Project, Eric Gossett
ACMS Conference Proceedings 1997
A bug tracking problem is used to introduce students to filtering and smoothing real-time data. A predictor-corrector filter/smoother algorithm is developed and a simulation platform is provided so that students can program and test implementations of the filter/smoother. The platform includes the ability to animate the simulation.
The tracking problem: A small computer bug is traveling around the $x-y$ plane trying to avoid detection. We can eliminate the bug if we can produce a reasonably accurate approximation to its trajectory.
We have a bug detecting device which can be pointed at the plane. It can measure the $x$ and $y$ …
A First Draft Of The History Of Acms, Robert Brabenec
A First Draft Of The History Of Acms, Robert Brabenec
ACMS Conference Proceedings 1997
This paper is a draft of the history of the Association of Christians in the Mathematical Sciences as told by Robert Brabenec.
History And Current Situation Of Russian Church, Ioann S. Goncharov, Gennadiy A. Kalyabin
History And Current Situation Of Russian Church, Ioann S. Goncharov, Gennadiy A. Kalyabin
ACMS Conference Proceedings 1997
This paper brief outlines the main periods in Russia's Orthodoxy including latest seven decades. In the Appendix a mathematical model is proposed for explaining the Divine Features such as Omniscience, Omnipotence, Predestination, and the free will of men.
Mathematics At Chartres Cathedral, Richard Stout
Mathematics At Chartres Cathedral, Richard Stout
ACMS Conference Proceedings 1997
Having had several opportunities to travel to France, often with groups of students, our trips have usually included a visit to Chartres, especially to visit the magnificent Gothic cathedral that dominates the town. On a recent visit I was again struck by the beauty, majesty and awe that the cathedral inspires. The building not only does a remarkable job of telling Biblical stories and of enclosing a space conducive to worship, it directs one's eyes and one's spirits upward. This is achieved not only by the beautiful stained glass windows and the striking sculptures, but also by the overall design …
An Investigation Of The Behavior Of Calculus Students Working Collaboratively In An Interactive Software Environment, Angela Hare
An Investigation Of The Behavior Of Calculus Students Working Collaboratively In An Interactive Software Environment, Angela Hare
ACMS Conference Proceedings 1997
Recent work in the area of cognitive research in mathematics education focuses on detailed examinations of the learning process of students and how this process is affected by current innovations in the classroom, including collaborative learning and the use of computers and interactive software. Much of this work is supported by the learning framework of constructivism, a school of thought which is based on the work and writings of Jean Piaget. Piaget, a French psychologist in the mid-twentieth century, observed the learning behavior of children and concluded that individuals construct their own knowledge by creating mental structures which explain their …
A Tale Of Two Transitions, David Klanderman, Sharon Robbert, Robert Wheeler
A Tale Of Two Transitions, David Klanderman, Sharon Robbert, Robert Wheeler
ACMS Conference Proceedings 1997
In this paper, we examine transitions to proof courses at two institutions. Bob Wheeler has taught the course at Northern Illinois University. Both Sharon Robbert and Dave Klanderman have taught a related course at Trinity Christian College. We analyze various features of these courses and offer suggestions for other colleges and universities.
Using Java And Html For Linear Algebra Instruction, Jonathan R. Senning
Using Java And Html For Linear Algebra Instruction, Jonathan R. Senning
ACMS Conference Proceedings 1997
This paper addresses some of the issues involved with using the HTML, JavaScript and Java to develop and serve a sequence of laboratory modules for use in teaching linear algebra. Attention is paid to the rationale for this approach as opposed to the more traditional approach of laboratory exercises executed using MATLAB or some similar computational tool. Several methods to display mathematics with HTML are described. Some implementation detail and a brief description of the HTML and Java based Linear Algebra Visualization Assistant (LAVA) is presented.
Fractal Geometry And Chaos Theory: From Old Problems To New Models And Methods, Terence H. Perciante
Fractal Geometry And Chaos Theory: From Old Problems To New Models And Methods, Terence H. Perciante
ACMS Conference Proceedings 1997
Fractal geometry and chaos theory are deeply rooted in significant problems in the history of mathematics and science. While mathematicians have geometrical descriptions of space with its properties, scientists have attempted to characterize the physical properties of fundamental entities present in space and time. The separate investigations frequently influenced each other and led to profound theories, answers, and models. However, at the same time new problems repeatedly arose internal to mathematics and externally in the applications to which mathematics was applied. Fractal geometry issues from these antecedents in response to features and processes in nature not easily represented by historical …
Introduction (1997), Association Of Christians In The Mathematical Sciences
Introduction (1997), Association Of Christians In The Mathematical Sciences
ACMS Conference Proceedings 1997
Eleventh ACMS Conference on Mathematics from a Christian Perspective
Table Of Contents (1997), Association Of Christians In The Mathematical Sciences
Table Of Contents (1997), Association Of Christians In The Mathematical Sciences
ACMS Conference Proceedings 1997
Eleventh ACMS Conference on Mathematics from a Christian Perspective
Schedule (1997), Association Of Christians In The Mathematical Sciences
Schedule (1997), Association Of Christians In The Mathematical Sciences
ACMS Conference Proceedings 1997
Eleventh ACMS Conference on Mathematics from a Christian Perspective
The Duals Of Warfield Groups, Peter Loth
The Duals Of Warfield Groups, Peter Loth
Mathematics Faculty Publications
A Warfield group is a direct summand of a simply presented abelian group. In this paper, we describe the Pontrjagin dual groups of Warfield groups, both for the p-local and the general case. A variety of characterizations of these dual groups is obtained. In addition, numerical invariants are given that distinguish between two such groups which are not topologically isomorphic.
Random Processes With Convex Coordinates On Triangular Graphs, J. N. Boyd, P. N. Raychowdhury
Random Processes With Convex Coordinates On Triangular Graphs, J. N. Boyd, P. N. Raychowdhury
Mathematics and Applied Mathematics Publications
Probabilities for reaching specified destinations and expectation values for lengths for random walks on triangular arrays of points and edges are computed. Probabilities and expectation values are given as functions of the convex (barycentric) coordinates of the starting point.
Diagonal Operators, S-Numbers, And Bernstein Pairs, Asuman Güven Aksoy, Grzegorz Lewicki
Diagonal Operators, S-Numbers, And Bernstein Pairs, Asuman Güven Aksoy, Grzegorz Lewicki
CMC Faculty Publications and Research
Replacing the nested sequence of ''finite" dimensional subspaces by the nested sequence of "closed" subspaces in the classical Bernstein lethargy theorem, we obtain a version of this theorem for the space B(X , Y) of all bounded linear maps. Using this result and some properties of diagonal operators, we investigate conditions under which a suitable pair of Banach spaces form an exact Bernstein pair.We also show that many "classical" Banach spaces, including the couple (Lp [O, 1] , Lq[O, 1]) form a Bernstein pair with respect to any sequence of s-numbers (sn) ,for 1 < p < ∞ and 1 ≤ q < ∞ …
Eigenfunction And Harmonic Function Estimates In Domains With Horns And Cusps, Michael Cranston, Yi Li
Eigenfunction And Harmonic Function Estimates In Domains With Horns And Cusps, Michael Cranston, Yi Li
Mathematics and Statistics Faculty Publications
No abstract provided.
Travelling Fronts In Cylinders And Their Stability, Jerrold W. Bebernes, Comgming Li, Yi Li
Travelling Fronts In Cylinders And Their Stability, Jerrold W. Bebernes, Comgming Li, Yi Li
Mathematics and Statistics Faculty Publications
No abstract provided.
Lyapunov Exponents Of Linear Stochastic Functional-Differential Equations. Ii. Examples And Case Studies, Salah-Eldin A. Mohammed, Michael K. R. Scheutzow
Lyapunov Exponents Of Linear Stochastic Functional-Differential Equations. Ii. Examples And Case Studies, Salah-Eldin A. Mohammed, Michael K. R. Scheutzow
Articles and Preprints
We give several examples and examine case studies of linear stochastic functional differential equations. The examples fall into two broad classes: regular and singular, according to whether an underlying stochastic semi-flow exists or not. In the singular case, we obtain upper and lower bounds on the maximal exponential growth rate $\overlineλ1$(σ) of the trajectories expressed in terms of the noise variance σ . Roughly speaking we show that for small σ, $\overlineλ1$(σ) behaves like -σ2 /2, while for large σ, it grows like logσ. In the regular case, it is shown that a discrete Oseledec …
Convolution And Fourier-Feynman Transforms, Chull Park, David Skough
Convolution And Fourier-Feynman Transforms, Chull Park, David Skough
Department of Mathematics: Faculty Publications
In this paper, for a class of funtionals on Wiener space of the form F(x) = exp{∫T0 f(t, x(t)) dt}, we show that the Fourier-Feynman transform of the convolution product is a product of Fourier-Feynman transforms. This allows us to compute the transform of the convolution product without computing the convolution product.
Positive Solution Curves Of Semipositone Problems With Concave Nonlinearities, Alfonso Castro, Sudhasree Gadam, Ratnasingham Shivaji
Positive Solution Curves Of Semipositone Problems With Concave Nonlinearities, Alfonso Castro, Sudhasree Gadam, Ratnasingham Shivaji
All HMC Faculty Publications and Research
We consider the positive solutions to the semilinear equation:
-Δu(x) = λf(u(x)) for x ∈ Ω
u(x) = 0 for x ∈ ∂Ω
where Ω denotes a smooth bounded region in RN (N > 1) and λ > 0. Here f :[0, ∞)→R is assumed to be monotonically increasing, concave and such that f(0) < 0 (semipositone). Assuming that f'(∞) ≡ lim t→∞ f'(t) > 0, we establish the stability and uniqueness of large positive solutions in terms of (f(t)/t)'. When Ω is a ball, we determine the exact number of positive solutions for each λ > 0. We also obtain the geometry of the branches of positive solutions completely and establish how …
The Nordstrom–Robinson Code Is Algebraic-Geometric, Judy L. Walker
The Nordstrom–Robinson Code Is Algebraic-Geometric, Judy L. Walker
Department of Mathematics: Faculty Publications
The techniques of algebraic geometry have been widely and successfully applied to the study of linear codes over finite field since the early 1980’s. Recently, there has been an increased interest in the study of linear codes over finite rings. In a previous paper [10], we combined these two approaches to coding theory by introducing and studying algebraic-geometric codes over rings. In this correspondence, we show that the Nordstrom–Robinson code is the image under the Gray mapping of an algebraic geometric code over Z = 4Z.