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2002

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Articles 31 - 60 of 140

Full-Text Articles in Physical Sciences and Mathematics

The Fourier Transform And Some Applications, Christopher Zion Sep 2002

The Fourier Transform And Some Applications, Christopher Zion

Masters Theses & Specialist Projects

none

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Tilings Of Low-Genus Surfaces By Quadrilaterals, John Gregoire, Isabel Averil Aug 2002

Tilings Of Low-Genus Surfaces By Quadrilaterals, John Gregoire, Isabel Averil

Mathematical Sciences Technical Reports (MSTR)

In contribution to the classification of all tilings of low-genus surfaces, the kaleidoscopic and non-kaleidoscopic tilings by quadrilaterals are given up to genus 12. As part of their classification, the algebraic structure of the conformal tiling groups and the geometric structure of the tiles are specified. In addition, several infinite classes of tilings and tiling groups are presented.

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Gradient Recovery And A Posteriori Estimate For Bilinear Element On Irregular Quadrilateral Meshes, Zhimin Zhang Aug 2002

Gradient Recovery And A Posteriori Estimate For Bilinear Element On Irregular Quadrilateral Meshes, Zhimin Zhang

Mathematics Research Reports

A polynomial preserving gradient recovery method is proposed and analyzed for bilinear element under general quadrilateral meshes. It has been proven that the recovered gradient converges at a rate O(h1+rho) for rho = min(alpha, 1) when the mesh is distorted O(h1+alpha) (alpha > 0) from a regular one. Consequently, the a posteriori error estimator based on the recovered gradient is asymptotically exact.

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On The Quantum Moduli Space Of M-Theory Compactifications, Tamar Friedmann Jul 2002

On The Quantum Moduli Space Of M-Theory Compactifications, Tamar Friedmann

Mathematics Sciences: Faculty Publications

We study the moduli space of M-theories compactified on G2 manifolds which are asymptotic to a cone over quotients of S3 × S3. We show that the moduli space is composed of several components, each of which interpolates smoothly among various classical limits corresponding to low energy gauge theories with a given number of massless U (1) factors. Each component smoothly interpolates among supersymmetric gauge theories with different gauge groups.

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Analogues Of Weyl’S Formula For Reduced Enveloping Algebras, J. E. Humphreys Jul 2002

Analogues Of Weyl’S Formula For Reduced Enveloping Algebras, J. E. Humphreys

Mathematics and Statistics Department Faculty Publication Series

In this note we study simple modules for a reduced enveloping algebra Ux (g) in the critical case when X E 2 g^x is “nilpotent”. Some dimension formulas computed by Jantzen suggest modified versions of Weyl’s dimension formula, based on certain reflecting hyperplanes for the affine Weyl group which might be associated to Kazhdan–Lusztig cells.

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A Restricted Partition Function Modulo 3, Naomi Utgof Jul 2002

A Restricted Partition Function Modulo 3, Naomi Utgof

Mathematical Sciences Technical Reports (MSTR)

The ordinary partition function p(n) counts the number of representations of a positive integer n as the sum of positive integers. We denote by p3(n) the number of partitions of n with no parts divisible by 3: We demonstrate congruence relations for arithmetic sequences qn+(2q2-2)/24 where q is a prime other than 3 congruent to 3 (mod 4): We also prove a result when q = 5 and make a conjecture about a generalization .

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Central Twisted Transformation Groups And Group C*-Algebras Of Central Group Extensions, Siegfried Echterhoff, Dana P. Williams Jul 2002

Central Twisted Transformation Groups And Group C*-Algebras Of Central Group Extensions, Siegfried Echterhoff, Dana P. Williams

Dartmouth Scholarship

We examine the structure of central twisted transformation group C∗-algebras C0(X) ⋊id,u G, and apply our results to the group C ∗-algebras of central group extensions. Our methods require that we study Moore’s cohomology group H2 (G, C(X,T)), and, in particular, we prove an inflation result for pointwise trivial cocyles which may be of use elsewhere.

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Analysis Of Recovery Type A Posteriori Error Estimators For Mildly Structured Grids, Jinchao Xu, Zhimin Zhang Jul 2002

Analysis Of Recovery Type A Posteriori Error Estimators For Mildly Structured Grids, Jinchao Xu, Zhimin Zhang

Mathematics Research Reports

Some recovery type error estimators for linear finite element method are analyzed under O(h1+alpha) (alpha greater than 0) regular grids. Superconvergence is established for recovered gradients by three different methods when solving general non-self-adjoint second-order elliptic equations. As a consequence, a posteriori error estimators based on those recovery methods are asymptotically exact.

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Global Stability Of Cycles: Lotka-Volterra Competition Model With Stocking, Saber Elaydi, Abdul-Aziz Yakubu Jun 2002

Global Stability Of Cycles: Lotka-Volterra Competition Model With Stocking, Saber Elaydi, Abdul-Aziz Yakubu

Mathematics Faculty Research

In this article, we prove that in connected metric spaces k - cycles are not globally attracting (where k>2). We apply this result to a two species discrete-time Lotka-Volterra competion model with stocking. In particular, we show that an k-cycle cannot be the ultimate life-history of evolution of all population sizes. This solves Yakubu's conjecture but the question on the structure of the boundary of the basins of attraction of the locally stable n-cycles is still open.

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Totally Magic Graphs, Geoffrey Exoo, Alan C. H. Ling, John P. Mcsorley, Nicholas C. Phillips, Walter D. Wallis Jun 2002

Totally Magic Graphs, Geoffrey Exoo, Alan C. H. Ling, John P. Mcsorley, Nicholas C. Phillips, Walter D. Wallis

Articles and Preprints

A total labeling of a graph with v vertices and e edges is defined as a one-to-one map taking the vertices and edges onto the integers 1, 2, · · · , v+e. Such a labeling is vertex magic if the sum of the label on a vertex and the labels on its incident edges is a constant independent of the choice of vertex, and edge magic if the sum of an edge label and the labels of the endpoints of the edge is constant. In this paper we examine graphs possessing a labeling that is simultaneously …

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Mini-Course On Stochastic Systems With Memory (University Of Campinas), Salah-Eldin A. Mohammed Jun 2002

Mini-Course On Stochastic Systems With Memory (University Of Campinas), Salah-Eldin A. Mohammed

Miscellaneous (presentations, translations, interviews, etc)

This is a mini-course consisting of three talks on the theme : ``Stochastic Systems with Memory", given at the Mathematics Institute, University of Campinas, Campinas, Brazil. My visit to Campinas was fully supported by a grant from FAPESP (of the State of Sao Paulo).

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Creating Successful Calculus Writing Assignments, Kris H. Green Jun 2002

Creating Successful Calculus Writing Assignments, Kris H. Green

Mathematical and Computing Sciences Faculty/Staff Publications

I discuss three different writing assignments that I have used in my calculus courses. These assignments are introduced with a discussion of purpose and audience. Defining these qualities of an assignment will ensure that your writing assignments are more successful. The assignments discussed and explored here represent three different purposes: personal, informational and a blend of the two. The audiences for these assignments are diverse and force the students to incorporate particular modes of writing that demonstrate much of their thinking. Assessment of student learning as a result of these assignments is discussed. A fourth writing assignment is developed from …

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Computational Geometry Column 43, Joseph O'Rourke Jun 2002

Computational Geometry Column 43, Joseph O'Rourke

Computer Science: Faculty Publications

The concept of pointed pseudo-triangulations is defined and a few of its applications described.

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The Mathematics Of T. Benny Rushing, James Keesling, Luis Montejano, Gerard A. Venema May 2002

The Mathematics Of T. Benny Rushing, James Keesling, Luis Montejano, Gerard A. Venema

University Faculty Publications and Creative Works

No abstract provided.

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Representing Homology Classes Of Simply Connected 4-Manifolds, Vo Thanh Liem, Gerard A. Venema May 2002

Representing Homology Classes Of Simply Connected 4-Manifolds, Vo Thanh Liem, Gerard A. Venema

University Faculty Publications and Creative Works

The main theorem asserts that every 2-dimensional homology class of a compact simply connected PL 4-manifold can be represented by a codimension-0 submanifold consisting of a contractible manifold with a single 2-handle attached. One consequence of the theorem is the fact that every map of S2 into a simply connected, compact PL 4-manifold is homotopic to an embedding if and only if the same is true for every homotopy equivalence. The theorem is also the main ingredient in the proof of the following result: If W is a compact, simply connected, PL submanifold of S4, then each element of H2(W;ℤ) …

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Nonorthogonal Polyhedra Built From Rectangles, Melody Donoso, Joseph O'Rourke May 2002

Nonorthogonal Polyhedra Built From Rectangles, Melody Donoso, Joseph O'Rourke

Computer Science: Faculty Publications

We prove that any polyhedron of genus zero or genus one built out of rectangular faces must be an orthogonal polyhedron, but that there are nonorthogonal polyhedra of genus seven all of whose faces are rectangles. This leads to a resolution of a question posed by Biedl, Lubiw, and Sun [BLS99].

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Local Rings Of Countable Cohen-Macaulay Type, Craig Huneke, Graham J. Leuschke May 2002

Local Rings Of Countable Cohen-Macaulay Type, Craig Huneke, Graham J. Leuschke

Mathematics - All Scholarship

We prove (the excellent case of) Schreyer's conjecture that a local ring with countable Cohen-Macaulay type has at most a one-dimensional singular locus. Furthermore we prove that the localization of a Cohen-Macaulay local ring of countable CM type is again of countable CM type.

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Σary, Minnesota State University Moorhead, Mathematics Department May 2002

Σary, Minnesota State University Moorhead, Mathematics Department

Math Department Newsletters

No abstract provided.

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On The Existence Of Multiple Positive Solutions For A Semilinear Problem In Exterior Domains, Yinbin Deng, Yi Li May 2002

On The Existence Of Multiple Positive Solutions For A Semilinear Problem In Exterior Domains, Yinbin Deng, Yi Li

Mathematics and Statistics Faculty Publications

In this paper, we study the existence and nonexistence of multiple positive solutions for problem where Ω=N\ω is an exterior domain in N, ω⊂N is a bounded domain with smooth boundary, and N>2. μ⩾0, p>1 are some given constants. K(x) satisfies: K(x)∈Cαloc(Ω) and ∃C, ϵ, M>0 such that |K(x)|⩽C |x|l for any |x|⩾M, with l⩽ −2−ϵ. Some existence and …

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Phase-Space Transport Of Stochastic Chaos In Population Dynamics Of Virus Spread, Lora Billings, Erik M. Bollt, Ira B. Schwartz May 2002

Phase-Space Transport Of Stochastic Chaos In Population Dynamics Of Virus Spread, Lora Billings, Erik M. Bollt, Ira B. Schwartz

Department of Mathematics Facuty Scholarship and Creative Works

A general way to classify stochastic chaos is presented and applied to population dynamics models. A stochastic dynamical theory is used to develop an algorithmic tool to measure the transport across basin boundaries and predict the most probable regions of transport created by noise. The results of this tool are illustrated on a model of virus spread in a large population, where transport regions reveal how noise completes the necessary manifold intersections for the creation of emerging stochastic chaos.

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The Uniform Convergence Of Special Standardized Distributions, Marcia Lami May 2002

The Uniform Convergence Of Special Standardized Distributions, Marcia Lami

Masters Theses & Specialist Projects

In this thesis, the uniform convergence of two special standardized distributions are examined. The Gamma distribution is standardized, and then the probability density function of the standardized Gamma distribution is shown to converge uniformly to the probability density function of the normal distribution. The F-distribution is standardized, and then the probability density function of the standardized F-distribution is shown to converge uniformly to the probability density function of the normal distribution. Along the way, some other interesting limits are observed.

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Boundary Value Problems On The Half Line In The Theory Of Colloids, Ravi P. Agarwal, Donal O'Regan Apr 2002

Boundary Value Problems On The Half Line In The Theory Of Colloids, Ravi P. Agarwal, Donal O'Regan

Mathematics and System Engineering Faculty Publications

No abstract provided.

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A Stirling Encounter With Harmonic Numbers, Arthur T. Benjamin, Gregory O. Preston '01, Jennifer J. Quinn Apr 2002

A Stirling Encounter With Harmonic Numbers, Arthur T. Benjamin, Gregory O. Preston '01, Jennifer J. Quinn

All HMC Faculty Publications and Research

No abstract provided in this article.

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Four-Person Envy-Free Chore Division, Elisha Peterson '00, Francis E. Su Apr 2002

Four-Person Envy-Free Chore Division, Elisha Peterson '00, Francis E. Su

All HMC Faculty Publications and Research

No abstract provided in this article

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Mathematisation Of The Science Of Motion And The Birth Of Analytical Mechanics : A Historiographical Note, Marco Panza Mar 2002

Mathematisation Of The Science Of Motion And The Birth Of Analytical Mechanics : A Historiographical Note, Marco Panza

MPP Published Research

Usually, one speaks of mathematization of a natural or social science to mean that mathematics comes to be a tool of such a science: the language of mathematics is used to formulate its results, and/or some mathematical techniques is employed to obtain these results.

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Structure Of The Malvenuto-Reutenauer Hopf Algebra Of Permutations (Extended Abstract), Marcelo Aguiar, Frank Sottile Mar 2002

Structure Of The Malvenuto-Reutenauer Hopf Algebra Of Permutations (Extended Abstract), Marcelo Aguiar, Frank Sottile

Mathematics and Statistics Department Faculty Publication Series

We analyze the structure of the Malvenuto-Reutenauer Hopf algebra of permutations in detail. We give explicit formulas for its antipode, prove that it is a cofree coalgebra, determine its primitive elements and its coradical filtration and show that it decomposes as a crossed product over the Hopf algebra of quasi-symmetric functions. We also describe the structure constants of the multiplication as a certain number of facets of the permutahedron. Our results reveal a close relationship between the structure of this Hopf algebra and the weak order on the symmetric groups.

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The Stable Manifold Theorem For Stochastic Differential Equations (Mathematics Colloquium, University Of North Carolina, Charlotte), Salah-Eldin A. Mohammed Mar 2002

The Stable Manifold Theorem For Stochastic Differential Equations (Mathematics Colloquium, University Of North Carolina, Charlotte), Salah-Eldin A. Mohammed

Miscellaneous (presentations, translations, interviews, etc)

No abstract provided.

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Boundary Layers Associated With Incompressible Navier-Stokes Equations: The Noncharacteristic Boundary Case, R. Temam, X. Wang Mar 2002

Boundary Layers Associated With Incompressible Navier-Stokes Equations: The Noncharacteristic Boundary Case, R. Temam, X. Wang

Mathematics and Statistics Faculty Research & Creative Works

The goal of this article is to study the boundary layer of wall bounded flows in a channel at small viscosity when the boundaries are uniformly non-characteristic, i.e., there is injection and/or suction everywhere at the boundary. Following earlier work on the boundary layer for linearized Navier-Stokes equations in the case where the boundaries are characteristic (non-slip at the boundary and non-permeable), we consider here the case where the boundary is permeable and thus non-characteristic. the form of the boundary layer and convergence results are derived in two cases: linearized equation and full nonlinear equations. We prove that there exists …

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Renewal Systems, Sharp-Eyed Snakes, And Shifts Of Finite Type, Aimee S. A. Johnson, K. M. Madden Mar 2002

Renewal Systems, Sharp-Eyed Snakes, And Shifts Of Finite Type, Aimee S. A. Johnson, K. M. Madden

Mathematics & Statistics Faculty Works

Johnson and Madden look at collections of bi-infinite strings of symbols that occur in several different areas of mathematics and ask whether these collections are the same in some sense. A dynamical systems property called entropy can be used to show that the shifts of finite type are not all conjugate to uniquely decipherable renewal systems.

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Mixed Partial Derivatives And Fubini's Theorem, Asuman Güven Aksoy, Mario Martelli Mar 2002

Mixed Partial Derivatives And Fubini's Theorem, Asuman Güven Aksoy, Mario Martelli

CMC Faculty Publications and Research

A most fascinating aspect of calculus is its power to surprise even an experienced mathemat ician. Just when it appears that all ideas, results and connections have been discovered and thorough ly analyzed, the horizon suddenly broadens and somebody cries the familiar "eureka". The reason could be either a new result, a simpler way to prove an existing theorem, or a previously missed connection between different ideas. This potential for enrichment is second to none, and it reaffirms the unparalleled educational value of this area of mathematics.

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