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Articles 20761 - 20790 of 27475

Full-Text Articles in Physical Sciences and Mathematics

On Energy And Expected Uncertainty Measures In Weighted Distributions, Broderick O. Oluyede, Mekki Terbeche Jan 2007

On Energy And Expected Uncertainty Measures In Weighted Distributions, Broderick O. Oluyede, Mekki Terbeche

Department of Mathematical Sciences Faculty Publications

In this note, bounds and inequalities for the comparisons of weighted energy functions, entropy, and discrimination information measures and their unweighted counterparts are presented. Inequalities for weighted expected uncertainty, cross-entropy or discrimination information measures are also presented. A useful result on the convergence of the weighted kernel density informational energy estimates is given and some informational energy applications presented.

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Closure Under Transfinite Extensions, Edgar Enochs, Alina Iacob, Overtoun Jenda Jan 2007

Closure Under Transfinite Extensions, Edgar Enochs, Alina Iacob, Overtoun Jenda

Department of Mathematical Sciences Faculty Publications

The closure under extensions of a class of objects in an abelian category is often an important property of that class. Recently the closure of such classes under transfinite extensions (both direct and inverse) has begun to play an important role in several areas of mathematics, for example, in Quillen's theory of model categories and in the theory of cotorsion pairs. In this paper we prove that several important classes are closed under transfinite extensions.

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On Comparability Of Random Permutations, Adam J. Hammett Jan 2007

On Comparability Of Random Permutations, Adam J. Hammett

Faculty Dissertations

No abstract provided.

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On Cosmall Abelian Groups, Brendan Goldsmith, O. Kolman Jan 2007

On Cosmall Abelian Groups, Brendan Goldsmith, O. Kolman

Articles

It is a well-known homological fact that every Abelian group G has the property that Hom(G,−) commutes with direct products. Here we investigate the ‘dual’ property: an Abelian group G is said to be cosmall if Hom(−,G) commutes with direct products. We show that cosmall groups are cotorsion-free and that no group of cardinality less than a strongly compact cardinal can be cosmall. In particular, if there is a proper class of strongly compact cardinals, then there are no cosmall groups.

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Estimating Winning Probabilities In Backgammon Races, Andrew M. Ross, Arthur T. Benjamin, Michael Munson '94 Jan 2007

Estimating Winning Probabilities In Backgammon Races, Andrew M. Ross, Arthur T. Benjamin, Michael Munson '94

All HMC Faculty Publications and Research

In modern backgammon, it is advantageous to know the chances each player has of winning, and to be able to compute the chances without the aid of calculators or pencil and paper. A simple model of backgammon is used to approximate those chances, and a readily computable and sufficiently accurate approximation of that is developed. From there, the model is compared to simulated backgammon games, and the previous approximation is modified to fit the real data.

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Conics In The Hyperbolic Plane, Trent Phillip Naeve Jan 2007

Conics In The Hyperbolic Plane, Trent Phillip Naeve

Theses Digitization Project

An affine transformation such as T(P)=Q is a locus of an affine conic. Any affine conic can be produced from this incidence construction. The affine type of conic (ellipse, parabola, hyperbola) is determined by the invariants of T, the determinant and trace of its linear part. The purpose of this thesis is to obtain a corresponding classification in the hyperbolic plane of conics defined by this construction.

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Seeking Bang-Bang Solutions Of Mixed Immuno-Chemotherapy Of Tumors, Lisette G. De Pillis, K Renee Fister, Weiqing Gu, Craig Collins, Michael Daub, David Gross '08, James Moore '07, Benjamin Preskill '09 Jan 2007

Seeking Bang-Bang Solutions Of Mixed Immuno-Chemotherapy Of Tumors, Lisette G. De Pillis, K Renee Fister, Weiqing Gu, Craig Collins, Michael Daub, David Gross '08, James Moore '07, Benjamin Preskill '09

All HMC Faculty Publications and Research

It is known that a beneficial cancer treatment approach for a single patient often involves the administration of more than one type of therapy. The question of how best to combine multiple cancer therapies, however, is still open. In this study, we investigate the theoretical interaction of three treatment types (two biological therapies and one chemotherapy) with a growing cancer, and present an analysis of an optimal control strategy for administering all three therapies in combination. In the situations with controls introduced linearly, we find that there are conditions on which the controls exist singularly. Although bang-bang controls (on-off) reflect …

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A Note On Clean Abelian Groups, Brendan Goldsmith, P. Vamos Jan 2007

A Note On Clean Abelian Groups, Brendan Goldsmith, P. Vamos

Articles

Nicholson defined a ring to be clean if every element is the sum of a unit and an idempotent. A module is clean if its endomorphism algebra is clean. We show that torsion-complete Abelian p-groups are clean and characterize the clean groups among the class of totally projective p-groups. An example is given of a clean p-group which is neither totally projective nor torsion- complete

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Lectures In Basic Computational Numerical Analysis, James M. Mcdonough Jan 2007

Lectures In Basic Computational Numerical Analysis, James M. Mcdonough

Mathematics Textbook Gallery

No abstract provided.

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A Generalization Of Ankeny And Rivlin's Result On The Maximum Modulus Of Polynomials Not Vanishing In The Interior Of The Unit Circle, V. K. Jain Jan 2007

A Generalization Of Ankeny And Rivlin's Result On The Maximum Modulus Of Polynomials Not Vanishing In The Interior Of The Unit Circle, V. K. Jain

Turkish Journal of Mathematics

For an arbitrary entire function f(z), let M(f,r) = max_{ z =r} f(z) . For a polynomial p(z) of degree n, it is known that M(p,R) \leq R^n M(p,1), R > 1. By considering the polynomial p(z) with no zeros in z < 1, Ankeny and Rivlin obtained the refinement M(p,R) \leq {(R^n+1)/2}M(p,1), R > 1. By considering the polynomial p(z) with no zeros in z < k, (k \geq 1) and simultaneously thinking of s^{\rm th} derivative (0 \leq s < n) of the polynomial, we have obtained the generalization \begin{displaymath} M(p^{(s)},R) \leq \left\{\begin{array}{l} (1/2){\frac{d^s}{dR^s}(R^n + k^n)}(2/(1+k))^nM(p,1), R \geq k,\ (1/(R^s+k^s))[{\frac{d^s}{dx^s}(1+x^n)}_{x=1}]((R+k)/(1+k))^nM(p,1), 1 \leq R \leq k,\end{array}\right. of Ankeny and Rivlin's result.

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Potts Model With Two Competing Binary Interactions, Nasir Ganikhodjaev, Hasan Akin, Seyi̇t Temi̇r Jan 2007

Potts Model With Two Competing Binary Interactions, Nasir Ganikhodjaev, Hasan Akin, Seyi̇t Temi̇r

Turkish Journal of Mathematics

The Potts model on a Cayley tree in the presence of competing two binary interactions and magnetic field is considered. We exactly solve a problem of phase transitions for the model,namely we calculate critical surface such that there is a phase transition above it,and a single Gibbs state found elsewhere.

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Symbolization Of Generating Functions; An Application Of The Mullin–Rota Theory Of Binomial Enumeration, Tian-Xiao He, Peter S, Leetsch Hsu Jan 2007

Symbolization Of Generating Functions; An Application Of The Mullin–Rota Theory Of Binomial Enumeration, Tian-Xiao He, Peter S, Leetsch Hsu

Scholarship

We have found that there are more than a dozen classical generating functions that could be suitably symbolized to yield various symbolic sum formulas by employing the Mullin–Rota theory of binomial enumeration. Various special formulas and identities involving well-known number sequences or polynomial sequences are presented as illustrative examples. The convergence of the symbolic summations is discussed.

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A Unifying Field In Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability And Statistics - 6th Ed., Florentin Smarandache Jan 2007

A Unifying Field In Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability And Statistics - 6th Ed., Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

It was a surprise for me when in 1995 I received a manuscript from the mathematician, experimental writer and innovative painter Florentin Smarandache, especially because the treated subject was of philosophy - revealing paradoxes - and logics. He had generalized the fuzzy logic, and introduced two new concepts: a) “neutrosophy” – study of neutralities as an extension of dialectics; b) and its derivative “neutrosophic”, such as “neutrosophic logic”, “neutrosophic set”, “neutrosophic probability”, and “neutrosophic statistics” and thus opening new ways of research in four fields: philosophy, logics, set theory, and probability/statistics. It was known to me his setting up in …

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Neutrosophy In Arabic Philosophy, Florentin Smarandache, Salah Osman Jan 2007

Neutrosophy In Arabic Philosophy, Florentin Smarandache, Salah Osman

Branch Mathematics and Statistics Faculty and Staff Publications

Is there an absolute reality? Yes, “God” is the only absolute reality. The three main religions: Judaism, Christianity and Islam have all claimed that God is a supreme reality, and that all other creatures are finite beings. Since they relatively continue and also relatively change, so they can not be absolute. The world is full of paradoxes, there is no absolute persistence, and also there is no change at a stretch. There is no absolute truth and there is no continuous falsehood. What exist are many faces or aspects between the two terms. Those faces are reduced to a neutral …

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Teaching Time Savers: Is Homework Grading On Your Nerves?, Lisette G. De Pillis, Michael E. Orrison Jr. Jan 2007

Teaching Time Savers: Is Homework Grading On Your Nerves?, Lisette G. De Pillis, Michael E. Orrison Jr.

All HMC Faculty Publications and Research

You have probably heard it said that we learn mathematics best when we do mathematics, or that mathematics is not a spectator sport. For most of our students, this means that their mathematics courses will involve a fair amount of homework. This homework is often used to evaluate individual student progress, but it can also be used, for example, as a catalyst for discussion, to emphasize a point made in class, and to identify common misunderstandings throughout the class as a whole. There is, however, the matter of grading homework.

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Domain Relaxation In Langmuir Films, James C. Alexander, Andrew J. Bernoff, Elizabeth K. Mann, J. Adin Mann Jr., Jacob R. Wintersmith '06, Lu Zou Jan 2007

Domain Relaxation In Langmuir Films, James C. Alexander, Andrew J. Bernoff, Elizabeth K. Mann, J. Adin Mann Jr., Jacob R. Wintersmith '06, Lu Zou

All HMC Faculty Publications and Research

We report on theoretical studies of molecularly thin Langmuir films on the surface of a quiescent subfluid and qualitatively compare the results to both new and previous experiments. The film covers the entire fluid surface, but domains of different phases are observed. In the absence of external forcing, the compact domains tend to relax to circles, driven by a line tension at the phase boundaries. When stretched (by a transient applied stagnation-point flow or by stirring), a compact domain elongates, creating a bola consisting of two roughly circular reservoirs connected by a thin tether. This shape will then relax slowly …

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Turing Patterns On Growing Spheres: The Exponential Case, Julijana Gjorgjieva, Jon T. Jacobsen Jan 2007

Turing Patterns On Growing Spheres: The Exponential Case, Julijana Gjorgjieva, Jon T. Jacobsen

All HMC Faculty Publications and Research

We consider Turing patterns for reaction-diffusion systems on the surface of a growing sphere. In particular, we are interested in the effect of dynamic growth on the pattern formation. We consider exponential isotropic growth of the sphere and perform a linear stability analysis and compare the results with numerical simulations.

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Sp-Scattered Spaces: A New Generalization Of Scattered Spaces, Melvin Henriksen, Robert M. Raphael, R. G. Woods Jan 2007

Sp-Scattered Spaces: A New Generalization Of Scattered Spaces, Melvin Henriksen, Robert M. Raphael, R. G. Woods

All HMC Faculty Publications and Research

The set of isolated points (resp. P-points) of a Tychonoff space X is denoted by Is(X) (resp. P(X)). Recall that X is said to be scattered if Is(A) ≠ ∅ whenever ∅ ≠ A ⊂ X. If instead we require only that P(A) has nonempty interior whenever ∅ ≠ A ⊂ X, we say that X is SP-scattered. Many theorems about scattered spaces hold or have analogs for SP-scattered spaces. For example, the union of a locally finite collection of SP-scattered spaces is SP-scattered. Some known theorems about Lindelöf or paracompact scattered spaces hold also in case the spaces …

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Removing Sets From Connected Spaces While Preserving Connectedness, Melvin Henriksen, Amir Nikou Jan 2007

Removing Sets From Connected Spaces While Preserving Connectedness, Melvin Henriksen, Amir Nikou

All HMC Faculty Publications and Research

As per the title, the nature of sets that can be removed from a product of more than one connected, arcwise connected, or point arcwise connected spaces while preserving the appropriate kind of connectedness is studied. This can depend on the cardinality of the set being removed or sometimes just on the cardinality of what is removed from one or two factor spaces. Sometimes it can depend on topological properties of the set being removed or its trace on various factor spaces. Some of the results are complicated to prove while being easy to state. Sometimes proofs for different kinds …

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Primary Decomposition Of Ideals In A Ring, Sola Oyinsan Jan 2007

Primary Decomposition Of Ideals In A Ring, Sola Oyinsan

Theses Digitization Project

The concept of unique factorization was first recognized in the 1840s, but even then, it was still fairly believed to be automatic. The error of this assumption was exposed largely through attempts to prove Pierre de Fermat's, 1601-1665, last theorem. Once mathematicians discovered that this property did not always hold, it was only natural for them to try to search for the strongest available alternative. Thus began the attempt to generalize unique factorization. Using the ascending chain condition on principle ideals, we will show the conditions under which a ring is a unique factorization domain.

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Frobenius Problem And The Covering Radius Of A Lattice, Lenny Fukshansky, Sinai Robins Jan 2007

Frobenius Problem And The Covering Radius Of A Lattice, Lenny Fukshansky, Sinai Robins

CMC Faculty Publications and Research

Abstract. Let N ≥ 2 and let 1 < a(1) < ... < a(N) be relatively prime integers. The Frobenius number of this N-tuple is defined to be the largest positive integer that cannot be expressed as Sigma(N)(i=1) a(i) x(i) where x(1),..., x(N) are non-negative integers. The condition that gcd(a(1),..., a(N)) = 1 implies that such a number exists. The general problem of determining the Frobenius number given N and a(1),..., a(N) is NP-hard, but there have been a number of different bounds on the Frobenius number produced by various authors. We use techniques from the geometry of numbers to produce a new bound, relating the Frobenius number to the covering radius of the null-lattice of this N-tuple. Our bound is particularly interesting in the case when this lattice has equal successive minima, which, as we prove, happens infinitely often.

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S-Toeplitz Composition Operators, Valentin Matache Jan 2007

S-Toeplitz Composition Operators, Valentin Matache

Mathematics Faculty Publications

Operators on function spaces acting by composition to the right with a fixed selfmap φ of some set are called composition operators of symbol φ.

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Emergence Of Singular Structures In Oldroyd-B Fluids, Becca Thomases, Michael Shelley Jan 2007

Emergence Of Singular Structures In Oldroyd-B Fluids, Becca Thomases, Michael Shelley

Mathematics Sciences: Faculty Publications

Numerical simulations reveal the formation of singular structures in the polymer stress field of a viscoelastic fluid modeled by the Oldroyd-B equations driven by a simple body force. These singularities emerge exponentially in time at hyperbolic stagnation points in the flow and their algebraic structure depends critically on the Weissenberg number. Beyond a first critical Weissenberg number the stress field approaches a cusp singularity, and beyond a second critical Weissenberg number the stress becomes unbounded exponentially in time. A local approximation to the solution at the hyperbolic point is derived from a simple ansatz, and there is excellent agreement between …

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Minimal Surfaces, Maria Guadalupe Chaparro Jan 2007

Minimal Surfaces, Maria Guadalupe Chaparro

Theses Digitization Project

The focus of this project consists of investigating when a ruled surface is a minimal surface. A minimal surface is a surface with zero mean curvature. In this project the basic terminology of differential geometry will be discussed including examples where the terminology will be applied to the different subjects of differential geometry. In addition the focus will be on a classical theorem of minimal surfaces referred to as the Plateau's Problem.

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An Upperbound On The Ropelength Of Arborescent Links, Larry Andrew Mullins Jan 2007

An Upperbound On The Ropelength Of Arborescent Links, Larry Andrew Mullins

Theses Digitization Project

This thesis covers improvements on the upperbounds for ropelength of a specific class of algebraic knots.

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Promoting Undergraduate Research In Mathematics At The University Of Nebraska – Lincoln, Judy L. Walker, Glenn Ledder, Richard Rebarber, Gordon S. Woodward Jan 2007

Promoting Undergraduate Research In Mathematics At The University Of Nebraska – Lincoln, Judy L. Walker, Glenn Ledder, Richard Rebarber, Gordon S. Woodward

Department of Mathematics: Faculty Publications

The Department of Mathematics at the University of Nebraska – Lincoln (UNL) has several programs which promote undergraduate research in a variety of ways. Two of these are summer programs which draw from a national applicant pool: The Nebraska REU in Applied Mathematics (Section 1) is a traditional NSF-funded REU site, and Nebraska IMMERSE (Section 2) offers a summer “bridge” program (with a research bent) for students about to start graduate school in mathematics. IMMERSE is a relatively new program, started in 2004 as part of the department’s Mentoring through Critical Transition Points (MCTP) grant from NSF. The MCTP grant …

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S-Extremal Additive F4 Codes, Evangeline P. Bautista, Philippe Gaborit, Jon-Lark Kim, Judy L. Walker Jan 2007

S-Extremal Additive F4 Codes, Evangeline P. Bautista, Philippe Gaborit, Jon-Lark Kim, Judy L. Walker

Department of Mathematics: Faculty Publications

Binary self-dual codes and additive self-dual codes over F4 have in common interesting properties, for example, Type I, Type II, shadows, etc. Recently Bachoc and Gaborit introduced the notion of s-extremality for binary self-dual codes, generalizing Elkies' study on the highest possible minimum weight of the shadows of binary self-dual codes. In this paper, we introduce a concept of s-extremality for additive self-dual codes over F4, give a bound on the length of these codes with even distance d, classify them up to minimum distance d = 4, give possible lengths and (shadow) weight …

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Graphics With Tikz, Andrew Mertz, William Slough Jan 2007

Graphics With Tikz, Andrew Mertz, William Slough

Faculty Research and Creative Activity

Beautiful and expressive documents often require beautiful and expressive graphics. PGF and its front-end TikZ walk a thin line between power, portability and usability, giving a TEX-like approach to graphics. While PGF and TikZ are extensively documented, first-time users may prefer learning about these packages using a collection of graduated examples. The examples presented here cover a wide spectrum of use and provide a starting point for exploration.

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Graphics With Pgf And Tikz, Andrew Mertz, William Slough Jan 2007

Graphics With Pgf And Tikz, Andrew Mertz, William Slough

Faculty Research and Creative Activity

Beautiful and expressive documents often require beautiful and expressive graphics. PGF and its front-end TikZ walk a fine line between power, portability and usability, giving a TEX-like approach to graphics. While PGF and TikZ are extensively documented, first-time users may prefer learning about these packages using a collection of graduated examples. The examples presented here cover a wide spectrum of use and provide a starting point for exploration.

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A Comparison Of Techniques To Forecast Consumer Satisfaction For Vehicle Ride, Elizabeth A. Cudney, David Drain, Kenneth M. Ragsdell, Kioumars Paryani Jan 2007

A Comparison Of Techniques To Forecast Consumer Satisfaction For Vehicle Ride, Elizabeth A. Cudney, David Drain, Kenneth M. Ragsdell, Kioumars Paryani

Engineering Management and Systems Engineering Faculty Research & Creative Works

This paper presents a comparison of methods for the identification of a reduced set of useful variables using a multidimensional system. the Mahalanobis-Taguchi System and a standard statistical technique are used reduce the dimensionality of vehicle ride based on consumer satisfaction ratings. the Mahalanobis-Taguchi System and cluster analysis are applied to vehicle ride. the research considers 67 vehicle data sets for the 6 vehicle ride parameters. This paper applies the Mahalanobis-Taguchi System to forecast consumer satisfaction and provides a comparison of results with those obtained from a standard statistical approach to the problem. Copyright © 2007 SAE International.

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