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Articles 20611 - 20640 of 27475

Full-Text Articles in Physical Sciences and Mathematics

Perturbations Of Roots Under Linear Transformations Of Polynomials, Branko Ćurgus, Vania Mascioni Apr 2007

Perturbations Of Roots Under Linear Transformations Of Polynomials, Branko Ćurgus, Vania Mascioni

Mathematics Faculty Publications

Let Pn be the complex vector space of all polynomials of degree at most n. We give several characterizations of the linear operators T:Pn→Pn for which there exists a constant C > 0 such that for all nonconstant f∈Pn there exist a root u of f and a root v of Tf with |u−v|≤C. We prove that such perturbations leave the degree unchanged and, for a suitable pairing of the roots of f and Tf, the roots are never displaced by more than a uniform constant independent on f. We show that such "good" operators T …

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Population Models In Almost Periodic Environments, Toka Diagana, Saber Elaydi, Abdul-Aziz Yakubu Apr 2007

Population Models In Almost Periodic Environments, Toka Diagana, Saber Elaydi, Abdul-Aziz Yakubu

Mathematics Faculty Research

We establish the basic theory of almost periodic sequences on Ζ+. Dichotomy techniques are then utilized to find sufficient conditions for the existence of a globally attracting almost periodic solution of a semilinear system of difference equations. These existence results are, subsequently, applied to discretely reproducing populations with and without overlapping generations. Furthermore, we access evidence for attenuance and resonance in almost periodically forced population models.

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A Spectral Order For Infinite Dimensional Quantum Spaces: A Preliminary Report, Joe Mashburn Apr 2007

A Spectral Order For Infinite Dimensional Quantum Spaces: A Preliminary Report, Joe Mashburn

Mathematics Faculty Publications

In 2002 Coecke and Martin created a Bayesian order for the finite dimensional spaces of classical states in physics and used this to define a similar order, the spectral order on the finite dimensional quantum states. These orders gave the spaces a structure similar to that of a domain. This allows for measuring information content of states and for determining which partial states are approximations of which pure states. In a previous paper the author extended the Bayesian order to infinite dimensional spaces of classical states. The order on infinite dimensional spaces retains many of the characteristics important to physics, …

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A Combinatorial Proof Of Vandermonde's Determinant, Arthur T. Benjamin, Gregory P. Dresden Apr 2007

A Combinatorial Proof Of Vandermonde's Determinant, Arthur T. Benjamin, Gregory P. Dresden

All HMC Faculty Publications and Research

No abstract provided in this article.

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Existence To Singular Boundary Value Problems With Sign Changing Nonlinearities Using An Approximation Method Approach, Haishen Lu, Donal O'Regan, Ravi P. Agarwal Apr 2007

Existence To Singular Boundary Value Problems With Sign Changing Nonlinearities Using An Approximation Method Approach, Haishen Lu, Donal O'Regan, Ravi P. Agarwal

Mathematics and System Engineering Faculty Publications

This paper studies the existence of solutions to the singular boundary value problem {−u′′=g(t,u)+(h,u),t∈(0,1),u(0)=0=u(1), {−u″=g(t,u)+(h,u),t∈(0,1),u(0)=0=u(1), , where g: (0, 1) × (0, ∞) → ℝ and h: (0, 1) × [0, ∞) → [0, ∞) are continuous. So our nonlinearity may be singular at t = 0, 1 and u = 0 and, moreover, may change sign. The approach is based on an approximation method together with the theory of upper and lower solutions.

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A Variational Principle For Discontinuous Potentials, Anna Mummert Apr 2007

A Variational Principle For Discontinuous Potentials, Anna Mummert

Mathematics Faculty Research

Let $X$ be a compact space, $f\colon X \to X$ a continuous map, and $\Lambda \subset X$ be any $f$-invariant subset. Assume that there exists a nested family of subsets $\{\Lambda_l\}_{l \geq 1}$ that exhaust $\Lambda$, that is $\Lambda_l \subset\Lambda_{l+1}$ and $\Lambda =\bigcup_{l \geq 1} \Lambda_l$. Assume that the potential $\varphi \colon X \to \mathbb{R}$ is continuous on the closure of each $\Lambda_l$ but not necessarily continuous on $\Lambda$. We define the topological pressure of $\varphi$ on $\Lambda$. This definition is shown to have a corresponding variational principle. We apply the topological pressure and variational principle to systems with non-zero …

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Rationalized Evaluation Subgroups Of A Map Ii: Quillen Models And Adjoint Maps, Gregory Lupton, Samuel Bruce Smith Apr 2007

Rationalized Evaluation Subgroups Of A Map Ii: Quillen Models And Adjoint Maps, Gregory Lupton, Samuel Bruce Smith

Mathematics and Statistics Faculty Publications

We identify the long exact sequence induced on rational homotopy groups by the evaluation map ω: map(X, Y ; f)→Y and in particular the rationalization of the evaluation subgroups off, in terms of derivations of Quillen models and adjoint maps. We consider a generalization of a question of Gottlieb within the context of rational homotopytheory. We also study the rationalization of the G-sequence of a map. In a separate result of independent interest, we give an explicit Quillen minimal model of a product A×X, in the case in which A is a rational co-H-space.

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Crossover Property Of The Nonperiodic Autocorrelation Of Quaternary Sequences, Michael Pohl Apr 2007

Crossover Property Of The Nonperiodic Autocorrelation Of Quaternary Sequences, Michael Pohl

Honors Theses

Sequences with identical nonperiodic autocorrelation functions have recently been used to construct Golay sequences different than the Davis-Jedwab construction. In this thesis, we construct infinite families of quaternary sequences with identical non periodic autocorrelation functions. These results demonstrate that current con­ structions for quaternary families are not all encompassing and need further study.

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The Computation Of Exact Green's Functions In Acoustic Analogy By A Spectral Collocation Boundary Element Method, Andrea D. Jones Apr 2007

The Computation Of Exact Green's Functions In Acoustic Analogy By A Spectral Collocation Boundary Element Method, Andrea D. Jones

Mathematics & Statistics Theses & Dissertations

Aircraft airframe noise pollution resulting from the take-off and landing of airplanes is a growing concern. Because of advances in numerical analysis and computer technology, most of the current noise prediction methods are computationally efficient. However, the ability to effectively apply an approach to complex airframe geometries continues to challenge researchers. The objective of this research is to develop and analyze a robust noise prediction method for dealing with geometrical modifications. This new approach for determining sound pressure involves computing exact, or tailored, Green's functions for use in acoustic analogy. The effects of sound propagation and scattering by solid surfaces …

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A Technique For Solving The Singular Integral Equations Of Potential Theory, Brian George Burns Apr 2007

A Technique For Solving The Singular Integral Equations Of Potential Theory, Brian George Burns

Mathematics & Statistics Theses & Dissertations

The singular integral equations of Potential Theory are investigated using ideas from both classical and contemporary mathematics. The goal of this semi-analytic approach is to produce numerical schemes that are both general and computationally simple. Previous works based on classical methods have yielded solutions only for very special cases while contemporary methods such as finite differences, finite elements and boundary element techniques are computationally extensive. Since the two-dimensional integral equations of interest exhibit structural invariance under a wide class of conformal mappings initial emphasis is placed on circular domains. By Fourier expansion with respect to the angular variable, such two-dimensional …

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A Study On Time/Memory Trade-Off Cryptanalysis., Sourav Mukhopadhyay Dr. Mar 2007

A Study On Time/Memory Trade-Off Cryptanalysis., Sourav Mukhopadhyay Dr.

Doctoral Theses

At the beginning of 2003, I was searching for a suitable area to do my PhD. My respected guide Prof. Palash Sarkar assigned me to do a survey work on block cipher cryptanalysis. I found myself very interested in this area. I am very lucky that I joined into a golden group – Cryptology Research Group of India formed by our beloved teacher Prof. Bimal Roy and had the opportunity to work with Prof. Palash Sarkar, Dr. Subhomoy Maitra, Prof. Rana Barua and many others. I have been inspired by many persons during my PhD work.I would like to begin …

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Extraction Of The Neutron Magnetic Form Factor From Quasielastic 3He(E , E') At Q2=0.1-0.6 (Gev/C)2, B. Anderson, L. Auberbach, T. Averett, W. Bertozzi, T. Black, J. Calarco, L. Cardman, G. D. Cates, Z. W. Chai, J. P. Chen, Seonho Choi, E. Chudakov, S. Churchwell, G. S. Corrado, C. Crawford, A. Deur, P. Djawotho, D. Dutta, J. M. Finn, H. Gao, J. Golak, J. Gomez, V. G. Gorbenko, J. O. Hansen, F. W. Hersman, D. W. Higinbotham, R. Holmes, C. R. Howell, E. Hughes, B. Humensky, S. Incerti, C. W. De Jager, J. S. Jensen, X. Jiang, C. E. Jones, M. Jones, R. Kahl, H. Kamada, A. Kievsky, I. Kominis, W. Korsch, K. Kramer, G. Kumbartzki, M. Kuss, Enkeleida K. Lakuriqi, M. Liang, N. Liyanange, J. Lerose, S. Malov, D. J. Margaziotis, J. W. Martin, K. Mccormick, R. D. Mckeown, K. Mcilhany, Z. E. Meziani, R. Michaels, G. W. Miller, J. Mitchell, S. Nanda, E. Pace, T. Pavlin, G. G. Petratos, R. I. Pomatsalyuk, D. Pripstein, D. Prout, R. D. Ransome, Y. Roblin, M. Rvachev, A. Saha, G. Salme, M. Schnee, J. Seely, T. Shin, K. Slifer, P. A. Souder, S. Strauch, R. Suleiman, M. Sutter, B. Tipton, L. Todor, M. Viviani, R. Gilman, A. V. Glamazdin, C. Glashausser, B. Vlahovic, J. Watson, C. F. Williamson, H. Witala, B. Wojsekhowski, F. Xiong, X. Wu, J. Yeh, P. Zolmierczuk Mar 2007

Extraction Of The Neutron Magnetic Form Factor From Quasielastic 3He(E , E') At Q2=0.1-0.6 (Gev/C)2, B. Anderson, L. Auberbach, T. Averett, W. Bertozzi, T. Black, J. Calarco, L. Cardman, G. D. Cates, Z. W. Chai, J. P. Chen, Seonho Choi, E. Chudakov, S. Churchwell, G. S. Corrado, C. Crawford, A. Deur, P. Djawotho, D. Dutta, J. M. Finn, H. Gao, J. Golak, J. Gomez, V. G. Gorbenko, J. O. Hansen, F. W. Hersman, D. W. Higinbotham, R. Holmes, C. R. Howell, E. Hughes, B. Humensky, S. Incerti, C. W. De Jager, J. S. Jensen, X. Jiang, C. E. Jones, M. Jones, R. Kahl, H. Kamada, A. Kievsky, I. Kominis, W. Korsch, K. Kramer, G. Kumbartzki, M. Kuss, Enkeleida K. Lakuriqi, M. Liang, N. Liyanange, J. Lerose, S. Malov, D. J. Margaziotis, J. W. Martin, K. Mccormick, R. D. Mckeown, K. Mcilhany, Z. E. Meziani, R. Michaels, G. W. Miller, J. Mitchell, S. Nanda, E. Pace, T. Pavlin, G. G. Petratos, R. I. Pomatsalyuk, D. Pripstein, D. Prout, R. D. Ransome, Y. Roblin, M. Rvachev, A. Saha, G. Salme, M. Schnee, J. Seely, T. Shin, K. Slifer, P. A. Souder, S. Strauch, R. Suleiman, M. Sutter, B. Tipton, L. Todor, M. Viviani, R. Gilman, A. V. Glamazdin, C. Glashausser, B. Vlahovic, J. Watson, C. F. Williamson, H. Witala, B. Wojsekhowski, F. Xiong, X. Wu, J. Yeh, P. Zolmierczuk

Enkeleida K. Lakuriqi

We have measured the transverse asymmetry AT' in the quasielastic 3He(e,e') process with high precision at Q2 values from 0.1 to 0.6 (GeV/c)2. The neutron magnetic form factor GnM was extracted at Q2 values of 0.1 and 0.2(GeV/c)2 using a nonrelativistic Faddeev calculation which includes both final-state interactions (FSI) and meson-exchange currents (MEC). Theoretical uncertainties due to the FSI and MEC effects were constrained with a precision measurement of the spin-dependent asymmetry in the threshold region of 3He(e,e'). We also extracted the neutron magnetic form factor …

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The Evaluation Subgroup Of A Fibre Inclusion, Gregory Lupton, Samuel Bruce Smith Mar 2007

The Evaluation Subgroup Of A Fibre Inclusion, Gregory Lupton, Samuel Bruce Smith

Mathematics and Statistics Faculty Publications

Let ξ: X j−→Ep−→B be a fibration of simply connected CW complexes of finite type with classifying map h: B→Baut1(X).We study the evaluation subgroup G n (E, X; j)of the fibre inclusion as an invariant of the fibre- homotopy type of ξ. For spherical fibrations, we show the evaluation subgroup may be expressed as an extension of the Gottlieb group of the fibre sphere provided the classifying map h induces the trivial map on homotopy groups. We extend this result after rationalization: We show that the decomposition G∗(E, X ; j)⊗Q=(G∗(X)⊗Q)⊕(π∗(B)⊗Q)is equivalent to the condition(h)Q=0.

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To Boldly Go: Current Work And Future Directions In Mathematics And Popular Culture, Christopher Goff, Sarah J. Greenwald Mar 2007

To Boldly Go: Current Work And Future Directions In Mathematics And Popular Culture, Christopher Goff, Sarah J. Greenwald

Christopher Goff

No abstract provided.

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Does Spelling Count? Reflections On Writing In The Mathematics Classroom, Christopher D. Goff Mar 2007

Does Spelling Count? Reflections On Writing In The Mathematics Classroom, Christopher D. Goff

College of the Pacific Faculty Presentations

The written word is scarce in the stereotypical mathematics course, which instead emphasizes the routine solving of problems. But having students explain their solutions in writing can pave the way to more critical mathematical thinking. This talk will examine the use of writing as a tool to learn mathematics. We will reflect on: reasons to incorporate writing in a mathematics class; which courses lend themselves to writing assignments; what types of assignments to use; samples of student work; and whether using writing can actually improve student learning. Depending on the assignments, writing can also incorporate several “Basic Principles” of AMATYC’s …

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Periodic Solutions Of Functional Dynamic Equations With Infinite Delay, Li Bi, Meng Fan, Martin Bohner Mar 2007

Periodic Solutions Of Functional Dynamic Equations With Infinite Delay, Li Bi, Meng Fan, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

In this paper, sufficient criteria are established for the existence of periodic solutions of some functional dynamic equations with infinite delays on time scales, which generalize and incorporate as special cases many known results for differential equations and for difference equations when the time scale is the set of the real numbers or the integers, respectively. The approach is mainly based on the Krasnosel'skilatin small letter i with breve fixed point theorem, which has been extensively applied in studying existence problems in differential equations and difference equations but rarely applied in studying dynamic equations on time scales. This study shows …

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Variational Analysis In Bilevel Programming, S Dempe, J Dutta, Boris S. Mordukhovich Mar 2007

Variational Analysis In Bilevel Programming, S Dempe, J Dutta, Boris S. Mordukhovich

Mathematics Research Reports

The paper is devoted to applications of advanced tools of modern variational analysis and generalized differentiation to problems of optimistic bilevel programming. In this way, new necessary optimality conditions are derived for two major classes of bilevel programs: those with partially convex and with fully convex lower-level problems. We provide detailed discussions of the results obtained and their relationships with known results in this area.

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Dynamics Of Asynchronous Random Boolean Networks With Asynchrony Generated By Stochastic Processes, Xutao Deng, Huimin Geng, Mihaela Teodora Matache Mar 2007

Dynamics Of Asynchronous Random Boolean Networks With Asynchrony Generated By Stochastic Processes, Xutao Deng, Huimin Geng, Mihaela Teodora Matache

Mathematics Faculty Publications

An asynchronous Boolean network with N nodes whose states at each time point are determined by certain parent nodes is considered. We make use of the models developed by Matache and Heidel [Matache, M.T., Heidel, J., 2005. Asynchronous random Boolean network model based on elementary cellular automata rule 126. Phys. Rev. E 71, 026232] for a constant number of parents, and Matache [Matache, M.T., 2006. Asynchronous random Boolean network model with variable number of parents based on elementary cellular automata rule 126. IJMPB 20 (8), 897–923] for a varying number of parents. In both these papers the authors consider an …

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The Time Invariance Principle, Ecological (Non)Chaos, And A Fundamental Pitfall Of Discrete Modeling, Bo Deng Mar 2007

The Time Invariance Principle, Ecological (Non)Chaos, And A Fundamental Pitfall Of Discrete Modeling, Bo Deng

Department of Mathematics: Faculty Publications

This paper is to show that most discrete models used for population dynamics in ecology are inherently pathological that their predications cannot be independently verified by experiments because they violate a fundamental principle of physics. The result is used to tackle an on-going controversy regarding ecological chaos. Another implication of the result is that all continuous dynamical systems must be modeled by differential equations. As a result it suggests that researches based on discrete modeling must be closely scrutinized and the teaching of calculus and differential equations must be emphasized for students of biology.

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Winning Paths In N-By-Infinity Hex, Walter Stromquist Mar 2007

Winning Paths In N-By-Infinity Hex, Walter Stromquist

Mathematics & Statistics Faculty Works

In n x ∞ Hex the player whose task is to complete a finite path can win, but the other player can ensure that any winning path contains at least n + [n−2/4] cells.

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On Edge Detection And Object Recognition In Color Images., Sarif Kumar Naik Dr. Feb 2007

On Edge Detection And Object Recognition In Color Images., Sarif Kumar Naik Dr.

Doctoral Theses

No abstract provided.

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Concatenative Text-To-Speech Synthesis: A Study On Standard Colloquial Bengali., Soumen Chowdhury Dr. Feb 2007

Concatenative Text-To-Speech Synthesis: A Study On Standard Colloquial Bengali., Soumen Chowdhury Dr.

Doctoral Theses

The primary communication process between human beings is Speech. Speech synthesis is the automatic and artificial generation of the speech signal by a machine. A TTS (Text-To-Speech) synthesis system is one which can generate speech signal from a string of text in a given language. The development in the speech synthesis systems in various languages has been going on for several decades. With the unprecedented expansion of IT (Information Technology) invading the life of the common man it is highly desirable that at least the information dissemination be made via the speech mode which is the most natural mode of …

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Quickest Flows Over Time, Lisa Fleischer, Martin Skutella Feb 2007

Quickest Flows Over Time, Lisa Fleischer, Martin Skutella

Dartmouth Scholarship

Flows over time (also called dynamic flows) generalize standard network flows by introducing an element of time. They naturally model problems where travel and transmission are not instantaneous. Traditionally, flows over time are solved in time‐expanded networks that contain one copy of the original network for each discrete time step. While this method makes available the whole algorithmic toolbox developed for static flows, its main and often fatal drawback is the enormous size of the time‐expanded network. We present several approaches for coping with this difficulty. First, inspired by the work of Ford and Fulkerson on maximal s‐t …

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On The Elimination Of The Sweeping Interactions From Theories Of Hydrodynamic Turbulence, Eleftherios Gkioulekas Feb 2007

On The Elimination Of The Sweeping Interactions From Theories Of Hydrodynamic Turbulence, Eleftherios Gkioulekas

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

In this paper, we revisit the claim that the Eulerian and quasi-Lagrangian same time correlation tensors are equal. This statement allows us to transform the results of an MSR quasi-Lagrangian statistical theory of hydrodynamic turbulence back to the Eulerian representation. We define a hierarchy of homogeneity symmetries between incremental homogeneity and global homogeneity. It is shown that both the elimination of the sweeping interactions and the derivation of the 4/5-law require a homogeneity assumption stronger than incremental homogeneity but weaker than global homogeneity. The quasi-Lagrangian transformation, on the other hand, requires an even stronger homogeneity assumption which is many-time rather …

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The Relationship Between Discrete Vector Quantization And The P-Median Problem, Allen G. Holder, G Lim, J Reese Feb 2007

The Relationship Between Discrete Vector Quantization And The P-Median Problem, Allen G. Holder, G Lim, J Reese

Mathematics Faculty Research

We show that a well studied problem in the engineering community is the same as a problem studied by mathematical combinatorialists. Specifically, we show that the question of optimally designing a vector quantizer, which is an important problem in coding theory, is the same as the p-median problem, which is a classic graph theory problem with important applications in operations research. The importance of the relationship lies in the fact that both communities have spent years developing solution methodologies, and this connection permits each community to glean new ideas from the other. We show that two of the most popular …

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Variational Principles For Set-Valued Mappings With Applications To Multiobjective Optimization, Truong Q. Bao, Boris S. Mordukhovich Feb 2007

Variational Principles For Set-Valued Mappings With Applications To Multiobjective Optimization, Truong Q. Bao, Boris S. Mordukhovich

Mathematics Research Reports

This paper primarily concerns the study of general classes of constrained multiobjective optimization problems (including those described via set-valued and vector-valued cost mappings) from the viewpoint of modern variational analysis and generalized differentiation. To proceed, we first establish two variational principles for set-valued mappings, which~being certainly of independent interest are mainly motivated by applications to multiobjective optimization problems considered in this paper. The first variational principle is a set-valued counterpart of the seminal derivative-free Ekeland variational principle, while the second one is a set-valued extension of the subdifferential principle by Mordukhovich and Wang formulated via an appropriate subdifferential notion for …

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An Unexpected Limit Of Expected Values, Branko Ćurgus, Robert I. Jewett Feb 2007

An Unexpected Limit Of Expected Values, Branko Ćurgus, Robert I. Jewett

Mathematics Faculty Publications

Let t⩾0. Select numbers randomly from the interval [0,1] until the sum is greater than t . Let α(t) be the expected number of selections. We prove that α(t)=et for 0⩽t⩽1. Moreover, . This limit is a special case of our asymptotic results for solutions of the delay differential equation f′(t)=f(t)-f(t-1) for t>1. We also consider four other solutions of this equation that are related to the above selection process.

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Galois Number Fields With Small Root Discriminant, John W. Jones, David P. Roberts Feb 2007

Galois Number Fields With Small Root Discriminant, John W. Jones, David P. Roberts

Mathematics Publications

We pose the problem of identifying the set K(G,Ω) of Galois number fields with given Galois group G and root discriminant less than the Serre constant Ω ≈ 44.7632. We definitively treat the cases G = A4. A5, A6, and S4, S5, S6, finding exactly 59, 78, 5 and 527, 192, 13 fields, respectively. We present other fields with Galois groups SL3(2), A7, S7, PGL2(7), SL2(8), ΣL2(8), PGL2(9), PSL2(11), and …

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Step-Up Simultaneous Tests For Identifying Active Effects In Orthogonal Saturated Designs, Samuel S. Wu, Weizhen Wang Feb 2007

Step-Up Simultaneous Tests For Identifying Active Effects In Orthogonal Saturated Designs, Samuel S. Wu, Weizhen Wang

Mathematics and Statistics Faculty Publications

A sequence of null hypotheses regarding the number of negligible effects (zero effects) in orthogonal saturated designs is formulated. Two step-up simultaneous testing procedures are proposed to identify active effects (nonzero effects) under the commonly used assumption of effect sparsity. It is shown that each procedure controls the experimentwise error rate at a given alpha level in the strong sense.

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Approximations Of Continuous Newton's Method: An Extension Of Cayley's Problem, Jon T. Jacobsen, Owen Lewis '05, Bradley Tennis '06 Feb 2007

Approximations Of Continuous Newton's Method: An Extension Of Cayley's Problem, Jon T. Jacobsen, Owen Lewis '05, Bradley Tennis '06

All HMC Faculty Publications and Research

Continuous Newton's Method refers to a certain dynamical system whose associated flow generically tends to the roots of a given polynomial. An Euler approximation of this system, with step size h=1, yields the discrete Newton's method algorithm for finding roots. In this note we contrast Euler approximations with several different approximations of the continuous ODE system and, using computer experiments, consider their impact on the associated fractal basin boundaries of the roots

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