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Articles 19171 - 19200 of 27485

Full-Text Articles in Physical Sciences and Mathematics

Oscillation Criteria For Second-Order Forced Dynamic Equations With Mixed Nonlinearities, Ravi P. Agarwal, Agacik Zafer Jun 2009

Oscillation Criteria For Second-Order Forced Dynamic Equations With Mixed Nonlinearities, Ravi P. Agarwal, Agacik Zafer

Mathematics and System Engineering Faculty Publications

We obtain new oscillation criteria for second-order forced dynamic equations on time scales containing mixed nonlinearities of the form (r(t) Φα (xΔ))Δ + f (t, xσ) = e(t), t ∈ [t0, ∞) T with f(t, x) = q(t)Φα(x) + ∑i=1nqi(t)Φβi (x), Φ* (u) = u *-1u, where [t0, ∞)T is a time scale interval with t0 ∈ T, the functions r, q, qi, e: [t0, ∞)T → ℝ are right-dense continuous with r > 0, σ is the forward jump operator, xσ(t) := x (σ(t)), and β1 > ⋯ > βm > α > βm+1 > ⋯ βn > 0. All results obtained are new even for …

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Variational Analysis In Semi-Infinite And Infinite Programming, I: Stability Of Linear Inequality Systems Of Feasible Solutions, M J. Cánovas, M A. Lopez, Boris S. Mordukhovich, J Parra Jun 2009

Variational Analysis In Semi-Infinite And Infinite Programming, I: Stability Of Linear Inequality Systems Of Feasible Solutions, M J. Cánovas, M A. Lopez, Boris S. Mordukhovich, J Parra

Mathematics Research Reports

This paper concerns applications of advanced techniques of variational analysis and generalized differentiation to parametric problems of semi-infinite and infinite programming, where decision variables run over finite-dimensional and infinite-dimensional spaces, respectively. Part I is primarily devoted to the study of robust Lipschitzian stability of feasible solutions maps for such problems described by parameterized systems of infinitely many linear inequalities in Banach spaces of decision variables indexed by an arbitrary set T. The parameter space of admissible perturbations under consideration is formed by all bounded functions on T equipped with the standard supremum norm. Unless the index set is finite, this …

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A Comparison Of Balanced Truncation Methods For Closed Loop Systems, John R. Singler, Belinda A. Batten Jun 2009

A Comparison Of Balanced Truncation Methods For Closed Loop Systems, John R. Singler, Belinda A. Batten

Mathematics and Statistics Faculty Research & Creative Works

Real-time control of a physical system necessitates controllers that are low order. In this paper, we compare two balanced truncation methods as a means of designing low order compensators for partial differential equation (PDE) systems. The first method is the application of balanced truncation to the compensator dynamics, rather than the state dynamics, as was done in cite{Skelton:1984}. The second method, LQG balanced truncation, applies the balancing technique to the Riccati operators obtained from a specific LQG design. We discuss snapshot-based algorithms for constructing the reduced order compensators and present numerical results for a two dimensional convection diffusion PDE system.

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Finite-Difference And Pseudo-Sprectral Methods For The Numerical Simulations Of In Vitro Human Tumor Cell Population Kinetics, Z. Jackiewicz, Barbara Zubik-Kowal, B. Basse Jun 2009

Finite-Difference And Pseudo-Sprectral Methods For The Numerical Simulations Of In Vitro Human Tumor Cell Population Kinetics, Z. Jackiewicz, Barbara Zubik-Kowal, B. Basse

Mathematics Faculty Publications and Presentations

Pseudo-spectral approximations are constructed for the model equations which describe the population kinetics of human tumor cells in vitro and their responses to radiotherapy or chemotherapy. These approximations are more efficient than finite-difference approximations. The spectral accuracy of the pseudo-spectral method allows us to resolve the model with a much smaller number of spatial grid-points than required for the finite-difference method to achieve comparable accuracy. This is demonstrated by numerical experiments which show a good agreement between predicted and experimental data.

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Research On Fractal Mathematics And Some Application In Mechanics, Yang Xiaojun Jun 2009

Research On Fractal Mathematics And Some Application In Mechanics, Yang Xiaojun

Xiao-Jun Yang

Since Mandelbrot proposed the concept of fractal in 1970s’, fractal has been applied in various areas such as science, economics, cultures and arts because of the universality of fractal phenomena. It provides a new analytical tool to reveal the complexity of the real world. Nowadays the calculus in a fractal space becomes a hot topic in the world. Based on the established definitions of fractal derivative and fractal integral, the fundamental theorems of fractal derivatives and fractal integrals are investigated in detail. The fractal double integral and fractal triple integral are discussed and the variational principle in fractal space has …

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Cutting A Pie Is Not A Piece Of Cake, J. B. Barbanel, S. J. Brams, Walter Stromquist Jun 2009

Cutting A Pie Is Not A Piece Of Cake, J. B. Barbanel, S. J. Brams, Walter Stromquist

Mathematics & Statistics Faculty Works

No abstract provided.

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Circular Nonlinear Subdivision Schemes For Curve Design, Jian-Ao Lian, Yonghui Wang, Yonggao Yang Jun 2009

Circular Nonlinear Subdivision Schemes For Curve Design, Jian-Ao Lian, Yonghui Wang, Yonggao Yang

Applications and Applied Mathematics: An International Journal (AAM)

Two new families of nonlinear 3-point subdivision schemes for curve design are introduced. The first family is ternary interpolatory and the second family is binary approximation. All these new schemes are circular-invariant, meaning that new vertices are generated from local circles formed by three consecutive old vertices. As consequences of the nonlinear schemes, two new families of linear subdivision schemes for curve design are established. The 3-point linear binary schemes, which are corner-cutting depending on the choices of the tension parameter, are natural extensions of the Lane-Riesenfeld schemes. The four families of both nonlinear and linear subdivision schemes are implemented …

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Analysis Of Rotating Flow Around A Growing Protein Crystal, Daniel N. Riahi, Charles W. Obare Jun 2009

Analysis Of Rotating Flow Around A Growing Protein Crystal, Daniel N. Riahi, Charles W. Obare

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

We consider the problem of steady flow around a growing protein crystal in a medium of its solution in a normal gravity environment. The whole flow system is assumed to be rotating with a constant angular velocity about a vertical axis which is anti-parallel to the gravity vector. Convective flow takes place due to the solute depletion around the growing crystal which leads to a buoyancy driven flow. Such convective flow can produce inhomogeneous solute concentration, which subsequently generate non-uniformities in the crystal’s structure finalizing lower quality protein crystal. Using scaling analysis within a diffusion boundary layer around the crystal, …

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Chemchains: A Platform For Simulation And Analysis Of Biochemical Networks Aimed To Laboratory Scientists, Tomáš Helikar, Jim A. Rogers Jun 2009

Chemchains: A Platform For Simulation And Analysis Of Biochemical Networks Aimed To Laboratory Scientists, Tomáš Helikar, Jim A. Rogers

Mathematics Faculty Publications

Background: New mathematical models of complex biological structures and computer simulation software allow modelers to simulate and analyze biochemical systems in silico and form mathematical predictions. Due to this potential predictive ability, the use of these models and software has the possibility to compliment laboratory investigations and help refine, or even develop, new hypotheses. However, the existing mathematical modeling techniques and simulation tools are often difficult to use by laboratory biologists without training in high-level mathematics, limiting their use to trained modelers. Results: We have developed a Boolean network-based simulation and analysis software tool, ChemChains, which combines the advantages of …

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Analytical Solution Of Time-Fractional Advection Dispersion Equation, Tariq O. Salim, Ahmad El-Kahlout Jun 2009

Analytical Solution Of Time-Fractional Advection Dispersion Equation, Tariq O. Salim, Ahmad El-Kahlout

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we get exact solution of the time-fractional advection-dispersion equation with reaction term, where the Caputo fractional derivative is considered of order α ϵ (0,2]. The solution is achieved by using a function transform, Fourier and Laplace transforms to get the formulas of the fundamental solution, which are expressed explicitly in terms of Fox’s H-function by making use of the relationship between Fourier and Mellin transforms. As special cases the exact solutions of time-fractional diffusion and wave equations are also obtained, and the solutions of the integer order equations are mentioned.

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Closed Knight's Tours With Minimal Square Removal For All Rectangular Boards, Joseph Demaio, Thomas Hippchen Jun 2009

Closed Knight's Tours With Minimal Square Removal For All Rectangular Boards, Joseph Demaio, Thomas Hippchen

Faculty Articles

A closed knight's tour of a chessboard uses legal moves of the knight to visit every square exactly once and return to its starting position. In 1991 Schwenk completely classified the rectangular chessboards that admit a closed knight's tour. For a rectangular chessboard that does not contain a closed knight's tour, this paper determines the minimum number of squares that must be removed in order to admit a closed knight's tour. Furthermore, constructions that generate a closed tour once appropriate squares are removed are provided.

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Mehler-Fock Transformation Of Ultradistribution, Deshna Loonker, P. K. Banerji Jun 2009

Mehler-Fock Transformation Of Ultradistribution, Deshna Loonker, P. K. Banerji

Applications and Applied Mathematics: An International Journal (AAM)

This paper deals with the testing function space Z and its dual Z', which is known as ultradistrbution. Some theorems and properties are investigated for the Mehler-Fock transformation and its inverse for the ultradistribution.

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Generalized Shifts On Cartesian Products, M. Rajagopalan, K. Sundaresan Jun 2009

Generalized Shifts On Cartesian Products, M. Rajagopalan, K. Sundaresan

Mathematics and Statistics Faculty Publications

It is proved that if E, F are infinite dimensional strictly convex Banach spaces totally incomparable in a restricted sense, then the Cartesian product E×F with the sum or sup norm does not admit a forward shift. As a corollary it is deduced that there are no backward or forward shifts on the Cartesian product`p1×`p2,1< p16=p2<∞, with the supremum norm thus settling a problem left open in Rajagopalan and Sundaresan in J. Analysis 7 (1999(, 75-81 and also a problem stated as unsolved in Rassias and Sundaresan.

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On Generalized Hurwitz-Lerch Zeta Distributions, Mridula Garg, Kumkum Jain, S. L. Kalla Jun 2009

On Generalized Hurwitz-Lerch Zeta Distributions, Mridula Garg, Kumkum Jain, S. L. Kalla

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we introduce a function which is an extension to the general Hurwitz-Lerch Zeta function. Having defined the incomplete generalized beta type-2 and incomplete generalized gamma functions, some differentiation formulae are established for these incomplete functions. We have introduced two new statistical distributions, termed as generalized Hurwitz-Lerch Zeta beta type-2 distribution and generalized Hurwitz-Lerch Zeta gamma distribution and then derived the expressions for the moments, distribution function, the survivor function, the hazard rate function and the mean residue life function for these distributions. Graphs for both these distributions are given, which reflect the role of shape and scale …

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Sequence Characterization Of Riordan Arrays, Tian-Xiao He, Renzo Sprugnoli Jun 2009

Sequence Characterization Of Riordan Arrays, Tian-Xiao He, Renzo Sprugnoli

Scholarship

In the realm of the Riordan group, we consider the characterization of Riordan arrays by means of the A- and Z-sequences. It corresponds to a horizontal construction of a Riordan array, whereas the traditional approach is through column generating functions. We show how the A- and Z-sequences of the product of two Riordan arrays are derived from those of the two factors; similar results are obtained for the inverse. We also show how the sequence characterization is applied to construct easily a Riordan array. Finally, we give the characterizations relative to some subgroups of the Riordan group, in particular, of …

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Gaussian Perturbations Of Circle Maps: A Spectral Approach, John Mayberry Jun 2009

Gaussian Perturbations Of Circle Maps: A Spectral Approach, John Mayberry

College of the Pacific Faculty Articles

In this work, we examine spectral properties of Markov transition operators corresponding to Gaussian perturbations of discrete time dynamical systems on the circle. We develop a method for calculating asymptotic expressions for eigenvalues (in the zero noise limit) and show that changes to the number or period of stable orbits for the deterministic system correspond to changes in the number of limiting modulus 1 eigenvalues of the transition operator for the perturbed process. We call this phenomenon a λ-bifurcation. Asymptotic expressions for the corresponding eigenfunctions and eigenmeasures are also derived and are related to Hermite functions. © Institute of Mathematical …

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Confidence Intervals For The Ratio Of Two Exponential Means With Applications To Quality Control, James Albert Polcer,Iii Jun 2009

Confidence Intervals For The Ratio Of Two Exponential Means With Applications To Quality Control, James Albert Polcer,Iii

Student Research Conference Select Presentations

We considered the problem of statistical quality control based on the ratio of two population means. We restrict the discussion for two exponential rates, which are commonly used for modeling failure times of components, machines, or systems. Closed form expressions via the moment generation function (MGF) technique will be presented, and numerical examples will be shown using engineering data sets.

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Sequence Characterization Of Riordan Arrays, Tian-Xiao He, Renzo Sprugnoli May 2009

Sequence Characterization Of Riordan Arrays, Tian-Xiao He, Renzo Sprugnoli

Tian-Xiao He

In the realm of the Riordan group, we consider the characterization of Riordan arrays by means of the A- and Z-sequences. It corresponds to a horizontal construction of a Riordan array, whereas the traditional approach is through column generating functions. We show how the A- and Z-sequences of the product of two Riordan arrays are derived from those of the two factors; similar results are obtained for the inverse. We also show how the sequence characterization is applied to construct easily a Riordan array. Finally, we give the characterizations relative to some subgroups of the Riordan group, in particular, of …

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Self Similar Flows In Finite Or Infinite Two Dimensional Geometries, Leonardo Xavier Espin Estevez May 2009

Self Similar Flows In Finite Or Infinite Two Dimensional Geometries, Leonardo Xavier Espin Estevez

Dissertations

This study is concerned with several problems related to self-similar flows in pulsating channels. Exact or similarity solutions of the Navier-Stokes equations are of practical and theoretical importance in fluid mechanics. The assumption of self-similarity of the solutions is a very attractive one from both a theoretical and a practical point of view. It allows us to greatly simplify the Navier-Stokes equations into a single nonlinear one-dimensional partial differential equation (or ordinary differential equation in the case of steady flow) whose solutions are also exact solutions of the Navier-Stokes equations in the sense that no approximations are required in order …

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Discreet Dynamical Population Models : Higher Dimensional Pioneer-Climax Models, Yogesh Joshi May 2009

Discreet Dynamical Population Models : Higher Dimensional Pioneer-Climax Models, Yogesh Joshi

Dissertations

There are many population models in the literature for both continuous and discrete systems. This investigation begins with a general discrete model that subsumes almost all of the discrete population models currently in use. Some results related to the existence of fixed points are proved. Before launching into a mathematical analysis of the primary discrete dynamical model investigated in this dissertation, the basic elements of the model - pioneer and climax species - are described and discussed from an ecological as well as a dynamical systems perspective. An attempt is made to explain why the chosen hierarchical form of the …

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Numerical Detection Of Complex Singularities In Two And Three Dimensions, Kamyar Malakuti May 2009

Numerical Detection Of Complex Singularities In Two And Three Dimensions, Kamyar Malakuti

Dissertations

Singularities often occur in solutions to partial differential equations; important examples include the formation of shock fronts in hyperbolic equations and self-focusing type blow up in nonlinear parabolic equations. Information about formation and structure of singularities can have significant role in interfacial fluid dynamics such as Kelvin-Helmholtz instability, Rayleigh-Taylor instability, and Hele-Shaw flow. In this thesis, we present a new method for the numerical analysis of complex singularities in solutions to partial differential equations. In the method, we analyze the decay of Fourier coefficients using a numerical form fit to ascertain the nature of singularities in two and three-dimensional functions. …

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Approximating Sums Of Infinite Series, Kara Garrison, Thomas E. Price May 2009

Approximating Sums Of Infinite Series, Kara Garrison, Thomas E. Price

ACMS Conference Proceedings 2009

The Euler-Maclaurin summation formula is frequently used to efficiently estimate sums of infinite series of the form $\sum_{j=1}^{\infty}f(j)$. The purpose of this article is to describe a modification of this numerical technique designed to simplify and reduce the computational effort required to obtain an acceptable estimate of the sum. The modified formula is obtained by replacing $f\left( x\right) $ with an easily constructed polynomial like interpolating function $a\left( x\right) $ designed to simplify the calculation of the integral and derivatives associated with Euler-Maclaurin. This approach provides a more tractable algorithm which can be written as a matrix equation. Examples are …

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Are Mathematical Entities Real?, Phillip E. Lestmann May 2009

Are Mathematical Entities Real?, Phillip E. Lestmann

ACMS Conference Proceedings 2009

This talk will introduce ontological questions related to mathematics. After surveying the views of Plato and Artistotle, other possible philosophical perspectives will be considered including realism, nominalism, conceptualism, and empiricism with their relative strengths and weaknesses. The discussion will conclude with a possible biblical foundation for mathematical ontology.

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History Of Mathematics In The Service Of School Mathematics Education, Calvin Jongsma May 2009

History Of Mathematics In The Service Of School Mathematics Education, Calvin Jongsma

ACMS Conference Proceedings 2009

This slide presentation outlines the author's use of history of mathematics in teaching a mathematics-content course to prospective middle school mathematics teachers. A pedagogical rationale for using history of mathematics is given, along with a case study illustrating its use for teaching the topic of ratio and proportion drawing upon the numerical and geometrical theories of such found in Euclid's Elements.

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A Career Preparation Course For Students In Mathematics And Computer Science, Donna Pierce, Peter A. Tucker May 2009

A Career Preparation Course For Students In Mathematics And Computer Science, Donna Pierce, Peter A. Tucker

ACMS Conference Proceedings 2009

As professors, we all want our students to succeed, and to be motivated to study. We all get questions from students that can be boiled down to, "What can I do with X degree?" Certainly, a quick answer is to point students to career websites, or to send them to the career services department on campus. However, we want to do better than that. We want students to learn how to investigate these future directions, and to have them think about their future more holistically--not just an effort to find a job. To that end, we have developed a course …

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Integrating Dynamic Software Into Geometry Courses At Middle School, High School, And College Levels: Ten Lesson Plan And Instruction Material Units Incorporating Geometer's Sketchpad Version 4.07, Jamie Blauw, Lauren Zylstra, Dave Klanderman May 2009

Integrating Dynamic Software Into Geometry Courses At Middle School, High School, And College Levels: Ten Lesson Plan And Instruction Material Units Incorporating Geometer's Sketchpad Version 4.07, Jamie Blauw, Lauren Zylstra, Dave Klanderman

ACMS Conference Proceedings 2009

This paper explores the use of dynamic geometry software (Geometer's Sketchpad) in the teaching and learning of Geometry at the high school and college level. As part of an honors project, two of the authors created a series of lesson activities to address specific geometric concepts. Each lesson implements Geometer's Sketchpad to create an engaging student-centered learning environment.

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A Vision For Acms, James Bradley May 2009

A Vision For Acms, James Bradley

ACMS Conference Proceedings 2009

This paper applies McGrath's and Heller's approach to the consideration of mathematics. It assumes that mathematics is not self-interpreting, but that, looked at from a framework informed by the Christian scriptures, it can be seen as having significant meaning and value and a transcendent purpose. In particular, it presents a classical interpretation of mathematics broadly conceived, presents two approaches to providing warrant for such an interpretation, and explores some implications. It argues, by means of the example of the classical interpretation, that the relationship between mathematics and theology is a viable area of scholarly inquiry encompassing profound and fascinating questions. …

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The Development Of Mathematical And Spiritual Maturity In The Undergraduate Mathematics Curriculum, Angela Hare May 2009

The Development Of Mathematical And Spiritual Maturity In The Undergraduate Mathematics Curriculum, Angela Hare

ACMS Conference Proceedings 2009

Colleges and universities that teach mathematics have a responsibility to develop in students an appreciation of the powerful tools they are studying in the mathematics curriculum. Beyond this fundamental responsibility, the Christian college or university has the richer task of equipping mathematics graduates to use their mathematical knowledge and skills to sharpen their spiritual insight, to serve others, and to promote justice and freedom in society. The growth in mathematical maturity that occurs during the undergraduate years is an asset that enables Christian students of mathematics to participate in the redemptive work of Jesus Christ through their discipline of study. …

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Monoids For Math Majors, Brian D. Beasley May 2009

Monoids For Math Majors, Brian D. Beasley

ACMS Conference Proceedings 2009

Inspired by an MAA PREP workshop on “The Art of Factorization in Multiplicative Structures”, this paper will treat the basics of congruence monoids and arithmetical congruence monoids with their potential for a Modern Algebra or capstone course.

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Professor Peacock's Symbolical Algebra: Glimpses Into The Life And Work Of A Mathematical Reformer, Richard Stout May 2009

Professor Peacock's Symbolical Algebra: Glimpses Into The Life And Work Of A Mathematical Reformer, Richard Stout

ACMS Conference Proceedings 2009

In his 1859 obituary of George Peacock (Royal Society of London, 1859),the nineteenth century mathematician and Dean of Ely Cathedral, his friend and long-time colleague J. F. W. Herschel not only lists Peacock's accomplishments as an educator, a churchman, and a mathematician, but also describes a man who embodies warmth and wisdom, the kind of person you would enjoy knowing and having as a colleague. Writing about Peacock in the Memoirs of the Royal Astronomical Society, Augustus DeMorgan echoes these sentiments when he says that "Whenever a man of safe judgment was wanted, who united kindness and courtesy to a …

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