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Articles 5941 - 5970 of 7941

Full-Text Articles in Applied Mathematics

Optimization Models For Designing Spatially Compact Ecological Reserve Systems, Lakmali Weerasena Aug 2009

Optimization Models For Designing Spatially Compact Ecological Reserve Systems, Lakmali Weerasena

All Theses

Over the past decades, a number of mathematical models and solution techniques have been developed to preserve reserve sites for species and their natural habitats. Two optimization models for designing spatially compact ecological reserve systems are addressed here as zero-one integer programming problems. These formulations have a bicriteria objective function that is a combination of both boundary length and distance. The two formulations cluster the sites into a relatively small number of compact groups while preserving a required number of sites that contain a certain species using a given amount of resources. Two general types of approaches have been developed …

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Variations On Graph Products And Vertex Partitions, Jobby Jacob Aug 2009

Variations On Graph Products And Vertex Partitions, Jobby Jacob

All Dissertations

In this thesis we investigate two graph products called double vertex graphs and complete double vertex graphs, and two vertex partitions called dominator partitions and rankings.
We introduce a new graph product called the complete double vertex graph and study its properties. The complete double vertex graph is a natural extension of the Cartesian product and a generalization of the double vertex graph.
We establish many properties of complete double vertex graphs, including results involving the chromatic number of a complete double vertex graph and the characterization of planar complete double vertex graphs. We also investigate the important problem of …

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Factoring Polynomials And Groebner Bases, Genhua (Yinhua) Guan Aug 2009

Factoring Polynomials And Groebner Bases, Genhua (Yinhua) Guan

All Dissertations

Factoring polynomials is a central problem in computational algebra and number theory and is a basic routine in most
computer algebra systems (e.g. Maple, Mathematica, Magma, etc). It has been extensively studied
in the last few decades by many mathematicians and computer scientists. The main approaches include Berlekamp's method
(1967) based on the kernel of Frobenius map, Niederreiter's method (1993) via an ordinary differential equation,
Zassenhaus's modular approach (1969), Lenstra, Lenstra and Lovasz's lattice reduction (1982), and Gao's method via a partial differential equation (2003). These methods and their recent improvements due to van Hoeij (2002) and
Lecerf et al …

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Quality Representation In Multiobjective Programming, Stacey Faulkenberg Aug 2009

Quality Representation In Multiobjective Programming, Stacey Faulkenberg

All Dissertations

In recent years, emphasis has been placed on generating quality representations of the nondominated set of multiobjective programming problems. This manuscript presents two methods for generating discrete representations with equidistant points for multiobjective programs with solution sets determined by convex cones. The Bilevel Controlled Spacing (BCS) method has a bilevel structure with the lower-level generating the nondominated points and the upper-level controlling the spacing. The Constraint Controlled Spacing (CCS) method is based on the epsilon-constraint method with an additional constraint to control the spacing of generated points. Both methods (under certain assumptions) are proven to produce (weakly) nondominated points. Along …

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Asymptotics Of Families Of Polynomials And Sums Of Hurwitz Class Numbers, Timothy Flowers Aug 2009

Asymptotics Of Families Of Polynomials And Sums Of Hurwitz Class Numbers, Timothy Flowers

All Dissertations

In a note in the American Mathematical Monthly in 1960, Strodt mentions a way to prove both the Euler-Maclaurin summation formula and the Boole summation formula using operators. In a 2009 article in the Monthly, Borwein, Calkin, and Manna expand on this idea. Therein, they define Strodt operators and Strodt polynomials and show that the classical Bernoulli polynomials and Euler polynomials are examples of Strodt polynomials.
It is well known that both Bernoulli polynomials and Euler polynomials on a fixed interval are asymptotically sinusoidal. Borwein, Calkin, and Manna show that a similar result holds for the uniform Strodt polynomials. We …

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Discrete Dynamics Over Finite Fields, Jang-Woo Park Aug 2009

Discrete Dynamics Over Finite Fields, Jang-Woo Park

All Dissertations

A dynamical system consists of a set V and a map f : V → V . The primary goal is to characterize points in V according to their limiting behaviors under iteration of the map f . Especially understanding dynamics of nonlinear maps is an important but difficult problem, and there are not many methods available. This work concentrates on dynamics of certain nonlinear maps over finite fields. First we study monomial dynamics over finite fields. We show that determining the number of fixed points of a boolean monomial dynamics is #P–complete problem and consider various cases in which …

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Using Works Of Visual Art To Teach Matrix Transformations, James Luke Akridge, Rachel Bowman, Peter Hamburger, Bruce Kessler Jul 2009

Using Works Of Visual Art To Teach Matrix Transformations, James Luke Akridge, Rachel Bowman, Peter Hamburger, Bruce Kessler

Mathematics Faculty Publications

The authors present a modern technique for teaching matrix transformations on $\R^2$ that incorporates works of visual art and computer programming. Two of the authors were undergraduate students in Dr. Hamburger's linear algebra class, where this technique was implemented as a special project for the students. The two students generated the images seen in this paper, and the movies that can be found on the accompanying webpage www.wku.edu/\~{\space}bruce.kessler/.

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Development Of Scoring Rubrics And Pre-Service Teachers Ability To Validate Mathematical Proofs, Timothy J. Middleton Jul 2009

Development Of Scoring Rubrics And Pre-Service Teachers Ability To Validate Mathematical Proofs, Timothy J. Middleton

Mathematics & Statistics ETDs

The basic aim of this exploratory research study was to determine if a specific instructional strategy, that of developing scoring rubrics within a collaborative classroom setting, could be used to improve pre-service teachers facility with proofs. During the study, which occurred in a course for secondary mathematics teachers, the primary focus was on creating and implementing a scoring rubric, rather than on direct instruction about proofs. In general, the study had very mixed results. Statistically, the quantitative data indicated no significant improvement occurred in participants' ability to validate proofs. However, the qualitative results and the considerable improvement by some participants …

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A Semilinear Wave Equation With Smooth Data And No Resonance Having No Continuous Solution, Jose F. Caicedo, Alfonso Castro Jul 2009

A Semilinear Wave Equation With Smooth Data And No Resonance Having No Continuous Solution, Jose F. Caicedo, Alfonso Castro

All HMC Faculty Publications and Research

We prove that a boundary value problem for a semilinear wave equation with smooth nonlinearity, smooth forcing, and no resonance cannot have continuous solutions. Our proof shows that this is due to the non-monotonicity of the nonlinearity.

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Variational Analysis In Semi-Infinite And Infinite Programming, Ii: Necessary Optimality Conditions, M J. Cánovas, M A. Lopez, Boris S. Mordukhovich, J Parra Jul 2009

Variational Analysis In Semi-Infinite And Infinite Programming, Ii: Necessary Optimality Conditions, 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 problems of semi-infinite and infinite programming with feasible solution sets defined by parameterized systems of infinitely many linear inequalities of the type intensively studied in the preceding development [5] from our viewpoint of robust Lipschitzian stability. We present meaningful interpretations and practical examples of such models. The main results establish necessary optimality conditions for a broad class of semi-infinite and infinite programs, where objectives are generally described by nonsmooth and nonconvex functions on Banach spaces and where infinite constraint inequality systems are indexed by arbitrary sets. …

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Modeling And Analysis Of Biological Populations, Joan Lubben Jul 2009

Modeling And Analysis Of Biological Populations, Joan Lubben

Department of Mathematics: Dissertations, Theses, and Student Research

Asymptotic and transient dynamics are both important when considering the future population trajectory of a species. Asymptotic dynamics are often used to determine whether the long-term trend results in a stable, declining or increasing population and even provide possible directions for management actions. Transient dynamics are important for estimating invasion speed of non-indigenous species, population establishment after releasing biocontrol agents, or population management after a disturbance like fire. We briefly describe here the results in this thesis.

(1) We consider asymptotic dynamics using discrete time linear population models of the form n(t + 1) = An(t) where …

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On The Rigidity Of The Cotangent Complex At The Prime 2, James M. Turner Jul 2009

On The Rigidity Of The Cotangent Complex At The Prime 2, James M. Turner

University Faculty Publications and Creative Works

In [D. Quillen, On the (co)homology of commutative rings, Proc. Symp. Pure Math. 17 (1970) 65-87; L. Avramov, Locally complete intersection homomorphisms and a conjecture of Quillen on the vanishing of cotangent homology, Annals of Math. 2 (150) (1999) 455-487] a conjecture was posed to the effect that if R → A is a homomorphism of Noetherian commutative rings then the flat dimension, as defined in the derived category of A-modules, of the associated cotangent complex LA / R satisfies: fdA LA / R < ∞ {long rightwards double arrow} fdA LA / R ≤ 2. The aim of this paper is to initiate an approach for solving this conjecture when R has characteristic 2 using simplicial algebra techniques. To that end, we obtain two results. First, we prove that the conjecture can be reframed in terms of certain nilpotence properties for the divided square γ2 and the André operation θ{symbol} as it acts on TorR (A, ℓ), ℓ any residue field of A. Second, we prove the conjecture is valid in two cases: when fdR A < ∞ and when R is a Cohen-Macaulay ring.

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An Adaptive Method For Calculating Blow-Up Solutions, Charles F. Touron Jul 2009

An Adaptive Method For Calculating Blow-Up Solutions, Charles F. Touron

Mathematics & Statistics Theses & Dissertations

Reactive-diffusive systems modeling physical phenomena in certain situations develop a singularity at a finite value of the independent variable referred to as "blow-up." The attempt to find the blow-up time analytically is most often impossible, thus requiring a numerical determination of the value. The numerical methods often use a priori knowledge of the blow-up solution such as monotonicity or self-similarity. For equations where such a priori knowledge is unavailable, ad hoc methods were constructed. The object of this research is to develop a simple and consistent approach to find numerically the blow-up solution without having a priori knowledge or resorting …

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Caching And Visualizing Statistical Analyses, Roger D. Peng, Duncan Temple Lang Jun 2009

Caching And Visualizing Statistical Analyses, Roger D. Peng, Duncan Temple Lang

Johns Hopkins University, Dept. of Biostatistics Working Papers

We present the cacher and CodeDepends packages for R, which provide tools for (1) caching and analyzing the code for statistical analyses and (2) distributing these analyses to others in an efficient manner over the web. The cacher package takes objects created by evaluating R expressions and stores them in key-value databases. These databases of cached objects can subsequently be assembled into “cache packages” for distribution over the web. The cacher package also provides tools to help readers examine the data and code in a statistical analysis and reproduce, modify, or improve upon the results. In addition, readers can easily …

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Sum Rules And Universality In Electron-Modulated Acoustic Phonon Interaction In A Free-Standing Semiconductor Plate, Shigeyasu Uno, Darryl H. Yong, Nobuya Mori Jun 2009

Sum Rules And Universality In Electron-Modulated Acoustic Phonon Interaction In A Free-Standing Semiconductor Plate, Shigeyasu Uno, Darryl H. Yong, Nobuya Mori

All HMC Faculty Publications and Research

Analysis of acoustic phonons modulated due to the surfaces of a free-standing semiconductor plate and their deformation-potential interaction with electrons are presented. The form factor for electron-modulated acoustic phonon interaction is formulated and analyzed in detail. The form factor at zero in-plane phonon wave vector satisfies sum rules regardless of electron wave function. The form factor is larger than that calculated using bulk phonons, leading to a higher scattering rate and lower electron mobility. When properly normalized, the form factors lie on a universal curve regardless of plate thickness and material.

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A Space Topologized By Functions From Omega To Omega, Akira Iwasa Jun 2009

A Space Topologized By Functions From Omega To Omega, Akira Iwasa

Computer Science and Mathematics Faculty Publications

No abstract provided.

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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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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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Analytical Solution For Nonlinear Gas Dynamic Equation By Homotopy Analysis Method, Hossein Jafari, Changbum Chun, S. Seifi, M. Saeidy Jun 2009

Analytical Solution For Nonlinear Gas Dynamic Equation By Homotopy Analysis Method, Hossein Jafari, Changbum Chun, S. Seifi, M. Saeidy

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, the Homotopy Analysis Method (HAM) is used to implement the homogeneous gas dynamic equation. The analytical solution of this equation is calculated in form of a series with easily computable components.

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Modeling And Analysis Of The Spread Of Japanese Encephalitis With Environmental Effects, Ram Naresh, Surabhi Pandey Jun 2009

Modeling And Analysis Of The Spread Of Japanese Encephalitis With Environmental Effects, Ram Naresh, Surabhi Pandey

Applications and Applied Mathematics: An International Journal (AAM)

A nonlinear mathematical model for the spread of Japanese Encephalitis, caused by infected mosquito feeding on susceptible human population incorporating demographic and environmental factors is proposed and analyzed. In the modeling process, it is assumed that the growth rates of reservoir animal population and vector mosquito population are enhanced due to environmental discharges caused by human population related factors. The model is analyzed by stability theory of differential equations and computer simulation. Both the disease-free and the endemic equilibria are found and their stability is investigated. It is found that whenever the disease-free equilibrium is locally asymptotically stable, the endemic …

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Linear Stability Of Thermosolutal Convection In A Micropolar Fluid Saturating A Porous Medium, R Reena, U. S. Rana Jun 2009

Linear Stability Of Thermosolutal Convection In A Micropolar Fluid Saturating A Porous Medium, R Reena, U. S. Rana

Applications and Applied Mathematics: An International Journal (AAM)

In the present paper, the theoretical investigation of the double-diffusive convection in a micropolar fluid layer heated and soluted from below saturating a porous medium is considered. For a flat fluid layer contained between two free boundaries, an exact solution is obtained. A linear stability analysis theory and normal mode analysis method have been used. For the case of stationary convection, the effect of various parameters like medium permeability, solute gradient and micropolar parameters (i.e., coupling parameter, spin diffusion parameter, micropolar heat conduction parameter and micropolar solute parameter arises due to coupling between spin and solute fluxes) has been analyzed …

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Effects Of Hematocrit On Impedance And Shear Stress During Stenosed Artery Catheterization, V. P. Srivastava, Rati Rastogi Jun 2009

Effects Of Hematocrit On Impedance And Shear Stress During Stenosed Artery Catheterization, V. P. Srivastava, Rati Rastogi

Applications and Applied Mathematics: An International Journal (AAM)

The flow of blood through a stenosed catheterized artery has been studied. To observe the effects of hematocrit, blood has been represented by a two-phase macroscopic model (i.e., a suspension of red cells in plasma). It is found that for any given catheter size, the impedance increases with hematocrit and also for a given hematocrit, the same increases with the catheter size. In the stenotic region, the wall shear stress increases in the upstream of the stenosis throat and decreases in the downstream in an uncatheterized artery but the same possesses an opposite character in the case of a catheterized …

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Variational Iteration Method For Solving Telegraph Equations, Syed T. Mohyud-Din, Muhammad A. Noor, Khalida I. Noor Jun 2009

Variational Iteration Method For Solving Telegraph Equations, Syed T. Mohyud-Din, Muhammad A. Noor, Khalida I. Noor

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we apply the variational iteration method (VIM) for solving telegraph equations, which arise in the propagation of electrical signals along a telegraph line. The suggested algorithm is more efficient and easier to handle as compare to the decomposition method. Numerical results show the efficiency and accuracy of the proposed VIM.

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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

Applications and Applied Mathematics: An International Journal (AAM)

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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Effect Of Glycocalyx On Red Blood Cell Motion In Capillary Surrounded By Tissue, Rekha Bali, Swati Mishra, P. N. Tandon Jun 2009

Effect Of Glycocalyx On Red Blood Cell Motion In Capillary Surrounded By Tissue, Rekha Bali, Swati Mishra, P. N. Tandon

Applications and Applied Mathematics: An International Journal (AAM)

The aim of the paper is to develop a simple model for capillary tissue fluid exchange system to study the effect of glycocalyx layer on the single file flow of red cells. We have considered the channel version of an idealized Krogh capillary-tissue exchange system. The glycocalyx and the tissue are represented as porous layers with different property parametric values. Hydrodynamic Lubrication theory is used to compute the squeezing flow of plasma within the small gap between the cell and the glycocalyx layer symmetrically surrounded by the tissue. The system of non linear partial differential equations has been solved using …

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A New Approach To Improve Inconsistency In The Analytical Hierarchy Process, Morteza Rahmami, Hamidreza Navidi Jun 2009

A New Approach To Improve Inconsistency In The Analytical Hierarchy Process, Morteza Rahmami, Hamidreza Navidi

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a new approach based on the generalized Purcell method for solving a system of homogenous linear equations is applied to improve near consistent judgment matrices. The proposed method relies on altering the components of the pairwise comparison matrix in such a way that the resulting sequences of improved matrices approach a consistent matrix. The complexity of the proposed method, together with examples, shows less cost and better results in computation than the methods in practice.

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Stability Of An Age-Structured Seir Epidemic Model With Infectivity In Latent Period, Xue-Zhi Li, Bin Fang Jun 2009

Stability Of An Age-Structured Seir Epidemic Model With Infectivity In Latent Period, Xue-Zhi Li, Bin Fang

Applications and Applied Mathematics: An International Journal (AAM)

We study an age-structured SEIR epidemic model with infectivity in the latent period. By using the theory and methods of Differential and Integral Equations, the explicit expression for the basic reproductive number R0 is first derived. It is shown that the disease-free equilibrium is locally and globally asymptotically stable if R0 < 1. It is then proved that only one endemic equilibrium exists if R0 > 1 and its stability conditions are also given.

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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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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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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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