Physical Sciences and Mathematics Commons^™

Elementary Differential Equations With Boundary Value Problems, William F. Trench

William F. Trench

Elementary Differential Equations with Boundary Value Problems is written for students in science, engineering, and mathematics who have completed calculus through partial differentiation. If your syllabus includes Chapter 10 (Linear Systems of Differential Equations), your students should have some prepa- ration in linear algebra. In writing this book I have been guided by the these principles: An elementary text should be written so the student can read it with comprehension without too much pain. I have tried to put myself in the student’s place, and have chosen to err on the side of too much detail rather than not enough. …

Elementary Differential Equations, William F. Trench

William F. Trench

Elementary Differential Equations with Boundary Value Problems is written for students in science, engineering, and mathematics who have completed calculus through partial differentiation. If your syllabus includes Chapter 10 (Linear Systems of Differential Equations), your students should have some preparation in linear algebra. In writing this book I have been guided by the these principles: An elementary text should be written so the student can read it with comprehension without too much pain. I have tried to put myself in the student’s place, and have chosen to err on the side of too much detail rather than not enough. An …

Student Solutions Manual For Elementary Differential Equations And Elementary Differential Equations With Boundary Value Problems, William F. Trench

William F. Trench

No abstract provided.

Introduction To Real Analysis, William F. Trench

William F. Trench

This is a text for a two-term course in introductory real analysis for junior or senior math- ematics majors and science students with a serious interest in mathematics. Prospective educators or mathematically gifted high school students can also benefit from the mathe- matical maturity that can be gained from an introductory real analysis course. The book is designed to fill the gaps left in the development of calculus as it is usually presented in an elementary course, and to provide the background required for insight into more advanced courses in pure and applied mathematics. The standard elementary calcu- lus sequence …

On The Data Of Images, Lori Ziegelmeier

Lori Beth Ziegelmeier

No abstract provided.

Free-Standing Inflatable Solar Chimney: Experiment And Theory, Peter Vorobieff, Andrea Mammoli, Nima Fathi, Vakhtang Putkaradze

Nima Fathi

Exact P-Adic Orders For Differences Of Motzkin Numbers, Tamas Lengyel

Tamas Lengyel

For any prime p, we establish congruences modulo pn+1 for the difference of the pn+1th and pnth Motzkin numbers and determine the p-adic order of the difference. The results confirm recent conjectures on the order. The applied techniques involve the use of congruences for the differences of certain Catalan numbers and binomial coefficients, congruential identities for sums of Catalan numbers, central binomial and trinomial coefficients, infinite incongruent disjoint covering systems and the solution of congruential recurrences.

Computing, Symbols And Math, Stephen M. Watt

Stephen M. Watt

No abstract provided.

A Chebyshev Pseudo-Spectral Method To Solve The Space-Time Tempered Fractional Diffusion Equation

Cecile M Piret

Predicting Severity And Periodicity Of Mountain Pine Beetle Outbreaks, Jacob P. Duncan

Jacob P Duncan

The relationship between the mountain pine beetle (Dendroctonus ponderosae) and lodgepole pine tree(Pinus contorta) has historically been normative: periodic small scale outbreaks of mountain pine beetle (MPB) would attack and kill old or weakened pine trees which subsequently led to new healthier forest growth. However, since MPB require moderate winter and warm summer to achieve synchronous emergence and successful attacks (Powell & Logan 2005), outbreaks have been more severe in recent decades due to global warming. These outbreaks can increase wildland fire risk and are likely the primary contributor to recent fires in Colorado. MPB-caused forest destruction may have significant …

Some Mathematical Problems In Numerical Relativity, Maria Babiuc-Hamilton, B´Ela Szilagyi, Jeffrey Winicour

Maria Babiuc-Hamilton

The main goal of numerical relativity is the long time simulation of highly nonlinear spacetimes that cannot be treated by perturbation theory. This involves analytic, computational and physical issues. At present, the major impasses to achieving global simulations of physical usefulness are of an analytic/ computational nature. We present here some examples of how analytic insight can lend useful guidance for the improvement of numerical approaches.

Generating A Dynamic Synthetic Population – Using An Age-Structured Two-Sex Model For Household Dynamics, Mohammad-Reza Namazi-Rad, Payam Mokhtarian, Pascal Perez

Payam Mokhtarian

Generating a reliable computer-simulated synthetic population is necessary for knowledge processing and decision-making analysis in agent-based systems in order to measure, interpret and describe each target area and the human activity patterns within it. In this paper, both synthetic reconstruction (SR) and combinatorial optimisation (CO) techniques are discussed for generating a reliable synthetic population for a certain geographic region (in Australia) using aggregated- and disaggregated-level information available for such an area. A CO algorithm using the quadratic function of population estimators is presented in this paper in order to generate a synthetic population while considering a two-fold nested structure for …

Construction Of Spline Type Orthogonal Scaling Functions And Wavelets, Tian-Xiao He, Tung Nguyen, '15

Tian-Xiao He

No abstract provided.

Purchasing Nonprescription Contraceptives: The Underlying Structure Of A Multi-Item Scale, Chris Manolis, Robert Winsor, Sheb True

Robert D. Winsor

The authors develop a multi-item scale measuring attitudes associated with purchasing nonprescription contraceptives. Although contraceptives represent a common as well as consequential purchase for many people, published research has not addressed measures of attitudes associated with this purchase decision. A scale development method is presented measuring both male and female consumer attitudes toward purchasing contraceptives. Ultimately, a multi-item scale demonstrating a high degree of invariance across 2 samples (men and women) is developed.

On The Least Significant P-Adic Digits Of Certain Lucas Numbers, Tamas Lengyel

Tamas Lengyel

We calculate the least significant p-ary digits of certain Lucas numbers Vn = Vn(P,Q)withV0 =2,V1 =PandVn =PVn1QVn2 forn2. Webase our study on an observation regarding these numbers: as m increases, more and more p-adic digits match in Vkpm with integer k 1. We use multi-section identities for generating functions and derive congruences for the underlying sequences.

An Algorithm In Computational Geometry And An Exploration In Computational Topology, Lori Ziegelmeier

Lori Beth Ziegelmeier

No abstract provided.

Critical Buckling Loads Of The Perfect Hollomon’S Power-Law Columns, Dongming Wei, Alejandro Sarria, Mohamed Elgindi

Dongming Wei

In this work, we present analytic formulas for calculating the critical buckling states of some plastic axial columns of constant cross-sections. The associated critical buckling loads are calculated by Euler-type analytic formulas and the associated deformed shapes are presented in terms of generalized trigonometric functions. The plasticity of the material is defined by the Holloman’s power-law equation. This is an extension of the Euler critical buckling loads of perfect elastic columns to perfect plastic columns. In particular, critical loads for perfect straight plastic columns with circular and rectangular cross-sections are calculated for a list of commonly used metals. Connections and …

On The Global Solvability Of A Class Of Fourth-Order Nonlinear Boundary Value Problems, M.B.M. Elgindi, Dongming Wei

Dongming Wei

In this paper we prove the global solvability of a class of fourth-order nonlinear boundary value problems that govern the deformation of a Hollomon’s power-law plastic beam subject to an axial compression and nonlinear lateral constrains. For certain ranges of the acting axial compression force, the solvability of the equations follows from the monotonicity of the fourth order nonlinear differential operator. Beyond these ranges the monotonicity of the operator is lost. It is shown that, in this case, the global solvability may be generated by the lower order nonlinear terms of the equations for a certain type of constrains.

A Priori Lρ Error Estimates For Galerkin Approximations To Porous Medium And Fast Diffusion Equations, Dongming Wei, Lew Lefton

Dongming Wei

Galerkin approximations to solutions of a Cauchy-Dirichlet prob- lem governed by a generalized porous medium equation.

Travelling Wave Solutions Of Burgers' Equation For Gee-Lyon Fluid Flows, Dongming Wei, Ken Holladay

Dongming Wei

In this work we present some analytic and semi-analytic traveling wave solutions of generalized Burger' equation for isothermal unidirectional flow of viscous non-Newtonian fluids obeying Gee-Lyon nonlinear rheological equation. The solution of Burgers' equation for Newtonian flow as a special case. We also derive estimates of shock thickness for non-Newtonian flows.

Analytic And Finite Element Solutions Of The Power-Law Euler-Bernoulli Beams, Dongming Wei, Yu Liu

Dongming Wei

In this paper, we use Hermite cubic finite elements to approximate the solutions of a nonlinear Euler-Bernoulli beam equation. The equation is derived from Hollomon’s generalized Hooke’s law for work hardening materials with the assumptions of the Euler-Bernoulli beam theory. The Ritz-Galerkin finite element procedure is used to form a finite dimensional nonlinear program problem, and a nonlinear conjugate gradient scheme is implemented to find the minimizer of the Lagrangian. Convergence of the finite element approximations is analyzed and some error estimates are presented. A Matlab finite element code is developed to provide numerical solutions to the beam equation. Some …

Some Generalized Trigonometric Sine Functions And Their Applications, Dongming Wei, Yu Liu, Mohamed B. Elgindi

Dongming Wei

In this paper, it is shown that D. Shelupsky's generalized sine function, and various general sine functions developed by P. Drabek, R. Manasevich and M. Otani, P. Lindqvist, including the generalized Jacobi elliptic sine function of S. Takeuchi can be defined by systems of first order nonlinear ordinary differential equations with initial conditions. The structure of the system of differential equations is shown to be related to the Hamilton System in Lagrangian Mechanics. Numerical solutions of the ODE systems are solved to demonstrate the sine functions graphically. It is also demonstrated that the some of the generalized sine functions can …

Existence, Uniqueness, And Numerical Analysis Of Solutions Of A Quasilinear Parabolic Problem, Dongming Wei

Dongming Wei

A quasilinear parabolic problem is studied. By using the method of lines, the existence and uniqueness of a solution to the initial boundary value problem with sufficiently smooth initial conditions are shown. Also given are L2 error estimates for the error between the extended fully discrete finite element solutions and the exact solution.

Finite Element Solutions Of Heat Transfer In Molten Polymer Flow In Tubes With Viscous Dissipation, Dongming Wei, Haibiao Luo

Dongming Wei

This paper presents the results of finite element analysis of a heat transfer problem of flowing polymer melts in a tube with constant ambient temperature. The rheological behavior of the melt is described by a temperature dependent power-law model. Aviscous dissipation term is included in the energy equation. Temperature profiles are obtained for different tube lengths and different entrance temperatures. The results are compared with some similar results in the literature.

Decay Estimates Of Heat Transfer To Melton Polymer Flow In Pipes With Viscous Dissipation, Dongming Wei, Zhenbu Zhang

Dongming Wei

In this work, we compare a parabolic equation with an elliptic equation both of which are used in modeling temperature profile of a power-law polymer flow in a semi-infinite straight pipe with circular cross section. We show that both models are well-posed and we derive exponential rates of convergence of the two solutions to the same steady state solution away from the entrance. We also show estimates for difference between the two solutions in terms of physical data.

A Behavioural Dynamic Model Of The Relative Age Effect, Kawika Pierson, Vittorio Addona, Phillip Yates

Vittorio Addona

No abstract provided.

Syllabus_Lecture_Notes_Collective_Phenomena_In_Laser_Plasmas_Ii_Phy998_Spring_2014, Serge Y. Kalmykov

Serge Youri Kalmykov

High-power laser radiation beams interacting with a rarefied, fully ionized plasmas are essentially unstable. This fact is mainly due to the excitation of various modes of plasma oscillations, most important of which are electron Langmuir waves and ion acoustic waves. The stimulated scattering processes destroy and deplete the pulse in the as it propagates. On the other hand, at the moderate level of instability, spectral properties of the scattered light may serve as optical diagnostics of the pulse propagation dynamics. Knowing the dynamics of the stimulated scattering processes is thus essential for such applications as inertial confinement fusion and laser-plasma …