Physical Sciences and Mathematics Commons^™

A Kind Of Symmetrical Iterative Methods To Solve Special Class Of Lcp (M, Q), Sa Edalatpanah, Hs Najafi

SA Edalatpanah

No abstract provided.

Nash Equilibrium Solution Of Fuzzy Matrix Game Solution Of Fuzzy Bimatrix Game, Sa Edalatpanah, Hs Najafi

SA Edalatpanah

In this paper, we propose a method for finding Nash equilibrium of fuzzy games. This method is based on ranking function of fuzzy linear programming which simplifies the solving process of fuzzy Nash equilibrium. Numerical results show that the proposed method is competitive to the state-of-the-art algorithms.

A New Two-Phase Method For The Fuzzy Primal Simplex Algorithm, Sa Edalatpanah, S Shahabi

SA Edalatpanah

Recently, Nasseri et al., [1, 2] proposed fuzzy two-phase method involving fuzzy artificial variables and fuzzy big-M method to obtain an initial fuzzy basic feasible solution to solve the linear programming with fuzzy variables (FVLP) problems. In this paper, we propose a new two-phase method for solving fuzzy linear programming. Our method needs not any artificial variables and has an advantage of the simple implementation. Furthermore this method is more effective and faster than above methods.

New Model For Preconditioning Techniques With Application To The Boundary Value Problems, Sa Edalatpanah, Hs Najafi

SA Edalatpanah

No abstract provided.

A Novel Approach To Processing Fractal Dynamical Systems Using The Yang-Fourier Transforms, Yang Xiaojun

Xiao-Jun Yang

In the present paper, local fractional continuous non-differentiable functions in fractal space are investigated, and the control method for processing dynamic systems in fractal space are proposed using the Yang-Fourier transform based on the local fractional calculus. Two illustrative paradigms for control problems in fractal space are given to elaborate the accuracy and reliable results.

On Soliton Interactions For A Hierarchy Of Generalized Heisenberg Ferromagnetic Models On Su(3)/S(U(1) $\Times$ U(2)) Symmetric Space, Vladimir Gerdjikov, Georgi Grahovski, Alexander Mikhailov, Tihomir Valchev

Articles

We consider an integrable hierarchy of nonlinear evolution equations (NLEE) related to linear bundle Lax operator L. The Lax representation is Z2 \times Z2 reduced and is naturally associated with the symmetric space SU(3)/S(U(1) \times U(2)). The simplest nontrivial equation in the hierarchy is a generalization of Heisenberg ferromagnetic model. We construct the N-soliton solutions for an arbitrary member of the hierarchy by using the Zakharov-Shabat dressing method with an appropriately chosen dressing factor. Two types of soliton solutions: quadruplet and doublet solitons are found. The one-soliton solutions of NLEEs with even and odd dispersion laws have different properties. In …

Exact Lambda-Numbers Of Generalized Petersen Graphs Of Certain Higher-Orders And On Mobius Strips, Sarah Spence Adams, Paul Booth, Harold Jaffe, Denise Troxell, Luke Zinnen

Sarah Spence Adams

An L(2,1)-labeling of a graph G is an assignment f of nonnegative integers to the vertices of G such that if vertices x and y are adjacent, |f(x)−f(y)|≥2, and if x and y are at distance two, |f(x)−f(y)|≥1. The λ-number of Gis the minimum span over all L(2,1)-labelings of G. A generalized Petersen graph (GPG) of order n consists of two disjoint copies of cycles on n vertices together with a perfect matching between the two vertex sets. By …

A Doubling Method For The Generalized Lambda Distribution, Todd C. Headrick, Mohan D. Pant

Mohan Dev Pant

This paper introduces a new family of generalized lambda distributions (GLDs) based on a method of doubling symmetric GLDs. The focus of the development is in the context of L-moments and L-correlation theory. As such, included is the development of a procedure for specifying double GLDs with controlled degrees of L-skew, L-kurtosis, and L-correlations. The procedure can be applied in a variety of settings such as modeling events and Monte Carlo or simulation studies. Further, it is demonstrated that estimates of L-skew, L-kurtosis, and L-correlation are substantially superior to conventional product-moment estimates of skew, kurtosis, and Pearson correlation in terms …

Effects Of Stochastic Freshwater Flux On The Atlantic Thermohaline Circulation, Alyssa Pampell, Alejandra Aceves

Mathematics Research

No abstract provided.

Heterogeneous Multiscale Modeling Of Advection-Diffusion Problems, David J. Gardner, Daniel R. Reynolds

Mathematics Research

No abstract provided.

Numerical Solution Of Integral Equations In Solidification And Laser Melting, Elizabeth Case, Johannes Tausch

Mathematics Research

No abstract provided.

Multilevel Schur Complement Preconditioner For Multi-Physics Simulations, Hilari Tiedeman, Daniel Reynolds

Mathematics Research

No abstract provided.

The Immersed Interface Method For Two-Fluid Problems, Miguel Uh, Sheng Xu

Mathematics Research

No abstract provided.

Block Preconditioning Of Stiff Implicit Models For Radiative Ionization In The Early Universe, Daniel R. Reynolds, Robert Harkness, Geoffrey So, Michael L. Norman

Mathematics Research

No abstract provided.

On The Stability Of A Microstructure Model, Mihhail Berezovski, Arkadi Berezovski

Publications

Abstract

The asymptotic stability of solutions of the Mindlin-type microstructure model for solids is analyzed in the paper. It is shown that short waves are asymptotically stable even in the case of a weakly non-convex free energy dependence on microdeformation.

Research highlights

The Mindlin-type microstructure model cannot describe properly short wave propagation in laminates. A modified Mindlin-type microstructure model with weakly non-convex free energy resolves this discrepancy. It is shown that the improved model with weakly non-convex free energy is asymptotically stable for short waves.

Estimation Of Performance Indices For The Planning Of Sustainable Transportation Systems, Pankaj Maheshwari, Alexander Paz, Pushkin Kachroo

Graduate Publications & Presentations

What is sustainable transportation system?

Fulfill the needs of current generations without compromising the ability of future generations

Utilize resources without compromising their health and productivity Leads to development that improves quality of life

Assimilate economic, ecological, social, and bio-physical components of resource ecosystems

Minimize the use of renewable and non-renewable resources, provide affordability and equity between generations

Characterizing Tukey H And Hh-Distributions Through L-Moments And The L-Correlation, Todd C. Headrick, Mohan D. Pant

Mohan Dev Pant

This paper introduces the Tukey family of symmetric h and asymmetric hh-distributions in the contexts of univariate L-moments and the L-correlation. Included is the development of a procedure for specifying nonnormal distributions with controlled degrees of L-skew, L-kurtosis, and L-correlations. The procedure can be applied in a variety of settings such as modeling events (e.g., risk analysis, extreme events) and Monte Carlo or simulation studies. Further, it is demonstrated that estimates of L-skew, L-kurtosis, and L-correlation are substantially superior to conventional product-moment estimates of skew, kurtosis, and Pearson correlation in terms of both relative bias and efficiency when heavy-tailed distributions …

Two Integration Of Faith And Mathematics Projects For Freshmen Mathematics Majors, Nicholas J. Willis

Faculty Publications - Department of Mathematics

Two projects will be presented that integrate faith and Mathematics in a freshman Introduction to Proofs class at George Fox University. The first project asks students to look at the life of a Christian Mathematician. The focus of this project is to show students that many great mathematicians also had immense faith. The second project asks students to take a close look at their own life. How do they plan to live a life of Christian faith in their chosen profession? Both projects are designed to encourage students to look at their careers in Mathematics as a vocation.

Singular Points Of Reducible Sextic Curves, David A. Weinberg, Nicholas J. Willis

Faculty Publications - Department of Mathematics

No abstract provided.

A Zeta Function For Juggling Sequences, Carsten Elsner, Dominic Klyve, Erik R. Tou

Mathematics Faculty Scholarship

We give a new generalization of the Riemann zeta function to the set of b-ball juggling sequences. We develop several properties of this zeta function, noting among other things that it is rational in b^−s. We provide a meromorphic continuation of the juggling zeta function to the entire complex plane (except for a countable set of singularities) and completely enumerate its zeroes. For most values of b, we are able to show that the zeroes of the b-ball zeta function are located within a critical strip, which is closely analogous to that of the Riemann zeta function.

Delay-Periodic Solutions And Their Stability Using Averaging In Delay-Differential Equations, With Applications, Thomas W. Carr, Richard Haberman, Thomas Erneux

Mathematics Research

Using the method of averaging we analyze periodic solutions to delay-differential equations, where the period is near to the value of the delay time (or a fraction thereof). The difference between the period and the delay time defines the small parameter used in the perturbation method. This allows us to consider problems with arbitrarily size delay times or of the delay term itself. We present a general theory and then apply the method to a specific model that has application in disease dynamics and lasers.

Influence Of Damping On Hyperbolic Equations With Parabolic Degeneracy, Katarzyna Saxton, Ralph Saxton

Mathematics Faculty Publications

This paper examines the effect of damping on a nonstrictly hyperbolic 2 x 2 system. It is shown that the growth of singularities is not restricted as in the strictly hyperbolic case where dissipation can be strong enough to preserve the smoothness of solutions globally in time. Here, irrespective of the stabilizing properties of damping, solutions are found to break down in finite time on a line where two eigenvalues coincide in state space.

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

Mathematics Faculty Publications

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

Mathematics Faculty Publications

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.

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

Mathematics Faculty Publications

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.

An H1 Model For Inextensible Strings, Stephen C. Preston, Ralph Saxton

Mathematics Faculty Publications

We study geodesics of the H¹ Riemannian metric (see article for equation) on the space of inextensible curves (see article for equation). This metric is a regularization of the usual L² metric on curves, for which the submanifold geometry and geodesic equations have been analyzed already. The H¹ geodesic equation represents a limiting case of the Pochhammer-Chree equation from elasticity theory. We show the geodesic equation is C^∞ in the Banach topology C¹ ([0,1], R²), and thus there is a smooth Riemannian exponential map. Furthermore, if we hold one of the curves fixed, …

Blow-Up Of Solutions To The Generalized Inviscid Proudman-Johnson Equation, Alejandro Sarria, Ralph Saxton

Mathematics Faculty Publications

For arbitrary values of a parameter --- finite-time blowup of solutions to the generalized, inviscid Proudman Johnson equation is studied via a direct approach which involves the derivation of representation formulae for solutions to the problem.

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

Mathematics Faculty Publications

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 …

Equivariant Degenerations Of Spherical Modules For Groups Of Type A, Stavros Argyrios Papadakis, Bart Van Steirteghem

Publications and Research

Let G be a complex reductive algebraic group. Fix a Borel subgroup B of G and a maximal torus T in B. Call the monoid of dominant weights L+ and let S be a finitely generated submonoid of L+. V. Alexeev and M. Brion introduced a moduli scheme MS which classifies affine G-varieties X equipped with a T-equivariant isomorphism SpecC[X]U → SpecC[S], where U is the unipotent radical of B. Examples of MS have been obtained by S. Jansou, P. Bravi and S. Cupit-Foutou. In this paper, we prove that MS is isomorphic to an affine space when S is …

Investigating Mountain Waves In Mtm Image Data At Cerro Pachon, Chile, Neal R. Criddle, M. J. Taylor, P.-D. Pautet, Y. Zhao, G. Swenson, A. Liu

Neal R Criddle

Gravity waves are important drivers of chemical species mixing, energy and momentum transfer into the MLT (~80 - 100 km) region. As part of a collaborative program involving instruments from several institutions Utah State University has operated a Mesospheric Temperature Mapper (MTM) at the new Andes Lidar Observatory (ALO) on Cerro Pachon (30.2°S, 70.7°W) Since August 2009. A primary goal of this program is to quantify the impact of mountain waves on the MLT region. The Andes region is an excellent natural laboratory for investigating gravity wave influences on the MLT region, especially the study of mountain waves, created by …