Applied Mathematics Commons^™

Resume, Anil Kumar Gupta

Dr. Anil Kumar

No abstract provided.

On The Analytical And Numerical Solutions Of Discretized Constrained Optimal Control Problem, Adeshina I. Adekunle

Adeshina I. Adekunle MR

The analytical and numerical solutions of continuous linear quadratic optimal control problem are presented. Numerical solutions are obtained by shooting method and the conjugate gradient method(CGM) via quadratic programming of the discretized continuous optimal control problem. Our results show that both analytical and numerical solutions agree favourably.

Thermocapillary Effects In Driven Dewetting And Self-Assembly Of Pulsed Laser-Irradiated Metallic Films, Mikhail Khenner

Mikhail Khenner

A mathematical model for the evolution of pulsed laser-irradiated, molten metallic films has been developed using the lubrication theory. The heat transfer problem that incorporates the absorbed heat from a single laser beam or the interfering laser beams is solved analytically. Using this temperature field, we derive the 3D long-wave evolution PDE for the film height. To get insights into dynamics of dewetting, we study the 2D version of the evolution equation by means of a linear stability analysis and by numerical simulations. The stabilizing and destabilizing effects of various system parameters, such as the reflectivity, the peak laser beam …

Modeling In Microbial Batch Culture And Its Parameter Identification, Zhaohua Gong, Chongyang Liu, Enmin Feng

Chongyang Liu

In this paper, the nonlinear dynamical system of batch fermentation is investigated in the bioconversion of glycerol to 1,3-propanediol(1,3-PD) by Klebsiella pneumoniae. Taking account of the kinetic behavior and experimental results in the batch cultures, we propose a two-stage dynamical system to formulate the fermentation process. Then some properties of the proposed system are proved. In view of the big errors between observations and numerical simulation results, we subsequently establish a parameter identification model to identify parameters in the system. The identifiability of the model is also discussed. Finally, in order to find the optimal parameters of the identification model, …

The Symmetric Positive Solutions Of Four-Point Problems For Nonlinear Boundary Value Second-Order Differential Equations, Qu Haidong

qu haidong

In this paper, we are concerned with the existence of symmetric positive solutions for second-order differential equations. Under the suitable conditions, the existence and symmetric positive solutions are established by using Krasnoselskii’s fixed-point theorems.

Logically Rectangular Finite Volume Methods With Adaptive Refinement On The Sphere, Marsha Berger, Donna Calhoun, Christiane Helzel, Randall Leveque

Donna Calhoun

The logically rectangular finite volume grids for two-dimensional partial differential equations on a sphere and for three-dimensional problems in a spherical shell introduced recently have nearly uniform cell size, avoiding severe Courant number restrictions. We present recent results with adaptive mesh refinement using the GEOCLAW software and demonstrate well-balanced methods that exactly maintain equilibrium solutions, such as shallow water equations for an ocean at rest over arbitrary bathymetry.

A Pair Of Operator Summation Formulas And Their Applications, Tian-Xiao He, Leetsch C. Hsu, Dongsheng Yin

Tian-Xiao He

Two types of symbolic summation formulas are reformulated using an extension of Mullin–Rota’s substitution rule in [R. Mullin, G.-C. Rota, On the foundations of combinatorial theory: III. Theory of binomial enumeration, in: B. Harris (Ed.), Graph Theory and its Applications, Academic Press, New York, London, 1970, pp. 167–213], and several applications involving various special formulas and identities are presented as illustrative examples.

Electron Self-Injection And Trapping Into An Evolving Plasma Bubble, Serguei Y. Kalmykov, Sunghwan A. Yi, Vladimir N. Khudik, Gennady Shvets

Serge Youri Kalmykov

The blowout (or bubble) regime of laser wakefield acceleration is promising for generating monochromatic high-energy electron beams out of low-density plasmas. It is shown analytically and by particle-in-cell simulations that self-injection of the background plasma electrons into the quasistatic plasma bubble can be caused by slow temporal expansion of the bubble. Sufficient criteria for the electron trapping and bubble’s expansion rate are derived using a semianalytic nonstationary Hamiltonian theory. It is further shown that the combination of bubble’s expansion and contraction results in monoenergetic electron beams.

On Sequences Of Numbers And Polynomials Defined By Linear Recurrence Relations Of Order 2, Tian-Xiao He, Peter J.-S. Shiue

Tian-Xiao He

Here we present a new method to construct the explicit formula of a sequence of numbers and polynomials generated by a linear recurrence relation of order 2. The applications of the method to the Fibonacci and Lucas numbers, Chebyshev polynomials, the generalized Gegenbauer-Humbert polynomials are also discussed. The derived idea provides a generalmethod to construct identities of number or polynomial sequences defined by linear recurrence relations. The applications using the method to solve some algebraic and ordinary differential equations are presented.

A Finite Volume Method For Solving Parabolic Equations On Curved Surfaces, Donna Calhoun

Donna Calhoun

No abstract provided.

Computing Sequences And Series By Recurrence, Stephen J. Sugden

Stephen Sugden

Extract: Many commonly-used mathematical functions may be computed via carefully-constructed recurrence formulas. Sequences are typically defined by giving a formula for the general term. Series is the mathematical name given to partial sums of sequences. In either case we may often take advantage of the great expressive power of recurrence relations to create code which is both lucid and compact. Further, this does not necessarily mean that we must use recursive code. In many instances, iterative code is adequate, and often more efficient.

A Sensitivity Matrix Methodology For Inverse Problem Formulation, Ariel Cintron-Arias, H. T. Banks, Alex Capaldi, Alun L. Lloyd

Alex Capaldi

We propose an algorithm to select parameter subset combinations that can be estimated using an ordinary least-squares (OLS) inverse problem formulation with a given data set. First, the algorithm selects the parameter combinations that correspond to sensitivity matrices with full rank. Second, the algorithm involves uncertainty quantification by using the inverse of the Fisher Information Matrix. Nominal values of parameters are used to construct synthetic data sets, and explore the effects of removing certain parameters from those to be estimated using OLS procedures. We quantify these effects in a score for a vector parameter defined using the norm of the …

Cayley-Dixon Projection Operator For Multi-Univariate Composed Polynomials, Arthur Chtcherba, Deepak Kapur, Manfred Minimair

Manfred Minimair

The Cayley-Dixon formulation for multivariate projection operators (multiples of resultants of multivariate polynomials) has been shown to be efficient (both exper- imentally and theoretically) for simultaneously eliminating many variables from a polynomial system. In this paper, the behavior of the Cayley-Dixon projection op- erator and the structure of Dixon matrices are analyzed for composed polynomial systems constructed from a multivariate system in which each variable is substi- tuted by a univariate polynomial in a distinct variable. Under some conditions, it is shown that a Dixon projection operator of the composed system can be expressed as a power of the resultant …

Multiple Loci Within The Major Histocompatibility Complex Confer Risk Of Psoriasis, Bing-Jian Feng, Liang-Dan Sun, Razieh Soltani-Arabshahi, Anne M. Bowcock, Rajan P. Nair, Philip Stuart, James T. Elder, Steven J. Schrodi, Ann B. Begovich, Goncalo R. Abecasis, Xue-Jun Zhang, Kristina P. Callis Duffin, Gerald G. Krueger, David E. Goldgar

Steven J Schrodi

Psoriasis is a common inflammatory skin disease characterized by thickened scaly red plaques. Previously we have performed a genome-wide association study (GWAS) on psoriasis with 1,359 cases and 1,400 controls, which were genotyped for 447,249 SNPs. The most significant finding was for SNP rs12191877, which is in tight linkage disequilibrium with HLA-Cw*0602, the consensus risk allele for psoriasis. However, it is not known whether there are other psoriasis loci within the MHC in addition to HLA-C. In the present study, we searched for additional susceptibility loci within the human leukocyte antigen (HLA) region through in-depth analyses of the GWAS data; …

Comic Books That Teach Mathematics, Bruce Kessler

Bruce Kessler

During the 2008--2009 academic year, the author embarked on an extremely non-standard curriculum path: developing comic books with embedded mathematics appropriate for 3rd through 6th grade students. With the help of an education professor to measure impact, an elementary-school principal, and talented undergraduate illustrators, this project came to fruition and the comics were implemented in elementary classrooms at Cumberland Trace Elementary in the Warren County School System in Bowling Green, Kentucky. This talk gives the motivation for the idea, introduces the characters, and how the comics integrated the math content into the stories.

Comic Books That Teach Mathematics, Bruce Kessler

Bruce Kessler

During the 2008--2009 academic year, the author embarked on an extremely non-standard curriculum path: developing comic books with embedded mathematics appropriate for 3rd through 6th grade students. With the help of an education professor to measure impact, an elementary-school principal, and talented undergraduate illustrators, this project came to fruition and the comics were implemented in elementary classrooms at Cumberland Trace Elementary in the Warren County School System in Bowling Green, Kentucky. This manuscript gives the history of this idea, the difficulties of developing the content of the comics and getting them illustrated, and the implementation plan in the school.

A …

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

Bruce Kessler

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/\~bruce.kessler/.

Wavelet Deconvolution In A Periodic Setting Using Cross-Validation, Leming Qu, Partha Routh, Kyungduk Ko

Kyungduk Ko

The wavelet deconvolution method WaveD using band-limited wavelets offers both theoretical and computational advantages over traditional compactly supported wavelets. The translation-invariant WaveD with a fast algorithm improves further. The twofold cross-validation method for choosing the threshold parameter and the finest resolution level in WaveD is introduced. The algorithm’s performance is compared with the fixed constant tuning and the default tuning in WaveD.

Bayesian Wavelet-Based Methods For The Detection Of Multiple Changes Of The Long Memory Parameter, Kyungduk Ko

Kyungduk Ko

Long memory processes are widely used in many scientific fields, such as economics, physics, and engineering. Change point detection problems have received considerable attention in the literature because of their wide range of possible applications. Here we describe a wavelet-based Bayesian procedure for the estimation and location of multiple change points in the long memory parameter of Gaussian autoregressive fractionally integrated moving average models (ARFIMA(p, d, q)), with unknown autoregressive and moving average parameters. Our methodology allows the number of change points to be unknown. The reversible jump Markov chain Monte Carlo algorithm is used for posterior inference. The method …

Comparison Between Direct Quadrature Method Of Moments And The Method Of Classes For Bubbly Flow, Brahim Selma, Rachid Bannari, Pierre Proulx

Rachid BANNARI

No abstract provided.

Design And Cfd Analysis Of Mass Transfer And Shear Stresses Distributions In Airlift Reactor, Rachid Bannari, Brahim Selma, Abdelfettah Bannari, Pierre Proulx

Rachid BANNARI

The design, scale-up and performance evaluation of biological reactors require accurate information about the gas-liquid flow dynamics. In this study, we use CFD techniques to investigate important parameters of the multiphase flow dynamics on an initial airlift bioreactor in order to improve its design. Such parameters are distributions of shear stresses and mass transfer. Our initial proposed design of the airlift bioreactor was used for biomass growing. Specifically to produce cellulase enzyme using the fungus Trichoderma Reesei. However, the morphology of the microorganism obtained in this bioreactor was not appropriated to produce cellulase. Since the microorganism morphology presented a small …

The Application Of Fuzzy Logic To The Modeling Of Product Density For Children Ready-Made Clothes, R. W. Hndoosh

R. W. Hndoosh

The main objective of this research is to design a program model for a new product density estimation by implementing fuzzy logic techniques. This model is designed depending upon some of the factors influencing product density. The model consists of conditional rules. Mamdani fuzzy inference system is used for reasoning process because it is an efficient type of fuzzy inference for knowledge to make decision processing. The model is designed using MATLAB as the programming tool for writing the model's programs. The model is applied to real data average taken from Mosul factory for children Ready-Made clothes. The results obtained …

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 …

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 …

A Simulated Annealing Approach To Communication Network Design, Stephen J. Sugden, Marcus Randall, Graham Mcmahon

Marcus Randall

This paper explores the use of the meta-heuristic search algorithm Simulated Annealing for solving a minimum cost network synthesis problem. This problem is a common one in the design of telecommunication networks. The formulation we use models a number of practical problems with hop-limit, degree and capacity constraints. Emphasis is placed on a new approach that uses a knapsack polytope to select amongst a number of pre-computed traffic routes in order to synthesise the network. The advantage of this approach is that a subset of the best routes can be used instead of the whole set, thereby making the process …

Elementary-Level Mathematics Content In Comic Book Format, Bruce Kessler, Janet Tassell, Mary Evans, Cathy Willoughby, Melissa Zimmer

Bruce Kessler

No abstract provided.

Proceedings Of The Scientific Conference On Energy And It At Alvsjo Fair, Stockholm March 11-12, 2009 In Connection With The “Energitinget 2009, Dr. Erik Dahlquist, Dr. Jenny Palm

Dr. Erik Dahlquist

This book contains the proceedings from the Energy and IT conference at Alvsjo Energy conference "Energitinget" arranged by Swedish Energy Agency, with approximately 2500 visitors. The papers contain both technical and social science papers, relating to both energy efficiency in buildings and in industry.

Axiomatic Equilibrium Selection For Generic Two-Player Games, Srihari Govindan, Robert B. Wilson

Robert B Wilson

We impose three conditions on refinements of the Nash equilibria of finite games with perfect recall that select closed connected subsets, called solutions. A. Each equilibrium in a solution uses undominated strategies; B. Each solution contains a quasi-perfect equilibrium; C. The solutions of a game map to the solutions of an embedded game, where a game is embedded if each player's feasible strategies and payoffs are preserved by a multilinear map. We prove for games with two players and generic payoffs that these conditions characterize each solution as an essential component of equilibria in undominated strategies, and thus a stable …

An Immune Self-Adaptive Differential Evolution Algorithm With Application To Estimate Kinetic Parameters For Homogeneous Mercury Oxidation, Chunping Hu, Xuefeng Yan

Chunping Hu

A new version of differential evolution (DE) algorithm, in which immune concepts and methods are applied to determine the parameter setting, named immune self-adaptive differential evolution (ISDE), is proposed to improve the performance of the DE algorithm. During the actual operation, ISDE seeks the optimal parameters arising from the evolutionary process, which enable ISDE to alter the algorithm for different optimization problems and improve the performance of ISDE by the control parameters’ self-adaptation. The performance of the proposed method is studied with the use of nine benchmark problems and compared with original DE algorithm and other well-known self-adaptive DE algorithms. …

A Coupled Cfd-Kinetic Models For Cellulase Production In Airlift Reactor, Rachid Bannari, Abdelfettah Bannari, Brahim Selma, Pierre Proulx

Rachid BANNARI

Cellulase production provides a catalyst for cellulose hydrolysis to glucose, to be used for eventual production of ethanol. The transport of reactants may influence the reaction rate remarkably, for the biological reaction, especially the enzymatic reaction, The transport behavior of the components in a biological system should be considered in the model. In this work, we propose a coupled model between hydrodynamics (twoPhaseEuler- Foam) and a kinetic model for batch and fed-batch cellulase enzyme production by T. reesei from cellulose/lactose substrate which is constructed from literature concepts and laboratory data. Good agreement is obtained between the results and experimental data.