Applied Mathematics Commons^™

Effect Of Network Structure On The Stability Margin Of Large Vehicle With Distributed Control, He Hao, Prabir Barooah, J. J. P. Veerman

Mathematics and Statistics Faculty Publications and Presentations

We study the problem of distributed control of a large network of double-integrator agents to maintain a rigid formation. A few lead vehicles are given information on the desired trajectory of the formation; while every other vehicle uses linear controller which only depends on relative position and velocity from a few other vehicles, which are called its neighbors. A predetermined information graph defines the neighbor relationships. We limit our attention to information graphs that are D-dimensional lattices, and examine the stability margin of the closed loop, which is measured by the real part of the least stable eigenvalue of …

Holomorphic Hardy Space Representations For Convex Domains In Cn, Jennifer West Paulk

Graduate Theses and Dissertations

This thesis deals with Hardy Spaces of holomorphic functions for a domain in several complex variables, that is, when the complex dimension is greater than or equal to two. The results we obtain are analogous to well known theorems in one complex variable. The domains we are concerned with are strongly convex with real boundary of class C^2. We obtain integral representations utilizing the Leray kernel for Hardy space (p=1) functions on such domains D. Next we define an operator to prove the non-tangential limits of a function in Hardy space (p between 1 and infinity, inclusive) of domain D …

A Comprehensive Uncertainty Analysis And Method Of Geometric Calibration For A Circular Scanning Airborne Lidar, Michael Oliver Gonsalves

Dissertations

This dissertation describes an automated technique for ascertaining the values of the geometric calibration parameters of an airborne lidar. A least squares approach is employed that adjusts the point cloud to a single planar surface which could be either a narrow airport runway or a dynamic sea surface. Going beyond the customary three boresight angles, the proposed adjustment can determine up to eleven calibration parameters to a precision that renders a negligible contribution to the point cloud’s positional uncertainty.

Presently under development is the Coastal Zone Mapping and Imaging Lidar (CZMIL), which, unlike most contemporary systems that use oscillating mirrors …

On Some Fractional Integral Operators Involving Generalized Gauss Hypergeometric Functions, N. Virchenko, O. Lisetska, S. L. Kalla

Applications and Applied Mathematics: An International Journal (AAM)

The object of this paper is to give a generalization of Gauss hypergeometric function, and to investigate its basic properties. Further, we define some fractional integral operators and their inverses in terms of the Mellin transform. Several well known integral operators, including Saigo operators can be derived from the results established here.

Exact Solutions Of The Generalized- Zakharov (Gz) Equation By The Infinite Series Method, N. Taghizadeh, M. Mirzazadeh, F. Farahrooz

Applications and Applied Mathematics: An International Journal (AAM)

The infinite series method is an efficient method for obtaining exact solutions of some nonlinear partial differential equations. This method can be applied to nonintegrable equations as well as to integrable ones. In this paper, the direct algebraic method is used to construct new exact solutions of generalized- Zakharov equation.

Application Of Differential Transform Method To The Generalized Burgers–Huxley Equation, J. Biazar, F. Mohammadi

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, the differential transform method (DTM) will be applied to the generalized Burgers-Huxley equation, and some special cases of the equation, say, Huxley equation and Fitzhugh-Nagoma equation. The DTM produces an approximate solution for the equation, with few and easy computations. Numerical comparison between differential transform method, Adomian decomposition method and Variational iteration method for Burgers-Huxley, Huxley equation and Fitzhugh-Nagoma equation reveal that differential transform method is simple, accurate and efficient.

A New Method For Fuzzy Critical Path Analysis In Project Networks With A New Representation Of Triangular Fuzzy Numbers, Amit Kumar, Parmpreet Kaur

Applications and Applied Mathematics: An International Journal (AAM)

The method for finding fuzzy optimal solution of fully fuzzy critical path (FFCP) problems i.e., critical path problems in which all the parameters are represented by fuzzy numbers, is at best scant; possibly non-existent. In this paper, a method is proposed to find the fuzzy optimal solution of FFCP problems, together with a new representation of triangular fuzzy numbers. This paper will show the advantages of using, the proposed representation over the existing representations of triangular fuzzy numbers and will present with great clarity the proposed method and illustrate its application to FFCP problems occurring in real life situations.

Differential Transform Method For Nonlinear Parabolic-Hyperbolic Partial Differential Equations, J. Biazar, M. Eslami, M. R. Islam

Applications and Applied Mathematics: An International Journal (AAM)

In the present paper an analytic solution of non-linear parabolic-hyperbolic equations is deduced with the help of the powerful differential transform method (DTM). To illustrate the capability and efficiency of the method four examples for different cases of the equation are solved. The method can easily be applied to many problems and is capable of reducing the size of computational work.

Exact Solutions For The Kdv6 And Mkdv6 Equations Via Tanh-Coth And Sech Methods, Alvaro H. Salas, Cesar. A. Gómez S

Applications and Applied Mathematics: An International Journal (AAM)

The tanh-coth method is used to seek solutions to obtain solutions to the new integrable sixthorder Korteweg-de Vries equation (KdV6). Following the analogy between the Korteweg-de Vries equation (KdV) and the modified Korteweg-de Vries equation (MKdV) we construct a new system equivalent to KdV6 from which exact solutions to original equation and derived, during the sech method.

An Analytical Technique For Solving Nonlinear Heat Transfer Equations, Hossein Aminikhah, Milad Hemmatnezhad

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, an analytic technique, namely the New Homotopy Perturbation Method (NHPM) is applied for solving the nonlinear differential equations arising in the field of heat transfer. In this method, the solution is considered as an infinite series expansion where converges rapidly to the exact solution. The nonlinear convective–radioactive cooling equation and nonlinear equation of conduction heat transfer with the variable physical properties are chosen as illustrative examples and the exact solutions have been found for each case.

Numerical Comparison Of Methods For Hirota-Satsuma Model, Syed T. Mohyud-Din, Ahmet Yildirim, Syed M. Mahdi Hosseini

Applications and Applied Mathematics: An International Journal (AAM)

This paper outlines the implementation of the modified decomposition method (MDM) to solve a very important physical model namely Hirota-Satsuma model which occurs quite often in applied sciences. Numerical results and comparisons with homotopy perturbation (HPM) and Adomian’s decomposition (ADM) methods explicitly reveal the complete reliability of the proposed MDM. It is observed that the suggested algorithm (MDM) is more user-friendly and is easier to implement compared to HPM and ADM.

Duality In Fuzzy Linear Programming With Symmetric Trapezoidal Numbers, S. H. Nasseri, E. Ebrahimnejad, S. Mizuno

Applications and Applied Mathematics: An International Journal (AAM)

Linear programming problems with trapezoidal fuzzy numbers have recently attracted much interest. Various methods have been developed for solving these types of problems. Here, following the work of Ganesan and Veeramani and using the recent approach of Mahdavi-Amiri and Nasseri, we introduce the dual of the linear programming problem with symmetric trapezoidal fuzzy numbers and establish some duality results. The results will be useful for post optimality analysis.

Global Stability Of Worms In Computer Network, Bimal Kumar Mishra, Aditya Kumar Singh

Applications and Applied Mathematics: An International Journal (AAM)

An attempt has been made to show the impact of non-linearity of the worms through SIRS (susceptible – infectious – recovered - susceptible) and SEIRS (susceptible – exposed – infectious – recovered - susceptible) e-epidemic models in computer network. A very general form of non-linear incidence rate has been considered satisfying the worm propagating behavior in computer network. The concavity conditions with a non-linear incidence rate and under the constant population size assumption are shown to be stable. Such systems have either a unique and stable endemic equilibrium state or no endemic equilibrium state at all; in the latter case, …

Reliability Measures Of A Three-State Complex System: A Copula Approach, Mangey Ram

Applications and Applied Mathematics: An International Journal (AAM)

Improvement in reliability and production play a very important role in system design. The two key factors, considered in predicting system reliability, are failure distribution of the component and system configuration. This research discusses the mathematical modeling of a highly reliable complex system, which is in three states i.e. normal, partial failed (degraded state) and complete failed state. The system, partial failed is due to the partial failure of internal components or redundancies and completely failed is due to catastrophic failure of the system. Repair rates are general functions of the time spent. All the transition rates are constant except …

Finite Element Analysis In Porous Media For Incompressible Flow Of Contamination From Nuclear Waste, Abbas Al-Bayati, Saad A. Manaa, Ekhlass S. Ahmed

Applications and Applied Mathematics: An International Journal (AAM)

A non-linear parabolic system is used to describe incompressible nuclear waste disposal contamination in porous media, in which both molecular diffusion and dispersion are considered. The Galerkin method is applied for the pressure equation. For the brine, radionuclide and heat, a kind of partial upwind finite element scheme is constructed. Examples are included to demonstrate certain aspects of the theory and illustrate the capabilities of the kind of partial upwind finite element approach.

Approximate Approach To The Das Model Of Fractional Logistic Population Growth, S. Das, P. K. Gupta, K. Vishal

Applications and Applied Mathematics: An International Journal (AAM)

In this article, the analytical method, Homotopy perturbation method (HPM) has been successfully implemented for solving nonlinear logistic model of fractional order. The fractional derivatives are described in the Caputo sense. Using initial value, the explicit solutions of population size for different particular cases have been derived. Numerical results show that the method is extremely efficient to solve this complicated biological model.

Optimal Correction Of Infeasible System In Linear Equality Via Genetic Algorithm, S. Ketabchi, H. Moosaei, S. Fallahi

Applications and Applied Mathematics: An International Journal (AAM)

This work is focused on the optimal correction of infeasible system of linear equality. In this paper, for correcting this system, we will make the changes just in the coefficient matrix by using l 􀬶 norm and show that solving this problem is equivalent to solving a fractional quadratic problem. To solve this problem, we use the genetic algorithm. Some examples are provided to illustrate the efficiency and validity of the proposed method.

Approximating Solutions For Ginzburg – Landau Equation By Hpm And Adm, J. Biazar, M. Partovi, Z. Ayati

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, an analytical approximation to the solution of Ginzburg-Landauis discussed. A Homotopy perturbation method introduced by He is employed to derive the analytic approximation solution and results compared with those of the Adomian decomposition method. Two examples are presented to show the capability of the methods. The results reveal that the methods are almost equally effective and promising.

The Möbius Geometry Of Hypersurfaces, Ii, Michael Bolt

University Faculty Publications and Creative Works

No abstract provided.

Application Of Homotopy Perturbation Method To Biological Population Model, Pradip Roul

Applications and Applied Mathematics: An International Journal (AAM)

In this article, a well-known analytical approximation method, so-called the Homotopy perturbation method (HPM) is adopted for solving the nonlinear partial differential equations arising in the spatial diffusion of biological populations. The resulting solutions are compared with those of the existing solutions obtained by employing the Adomian’s decomposition method. The comparison reveals that our approximate solutions are in very good agreement with the solutions by Adomian’s method. Moreover, the results show that the proposed method is a more reliable, efficient and convenient one for solving the non-linear differential equations.