Showing papers in "Applied Mathematics-a Journal of Chinese Universities Series B in 2011"

On modeling with multiplicative differential equations

Abstract: This work is aimed to show that various problems from different fields can be modeled more efficiently using multiplicative calculus, in place of Newtonian calculus. Since multiplicative calculus is still in its infancy, some effort is put to explain its basic principles such as exponential arithmetic, multiplicative calculus, and multiplicative differential equations. Examples from finance, actuarial science, economics, and social sciences are presented with solutions using multiplicative calculus concepts. Based on the encouraging results obtained it is recommended that further research into this field be vested to exploit the applicability of multiplicative calculus in different fields as well as the development of multiplicative calculus concepts.

Dynamics of a Heroin Epidemic Model with Very Population

Abstract: Based on the model provided by the Mulone and Straughan [1], we relax the population which are constant and obtain the drug-free equilibrium which is global asymptotically stable under some conditions. The system has only uniqueness positive endemic equilibrium which is globally asymptotically stable by using the second compound matrix.

Expanding the Tanh-Function Method for Solving Nonlinear Equations

Abstract: In this paper, using the tanh-function method, we introduce a new approach to solitary wave solutions for solving nonlinear PDEs. The proposed method is based on adding integration constants to the resulting nonlinear ODEs from the nonlinear PDEs using the wave transformation. Also, we use a transformation related to those integration constants. Some examples are considered to find their exact solutions such as KdV- Burgers class and Fisher, Boussinesq and Klein-Gordon equations. Moreover, we discuss the geometric interpretations of the resulting exact solutions.

Approximate Analytical Solutions for the Nonlinear Brinkman-Forchheimer-Extended Darcy Flow Model

Abstract: New approximate analytical solutions for steady flow in parallel-plates channels filled with porous materials governed by non-linear Brinkman-Forchheimer extended Darcy model for three different physical situations are presented. These results are compared with those obtained from an implicit finite-difference solution of the corresponding time dependent flow problem. It is seen that the time dependent flow solutions yield the almost same steady state values as obtained by using the new approximate analytical solutions

Septic B-Spline Collocation Method for the Numerical Solution of the Modified Equal Width Wave Equation

Abstract: Numerical solutions of the modified equal width wave equation are obtained by using collocation method with septic B-spline finite elements with three different linearization techniques. The motion of a single solitary wave, interaction of two solitary waves and birth of solitons are studied using the proposed method. Accuracy of the method is discussed by computing the numerical conserved laws error norms L2 and L∞. The numerical results show that the present method is a remarkably successful numerical technique for solving the MEW equation. A linear stability analysis shows that this numerical scheme, based on a Crank Nicolson approximation in time, is unconditionally stable.

An Extension of Hardy–Hilbert’s Inequality

Abstract: By using the way of weight coefficient and the improved Euler-Maclaurin’s summation formula, a new extension of Hardy–Hilbert’s inequality with multi-parameter and a best constant factor is obtained, and the equivalent form is considered

Boundary Layer Flow and Heat Transfer of a Dusty Fluid over a Stretching Vertical Surface

Abstract: This paper presents the study of convective heat transfer characteristics of an incompressible dusty fluid past a vertical stretching sheet The governing partial differential equations are reduced to nonlinear ordinary differential equations by using similarity transformation The transformed equations are solved numerically by applying Runge Kutta Fehlberg fourth-fifth order method (RKF45 Method) Here obtained non-dimensional velocity and temperature profiles has been carried out to study the effect of different physical parameters such as fluid-particle interaction parameter, Grashof number, Prandtl number, Eckert number Comparison of the obtained numerical results is made with previously published results

A New Bandwidth Interval Based Forecasting Method for Enrollments Using Fuzzy Time Series

Abstract: In this paper, we introduce the concept of (4/3)? bandwidth interval based forecasting. The historical enrollments of the university of Alabama are used to illustrate the proposed method. In this paper we use the new simplified technique to find the fuzzy logical relations.

Fuzzy Fault Tree Analysis for Fault Diagnosis of Cannula Fault in Power Transformer

Abstract: Being one of the most expensive components of an electrical power plant, the failures of a power transformer can result in serious power system issues. So fault diagnosis for power transformer is highly important to ensure an uninterrupted power supply. Due to information transmission mistakes as well as arisen errors while processing data in surveying and monitoring state information of transformer, uncertain and incomplete information may be produced. Based on these points, this paper presents an intelligent fault diagnosis method of power transformer using fuzzy fault tree analysis (FTA) and beta distribution for failure possibility estimation. By using the technique we proposed herein, the continuous attribute values are transformed into the fuzzy numbers to give a realistic estimate of failure possibility of a basic event in FTA. Further, it explains a new approach based on Euclidean distance between fuzzy numbers, to rank the basic events in accordance with their Fuzzy Importance Index.

Meshless Method of Lines for Numerical Solution of Kawahara Type Equations

Abstract: In this work, an algorithm based on method of lines coupled with radial basis functions namely meshless method of lines (MMOL) is presented for the numerical solution of Kawahara, modified Kawahara and KdV Kawahara equations. The motion of a single solitary wave, interaction of two and three solitons and the phenomena of wave generation is discussed. The results are compared with the exact solution and with the results in the relevant literature to show the efficiency of the method.

Mathematical Model of Blood Flow in Small Blood Vessel in the Presence of Magnetic Field

Abstract: A mathematical model for blood flow in the small blood vessel in the presence of magnetic field is presented in this paper. We have modeled the two phase model for the blood flow consists of a central core of suspended erythrocytes and cell-free layer surrounding the core. The system of differential equations has been solved analytically. We have obtained the result for velocity, flow rate and effective viscosity in presence of peripheral layer and magnetic field .All the result has been obtained and discussed through graphs.

On the Behavior of Solutions of the System of Rational Difference Equations x n+1 =x n-1 /y n x n-1 -1, y n+1 =y n-1 /x n y n-1 -1, z n+1 =x n /y n z n-1

Abstract: In this paper, we investigate the solutions of the system of difference equations xn+1=xn-1/ynxn-1-1,yn+1=yn-1/xnyn-1-1,zn+1=xn/ynzn-1 where x0,x-1,y0,y-1,z0,z-1∈R.

Uses of the Buys-Ballot Table in Time Series Analysis

Abstract: Uses of the Buys-Ballot table for choice of appropriate transformation (using the Bartlett technique), assessment of trend and seasonal components and choice of model for time series decomposition are discussed in this paper. Uses discussed are illustrated with numerical examples when trend curve is linear, quadratic and exponential.

Mathematical Modeling and Analysis of Tumor Therapy with Oncolytic Virus

Abstract: In this paper, we have proposed and analyzed a nonlinear mathematical model for the study of interaction between tumor cells and oncolytic viruses. The model is analyzed using stability theory of differential equa- tions. Positive equilibrium points of the system are investigated and their stability analysis is carried out. Moreover, the numerical simulation of the proposed model is also performed by using fourth order Runge- Kutta method which supports the theoretical findings. It is found that both infected and uninfected tumor cells and hence tumor load can be eliminated with time, and complete recovery is possible because of virus therapy, if certain conditions are satisfied. It is further found that the system appears to exhibit periodic limit cycles and chaotic attractors for some ranges of the system parameters.

On the Periodicity of Solutions of the System of Rational Difference Equations

Abstract: In this paper, we have investigated the periodicity of the solutions of the system of difference equations , where .

A Note on Crank-Nicolson Scheme for Burgers’ Equation

Abstract: In this work we generate the numerical solutions of the Burgers’ equation by applying the Crank-Nicolson method directly to the Burgers’ equation, i.e., we do not use Hopf-Cole transformation to reduce Burgers’ equation into the linear heat equation. Absolute error of the present method is compared to the absolute error of the two existing methods for two test problems. The method is also analyzed for a third test problem, nu-merical solutions as well as exact solutions for different values of viscosity are calculated and we find that the numerical solutions are very close to exact solution.

Cryptographic PRNG Based on Combination of LFSR and Chaotic Logistic Map

Abstract: The random sequence generated by linear feedback shift register can’t meet the demand of unpredictability for secure paradigms. A combination logistic chaotic equation improves the linear property of LFSR and constructs a novel random sequence generator with longer period and complex architecture. We present the detailed result of the statistical testing on generated bit sequences, done by very strict tests of randomness: the NIST suite tests, to detect the specific characteristic expected of truly random sequences. The results of NIST’s statistical tests show that our proposed method for generating random numbers has more efficient performance.

A Strong Method for Solving Systems of Integro-Differential Equations

Abstract: The introduced method in this paper consists of reducing a system of integro-differential equations into a system of algebraic equations, by expanding the unknown functions, as a series in terms of Chebyshev wavelets with unknown coefficients. Extension of Chebyshev wavelets method for solving these systems is the novelty of this paper. Some examples to illustrate the simplicity and the effectiveness of the proposed method have been presented.

Precision of a Parabolic Optimum Calculated from Noisy Biological Data, and Implications for Quantitative Optimization of Biventricular Pacemakers (Cardiac Resynchronization Therapy)

Abstract: In patients with heart failure and disordered intracardiac conduction of activation, doctors implant a biven- tricular pacemaker (“cardiac resynchronization therapy”, CRT) to allow adjustment of the relative timings of activation of parts of the heart. The process of selecting the pacemaker timings that maximize cardiac function is called “optimization”. Although optimization—more than any other clinical assessment—needs to be precise, it is not yet conventional to report the standard error of the optimum alongside its value in clinical practice, nor even in research, because no method is available to calculate precision from one optimization dataset. Moreover, as long as the determinants of precision remain unknown, they will remain unconsidered, preventing candidate haemodynamic variables from being screened for suitability for use in optimization. This manuscript derives algebraically a clinically-applicable method to calculate the precision of the optimum value of x arising from fitting noisy biological measurements of y (such as blood flow or pressure) obtained at a series of known values of x (such as atrioventricular or interventricular delay) to a quadratic curve. A formula for uncertainty in the optimum value of x is obtained, in terms of the amount of scatter (irreproducibility) of y, the intensity of its curvature with respect to x, the width of the range and number of values of x tested, the number of replicate measurements made at each value of x, and the position of the optimum within the tested range. The ratio of scatter to curvature is found to be the overwhelming practical determinant of precision of the optimum. The new formulae have three uses. First, they are a basic science for anyone desiring time-efficient, reliable optimization protocols. Second, asking for the precision of every reported optimum may expose optimization methods whose precision is unacceptable. Third, evaluating precision quantitatively will help clinicians decide whether an apparent change in optimum between successive visits is real and not just noise.

Estimation in Interacting Diffusions: Continuous and Discrete Sampling

Abstract: Consistency and asymptotic normality of the sieve estimator and an approximate maximum likelihood estimator of the drift coefficient of an interacting particles of diffusions are studied. For the sieve estimator, observations are taken on a fixed time interval [0,T] and asymptotics are studied as the number of interacting particles increases with the dimension of the sieve. For the approximate maximum likelihood estimator, discrete observations are taken in a time interval [0,T] and asymptotics are studied as the number of interacting particles increases with the number of observation time points.

Effect of Point Source, Self-Reinforcement and Heterogeneity on the Propagation of Magnetoelastic Shear Wave

Abstract: This paper investigates the propagation of horizontally polarised shear waves due to a point source in a magnetoelastic self-reinforced layer lying over a heterogeneous self-reinforced half-space. The heterogeneity is caused by consideration of quadratic variation in rigidity. The methodology employed combines an efficient derivation for Green’s functions based on algebraic transformations with the perturbation approach. Dispersion equation has been obtained in the closed form. The dispersion curves are compared for different values of magnetoelastic coupling parameters and inhomogeneity parameters. Also, the comparative study is being made through graphs to find the effect of reinforcement over the reinforced-free case on the phase velocity. It is observed that the dispersion equation is in assertion with the classical Love-type wave equation in the absence of reinforcement, magnetic field and heterogeneity. Moreover, some important peculiarities have been observed in graphs.

Intersection Curves of Implicit and Parametric Surfaces in R 3

Abstract: We present algorithms for computing the differential geometry properties of Frenet apparatus {t,n,b,κ,τ} and higher-order derivatives of intersection curves of implicit and parametric surfaces in R3 for transversal and tangential intersection. This work is considered as a continuation to Ye and Maekawa [1]. We obtain a classification of the singularities on the intersection curve. Some examples are given and plotted.

Multi-Item EOQ Model with Both Demand-Dependent Unit Cost and Varying Leading Time via Geometric Programming

Abstract: The objective of this paper is to derive the analytical solution of the EOQ model of multiple items with both demand-dependent unit cost and leading time using geometric programming approach. The varying purchase and leading time crashing costs are considered to be continuous functions of demand rate and leading time, respectively. The researchers deduce the optimal order quantity, the demand rate and the leading time as decision variables then the optimal total cost is obtained.

On the Zeros of a Polynomial

Abstract: In this paper we consider the problem of finding the estimate of maximum number of zeros in a prescribed region and the results which we obtain generalizes and improves upon some well known results.

A new type of the generalized Bézier curves

Abstract: In this paper, we improve the generalized Bernstein basis functions introduced by Han, et al. The new basis functions not only inherit the most properties of the classical Bernstein basis functions, but also reserve the shape parameters that are similar to the shape parameters of the generalized Bernstein basis functions. The degree elevation algorithm and the conversion formulae between the new basis functions and the classical Bernstein basis functions are obtained. Also the new Q-Bezier curve and surface constructed by the new basis functions are given and their properties are discussed.

A Problem of a Semi-Infinite Medium Subjected to Exponential Heating Using a Dual-Phase-Lag Thermoelastic Model

Abstract: The problem of a semi-infinite medium subjected to thermal shock on its plane boundary is solved in the context of the dual-phase-lag thermoelastic model. The expressions for temperature, displacement and stress are presented. The governing equations are expressed in Laplace transform domain and solved in that domain. The solution of the problem in the physical domain is obtained by using a numerical method for the inversion of the Laplace transforms based on Fourier series expansions. The numerical estimates of the displacement, temperature, stress and strain are obtained for a hypothetical material. The results obtained are presented graphically to show the effect phase-lag of the heat flux and a phase-lag of temperature gradient on displacement, temperature, stress.

A Primal-Dual Simplex Algorithm for Solving Linear Programming Problems with Symmetric Trapezoidal Fuzzy Numbers

Abstract: Two existing methods for solving a class of fuzzy linear programming (FLP) problems involving symmetric trapezoidal fuzzy numbers without converting them to crisp linear programming problems are the fuzzy primal simplex method proposed by Ganesan and Veeramani [1] and the fuzzy dual simplex method proposed by Ebrahimnejad and Nasseri [2]. The former method is not applicable when a primal basic feasible solution is not easily at hand and the later method needs to an initial dual basic feasible solution. In this paper, we develop a novel approach namely the primal-dual simplex algorithm to overcome mentioned shortcomings. A numerical example is given to illustrate the proposed approach.

Thermal Effect on Vibration of Parallelogram Plate of Bi-Direction Linearly Varying Thickness

Abstract: In this paper, the effect of thermal gradient on the vibration of parallelogram plate with linearly varying thickness in both direction having clamped boundary conditions on all the four edges is analyzed. Thermal effect on vibration of such plate has been taken as one-dimensional distribution in linear form only. An approximate but quiet convenient frequency equation is derived using Rayleigh-Ritz technique with a two-term deflection function. The frequencies corresponding to the first two modes of vibration of a clamped parallelogram plate have been computed for different values of aspect ratio, thermal gradient, taper constants and skew angle. The results have been presented in tabular forms. The results obtained in this study are reduced to that of unheated parallelogram plates of uniform thickness and have generally been compared with the published one.

The Traveling Wave Solutions for Some Nonlinear PDEs in Mathematical Physics

Abstract: In the present article, we construct the exact traveling wave solutions of some nonlinear PDEs in the mathematical physics via (1 + 1) dimensional Kaup Kupershmit equation, the (1 + 1) dimensional seventh order KdV equation and (1 + 1) dimensional Kersten-Krasil Shchik equations by using the modified truncated expansion method. New exact solutions of these equations are found.

Solution of the Fuzzy Equation A + X = B Using the Method of Superimposition

Abstract: Fuzzy equations were solved by using different standard methods. One of the well-known methods is the method of -cut. The method of superimposition of sets has been used to define arithmetic operations of fuzzy numbers. In this article, it has been shown that the fuzzy equation AX B   , where A, X, B are fuzzy numbers can be solved by using the method of superimposition of sets. It has also been shown that the method gives same result as the method of -cut.