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Mathematical Sciences Letters
An International Journal



A Note on FS Isometry Operators

Hanan Hassan Sakr,
Abstract :
In this work, we introduce the definition of the FS isometry operator, a special type of the FS linear operators in the FS Hilbert space, initiated by Faried, Ali and Sakr [5]. Furthermore, related theorems of the FS spectral theory are introduced.


Regional controllability for hyperbolic systems with output constraints

Ali Boutoulout,
Abstract :
The aim of this paper is to characterize the minimum energy control that steers a hyperbolic system to a final state between two prescribed functions only on a subregion $\omega$ of the evolution system domain $\Omega$. We give some definitions and properties of this new concept, and then we concentrate on the determination of the control which would realize a given final state with output constraints in $\omega$ with minimum energy. This problem is solved using the Lagrangian approach and leads to an algorithm for the computation of the optimal control. The obtained results are illustrated by numerical simulations which lead to some conjectures.



Muhammad Amer Latif,
Abstract :
Several new weighted inequalities connected with Hermite-Hadamard and Fejér type inequalities are established for functions whose derivatives in absolute value are preinvex. The results presented in this paper provide extensions of those given in earlier works.


Numerical solution of model of cancer invasion with tissue

Mohammad Bagher Ghaemi,
Abstract :
Chemotaxis-haptotaxis model of cancer invasion with tissue remodeling is one of the important PDE’s system in medicine, mathematics and biomathematics. In this paper we find the solution of chemotaxis-haptotaxis model of cancer invasion using the new homotopy perturbation method (NHPM). Then by comparing some estimated numerical result with simulation laboratory result, its shown that NHPM is an efficient and exact way for solving cancer PDE’s system.


Mathematical analysis of virus dynamics model with multitarget cells in vivo

Ahmed Bakr,
Abstract :
This paper investigates the qualitative behavior of viral infection model with multiple delays in vivo. The infection rate is given by Crowley-Martin functional response. By assuming that the virus attack $n$ classes of uninfected target cells, we study a viral infection model of dimension $2n+1$ with discrete delay. To describe the latent period for the contacted target cells with viruses to begin producing viruses, two types of discrete delay are incorporated into the model. The basic reproduction number $R_{0}$ of the model is defined which determines the dynamical behaviors of the model. Utilizing Lyapunov functionals and LaSalles invariance principle, we have proven that if $R_{0}\le{1}$ then the uninfected steady state is globally asymptotically stable, and if $R_{0}>1$ then the infected steady state is globally asymptotically stable.


Some Modifications of Adomian’s Decomposition Method for Fractional Partial Differential Equations

Jamshad Ahmad,
Abstract :
In this paper, we present some modifications of Adomian’s Decomposition Method (ADM) to obtain analytical exact and approximate solutions for initial value problems of fractional order. The fractional derivative is defined in the Jumarie’s sense. The results are compared with those obtained using the Fractional Adomian’s Decomposition Method (ADM). The effectiveness and good accuracy of each modified is verified by the numerical results.


Some integral inequalities in terms of supremum norms of $n$-time differentiable functions

Shu-Hong Wang, Bo-Yan Xi, Feng Qi,
Abstract :
In the paper, the authors establish identities for $n$-time differentiable functions and obtain some integral inequalities in terms of supremum norms of $n$-time differentiable functions. These results generalize Ostrowskis and Simpsons inequalities.


Higher order schemes for Solving Optimal Control Problems

Mostafs. A. El-Khateb,
Abstract :
We shall present a numerical procedure for solving optimal control problems with the extended-one step method. A control system is considered, and a cost functional is minimized. A class of optimal control problems governed by ordinary differential equations is presented. The control variables are approximated by a polynomial function and the state variables are obtained by solving a system of ordinary differential equations using extended one-step methods of order five and six. These methods are A- and L-stable methods. The problem is reduced to either a constrained or unconstrained optimization problem according to the nature of the dynamic system and the given conditions, which can be solved using Hybrid penalty partial quadratic interpolation technique.


Solving a class of nonlinear two-dimensional Volterra integral equations by two-dimensional triangular orthogonal functions

Farshid Mirzaee,
Abstract :
Two-dimensional triangular orthogonal functions (2D-TFs) are applied to solving a class of nonlinear two-dimensional Volterra integral equations. Using 2D-TFs, nonlinear two-dimensional Volterra integral equations reduce to algebraic equations. The comparison of the results with the other numerical methods shows the efficiency and accuracy of this method.


Global Nonexistence of Solutions for Systems of Quasilinear Hyperbolic Equations with Damping and Source Terms

Yaojun YE,
Abstract :
The initial-boundary value problem for a class of quasilinear hyperbolic equations system in bounded domain is studied. We prove that the solutions with the positive initial energy blow up in finite time under some conditions. The estimates of the lifespan of solutions are given.


Numerical approximation solutions for space-symmetric fractional diffusion equation with variable step-size in Riesz spaces

Youwei Zhang,
Abstract :
This paper presents numerical solution of Riesz fractional diffusion equation and Riesz fractional advection-dispersion equation on a bounded domain, our main concern is to obtain a general numerical approximation schemes to solve these equations by introducing a variable space step-size numerical approximation schemes. Two numerical methods are provided to deal with numerical solution of the Riesz space fractional derivatives, and an example are included to illustrate the results obtained.


Bernoulli Matrix Approach for Solving Two Dimensional Linear Hyperbolic Partial Differential Equations with Constant Coefficients

Abstract :
The purpose of this study is to give a Bernoulli polynomial approximation for the solution of hyperbolic partial differential equations with three variables and constant coefficients. For this purpose, a Bernoulli matrix approach is introduced. This method is based on taking the truncated Bernoulli expansions of the functions in the partial differential equations. After replacing the approximations of functions in the basic equation, we deal with a linear algebraic equation. Hence, the result matrix equation can be solved and the unknown Bernoulli coefficients can be found approximately. The efficiency of the proposed approach is demonstrated with one example.


Unsteady Simulation of Rotor-Stator Interaction in Axial Flow Pump Based on Computational Fluid Dynamics

Zhang Hua, Shi Weidong, Li Tongtong, Yao Jie,
Abstract :
Investigations of the Rotor-Stator Interaction in a axial-flow pump at different conditions are presented in the paper. The numerical simulation of the unsteady flow field is performed with FLUENT codes based on RNG k-ε model and SIMPLEC arithmetic. Numerical results show that the strong-coupling evolutions of static pressure and axial velocity distribution between rotor and stator in multi-conditions are periodic with the rotation of rotor. The interaction of stationary and rotating pressure field leads to periodic flow field distortions and induces pressure fluctuation. It is found that the maximum pressure amplitude of blade passing frequency occurs in the rotor inlet zone, but it deceases very fast backward to the stator. The dominant frequency at monitoring points located at rotor inlet, outlet and stator outlet, corresponds to the blade passage frequency. The axial velocity distortion resulting from the modulation of the interacting stationary and rotating flow field is affected by the blade numbers and thickness of both rotor and stator. The axial velocity shows different distributions at different conditions, and the phase of it changes cyclically.


T, S-intuitionistic Fuzzy Finite State Machines

Masumeh Sadeghi, Hamid Alinejad-Rokny,
Abstract :
The aim of this paper is the study of the notions of covering and direct product in T-S-intuitionistic fuzzy finite state machines. In this regards various kinds of products in such machines are defined and aim of algebraic properties of them are investigated.


Anomaly intrusion Detection Based on PLS Feature Extraction and Core Vector Machine

Gan Xu-sheng et al, Gan Xu-sheng et al,
Abstract :
To improve the ability of detecting anomaly intrusions, a combined algorithm is proposed based on Partial Least Square (PLS) feature extraction and Core Vector Machine (CVM) algorithms. Principal elements are firstly extracted from the data set using the feature extraction of PLS algorithm to construct the feature set, and then the anomaly intrusion detection model for the feature set is established by virtue of the speediness superiority of CVM algorithm in processing large-scale sample data. Finally, anomaly intrusion actions are checked and judged using this model. Experiments based on KDD99 data set verify the feasibility and validity of the combined algorithm.


Closed form solution of electromagnetic wave diffraction in a homogeneous bi-isotropic medium

Rab Nawaz,
Abstract :
We have presented a theoretical analysis of an electromagnetic scattering problem by a perfectly conducting strip surrounded by a homogeneous bi-isotropic medium. This study is focused on the exact and concise formulation for the acquisition of a closed form solution in complex domain. The complete solution of electromagnetic plane wave is presented by a series one whose eigenfunctions are the generalized Gamma functions occurring in the finite diffraction theory. The scattered field is discussed in physical domain by obtaining the convergence history of the problem in transformed domain. This analysis provides the higher order accuracy solution in closed form in physical domain.


A novel proof of Watsons contour integral representations

Dong-Fang Liu, Xiang-Li Wang,
Abstract :
In this paper we give a simple proof of Watsons contour integral representations for $_{r+1}\phi_{r}$ by applying Cauchys operators, and obtain an interesting formula of contour integral representation for $(q;q)^r_\infty$.


The approximate solution of Fredholm integralequations by using Chebyshev polynomials

Abstract :
In this paper, a numerical solution for solving the Fredholm integral equations of the second kind is considered. An application of Chebyshev polynomial method is applied to solve the Fredholm integral equations. Numerical examples are presented to illustrate the efficiency and accuracy of the method.


Exact solution for fractionalized Maxwell fluid using Fox H-function

Muhammad Jamil,
Abstract :
The unsteady flow of a viscoelastic fractionalized (this word is suitable when fractional derivative is used in constitutive or governing equations) Maxwell fluid model, between two infinite coaxial circular cylinders, is studied by means of the Laplace and finite Hankel transforms. The motion is produced by the inner cylinder that at the initial moment is subject to a torsional time dependent shear stress. The solutions that have been obtained, presented under series form in terms of Fox H-functions, satisfy all imposed initial and boundary conditions. Moreover, the corresponding solutions for ordinary Maxwell and Newtonian fluids appear as special cases of the present results. Finally, the influence of the pertinent parameters on the fluid motion, as well as a comparison between models, is shown by graphical illustrations.



Abdon Atangana,
Abstract :
Fractional advection-dispersion equations are used in groundwater hydrology to model the transport of passive tracers carried by fluid flow in a porous medium. A space-time fractional advection-dispersion equation (FADE) is a generalization of the classical ADE in which the first-order space derivative is replaced with Caputo or Riemann-Liouville derivative of order 0

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