Search results for: Differential Forms
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 1293

Search results for: Differential Forms

1263 Differential Sandwich Theorems with Generalised Derivative Operator

Authors: Maslina Darus, Khalifa Al-Shaqsi

Abstract:

In this paper, a generalized derivatives operator n λ,βf introduced by the authors will be discussed. Some subordination and superordination results involving this operator for certain normalized analytic functions in the open unit disk will be investigated. Our results extend corresponding previously known results.

Keywords: Analytic functions, Univalent functions, Derivative operator, Differential subordination, Differential superordination.

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1262 Engineering Optimization Using Two-Stage Differential Evolution

Authors: K. Y. Tseng, C. Y. Wu

Abstract:

This paper employs a heuristic algorithm to solve engineering problems including truss structure optimization and optimal chiller loading (OCL) problems. Two different type algorithms, real-valued differential evolution (DE) and modified binary differential evolution (MBDE), are successfully integrated and then can obtain better performance in solving engineering problems. In order to demonstrate the performance of the proposed algorithm, this study adopts each one testing case of truss structure optimization and OCL problems to compare the results of other heuristic optimization methods. The result indicates that the proposed algorithm can obtain similar or better solution in comparing with previous studies.

Keywords: Differential evolution, truss structure optimization, optimal chiller loading, modified binary differential evolution.

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1261 The Strict Stability of Impulsive Stochastic Functional Differential Equations with Markovian Switching

Authors: Dezhi Liu Guiyuan Yang Wei Zhang

Abstract:

Strict stability can present the rate of decay of the solution, so more and more investigators are beginning to study the topic and some results have been obtained. However, there are few results about strict stability of stochastic differential equations. In this paper, using Lyapunov functions and Razumikhin technique, we have gotten some criteria for the strict stability of impulsive stochastic functional differential equations with markovian switching.

Keywords: Impulsive; Stochastic functional differential equation; Strict stability; Razumikhin technique.

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1260 Design of a CMOS Differential Operational Transresistance Amplifier in 90 nm CMOS Technology

Authors: Hafiz Muhammad Obaid, Umais Tayyab, Shabbir Majeed Ch.

Abstract:

In this paper, a CMOS differential operational transresistance amplifier (OTRA) is presented. The amplifier is designed and implemented in a standard umc90-nm CMOS technology. The differential OTRA provides wider bandwidth at high gain. It also shows much better rise and fall time and exhibits a very good input current dynamic range of 50 to 50 μA. The OTRA can be used in many analog VLSI applications. The presented amplifier has high gain bandwidth product of 617.6 THz Ω. The total power dissipation of the presented amplifier is also very low and it is 0.21 mW.

Keywords: CMOS, differential, operational transresistance amplifier, OTRA, 90 nm, VLSI.

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1259 A New Method to Solve a Non Linear Differential System

Authors: Seifedine Kadry

Abstract:

In this article, our objective is the analysis of the resolution of non-linear differential systems by combining Newton and Continuation (N-C) method. The iterative numerical methods converge where the initial condition is chosen close to the exact solution. The question of choosing the initial condition is answered by N-C method.

Keywords: Continuation Method, Newton Method, Finite Difference Method, Numerical Analysis and Non-Linear partial Differential Equation.

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1258 Existence of Solution for Four-Point Boundary Value Problems of Second-Order Impulsive Differential Equations (III)

Authors: Li Ge

Abstract:

In this paper, we study the existence of solution of the four-point boundary value problem for second-order differential equations with impulses by using Leray-Schauder theory:

Keywords: impulsive differential equations, impulsive integraldifferential equation, boundary value problems

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1257 Existence of Solution for Four-Point Boundary Value Problems of Second-Order Impulsive Differential Equations (I)

Authors: Li Ge

Abstract:

In this paper, we study the existence of solution of the four-point boundary value problem for second-order differential equations with impulses by using leray-Schauder theory:

Keywords: impulsive differential equations, impulsive integraldifferentialequation, boundary value problems

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1256 Existence of Solution for Four-Point Boundary Value Problems of Second-Order Impulsive Differential Equations (II)

Authors: Li Ge

Abstract:

In this paper, we study the existence of solution of the four-point boundary value problem for second-order differential equations with impulses by using leray-Schauder theory:

Keywords: impulsive differential equations, impulsive integraldifferentialequation, boundary value problems

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1255 Simulink Approach to Solve Fuzzy Differential Equation under Generalized Differentiability

Authors: N. Kumaresan , J. Kavikumar, Kuru Ratnavelu

Abstract:

In this paper, solution of fuzzy differential equation under general differentiability is obtained by simulink. The simulink solution is equivalent or very close to the exact solution of the problem. Accuracy of the simulink solution to this problem is qualitatively better. An illustrative numerical example is presented for the proposed method.

Keywords: Fuzzy differential equation, Generalized differentiability, H-difference and Simulink.

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1254 The Differential Transform Method for Advection-Diffusion Problems

Authors: M. F. Patricio, P. M. Rosa

Abstract:

In this paper a class of numerical methods to solve linear and nonlinear PDEs and also systems of PDEs is developed. The Differential Transform method associated with the Method of Lines (MoL) is used. The theory for linear problems is extended to the nonlinear case, and a recurrence relation is established. This method can achieve an arbitrary high-order accuracy in time. A variable stepsize algorithm and some numerical results are also presented.

Keywords: Method of Lines, Differential Transform Method.

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1253 On a Class of Inverse Problems for Degenerate Differential Equations

Authors: Fadi Awawdeh, H.M. Jaradat

Abstract:

In this paper, we establish existence and uniqueness of solutions for a class of inverse problems of degenerate differential equations. The main tool is the perturbation theory for linear operators.

Keywords: Inverse Problem, Degenerate Differential Equations, Perturbation Theory for Linear Operators

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1252 On the Approximate Solution of Continuous Coefficients for Solving Third Order Ordinary Differential Equations

Authors: A. M. Sagir

Abstract:

This paper derived four newly schemes which are combined in order to form an accurate and efficient block method for parallel or sequential solution of third order ordinary differential equations of the form y''' = f(x, y, y', y''), y(α)=y0, y'(α)=β, y''(α)=η with associated initial or boundary conditions. The implementation strategies of the derived method have shown that the block method is found to be consistent, zero stable and hence convergent. The derived schemes were tested on stiff and non – stiff ordinary differential equations, and the numerical results obtained compared favorably with the exact solution.

Keywords: Block Method, Hybrid, Linear Multistep, Self starting, Third Order Ordinary Differential Equations.

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1251 Position Vector of a Partially Null Curve Derived from a Vector Differential Equation

Authors: Süha Yılmaz, Emin Özyılmaz, Melih Turgut, Şuur Nizamoğlu

Abstract:

In this paper, position vector of a partially null unit speed curve with respect to standard frame of Minkowski space-time is studied. First, it is proven that position vector of every partially null unit speed curve satisfies a vector differential equation of fourth order. In terms of solution of the differential equation, position vector of a partially null unit speed curve is expressed.

Keywords: Frenet Equations, Partially Null Curves, Minkowski Space-time, Vector Differential Equation.

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1250 Existence of Solution of Nonlinear Second Order Neutral Stochastic Differential Inclusions with Infinite Delay

Authors: Yong Li

Abstract:

The paper is concerned with the existence of solution of nonlinear second order neutral stochastic differential inclusions with infinite delay in a Hilbert Space. Sufficient conditions for the existence are obtained by using a fixed point theorem for condensing maps.

Keywords: Mild solution, Convex multivalued map, Neutral stochastic differential inclusions.

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1249 Positive Solutions for Three-Point Boundary Value Problems of Third-Order Nonlinear Singular Differential Equations in Banach Space

Authors: Li Xiguang

Abstract:

In this paper, by constructing a special set and utilizing fixed point index theory, we study the existence of solution for singular differential equation in Banach space, which improved and generalize the result of related paper.

Keywords: Banach space, cone, fixed point index, singular differential equation.

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1248 The Homotopy Analysis Method for Solving Discontinued Problems Arising in Nanotechnology

Authors: Hassan Saberi-Nik, Mahin Golchaman

Abstract:

This paper applies the homotopy analysis method method to a nonlinear differential-difference equation arising in nanotechnology. Continuum hypothesis on nanoscales is invalid, and a differential-difference model is considered as an alternative approach to describing discontinued problems. Comparison of the approximate solution with the exact one reveals that the method is very effective.

Keywords: Homotopy analysis method, differential-difference, nanotechnology.

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1247 Reduction of Differential Column Shortening in Tall Buildings

Authors: Hansoo Kim, Seunghak Shin

Abstract:

The differential column shortening in tall buildings can be reduced by improving material and structural characteristics of the structural systems. This paper proposes structural methods to reduce differential column shortening in reinforced concrete tall buildings; connecting columns with rigidly jointed horizontal members, using outriggers, and placing additional reinforcement at the columns. The rigidly connected horizontal members including outriggers reduce the differential shortening between adjacent vertical members. The axial stiffness of columns with greater shortening can be effectively increased by placing additional reinforcement at the columns, thus the differential column shortening can be reduced in the design stage. The optimum distribution of additional reinforcement can be determined by applying a gradient based optimization technique.

Keywords: Column shortening, long-term behavior, optimization, tall building.

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1246 Instability of a Nonlinear Differential Equation of Fifth Order with Variable Delay

Authors: Cemil Tunc

Abstract:

In this paper, we study the instability of the zero solution to a nonlinear differential equation with variable delay. By using the Lyapunov functional approach, some sufficient conditions for instability of the zero solution are obtained.

Keywords: Instability, Lyapunov-Krasovskii functional, delay differential equation, fifth order.

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1245 Posture Stabilization of Kinematic Model of Differential Drive Robots via Lyapunov-Based Control Design

Authors: Li Jie, Zhang Wei

Abstract:

In this paper, the problem of posture stabilization for a kinematic model of differential drive robots is studied. A more complex model of the kinematics of differential drive robots is used for the design of stabilizing control. This model is formulated in terms of the physical parameters of the system such as the radius of the wheels, and velocity of the wheels are the control inputs of it. In this paper, the framework of Lyapunov-based control design has been used to solve posture stabilization problem for the comprehensive model of differential drive robots. The results of the simulations show that the devised controller successfully solves the posture regulation problem. Finally, robustness and performance of the controller have been studied under system parameter uncertainty.

Keywords: Differential drive robots, nonlinear control, Lyapunov-based control design, posture regulation.

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1244 Fractional Delay FIR Filters Design with Enhanced Differential Evolution

Authors: Krzysztof Walczak

Abstract:

Fractional delay FIR filters design method based on the differential evolution algorithm is presented. Differential evolution is an evolutionary algorithm for solving a global optimization problems in the continuous search space. In the proposed approach, an evolutionary algorithm is used to determine the coefficients of a fractional delay FIR filter based on the Farrow structure. Basic differential evolution is enhanced with a restricted mating technique, which improves the algorithm performance in terms of convergence speed and obtained solution. Evolutionary optimization is carried out by minimizing an objective function which is based on the amplitude response and phase delay errors. Experimental results show that the proposed algorithm leads to a reduction in the amplitude response and phase delay errors relative to those achieved with the Least-Squares method.

Keywords: Fractional Delay Filters, Farrow Structure, Evolutionary Computation, Differential Evolution

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1243 Free Vibration of Axially Functionally Graded Simply Supported Beams Using Differential Transformation Method

Authors: A. Selmi

Abstract:

Free vibration analysis of homogenous and axially functionally graded simply supported beams within the context of Euler-Bernoulli beam theory is presented in this paper. The material properties of the beams are assumed to obey the linear law distribution. The effective elastic modulus of the composite was predicted by using the rule of mixture. Here, the complexities which appear in solving differential equation of transverse vibration of composite beams which limit the analytical solution to some special cases are overcome using a relatively new approach called the Differential Transformation Method. This technique is applied for solving differential equation of transverse vibration of axially functionally graded beams. Natural frequencies and corresponding normalized mode shapes are calculated for different Young’s modulus ratios. MATLAB code is designed to solve the transformed differential equation of the beam. Comparison of the present results with the exact solutions proves the effectiveness, the accuracy, the simplicity, and computational stability of the differential transformation method. The effect of the Young’s modulus ratio on the normalized natural frequencies and mode shapes is found to be very important.

Keywords: Differential transformation method, functionally graded material, mode shape, natural frequency.

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1242 Critical Buckling Load of Carbon Nanotube with Non-Local Timoshenko Beam Using the Differential Transform Method

Authors: Tayeb Bensattalah, Mohamed Zidour, Mohamed Ait Amar Meziane, Tahar Hassaine Daouadji, Abdelouahed Tounsi

Abstract:

In this paper, the Differential Transform Method (DTM) is employed to predict and to analysis the non-local critical buckling loads of carbon nanotubes with various end conditions and the non-local Timoshenko beam described by single differential equation. The equation differential of buckling of the nanobeams is derived via a non-local theory and the solution for non-local critical buckling loads is finding by the DTM. The DTM is introduced briefly. It can easily be applied to linear or nonlinear problems and it reduces the size of computational work. Influence of boundary conditions, the chirality of carbon nanotube and aspect ratio on non-local critical buckling loads are studied and discussed. Effects of nonlocal parameter, ratios L/d, the chirality of single-walled carbon nanotube, as well as the boundary conditions on buckling of CNT are investigated.

Keywords: Boundary conditions, buckling, non-local, the differential transform method.

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1241 Stability Analysis of Two-delay Differential Equation for Parkinson's Disease Models with Positive Feedback

Authors: M. A. Sohaly, M. A. Elfouly

Abstract:

Parkinson's disease (PD) is a heterogeneous movement disorder that often appears in the elderly. PD is induced by a loss of dopamine secretion. Some drugs increase the secretion of dopamine. In this paper, we will simply study the stability of PD models as a nonlinear delay differential equation. After a period of taking drugs, these act as positive feedback and increase the tremors of patients, and then, the differential equation has positive coefficients and the system is unstable under these conditions. We will present a set of suggested modifications to make the system more compatible with the biodynamic system. When giving a set of numerical examples, this research paper is concerned with the mathematical analysis, and no clinical data have been used.

Keywords: Parkinson's disease, stability, simulation, two delay differential equation.

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1240 A Study of Hamilton-Jacobi-Bellman Equation Systems Arising in Differential Game Models of Changing Society

Authors: Weihua Ruan, Kuan-Chou Chen

Abstract:

This paper is concerned with a system of Hamilton-Jacobi-Bellman equations coupled with an autonomous dynamical system. The mathematical system arises in the differential game formulation of political economy models as an infinite-horizon continuous-time differential game with discounted instantaneous payoff rates and continuously and discretely varying state variables. The existence of a weak solution of the PDE system is proven and a computational scheme of approximate solution is developed for a class of such systems. A model of democratization is mathematically analyzed as an illustration of application.

Keywords: Differential games, Hamilton-Jacobi-Bellman equations, infinite horizon, political-economy models.

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1239 Positive Solutions for Boundary Value Problems of Fourth-Order Nonlinear Singular Differential Equations in Banach Space

Authors: Li Xiguang

Abstract:

In this paper, by constructing a special non-empty closed convex set and utilizing M¨onch fixed point theory, we investigate the existence of solution for a class of fourth-order singular differential equation in Banach space, which improved and generalized the result of related paper.

Keywords: Banach space, cone, fixed point index, singular differential equation.

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1238 Group Invariant Solutions of Nonlinear Time-Fractional Hyperbolic Partial Differential Equation

Authors: Anupma Bansal, Rajeev Budhiraja, Manoj Pandey

Abstract:

In this paper, we have investigated the nonlinear time-fractional hyperbolic partial differential equation (PDE) for its symmetries and invariance properties. With the application of this method, we have tried to reduce it to time-fractional ordinary differential equation (ODE) which has been further studied for exact solutions.

Keywords: Nonlinear time-fractional hyperbolic PDE, Lie Classical method, exact solutions.

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1237 Biodegradable Cellulose-Based Materials for the Use in Food Packaging

Authors: Azza A. Al-Ghamdi, Abir S. Abdel-Naby

Abstract:

Cellulose acetate (CA) is a natural biodegradable polymer. It forms transparent films by the casting technique. CA suffers from high degree of water permeability as well as the low thermal stability at high temperatures. To adjust the CA polymeric films to the manufacture of food packaging, its thermal and mechanical properties should be improved. The modification of CA by grafting it with N-Amino phenyl maleimide (N-APhM) led to the construction of hydrophobic branches throughout the polymeric matrix which reduced its wettability as compared to the parent CA. The branches built onto the polymeric chains had been characterized by UV/Vis, 13C-NMR and ESEM. The improvement of the thermal properties was investigated and compared to the parent CA using thermal gravimetric analysis (TGA), differential scanning calorimetry (DSC), differential thermal analysis (DTA), contact angle and mechanical testing measurements. The results revealed that the water-uptake was reduced by increasing the graft percentage. The thermal and mechanical properties were also improved.

Keywords: Cellulose acetate, food packaging, graft copolymerization.

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1236 Combating and Preventing Unemployment in Sweden

Authors: Beata Wentura-Dudek

Abstract:

In Sweden the needs of the labor market are regularly monitored. Test results and forecasts translate directly into the education system in this country, which is largely a state system. Sweden is one of the first countries in Europe that has used active labor market policies. It is realized that there is an active unemployment which includes a wide range of activities that can be divided into three groups: Active forms of influencing the creation of new jobs, active forms that affect the labor supply and active forms for people with disabilities. Most of the funding is allocated there for subsidized employment and training. Research conducted in Sweden shows that active forms of counteracting unemployment focused on the long-term unemployed can significantly raise the level of employment in this group.

Keywords: Sweden, research conducted in Sweden, labour market, labour market policies, unemployment, active forms of influencing the creation of new jobs, active forms of counteracting unemployment, employment, subsidized employment education.

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1235 Research of a Multistep Method Applied to Numerical Solution of Volterra Integro-Differential Equation

Authors: M.Imanova, G.Mehdiyeva, V.Ibrahimov

Abstract:

Solution of some practical problems is reduced to the solution of the integro-differential equations. But for the numerical solution of such equations basically quadrature methods or its combination with multistep or one-step methods are used. The quadrature methods basically is applied to calculation of the integral participating in right hand side of integro-differential equations. As this integral is of Volterra type, it is obvious that at replacement with its integrated sum the upper limit of the sum depends on a current point in which values of the integral are defined. Thus we receive the integrated sum with variable boundary, to work with is hardly. Therefore multistep method with the constant coefficients, which is free from noted lack and gives the way for finding it-s coefficients is present.

Keywords: Volterra integro-differential equations, multistepmethods, finite-difference methods, initial value problem

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1234 Research Analysis in Eclectic Theory (Kaboudan and Sfandiar)

Authors: Farideh Alizadeh, Mohd Nasir Hashim

Abstract:

Present research investigates eclecticism in Iranian theatre on the basis of eclectic theory. Eclectic theatre is a new theory in postmodernism. The theory appeared during 60th – 70th century in some theatres such as “Conference of the Birds”. Special theatrical forms have been developed in many geographical- cultural areas of the world and are indigenous to that area. These forms, as compared with original forms, are considered to be traditional while being comprehensive, the form is considered to be national. Kaboudan and Sfandiar theatre has been influenced by elements of traditional form of Iran.

Keywords: Eclectic theatre, theatrical forms, tradition, play.

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