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In this paper, we use the decomposition technique of Noor and Noor [M. A. Noor and K. I. Noor, Three-step iterative methods for nonlinear equations, preprint (2006)] to suggest and analyze a new iterative methods for solving the integral equations. Our method of developing this new method is very simple as compared with other methods. Several numerical examples are given to illustrate the efficiency and performance of the new method. Results reveal that the proposed method is very effective and simple. Our method can be considered as an improvement of the existing methods. [ABSTRACT FROM AUTHOR]

This paper investigates the global synchronization problem of master-slave coupled multi-scroll saturated chaotic systems via single-state linear feedback control. An algebraic criterion for global synchronization is rigorously proven by means of the absolute stability theory. The obtained algebraic criterion is then optimized thereby deriving a less-conservative result, which is finally verified by numerical examples. [ABSTRACT FROM AUTHOR]

The predictions of the Quantum Theory have been verified so far with astonishingly high accuracy. Despite of its impressive successes, the theory still presents mysterious features such as the border line between the classical and quantum world, or the deep nature of quantum nonlocality. These open questions motivated in the past several proposals of alternative and/or generalized approaches. We shall discuss in the present paper alternative theories that can be infered from a reconsideration of the status of time in quantum mechanics. Roughly speaking, quantum mechanics is usually formulated as a memory free (Markovian) theory at a fundamental level, but alternative, nonMarkovian, formulations are possible, and some of them can be tested in the laboratory. In our paper we shall give a survey of these alternative proposals, describe related experiments that were realized in the past and also formulate new experimental proposals. [ABSTRACT FROM AUTHOR]

The Šil'nikov homoclinic theorem provides one analytic criterion for proving the existence of chaos in three-dimensional autonomous nonlinear systems. In applications of the theorem, however, the existence of a homoclinic orbit that usually determines the geometric structure of the chaotic attractor is not easily verified mainly because there are no available efficient methods. In this paper, based on the undetermined coefficient approach we present a framework of how to find homoclinic orbits in two classes of three-dimensional autonomous nonlinear systems of normal forms, including how to set a reasonable form of expanding series of the homoclinic orbit, how to determine all coefficients in the expansion, and how to find a numerical homoclinic orbit. Numerical examples show that the proposed framework in combination with computer simulation is very efficient. [ABSTRACT FROM AUTHOR]

This paper is concerned with modified integration algorithm in the strain space for rate and temperature dependent elasto-plastic constitutive relations in order to obtain more accurate results in numerical implementation. The proposed algorithm adopts both the 2-stage Lobatto IIIA with second-order accuracy and the iteration procedure using the Newton–Raphson method to enfoce consistency at the end of the step. The algorithm enables to consider the convective stress rates on the yield surface in the strain space in the numerical integration of the constitutive model. Accuracy assessment using the isoerror maps and FEM analysis of the adiabatic shear band is carried out in order to demonstrate the accuracy of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, a fractional-order hyperchaotic system evolved from Liu system is proposed. Based on the theory of fractional calculus, a novel circuit diagram is designed for hardware implementation of the fractional-order hyperchaotic Liu system. Furthermore, implementation results reveal that hyperchaos can be generated in the hyperchaotic Liu system with the system order as low as 3.6 and numerical analysis results demonstrate that the lowest order of the fractional-order Liu system is 0.4. [ABSTRACT FROM AUTHOR]

In this paper, the orbital forming simulation of an automotive hub bearing was studied to predict forming conditions and performances using the explicit finite element method. To set up an efficient solution technique for the orbital forming, axisymmetric finite element models and 3D solid element models were numerically solved and compared to each other. The time scaling and mass scaling techniques were introduced to reduce the excessive computational time caused by small element size in case of the explicit finite element method. It was found from the numerical results on the orbital forming that the axisymmetric element models showed the similar results to the 3D solid element models in forming loads whereas the deformations at the bearing inner race were quite different. Finally the strains at the bearing inner race and the forming forces of the peen were measured by test for the same product used in the numerical analysis, and were compared with the 3D solid element results. It was shown that the test results were in good agreements with the numerical ones. [ABSTRACT FROM AUTHOR]

This contribution addresses a possible description of the chaotic behavior in multivalued dynamical systems. For the multivalued system formulated via differential inclusion the practical conditions on the right-hand side are derived to guarantee existence of a solution, which leads to the chaotic behavior. Our approach uses the notion of the generalized semiflow but it does not require construction of a selector on the set of solutions. Several applications are provided by concrete examples of multivalued dynamical systems including the one having a clear physical motivation. [ABSTRACT FROM AUTHOR]

Based on a variable separated ODE method presented by Sirendaoreji and Sun, a modified variable separated ODE method is developed to uniformly construct the explicit exact solutions of sine-Gordon type equations by introducing a more general additional variable separated ODE. We demonstrate the effectiveness of our approach by applications to certain physically significant sine-Gordon type equations comprising the sine-Gordon equation and double sine-Gordon equation as particular examples. As a result, we cannot only recover the previously known exact solutions, but also pick up some new formal solutions for the sine-Gordon equation and double sine-Gordon equation by means of this approach. [ABSTRACT FROM AUTHOR]

Two-dimensional problem is systematically investigated for the coupled equations in two-dimensional decagonal quasicrystals, and three general solutions are presented by an operator method. To simplify governing equations, each general solution shall take three different forms expressed in terms of three displacement functions, which satisfy partial three differential equations of second order. To illustrate its utility, the closed-form solutions are obtained for problems of point phonon forces and phason force acting at the apex of a quasicrystal wedge, all in terms of the general solutions. Furthermore, these solutions can be degenerated to those of problems of point forces applied on the boundary of a quasicrystal half-plane. [ABSTRACT FROM AUTHOR]

For second order elliptic equations with rapidly oscillating coefficients, we make some theoretical analysis for a multi-scale finite element algorithm on condition that rapidly oscillating coefficients aij belong to Sobolev spaces W1, p(Q)(1≤p<2). Finally, we employ some numerical experiments to demonstrate those theoretical results. [ABSTRACT FROM AUTHOR]

Exact analytical expressions for the Dirac-Slater-Marvin radial integrals of the type $DF_k^{(\mu, \nu)}(1;1)$, $DF_k^{(\mu, \nu)}(1;2)$ and $DG_k^{(\mu, \nu)}(1, 2)$ by means of Gauss's functions 2F1(z) and also their exact numerical values are first given. (Author has all the values of these integrals for arbitrary nlj-states of H-like for Z≤137, i.e., actually for all Mendeleev's table.) [ABSTRACT FROM AUTHOR]

A lattice BGK model for simulating solitary waves of the combined KdV-MKDV equation, ut+αuux-βu2ux+δuxxx = 0, is established. The tunable parameters in Chapman-Enskog expansion of the local equilibrium distribution function are determined by the coefficient of the combined KdV-MKDV equation. Simulating results fit close in with the theoretical results. [ABSTRACT FROM AUTHOR]

The Barabási–Albert (BA) model is extended to include the concept of local world and the microscopic event of adding edges. With probability p, we add a new node with m edges which preferentially link to the nodes presented in the network; with probability 1-p, we add m edges among the present nodes. A node is preferentially selected by its degree to add an edge randomly among its neighbors. Using the continuum theory and the rate equation method we get the analytical expressions of the power-law degree distribution with exponent γ=3 and the clustering coefficient c(k)~k-1+c. The analytical expressions are in good agreement with the numerical calculations. [ABSTRACT FROM AUTHOR]