In this paper a modification of He's variational iteration method (VIM) has been employed to solve Dung and Riccati equations. Sometimes, it is not easy or even impossible, to obtain the first few iterations of VIM, therefore, we suggest to approximate the integrand by using suitable expansions such as Taylor or Chebyshev expansions.

This paper is an elementary introduction to the methods of Landsberg and Manivel, [3] for finding the ideals of secant varieties to Segre varieties. We cover only the most basic topics from [3], but hope that since this is a topic which is rarely made explicit, these notes will be of some use. We assume the reader is familiar with the basic operations of multilinear algebra: tensor, symmetric, ...

To provide a geometrical description of the classification theory and the structure theory of varieties of almost minimal degree, that is of non-degenerate irreducible projective varieties whose degree exceeds the codimension by precisely 2, a natural approach is to investigate simple projections of varieties of minimal degree. Let X̃ ⊂ P K be a variety of minimal degree and of codimension at le...

Standard general relativity fails to take into account the changes in coordinates induced by the variation of metric in the Hilbert action principle. We propose to include such changes by introducing a fundamental compensating tensor field uniquely associated with any given coordinatization procedure.

Solving the static equilibrium position is one of the most important parts of dynamic coefficients calculation and further coupled calculation of rotor system. The main contribution of this study is testing the superlinear iteration convergence method—twofold secant method, for the determination of the static equilibrium position of journal bearing with finite length. Essentially, the Reynolds ...

This paper considers the backward error analysis of stochastic differential equations (SDEs), a technique that has been of great success in interpreting numerical methods for ODEs. It is possible to fit an ODE (the so called modified equation) to a numerical method to very high order accuracy. Backward error analysis has been particularly valuable for Hamiltonian systems, where symplectic numer...

This paper is concerned with a class of functional differential equations whose argument transforms are involutions. In contrast to the earlier works in this area, which have used only involutions with a fixed point, we also admit involutions without a fixed point. In the first case, an initial value problem for a differential equation with involution is reduced to an initial value problem for ...

Another new family of Secant-like method is proposed in this paper. Analysis of convergence shows that the method has a super-linear convergence as Secant method. Numerical experiments show that the efficiency of the method is depended on the value of its parameter. AMS Subject Classification: 65D99, 65H05

We show that the secant variety of the Segre variety gives useful information about the geometrical structure of an arbitrary multipartite quantum system. In particular, we investigate the relation between arbitrary bipartite and three-partite entangled states and this secant variety. We also discuss the geometry of an arbitrary general multipartite state.

In this work some interesting relations between results on basic optimization and algorithms for nonconvex functions (such as BFGS and secant methods) are pointed out. In particular, some innovative tools for improving our recent secant BFGS-type and LQN algorithms are described in detail. © 2006 Elsevier B.V. All rights reserved. MSC: 51M04; 65H20; 65F30; 90C53