We derive a general expression for an interface parameter which makes possible the design of a neutral elliptic inhomogeneity when the stress field in the surrounding matrix is a polynomial function of nth order and the composite is subjected to antiplane shear deformations. © 2005 Elsevier Ltd. All rights reserved.

The distribution of the initial short-time displacements of a single particle is considered for a class of classical systems of particles under rather general conditions. This class of systems contains canonical equilibrium of a multi-component Hamiltonian system as a special case. We prove that for this class of systems the nth order cumulant of the initial short-time displacements behaves as ...

A tiie-differencing scheme consisting of an initializing step and N repetitions of a set of steps is proposed. For linear equations, the scheme is of Nth order. It is easily programmed and uses a minimal amount of storage space. The order may be changed by changing one parameter. An improved scheme is of Nth order even for nonlinear equations , for N 54.

An experimental design involving sequences of m distinct events can be conceptualized as an nth-order transition probability matrix specifying the probabilities with which each of the m distinct events is to follow certain n-grams. This paper describes a general method for constructing sequences of shortest possible length that satisfy any such matrix and presents a computer program that random...

A nonlinear system possesses an invariancewith respect to a set of transformations if its output dynamics remain invariant when transforming the input, and adjusting the initial condition accordingly. Most research has focused on invariances with respect to time-independent pointwise transformations like translational-invariance (u(t) → u(t) + p, p ∈ R) or scale-invariance (u(t) → pu(t), p ∈ ...

In this letter we present a technique for the implementation of Nth-order ultrafast temporal differentiators. This technique is based on two oppositely chirped fiber Bragg gratings in which the grating profile maps the spectral response of the Nth-order differentiator. Examples of 1(st), 2(nd), and 4(th) order differentiators are designed and numerically simulated.

approximating the solution of differential equations of fractional order is necessary because fractional differential equations have extensively been used in physics, chemistry as well as engineering fields. in this paper with central difference approximation and newton cots integration formula, we have found approximate solution for a class of boundary value problems of fractional order. three...

Wide classes of nonlinear mathematical physics equations are described that admit order reduction through the use of the Crocco transformation, with a first-order partial derivative taken as a new independent variable and a second-order partial derivative taken as the new dependent variable. Associated Bäcklund transformations are constructed for evolution equations of general form (special cas...

This paper is devoted to the derivation of expansion and sampling theorems associated with nth order discontinuous eigenvalue problems defined on [−1, 1], illustrated with detailed examples. The problem consists of nth order differential expressions and n boundary and n compatibility conditions at x = 0. The differential expressions are defined, in general, in two different ways throughout [−1,...

We present a general framework to systematically study the derivative expansion of asymptotically safe quantum gravity. It is based on an exact decoupling and cancellation different modes in Landau limit, implements correct mode count as well regularisation geometrical considerations. applicable independent truncation order. To illustrate power framework, we discuss quartic order its fixed poin...