consider an n × n matrix polynomial p(λ). a spectral norm distance from p(λ) to the set of n × n matrix polynomials that havea given scalar µ ∈ c as a multiple eigenvalue was introducedand obtained by papathanasiou and psarrakos. they computedlower and upper bounds for this distance, constructing an associated perturbation of p(λ). in this paper, we extend this resultto the case of two given di...

States with v 1 = λ, v 2 = −λ and reciprocal equations in the six-vertex model Abstract The eigenvalues of the transfer matrix in a six-vertex model (with periodic boundary conditions) can be written in terms of n constants v 1 ,. .. , v n , the zeros of the function Q(v). A peculiar class of eigenvalues are those in which two of the constants v 1 , v 2 are equal to λ, −λ , with ∆ = − cosh λ an...

In this paper, the stress concentration around a hole in the single layer composite materials with long fibers is examined. The single layer has an infinite length, limited with and instant thickness and is loaded by a constant tension force p at infinity. The width of the lamina is considered to be finite and bears a hole as a defect. Due to presence of excessive shear stress in the matrix bay...

Recent studies by mathematicians and physicists have identified a close association between the distribution of prime numbers and quantum mechanical laws governing the subatomic dynamics of quantum systems such as the electron or the photon. It is now recognised that Cantorian fractal space-time fluctuations characterise dynamical systems of all space-time scales ranging from the microscopic su...

Fractal geometry (fractional Brownian motion—FBM) is introduced to characterize the pore distribution of porous material. Based on this fractal characterization, a mathematical model of heat conduction is presented to study heat conduction behaviors in porous material with a focus on effective thermal conductivity. The role of pore structure on temperature distribution and heat flux is examined...

We consider aane systems in R n constructed from a given integral invertible and expansive matrix R, and a nite set B of translates, b x := R ?1 x + b; the corresponding measure on R n is a probability measure and xed by the selfsimilarity = jBj ?1 P b2B ?1 b. There are two a priori candidates for an associated orthogonal harmonic analysis : (i) the existence of some subset in R n such that the...

Many basalts from oceanic islands, ridges, and arcs show strong trace element evidence for melting at great depths, where garnet is a stable phase in mantle peridotites. If partial melts ascend to the surface by porous (intergranular) flow processes, the high-pressure garnet signature will be obliterated by diffusive reequilibration at shallower depths in the mantle. Spiegelman and Kenyon [Spie...

This paper addresses the problem of dielectric breakdown in composite materials. The dielectric breakdown model was generalized to describe dielectric breakdown patterns in conductor-loaded composites. Conducting particles are distributed at random in the insulating matrix, and the dielectric breakdown propagates according to new rules to take into account electrical properties and particle siz...