on the distribution of a random variable occurring in 1d disordered systems the authors consider the random variable z 1 x1 x1x2 x1x2x3 where the xi are independent identically distributed variables they derive some asymptotic properties of the distribution of z which are related e g to the low temperature behaviour of the random field ising chain for a special class of distributions of the xi exact solutions are presented they also study the cases where the distribution function of z exhibits a power law fall off modulated by a periodic critical amplitude

eventual practical stability of impulsive differential equations with time delay in terms of two measurements in this paper we introduce a new stability eventual practical stability for impulsive differential equations with time delay by using lyapunov functions and comparison principle we will get some criteria of eventual practical stability eventual practical quasistability and strong eventual practical stability for impulsive differential equations with time delay in terms of two measurements

a numerical study of diffusion and conduction in a 2d random medium investigates numerically the diffusion and conduction properties of a two dimensional random lattice hopping model the results are compared with a recent field theoretical renormalisation group approach showing that two is the upper critical dimension for such models the predicted scaling law with a universal logarithmic behaviour of the velocity is clearly observed the finiteness of the diffusion constant are well as its regular dependence versus the strength of randomness are evenly in good agreement with analytical results the author also determines the frequency dependence of the ac conductivity tensor

sound scattering by cylinders of noncircular cross section a conformal mapping approach a new method for predicting the far field scattered pressure due to a plane wave incident upon an infinitely long cylinder of noncircular cross section is presented the method referred to herein as the fourier matching method fmm involves conformally mapping the exterior and interior of a closed surface to a semi infinite strip this method is new in that the boundary conditions are satisfied using constraints described in the new angular variable the resultant formulation is numerically efficient much more so than the t matrix method under certain conditions for example and works well for both small and large deviations from a circular cross section as well as penetrable and impenetrable materials furthermore the basis functions generated in the calculation can also improve the efficiency of other methods such as the t matrix method example calculations are presented for elliptic square and three leaf clover cross sections for several types of boundary conditions in all cases the results compare extremely well with exact or high frequency asymptotic results

iterative extended boundary condition method for scattering by objects of high aspect ratios the limitations of the t matrix procedure or the extended boundary condition method ebcm for wave scattering problems when used for long slender objects are due to the shrinking volume over which the incident field is extinguished the resulting ill conditioning of the matrices involved makes it impossible to invert them for nondissipative objects only we observe that the reinforced modified gram schmidt rmgs orthogonalization procedure works best of all such unitary approaches investigated but information about the surface and the internal fields is lost in the process an alternate approach called the iterative ebcm iebcm is more general in its scope since it provides convergent surface and internal field values and can also work for dissipative targets this success of the iebcm results because it extends the interior volume over which the incident field is extinguished

oscillatory critical amplitudes in hierarchical models we study the oscillatory critical amplitudes of theq states potts model on a diamond hierarchical lattice we consider an example of the generic case finite critical index as well as the degenerate case essential singularity in both cases we compare the magnitude of the oscillations with geometrical characteristics of the julia set of zeroes of the partition function

stability of impulsive functional differential equations abstract in this paper the stability of impulsive functional differential equations in which the state variables on the impulses are related to the time delay is studied by using lyapunov functions and razumikhin techniques some criteria of stability asymptotic stability and practical stability for impulsive functional differential equations in which the state variables on the impulses are related to the time delay are provided some examples are also presented to illustrate the efficiency of the results obtained

about some new integral inequalities of wendroff type for discontinuous functions abstract in this article we obtain some new nonlinear integral inequalities for discontinuous functions of two independent variables wendroff type by including also inequalities with delay we deduce new generalizations of earlier results given by r p agarwal r bellman i bihari b k bondge v lakshmikantham s leela b g pachpatte for continuous and discrete functions furthermore generalizations of some results for integro sum inequalities are obtained as well

analytical solution for a reinforcement layer bonded to an elliptic hole under a remote uniform load a general solution to a reinforced elliptic hole embedded in an infinite matrix subjected to a remote uniform load is provided in this paper investigations on the present elasticity problem are rather tedious due to the presence of material inhomogeneities and complex geometric configurations based on the technique of conformal mapping and the method of analytical continuation in conjunction with the alternating technique the general expressions of the displacement and stresses in a reinforcement layer and the matrix are derived explicitly in a series form some numerical results are provided to investigate the effects of the material combinations and geometric configurations on the interfacial stresses the results show that there exists an optimum design of a reinforcement layer such that both the magnitude of stress concentration and the interfacial stresses could be fairly reduced

discontinuous galerkin methods for the helmholtz equation with large wave number this paper develops and analyzes some interior penalty discontinuous galerkin ipdg methods using piecewise linear polynomials for the helmholtz equation with the first order absorbing boundary condition in two and three dimensions it is proved that the proposed discontinuous galerkin methods are stable hence well posed without any mesh constraint for each fixed wave number k optimal order with respect to h error estimate in the broken h 1 norm and suboptimal order estimate in the l 2 norm are derived without any mesh constraint the latter estimate improves to optimal order when the mesh size h is restricted to the preasymptotic regime i e k 2 h gtrsim 1 numerical experiments are also presented to gauge the theoretical result and to numerically examine the pollution effect with respect to k in the error bounds the novelties of the proposed ipdg methods include the following first the methods penalize not only the jumps of the function values across the element edges but also the jumps of the normal and tangential derivatives second the penalty parameters are taken as complex numbers of positive imaginary parts so essentially and practically no constraint is imposed on the penalty parameters since the helmholtz problem is a non hermitian and indefinite linear problem as expected the crucial and the most difficult part of the whole analysis is to establish the stability estimates i e a priori estimates for the numerical solutions to this end the cruxes of our analysis are to establish and to make use of a local version of the rellich identity for the laplacian and to mimic the stability analysis for the pde solutions given in p cummings analysis of finite element based numerical methods for acoustic waves elastic waves and fluid solid interactions in the frequency domain ph d thesis the university of tennessee knoxville tn 2001 p cummings and x feng math models methods appl sci 16 2006 pp 139 160 u hetmaniuk commun math sci 5 2007 pp 665 678

random walk in a one dimensional random medium abstract the random walk of a particle in a one dimensional random medium is examined by means of the equivalent transfer rates technique in the discrete as well as in the continuous version of the model the probability distributions of the energy dependent equivalent transfer rates are found analytically either by a matching procedure in the discrete case or exactly in the continuous model both discrete and continuous models are shown to belong to the same universality class the average probability of presence of the particle at its initial point is then computed for a non zero global bias it decreases at large times according to a negative power law with an exponent depending on disorder and bias when there is no global bias sinai s model the decay at large times follows a logarithmic law

investigations of the properties motion for essential nonlinear systems perturbed by impulses on some hypersurfaces abstract in this work sufficiently conditions boundedness stability asymptotical stability exponential stability attraction practical stability nondisturbed motion systems with impulse perturbations on some hypersurfaces are obtained we formulate the conditions which guarantee that no beating motion of hypersurfaces will be present estimates of cauchy matrix system of variation for approximated system are obtained for different kinds of right side shorted system these estimates are used as one parametric scale increasing functions moreover we also consider two parametric scale such as proposed by demidovich

singular behaviour of certain infinite products of random 2 2 matrices the authors consider an infinite product of random matrices which appears in several physical problems in particular the ising chain in a random field the random matrices depend analytically on a parameter epsilon in such a way that for 0 they all commute under certain conditions they find that the lyapunov index of this product behaves approximately as c 2 for to 0 their approach is based on the decomposition of an exact integral equation for this problem into two reduced equations they give an expression for the exponent alpha in terms of the probability distribution of the matrices and for the proportionality constant c in terms of the solutions of the reduced integral equations in cases where exact results are available agreement is obtained the physical consequences for disordered one dimensional systems are pointed out

singular behavior of the density of states and the lyapunov coefficient in binary random harmonic chains we study the integrated density of statesh 2 of a chain of harmonic oscillators with a binary random distribution of the masses we show in particular that there is a dense set of values of the squared frequency for which the differenceh 2 h 2 has a singularity of the type 2 multiplied by a periodic function of ln where the exponent and the period depend continuously on 2 in the region where 1 2 h is not differentiate on a dense set of points the same type of singularities is also present in the lyapunov coefficient

on the stability of invariant sets of functional differential equations abstract a system of functional differential equations with delay dz dt z t zt where z x y x rn y rm and z is the vector valued functional is considered it is supposed that this system has a positive invariant set x 0 definitions of its stability asymptotic stability and uniform asymptotic stability are given theorems on the uniform asymptotic stability are formulated and proved

periodic solutions to impulsive differential inclusions with constraints abstract the existence of a periodic solution to an impulsive differential inclusion being invariant with respect to a non convex set of state constraints is established by the use a lefschetz type fixed point theorem for set valued maps

about a generalization of bellman bihari type inequalities for discontinuous functions and their applications abstract in the present paper we introduce the conditions of solvability for chaplygin s problem with discontinuous functions in two independent variables satisfying integro sum inequalities the new type of nonlinear integral and wendroff s inequality for discontinuous functions are investigated as applications the conditions of boundedness solutions of partial differential equations of hyperbolic type with impulse influence on some hypersurfaces j r 2 are obtained some historical aspects of the theory of integro sum inequalities are presented

on quasi stability for impulsive differential systems on developpe une theorie de la stabilite relativement a une solution donnee de systemes differentiels impulsifs une telle etude conduit a un mecanisme complique et les notions de stabilite doivent etre modifiees

diffusion in a one dimensional lattice with random asymmetric transition rates the authors study one dimensional continuous time random walks for which the pairs wn wn 1 of nearest neighbour transition rates are assumed to be independent equally distributed random variables the long time asymptotic behaviour of the mean displacement x t is determined exactly for a specific model system in which diodes u 0 and two way bonds lambda v v occur with probabilities p and 1 p respectively for lambda 1 p we find that x t approximately tnu f beta 1ln t where nu ln 1 p ln lambda and beta ln lambda and where f is a periodic function with period 1 the mean displacement thus not only increases slower than linearly in time but exhibits superimposed non decaying oscillations

comments on recent criticism of the t matrix method recently the t matrix method has been criticized in this journal this letter will point out that such criticisms are invalid since they involve comparison with data computed using older versions of the t matrix method furthermore through an extensive bibliography attention is drawn to the wide variety of problems that have been solved using this method

fine structure and complex exponents in power law distributions from random maps discrete scale invariance dsi has recently been documented in time to failure rupture earthquake processes and financial crashes in the fractal geometry of growth processes and in random systems the main signature of dsi is the presence of log periodic oscillations correcting the usual power laws corresponding to complex exponents log periodic structures are important because they reveal the presence of preferred scaling ratios of the underlying physical processes here we present new evidence of log periodicity overlaying the leading power law behavior of probability density distributions of affine random maps with parametric noise the log periodicity is due to intermittent amplifying multiplicative events we quantify precisely the progressive smoothing of the log periodic structures as the randomness increases and find a large robustness our results provide useful markers for the search of log periodicity in numerical and experimental data

shear compliance of two dimensional pores possessing n fold axis of rotational symmetry we use the complex variable method and conformal mapping to derive a closed form expression for the shear compliance parameters of some two dimensional pores in an elastic material the pores have

field induced drift and trapping in percolation networks the authors study the effects of a bias producing external field on a random walk on the infinite cluster in the percolation problem there are two competing physical effects drift and trapping which result in a drift velocity nu which rises and then falls as the field increases they study these effects on a one dimensional lattice with random length branches and on the diluted bethe lattice they calculate nu in the first model with a maximum allowed length for each branch in the limit that this cutoff length becomes infinite they find that the velocity vanishes identically above a finite critical value of the field for the bethe lattice they derive an upper bound on the critical field which varies as p pc 1 2 as the percolation concentration pc is approached in the one dimensional model they also investigate the anomalous regime in which the velocity vanishes they discuss the distribution of steady state times required to traverse n sites and find that it can be described in terms of a stable distribution of index x with superimposed oscillations the index x of the stable distribution is given by l xi where xi is a characteristic branch length and l is a bias induced length which describes the exponential buildup of the steady state density of particles towards the end of a branch

diffusion in random one dimensional systems diffusion on the one dimensional lattice is described by a master equation with nearest neighbor transfer rates symmetric or asymmetric the transfer rates associated with bonds are assumed to be independent equally distributed random variables under various conditions on their common distribution the large time behavior of averaged site probabilities and or related quantities is exhibited

conformal mapping for the helmholtz equation acoustic wave scattering by a two dimensional inclusion with irregular shape in an ideal fluid the complex variables method with mapping function was extended to solve the linear acoustic wave scattering by an inclusion with sharp smooth corners in an infinite ideal fluid domain the improved solutions of helmholtz equation shown as bessel function with mapping function as the argument and fractional order bessel function were analytically obtained based on the mapping function the initial geometry as well as the original physical vector can be transformed into the corresponding expressions inside the mapping plane as all the physical vectors are calculated in the mapping plane this method can lead to potential vast savings of computational resources and memory in this work the results are validated against several published works in the literature the different geometries of the inclusion with sharp corners based on the proposed mapping functions for irregular polygons are studied and discussed the findings show that the variation of angles and frequencies of the incident waves ha

transition operators in electromagnetic wave diffraction theory ii applications to optics this paper is the second of a series the first g e hahne phys rev a 45 7526 1992 developed a general theory of the transition operator approach to diffraction of time harmonic electromagnetic waves from fixed obstacles such that the response of the obstacle denoted by ensuremath omega to an impinging electromagnetic signal with wave number mathit k 0 was simulated by nonlocal homogeneous leontovich i e impedance boundary conditions on the obstacle s surface which surface is called ensuremath partial ensuremath omega moreover the exterior region called mathrm ensuremath omega mathrm ex was presumed to be unbounded empty space and has an electromagnetic response that can be expressed in terms of the so called radiation impedance operator denoted z mathrm ifmmode breve else u fi mathit k 0 z mathrm ifmmode breve else u fi mathit k 0 is a certain invertible linear functional operator that maps the space of complex tangent vector fields on ensuremath partial ensuremath omega into itself

bifurcations of periodic solutions of delay differential equations abstract in this paper we develop kaplan yorke s method and consider the existence of periodic solutions for some delay differential equations we especially study hopf and saddle node bifurcations of periodic solutions with certain periods for these equations with parameters and give conditions under which the bifurcations occur we also give application examples and find that hopf and saddle node bifurcations often occur infinitely many times

integro sum inequalities and motion stability of systems with impulse perturbations abstract this article is devoted to the investigation of the properties of motion represented by essential nonlinear system of differential equations with impulse effect the results based on the solvability problem by s a chaplygin for discontinuous functions satisfy integro sum inequalities the conditions of boundedness stability asymptotical stability practical stability attraction motion for different kinds of nonlinearities of systems are obtained

existence of optimal controls for a general class of impulsive systems on banach spaces this paper presents some results on the question of existence of optimal controls for a large class of semilinear impulsive systems in infinite dimensional spaces with admissible controls from the space of vector measures this also includes as a special case the class of purely impulsive controls two physical examples are presented for illustration

some problems in plane thermopiezoelectric materials with holes piezoelectric materials have recently attracted considerable attention due to their potential use in intelligent structural systems in this paper we treat the plane problem of thermopiezoelasticity with various holes and subject to coupled mechanical electric and thermal loads an analytical solution is obtained by applying the technique of conformal mapping and some identities in the stroh formalism the solution has a simple unified form for various holes such as ellipse circle triangle and square by way of the solution the expressions for the energy release rate and stress intensity factors of cracks are presented numerical results for concentration coefficients of stress and electric displacement along the hole boundary are given to assess the acceptability of the proposed method

compressibility of two dimensional pores having n fold axes of symmetry the complex variable method and conformal mapping are used to derive a closed form expression for the compressibility of an isolated pore in an infinite two dimensional isotropic elastic body the pore is assumed to have an n fold axis of symmetry and be represented by at most four terms in the mapping function that conformally maps the exterior of the pore into the interior of the unit circle the results are validated against some special cases available in the literature and against boundary element calculations by extrapolation of the results for pores obtained from three and four terms of the schwarz christoffel mapping function for regular polygons the compressibilities of a triangle square pentagon and hexagon are found to at least three digits specific results for some other pore shapes more general than the quasi polygons obtained from the schwarz christoffel mapping are also presented an approximate scaling law for the compressibility in terms of the ratio of perimeter squared to area is also tested this expression gives a reasonable approximation to the pore compressibility but may overestimate it by as much as 20

p moment stability of stochastic differential equations with impulsive jump and markovian switching this paper introduces some new concepts of p moment stability for stochastic differential equations with impulsive jump and markovian switching some stability criteria of p moment stability for stochastic differential equations with impulsive jump and markovian switching are obtained by using liapunov function method an example is also discussed to illustrate the efficiency of the obtained results

impulsive differential systems the problem of stability and practical stability abstract this article is devoted to the analysis properties of the solutions of nonlinear impulsive differential systems with perturbations on some hypersurfaces t i x the conditions of boundedness practical stability uniformly attractive stability uniformly asymptotical attraction of the solutions perturbed system by using linear approximation are obtained

t matrix methods in acoustic scattering some further refinements are described for the t matrix approach to acoustic scattering from the structure of the matrices involved one can infer the rayleigh limit explicitly for objects having no density contrast one finds tray ir r2 where the r matrix involves integrals of the regular spherical wave functions over the object s surface the index of refraction and loss factor can be chosen as desired and energy balance and reciprocity requirements are found to be met the derivation can be extended to obtain the rayleigh expansion effectively describing t as a series in ascending powers of the ratio of object size to wavelength in trial cases the series converges throughout the rayleigh region and somewhat beyond bodies of high aspect ratio are also considered where difficulties arise due to precision loss during numerical integration loss ranges from 4 or 5 significant figures 2 1 spheroid to 22 figures 40 1 spheroid or more a class of surfaces has been found for which this problem can

stability criteria for impulsive differential equations in terms of two measures in general the stability notions of a given solution d t of an impulsive differential system cannot be transferred to the stability notions of the trivial solution by change of variables this is because of the fact that moments of impulse effects of 4 t need not be the same as that of a different solution x t and therefore demanding that the difference lx t d t 1 be small for all future time seems unnatural see 4 73 as a result the definitions of stability require suitable changes in the general situations and the corresponding theory has not yet been developed however in the case of impulsive differential systems with fixed moments of impulse effects such a problem does not arise and hence the standard definitions of stability will suffice employing suitable discontinuous lyapunov functions stability theory has recently been developed for such systems 1 2 3 51 in this paper we shall discuss stabiliy theory of impulsive differential systems with fixed moments of impulse effects in terms of two measures since such a theory enables us to unify a variety of stability results found in the literature we shall employ theory of impulsive differential inequalities as well as a direct approach to bring out the advantages of each approach

some new integral inequalities of bellman bihari type with delay for discontinuous functions abstract in this article we investigate some integral functional inequalities of bellman bihari type for piecewise continuous functions with some fixed points of discontinuity we also prove a new analogy and generalization of results which were obtained by bellman and bihari to integro sum inequalities with delay and discontinuities that do not belong to lipschitz s type

practical and asymptotic stabilization of chained systems by the transverse function control approach a control approach for the practical and asymptotic stabilization of nonlinear driftless systems subjected to additive perturbations is proposed such perturbations arise naturally for instance in the modeling of trajectory stabilization problems for controllable driftless systems on lie groups the objective of the approach is to provide practical stability of an arbitrary given point in the state space whatever the perturbations and asymptotic stability resp convergence to the point when the perturbations are absent resp tend to zero a general framework is presented in this paper and a control solution is proposed for the class of the chained systems

a boundary integral equation method using auxiliary interior surface approach for acoustic radiation and scattering in two dimensions this paper presents an effective solution method for predicting acoustic radiation and scattering fields in two dimensions the difficulty of the fictitious characteristic frequency is overcome by incorporating an auxiliary interior surface that satisfies certain boundary condition into the body surface this process gives rise to a set of uniquely solvable boundary integral equations distributing monopoles with unknown strengths over the body and interior surfaces yields the simple source formulation the modified boundary integral equations are further transformed to ordinary ones that contain nonsingular kernels only this implementation allows direct application of standard quadrature formulas over the entire integration domain that is the collocation points are exactly the positions at which the integration points are located selecting the interior surface is an easy task moreover only a few corresponding interior nodal points are sufficient for the computation numerical calculations consist of the acoustic radiation and scattering by acoustically hard elliptic and rectangular cylinders comparisons with analytical solutions are made numerical results demonstrate the efficiency and accuracy of the current solution method