Codes with a Disparity Property

Kth order zero disparity codes have been considered in several recent papers. In the first part of this paper we remove the zero disparity condition and consider the larger class of codes, Kth order disparity D codes. We establish properties of disparity D codes showing that they have many of the properties of zero disparity codes. We give existence criteria for them, and discuss how new codewords may be formed from ones already known. We then discuss Kth order disparity D codes that have the same number of codewords. We discuss the minimum distance properties of these new codes and present a decoding algorithm for them. In the second part of the paper we look at how the minimum distance of disparity D codes can be improved. We consider subsets of a very specialised subclass, namely first order zero disparity codes over alphabet Aq of size q. These particular subsets have q codewords of length n and minimum Hamming distance n. We show that such a subset exists when q is even and nis a multiple of 4, and also when q is odd and n is even. These subsets have the best error correction capabilities of any subset of q first order zero disparity codewords.     

How to change a boundary condition in a problem to make the problem have a prescribed spectrum

We consider a boundary value problem for an ordinary differential equation of order n with a spectral parameter in n boundary conditions. We suggest a method for changing one of the boundary conditions so as to make the problem have a prescribed spectrum.     

Thermal stress state of a bimaterial with a closed interfacial crack having rough surfaces

We have formulated the problem of thermoelasticity for a bimaterial whose components differ only in their shear moduli, with a closed interfacial crack having rough surfaces. The bimaterial is subjected to the action of compressive loads and heat flow normal to the interfacial surface. We have taken into account the dependence of thermal conductance of the defect on the contact pressure of its faces and heat conductivity of the medium that fills it. The problem is reduced to a Prandtl-type nonlinear singular integro-differential equation for temperature jump between the crack surfaces. An analytical solution of this problem has been constructed for the case of action of the heat flow only. We have analyzed the dependence of contact pressure of the defect faces, temperature jump between them, and the intensity factor of tangential interfacial stresses on the value of given heat flow, roughness of the surfaces, and ratio between the shear moduli of joined materials.     

Perturbation of a periodic operator by a narrow potential

We consider perturbations of a second-order periodic operator on the line; the Schr?dinger operator with a periodic potential is a specific case of such an operator. The perturbation is realized by a potential depending on two small parameters, one of which describes the length of the potential support, and the inverse value of other corresponds to the value of the potential. We obtain sufficient conditions for the perturbing potential to have eigenvalues in the gaps of the continuous spectrum. We also construct their asymptotic expansions and present sufficient conditions for the eigenvalues of the perturbing potential to be absent.     

Boundary value problem for a parabolic system in a domain with a conical point on the boundary

We study the first initial-boundary value problem for strongly parabolic systems in cylinders whose bases have conical points. An illustrating example for the heat equation is presented.     

Isochronicity of centers in a switching Bautin system

In this paper isochronicity of centers is discussed for a class of discontinuous differential system, simply called switching system. We give some sufficient conditions for the system to have a regular isochronous center at the origin and, on the other hand, construct a switching system with an irregular isochronous center at the origin. We give a computation method for periods of periodic orbits near the center and use the method to discuss a switching Bautin system for center conditions and isochronous center conditions. We further find all of those systems which have an irregular isochronous center.     

The Hilbert boundary-value problem with a finite index and a countable set of jump discontinuities in coefficients

We consider the Hilbert boundary-value problem with a finite index for the case, when the coefficients in the boundary condition have two infinite sequences of discontinuity points of the first kind. We obtain a formula for the general solution and study the solvability issues.     

Soliton interaction in a dispersion-decreasing fiber with effective gain and effective phase modulation

We have considered soliton pulse compression in a hyperbolic dispersion-decreasing fiber with fiber loss and phase modulation. We have shown that there is exact balancing between the effective gain and the effective phase modulation as it provides fairly good compression even after compensating for the fiber loss. We have also considered the interaction scenario in detail.     

On a question of Pereira

Answering a question of Pereira we show that it is possible to have a model violating the Singular Cardinal Hypothesis without a tree-like continuous scale. We are grateful to Luis Pereira for asking an interesting question and his comments on the paper. We would like to thank to the referee of the paper for his comments and corrections.     

Optimal static pricing for a tree network

We study the static pricing problem for a network service provider in a loss system with a tree structure. In the network, multiple classes share a common inbound link and then have dedicated outbound links. The motivation is from a company that sells phone cards and needs to price calls to different destinations. We characterize the optimal static prices in order to maximize the steady-state revenue. We report new structural findings as well as alternative proofs for some known results. We compare the optimal static prices versus prices that are asymptotically optimal, and through a set of illustrative numerical examples we show that in certain cases the loss in revenue can be significant. Finally, we show that static prices obtained using the reduced load approximation of the blocking probabilities can be easily obtained and have near-optimal performance, which makes them more attractive for applications.     

Scalars convected by a two‐dimensional incompressible flow

We provide a test for numerical simulations, for several two dimensional incompressible flows, that appear to develop sharp fronts. We show that in order to have a front the velocity has to have uncontrolled velocity growth. © 2001 John Wiley & Sons, Inc.     

Numerical solution for a sub-diffusion equation with a smooth kernel

In this paper we study the numerical solution of an initial value problem of a sub-diffusion type. For the time discretization we apply the discontinuous Galerkin method and we use continuous piecewise finite elements for the space discretization. Optimal order convergence rates of our numerical solution have been shown. We compare our theoretical error bounds with the results of numerical computations. We also present some numerical results showing the super-convergence rates of the proposed method.     

The Drazin Inverse of a Morphism with a Sequence of (epic, monic) Factorizations

§ 1.Ｉｎｔｒｏｄｕｃｔｉｏｎ　Ｉｎ [1 ],ｔｈｅａｕｔｈｏｒｄｅｆｉｎｅｄａｃｃｕｒａｔｅｌｙｔｈｅＤｒａｚｉｎｉｎｖｅｒｓｅｏｆａｍｏｒｐｈｉｓｍ .Ｐｒｅｖｉｏｕｓｌｙ ,ｓｏｍｅｎｅｃｅｓｓａｒｙａｎｄｓｕｆｆｉｃｉｅｎｔｃｏｎｄｉｔｉｏｎｓｗｅｒｅｏｂｔａｉｎｅｄｆｏｒａｍｏｒｐｈｉｓｍｗｉｔｈ (ｅｐｉｃ ,ｍｏｎｉｃ)ｆａｃｔｏｒｉｚａｔｉｏｎｔｏｈａｖｅｔｈｅｇｒｏｕｐｉｎｖｅｒｓｅ (ｓｅｅ [2 ],Ｔｈｅｏｒｅｍ 1 )ａｎｄｔｈｅＤｒａｚｉｎｉｎｖｅｒｓｅｏｆａｍａｔｒｉｘｏｖｅｒｔｈｅｃｏｍｐ…     

Banach空间中的X_d框架与Reisz基

本文引入并研究了Banach空间中的X_d框架,X_d Bessel列,紧X_d框架,独立X_d框架和X_d Riesz基等概念,给出了X_d框架和独立X_d框架的算子等价刻画,Banach空间X中存在X_d框架或X_d Riesz基的充要条件以及X_d框架的对偶框架存在的充要条件,讨论了Banach空间的基和X_d框架,X_d Riesz基之间的关系．     

Application of a posteriori error estimates for Navier‐Stokes equations to fluid flow in a channel with corners

We investigate a posteriori error estimates for the Stokes and Navier‐Stokes equations for incompressible fluid problem on 2D polygonal domains. We have determined accurately the constant that appears in the estimates. We apply these results to the technique of adaptive mesh refinement ‐ we solve an incompressible flow problem in a domain with corners that cause singularities in the solution.     

Product-form characterization for a two-dimensional reflecting random walk

We consider a two-dimensional skip-free reflecting random walk on the non-negative integers, which is referred to as a 2-d reflecting random walk. We give necessary and sufficient conditions for the stationary distribution to have a product-form. We also derive simpler sufficient conditions for the product-form for a restricted class of 2-d reflecting random walks. We apply these results and obtain a product-form approximation of the stationary distribution through a suitable modification of the parameters of the random walk.     

On a global analytic Positivstellensatz

We consider several modified versions of the Positivstellensatz for global analytic functions that involve infinite sums of squares and/or positive semidefinite analytic functions. We obtain a general local-global criterion which localizes the obstruction to have such a global result. This criterion allows us to get completely satisfactory results for analytic curves, normal analytic surfaces and real coherent analytic sets whose connected components are all compact.     

Stressed state of an elastoplastic isotropic shell with a through crack with regard for material hardening

We have solved the problem of determining the stressed state of an elastoplastic isotropic shell of arbitrary curvature with a through crack with regard for material hardening. We have obtained a system of singular integral equations and solved it numerically by the method of mechanical quadratures. We have also studied the influence of material hardening on the general characteristics of the stressed state.     

On Functions with a Unique Identification Minor

We shed some new light to the problem of characterizing those functions of several arguments that have a unique identification minor. The 2-set-transitive functions are known to have this property. We describe another class of functions that have a unique identification minor, namely functions determined by the order of first occurrence. We also present some examples of other kinds of functions with a unique identification minor. These examples have a relatively small arity.     

Green functions of three-dimensional static thermoelasticity problems for a piecewise homogeneous space

The Green functions of thermoelasticity problems for a piecewise homogeneous body, composed of two perfectly contacting semiinfinite isotropic bodies, have been constructed in closed form. We have used here generalized functions and Green functions for the corresponding systems of ordinary differential equations. As the limiting cases, we have obtained the Green functions of thermoelasticity problems for a semiinfinite body, when its surface, thermally insulated or maintained at zero temperature, is load-free or rigidly restrained. We also present some results of numerical studies.