an inverse pollution problem in porous media abstract in this paper we deal with an inverse source problem of integro differential parabolic equations which comes from nonlinear pollution problems in porous media we study the existence and uniqueness of solutions for the direct problem as well as the existence of quasisolutions of the inverse source problem in an appropriate class of admissible source functions

delay independent stability test for systems with multiple time delays delay independent stability dis of a general class of linear time invariant lti multiple time delay system mtds is investigated in the entire delay parameter space stability of such systems may be lost only if their spectrum lies on the imaginary axis for some delays we build an analytical approach that requires the inspection of the roots of finite number of single variable polynomials in order to detect if the spectrum ever lies on the imaginary axis for some delays excluding infinite delays the approach enables to test the necessary and sufficient conditions of dis of lti mtds technically known as weak dis as well as the robust stability of single delay systems against all variations in delay ratios the proposed approach which does not require any parameter sweeping and graphical display becomes possible by establishing a link between the infinite spectrum and algebraic geometry case studies are provided to show the effectiveness of the approach

error analysis of an equation error method for the identification of the diffusion coefficient in a quasi linear parabolic differential equation we consider the inverse problem of reconstructing the diffusion coefficient in a quasi linear parabolic differential equation in divergence form from measurements of the solution at a finite number of points in the interior of the domain an equation error method is developed which transforms the inverse problem into a system of linear operator equations for the diffusion coefficient and which can be solved by the conjugate gradient method in a very efficient and stable manner a detailed error analysis relates the required number of measurements with their accuracy numerical results illustrate the performance of the method

nonbinary quantum codes we present several results on quantum codes over general alphabets that is in which the fundamental units may have more than two states in particular we consider codes derived from finite symplectic geometry assumed to have additional global symmetries from this standpoint the analogs of calderbank shor steane codes and of gf 4 linear codes turn out to be special cases of the same construction this allows us to construct families of quantum codes from certain codes over number fields in particular we get analogs of quadratic residue codes including a single error correcting code encoding one letter in five for any alphabet size we also consider the problem of fault tolerant computation through such codes generalizing ideas of gottesman see phys rev a vol 57 no 1 p127 37 1998

the asymptotic probability distribution of the relative distance of additive quantum codes abstract for given information rate r it is proved as n tends to infinite that almost all additive n n r quantum codes pure and impure are the codes with their relative distance tending to h 1 1 r where h x x log 2 x 3 1 x log 2 1 x is an entropy function

asymptotically good quantum codes exceeding the ashikhmin litsyn tsfasman bound it is known that quantum error correction can be achieved using classical binary codes or additive codes over f sub 4 asymptotically good quantum codes have been constructed from algebraic geometry codes and a bound on spl delta r was computed from the tsfasman vladut zink bound of the theory of classical algebraic geometry codes in this correspondence by the use of a concatenation technique we construct a family of asymptotically good quantum codes exceeding the bound in a small interval

nonbinary quantum stabilizer codes we define and show how to construct nonbinary quantum stabilizer codes our approach is based on nonbinary error bases it generalizes the relationship between self orthogonal codes over f sub 4 and binary quantum codes to one between self orthogonal codes over f q sup 2 and q ary quantum codes for any prime power q

stability and bifurcations of equilibria in a multiple delayed differential equation the influence of multiple negative delayed feedback loops on the stability of a single action mechanism are considered a characteristic equation for the linearized stability of the equilibrium is completely analyzed as a function of two parameters describing a delay in one loop and a ratio of the gains in the two feedback loops the bifurcations occurring as the linear stability is lost are analyzed by the construction of a centre manifold in particular the nature of hopf and more degenerate higher codimension bifurcations are explicitly determined

frequency sweeping tests for stability independent of delay in this paper we study the stability properties of linear time invariant delay systems given in a state space form we consider specifically the notion of asymptotic stability independent of delay systems with both commensurate and noncommensurate delays are investigated we present for each class of systems a necessary and sufficient condition in terms of structured singular values and further we demonstrate how these conditions may be extended to study stability independent of delay for uncertain systems our results consist of several frequency sweeping tests that can be systematically implemented and that should complement the previous work

concatenated quantum codes constructible in polynomial time efficient decoding and error correction a method for concatenating quantum error correcting codes is presented the method is applicable to a wide class of quantum error correcting codes known as calderbank shor steane css codes as a result codes that achieve a high rate in the shannon theoretic sense and that are decodable in polynomial time are presented the rate is the highest among those known to be achievable by css codes moreover the best known lower bound on the greatest minimum distance of codes constructible in polynomial time is improved for a wide range

the existence of binary linear concatenated codes with reed solomon outer codes which asymptotically meet the gilbert varshamov bound binary linear concatenated codes with reed solomon codes as the outer code and varying nonsystematic inner codes are investigated it is shown that codes exist in this class which asymptotically meet the gilbert varshamov bound

an unstable mode selection rule frustrated optical instability due to competing boundary conditions abstract self oscillation phenomenon which occurs in a system with more than one spatial boundary condition may fall into frustration from competition between resonance conditions due to the multiple boundaries in this paper we study a nonlinear optical instability in a compound resonator which is a typical example of this phenomenon in this system for a fixed control parameter the asymptotic behaviour is just oscillation at a single frequency however as the rule which determines the oscillation frequency contains chaos the final oscillation frequency shows a very sensitive dependence on the ratio of lengths of the resonators in the compound cavity elementary number theoretic method is successfully applied to the analysis of this phenomenon and an almost complete selection rule for the oscillating mode is established the selection rule explains very well the recent experiments this can be regarded as a typical example of a system in which the final pattern itself is dynamically stable but the choice of the pattern is unstable with respect to noise in the environment

a note on delay independent stability of a predator prey model abstract this paper analyzes the delay independent stability of a predator prey model with the assistance of the delay independent stability criteria for a class of retarded dynamical systems an interesting result is obtained that the delay independent stability condition is equivalent to the zero delay stability condition in this model the physical meaning of this result is also given

anti periodic solutions to nonlinear evolution equations abstract we deal with anti periodic problems for nonlinear evolution equations with nonmonotone perturbations the main tools in our study are the maximal monotone property of the derivative operator with anti periodic conditions and the theory of pseudomonotone perturbations of maximal monotone mappings

anti periodic solutions to a class of nonlinear differential equations in hilbert space abstract a broad class of nonlinear non monotone anti periodic boundary value problems in a hilbert space is considered as a preliminary step the existence uniqueness and continuous dependence upon data of anti periodic solutions to some first and second order evolution equations associated to odd noncoercive monotone operators is established applications of the theory to nonlinear partial differential equations are also discussed

quantum error detection ii bounds for pt i see ibid vol 46 no 3 p 778 88 2000 in part i of this paper we formulated the problem of error detection with quantum codes on the depolarizing channel and gave an expression for the probability of undetected error via the weight enumerators of the code in this part we show that there exist quantum codes whose probability of undetected error falls exponentially with the length of the code and derive bounds on this exponent the lower existence bound is proved for stabilizer codes by a counting argument for classical self orthogonal quaternary codes upper bounds are proved by linear programming first we formulate two linear programming problems that are convenient for the analysis of specific short codes next we give a relaxed formulation of the problem in terms of optimization on the cone of polynomials in the krawtchouk basis we present two general solutions of the problem together they give an upper bound on the exponent of undetected error the upper and lower asymptotic bounds coincide for a certain interval of code rates close to 1

concatenated quantum codes can attain the quantum gilbert varshamov bound a family of quantum codes of increasing block length with positive rate is asymptotically good if the ratio of its distance to its block length approaches a positive constant the asymptotic quantum gilbert varshamov gv bound states that there exist q ary quantum codes of sufficiently long block length n having fixed rate r with distance at least n h 1 q 2 1 r 2 where h q 2 is the q 2 ary entropy function for q only random quantum codes are known to asymptotically attain the quantum gv bound however random codes have little structure in this paper we generalize the classical result of thommesen to the quantum case thereby demonstrating the existence of concatenated quantum codes that can asymptotically attain the quantum gv bound the outer codes are quantum generalized reed solomon codes and the inner codes are random independently chosen stabilizer codes where the rates of the inner and outer codes lie in a specified feasible region

stability bifurcation and multistability in a system of two coupled neurons with multiple time delays a system of delay differential equations representing a model for a pair of neurons with time delayed connections between the neurons and time delayed feedback from each neuron to itself is studied conditions for the linear stability of the trivial solution of this system are represented in a parameter space consisting of the sum of the time delays between the elements and the product of the strengths of the connections between the elements it is shown that the trivial fixed point may lose stability via a pitchfork bifurcation a hopf bifurcation or one of three types of codimension two bifurcations multistability near these latter bifurcations is predicted using center manifold analysis and confirmed using numerical simulations

a family of asymptotically good quantum codes based on code concatenation we explicitly construct an infinite family of asymptotically good concatenated quantum stabilizer codes where the outer codes use quantum reed solomon codes and the inner codes use a set of special quantum codes in the field of quantum error correcting codes this is the first time that a family of asymptotically good quantum codes is derived from bad codes its occurrence supplies a gap in quantum coding theory

delay independent stability criteria for a class of retarded dynamical systems with two delays in this paper sufficient and necessary delay independent stability criteria are given for a class of retarded dynamical systems with two discrete time delays and parameters the delay independent stability problem of the system is discussed in terms of the stability of the characteristic function which is determined by checking the existence of real roots for some polynomials the criteria are also illustrated by examples

the existence of concatenated codes list decodable up to the hamming bound it is proven that binary linear concatenated codes with an outer algebraic code specifically a folded reed solomon code and independently and randomly chosen linear inner codes achieve with high probability the optimal tradeoff between rate and list decoding radius in particular for any 0 0 there exist concatenated codes of rate at least 1 h e that are combinatorially list decodable up to a fraction of errors the hamming bound states that the best possible rate for such codes cannot exceed 1 h and standard random coding arguments show that this bound is approached by random codes with high probability a similar result with better list size guarantees holds when the outer code is also randomly chosen the methods and results extend to the case when the alphabet size is any fixed prime power q 2

delay independent stability of retarded dynamic systems of multiple degrees of freedom on the basis of generalized sturm theory this paper presents a simple but systematic approach to the delay independent stability analysis of the linear dynamic systems involving multiple degrees of freedom and possibly two time delays the approach enables one to complete the stability analysis in a much simpler way than before through the use of a maple routine given in the paper to demonstrate the approach the paper gives a detailed analysis the corresponding sufficient and necessary conditions as well as stable regions in parameter space of concern for the delay independent stability of a vibrating system with time delays in state feedback an active tendon for a tall structure and an active suspension of a quarter car model

anti periodic solutions for semilinear evolution equations in this paper we use the homotopy method to establish the existence and uniqueness of anti periodic solutions for the nonlinear anti periodic problem a t x bx f t a e t r x t t x t where a t x is a nonlinear map and b is a bounded linear operator from r n to r n sufficient conditions for the existence of the solution set are presented also we consider the nonlinear evolution problems with a perturbation term which is multivalued we show that for this problem the solution set is nonempty and weakly compact in w 1 2 i r n for the case of convex valued perturbation and prove the existence theorems of anti periodic solutions for the nonconvex case all illustrative examples are provided

communicating over adversarial quantum channels using quantum list codes in this correspondence we study quantum communication in the presence of adversarial noise in this setting communicating with perfect fidelity requires a quantum code of bounded minimum distance for which the best known rates are given by the quantum gilbert varshamov qgv bound asking only for arbitrarily high fidelity and letting the sender and receiver use a secret key of length logarithmic in the number of qubits sent we find a dramatic improvement over the qgv rates in fact our protocols allow high fidelity transmission at noise levels for which perfect fidelity is impossible to achieve such rates we introduce fully quantum list codes which may be of independent interest

stability in linear delay equations abstract for linear autonomous differential difference equations of retarded or neutral type necessary and sufficient conditions are given for the zero solution to be stable hyperbolic for all values of the delays

a finite gilbert varshamov bound for pure stabilizer quantum codes a finite gilbert varshamov gv bound for pure stabilizer binary and nonbinary quantum error correcting codes is presented in analogy to the gv bound for classical codes by using several enumerative results in finite unitary geometry from this quantum gv bound we obtain several new binary quantum codes in a nonconstructive way having better parameters than the known codes