extensions of the method of poles for code construction the method of poles is a method introduced by franaszek 1969 for constructing a rate 1 1 finite state code from k ary data into a constrained channel of finite type whose capacity is strictly greater than log k the method is based on the computation of a set of states called poles with each pole is associated a set of paths going from this pole to others each set verifies an entropy condition the code produced by the method of poles has a sliding block decoder if each set of paths satisfies moreover an optimization condition based on the sum of the path lengths of the set we give a new optimization condition which guarantees the sliding block window decoding property and has a lower computational complexity than the previous one we also extend the method of poles to the more general case of sofic constrained channels

nonclassical properties of semi coherent quantum states we study the properties of semi coherent quantum states introduced by mathews and eswaran in 1973 establishing relations between them and other families of nonclassical states such as displaced number states and multiphoton states we also analyse the photon number distribution photon statistics the wigner and marginal distribution functions and show the ways for possible further generalizations

uniform preconditioners for a parameter dependent saddle point problem with application to generalized stokes interface equations we consider an abstract parameter dependent saddle point problem and present a general framework for analyzing robust schur complement preconditioners the abstract analysis is applied to a generalized stokes problem which yields robustness of the cahouet chabard preconditioner motivated by models for two phase incompressible flows we consider a generalized stokes interface problem application of the general theory results in a new schur complement preconditioner for this class of problems the robustness of this preconditioner with respect to several parameters is treated results of numerical experiments are given that illustrate robustness properties of the preconditioner

dual primal feti methods for three dimensional elliptic problems with heterogeneous coefficients in this paper certain iterative substructuring methods with lagrange multipliers are considered for elliptic problems in three dimensions the algorithms belong to the family of dual primal finite element tearing and interconnecting feti methods which recently have been introduced and analyzed successfully for elliptic problems in the plane the family of algorithms for three dimensions is extended and a full analysis is provided for the new algorithms particular attention is paid to finding algorithms with a small primal subspace since that subspace represents the only global part of the dual primal preconditioner it is shown that the condition numbers of several of the dual primal feti methods can be bounded polylogarithmically as a function of the dimension of the individual subregion problems and that the bounds are otherwise independent of the number of subdomains the mesh size and jumps in the coefficients these results closely parallel those of other successful iterative substructuring methods of primal as well as dual type

complexity and sliding block decodability a constrained system or sofic system s is the set of symbol strings generated by the finite length paths through a finite labeled directed graph karabed and marcus 1988 extending the work of adler coppersmith and hassner 1983 used the technique of state splitting to prove the existence of a noncatastrophic rate p q finite state encoder from binary data into s for any input word length p and codeword length q satisfying p q spl les cap s the shannon 1948 capacity for constrained systems that are almost finite type they further proved the existence of encoders enjoying a stronger form of decodability namely sliding block decodability in particular their result implies the existence of a 100 efficient rate 1 2 sliding block code for the charge constrained runlength limited constraint with parameters d k c 1 3 3 an almost finite type system with capacity precisely 1 2 we describe two quite different constructions of such codes the constructions highlight connections between the problem of determining sliding block decodability of a finite state encoder and certain problems of colorability for graphs and sets using these connections we show that the problem of determining the existence of a block decodable input tag assignment for a given rate p q finite state encoder is np complete for p 1 we also prove np completeness results for several related problems in combinatorics and coding

sofic systems and encoding data techniques of symbolic dynamics are applied to prove the existence of codes suitable for certain input restricted channels this generalizes the earlier work of adler coppersmith and hassner on the same problem

convergence estimates for multigrid algorithms without regularity assumptions a new technique for proving rate of convergence estimates of multi grid algorithms for symmetric positive definite problems will be given in this paper the standard multigrid theory requires a regularity and approxima tion assumption in contrast the new theory requires only an easily verified approximation assumption this leads to convergence results for multigrid re finement applications problems with irregular coefficients and problems whose coefficients have large jumps in addition the new theory shows why it suffices to smooth only in the regions where new nodes are being added in multigrid refinement applications

an unfitted finite element method based on nitsche s method for elliptic interface problems in this paper we propose a method for the finite element solution of elliptic interface problem using an approach due to nitsche the method allows for discontinuities internal to the elements in the approximation across the interface we show that optimal order of convergence holds without restrictions on the location of the interface relative to the mesh further we derive a posteriori error estimates for the purpose of controlling functionals of the error and present some numerical examples

optimized interface conditions in domain decomposition methods for problems with extreme contrasts in the coefficients when the coefficients of a problem have jumps of several orders of magnitude and are anisotropic many preconditioners and domain decomposition methods ddm suffer from plateaus in the convergence due to the presence of very small isolated eigenvalues in the spectrum of the preconditioned linear system one way to improve the preconditioner is to use a linear algebra technique called deflation or very similarly coarse grid corrections in both cases it is necessary to identify and compute at least approximately all the eigenvectors corresponding to the bad eigenvalues in the framework of ddm we propose a way to design interface conditions so that convergence is fast and does not have any plateau the method relies only on the knowledge of the smallest and largest eigenvalues of an auxiliary matrix the eigenvectors are not used the method relies on van der sluis result on a quasi optimal diagonal preconditioner for a symmetric positive definite matrix it is then possible to design robin interface conditions using only one real parameter for the entire interface by adding a second real parameter and more general interface conditions it is possible to take into account highly heterogeneous and anisotropic media numerical results are given and compared with other approaches

variable length state splitting with applications to average runlength constrained arc codes a new class of constrained systems average runlength constraints arcs is defined by requiring that the sum of n consecutive run lengths be bounded above by a linear function of n in particular the running average runlength of every sequence in the system is bounded above by a constant a general result is given on the capacity of arc systems the state splitting algorithm is then improved for variable length graphs this is then applied to obtain high fixed rate codes from the free binary source to arc systems as an example a rate 1 2 d k

finite element discretization of the navier stokes equations with a free capillary surface the instationary navier stokes equations with a free capillary boundary are considered in 2 and 3 space dimensions a stable finite element discretization is presented the key idea is the treatment of the curvature terms by a variational formulation in the context of a discontinuous in time space time element discretization stability in weak energy norms can be proved numerical examples in 2 and 3 space dimensions are given

optimized schwarz methods without overlap for highly heterogeneous media in this paper an original variant of the schwarz domain decomposition method is introduced for heterogeneous media this method uses new optimized interface conditions specially designed to take into account the heterogeneity between the sub domains on each sides of the interfaces numerical experiments illustrate the dependency of the proposed method with respect to several parameters and confirm the robustness and efficiency of this method based on such optimized interface conditions several mesh partitions taking into account multiple cross points are considered in these experiments

temporally stable coherent states for infinite well and poschl teller potentials this article is a direct illustration of a construction of coherent states which has been recently proposed by two of us jpg and jk we have chosen the example of a particle trapped in an infinite square well and also in poschl teller potentials of the trigonometric type in the construction of the corresponding coherent states we take advantage of the simplicity of the solutions which ultimately stems from the fact they share a common su 1 1 symmetry a la barut girardello many properties of these states are then studied both from mathematical and from physical points of view

bounded delay encodable block decodable codes for constrained systems we introduce and investigate the class of bounded delay encodable block decodable bdb codes several characterizations for this class of codes are given and some construction methods especially for one symbol look ahead bdb codes are described in another direction we use our results to show the existence of a decision procedure for some basic coding problems

a note on the method of poles for code construction the method of poles is a method for constructing a rate 1 1 finite state code from k ary data into a constrained channel s where s is recognized by a given local automaton and s has capacity at least log k we characterize those automata to which the method of poles applies in the case where h s log k the code produced by the method of poles has a sliding block decoder we also give an upper bound on the window length of the decoder that applies when h s spl ges log k

balancing domain decomposition for problems with large jumps in coefficients the balancing domain decomposition algorithm uses in each iteration solution of local problems on the subdomains coupled with a coarse problem that is used to propagate the error globally and to guarantee that the possibly singular local problems are consistent the abstract theory introduced recently by the first named author is used to develop condition number bounds for conforming linear elements in two and three dimensions the bounds are independent of arbitrary coefficient jumps between subdomains and of the number of subdomains and grow only as the squared logarithm of the mesh size h computational experiments for two and three dimensional problems confirm the theory

photon added coherent states as nonlinear coherent states the states m defined as up to a normalization constant and where m is a non negative integer are shown to be the eigenstates of where is a nonlinear function of the number operator the explicit form of is constructed the eigenstates of this operator for negative values of m are introduced the properties of these states are discussed and compared with those of the state m the eigenstates corresponding to the positive and negative values of m are shown to be the result of nonunitarily deforming the number states m and 0 respectively

sliding block coding for input restricted channels work on coding arbitrary sequences into a constrained system of sequences called a sofic system is presented such systems model the input constraints for input restricted channels e g run length limits and spectral constraints for the magnetic recording channel in this context it is important that the code be noncatastrophic to ensure that the decoder has limited error propagation a constructive proof is given of the existence of finite state invertible noncatastrophic codes from arbitrary n ary sequences to a sofic system s at constant rate p q provided only that shannon s condition p q

a linear bound for sliding block decoder window size ii for pt i see ibid vol 34 p 389 99 1988 an input constrained channel is the set s of finite sequences of symbols generated by the walks on a labeled finite directed graph g which is said to present s we introduce a new construction of finite state encoders for input constrained channels the construction is a hybrid of the state splitting technique of adler coppersmith and hassner 1983 and the stethering technique of ashley marcus and roth see ibid vol 41 p 55 76 1995 when s has finite memory and p and g are integers where p g is at most the capacity of s the construction guarantees an encoder at rate p g and having a sliding block decoder literally at rate q p with look ahead that is linear in the number of states of the smallest graph g presenting s this contrasts with previous constructions the straight adler coppersmith and hassner construction provides an encoder having a sliding block decoder at rate q p but the best proven upper bound on the decoder look ahead is exponential in the number of states of g a previous construction of ashley provides an encoder having a sliding block decoder whose look ahead has been proven to be linear in the number of states of g but the decoding is at rate tq tp where t is linear in the number of states of g

coherent states for systems with discrete and continuous spectrum for a system with one degree of freedom coherent states that are parametrized by classical canonical action angle variables are introduced these states also possess continuity of labelling a resolution of unity and temporal stability the insistence on canonical action angle variables strongly restricts any remaining arbitrariness in the coherent state definition such states are introduced for semibounded hamiltonian operators having either a discrete or a continuous spectrum hamiltonians that have both discrete and continuous parts in their spectrum are also discussed

the method of poles a coding method for constrained channels a method for solving coding problems involving channels restricted by finite state constraints is presented the method was introduced by p a franaszek 1969 and is based on the computation of a set of principal states it is proved that state independent decoding is guaranteed the main result is that the transducer constructed using the method is a local automaton in its output the method is also related to recent work in symbolic dynamics by r l adler 1987 b marcus 1985 and others typical applications are coding methods for magnetic storage

new physics in landau levels the most general displaced number coherent states based on the heisenberg su 2 and su 1 1 lie algebras symmetries are constructed they depend on two parameters and can be converted into the well known photon added two variable glauber coherent states and displaced number states respectively depending on which of the parameters is equal to zero the relations of the weyl heisenberg algebra guarantee a corresponding resolution of the identity conditions a discussion of the statistical properties of these states is included significant are their squeezing properties which can be raised by increasing the energy and angular momentum quantum numbers n and m the maximum squeezing is obtained for bext 0 depending on the particular choice of parameters in the above scenarios we are able to determine the status of compliance with poissonian statistics in the limiting case we obtain a major result about the non classical properties of the glauber minimum uncertainty coherent states in other words in addition to the requirement to minimize uncertainty conditions they carry non classical features too finally a theoretical framework is proposed to generate them

a boundary condition capturing method for poisson s equation on irregular domains interfaces have a variety of boundary conditions or jump conditions that need to be enforced the ghost fluid method gfm was developed to capture the boundary conditions at a contact discontinuity in the inviscid euler equations and has been extended to treat more general discontinuities such as shocks detonations and deflagrations and compressible viscous flows in this paper a similar boundary condition capturing approach is used to develop a new numerical method for the variable coefficient poisson equation in the presence of interfaces where both the variable coefficients and the solution itself may be discontinuous this new method is robust and easy to implement even in three spatial dimensions furthermore the coefficient matrix of the associated linear system is the standard symmetric matrix for the variable coefficient poisson equation in the absence of interfaces allowing for straightforward application of standard black box solvers

an asymptotic solution approach for elliptic equations with discontinuous coefficients when the coefficients of an elliptic problem have jumps of several orders of magnitude across an embedded interface many iterative solvers exhibit deteriorated convergence properties or a loss of efficiency and it is difficult to achieve high solution accuracies in the whole domain in this paper we present an asymptotic solution approach for the elliptic problem b x u x f x on a domain w w w with piecewise constant coefficients b b with b b and prescribed jump conditions at an embedded interface c separating the domains w and w we are in particular focusing on a problem related to fluid mechanics namely incompressible two phase flow with a large density ratio across the phase boundary where an accurate solution of the velocity depends on the accurate solution of a pressure poisson equation with equal local relative errors in the whole domain instead of solving the equation in a single solution step we decompose the problem into two consecutive problems based on an asymptotic analysis of the physical problem where each problem is asymptotically independent of the ratio of coefficients e b b the proposed methods lead to a robust and accurate solution of the elliptic problem using standard black box iterative solvers

new nonlinear coherent states based on hypergeometric type operators the main goal of this paper is to present an alternative method to construct new kinds of nonlinear coherent states to do this we first establish a class of hypergeometric type of generalized displacement operators 1fr 0 0 1 r 1 za act on the vacuum state of the harmonic oscillator and generate normalized quantum states of the fock space which admit a resolution of the identity through a positive definite measure on the complex plane furthermore realization of the compact form of these states as functions of the position coordinate x for r 2 leads to a generating function of the hermite polynomials in terms of the modified bessel function finally studying some statistical characters reveals that they have indeed non classical features such as squeezing an anti bunching effect and sub poissonian statistics too

on the construction of bounded delay encodable codes for constrained systems we present a new technique to construct sliding block modulation codes with a small decoding window our method which involves both state splitting and look ahead encoding crucially depends on a new local construction method for bounded delay codes we apply our method to construct several new codes all with a smaller decoding window than previously known codes for the same constraints at the same rate

a numerical method for solving variable coefficient elliptic equation with interfaces a new 2nd order accurate numerical method on non body fitting grids is proposed for solving the variable coefficient elliptic equation in disjoint subdomains w separated by interfaces c the variable coefficients the source term and hence the solution itself and its derivatives may be discontinuous across the interfaces jump conditions in solution and its co normal derivative at interface are prescribed instead of smooth the interfaces are only required to be lipschitz continuous as submanifold a weak formulation is developed the existence uniqueness and regularity of the solutions are studied the numerical method is derived by discretizing the weak formulation the method is different from traditional finite element methods extensive numerical experiments are presented and show that the method is 2nd order accurate in solution and 1st order accurate in its gradient in l norm if the interface is c 2 and solutions are c 2 on the closures of the subdomains the method can handle the problems when the solutions and or the interfaces are weaker than c 2 for example email protected h 2 w c is lipschitz continuous and their singularities coincide see example 18 in section 4 the accuracies of the method under various circumstances are listed in table 19