extension of the berlekamp massey algorithm to n dimensions abstract we present an algorithm for finding a minimal set of linear recurring relations which are valid for a given n dimensional array over any field where the minimality is defined with respect to the partial order over the n dimensional lattice the algorithm is an extension of our two dimensional version of the berlekamp massey algorithm to more than two dimensions the n dimensional theory is based on more general concepts which can be reduced into those of the two dimensional theory in the previous paper in a typical case the resulting set of polynomials characterizing the minimal linear recurring relations proves to be a groebner basis of the ideal defined by the array and consequently the structure of an n dimensional linear feedback shift register with the minimum number of storage devices which can generate the array is determined by it

fast high order ader schemes for linear hyperbolic equations a reformulation of the ader approach arbitrary high order schemes using derivatives for linear hyperbolic pde s is presented this reformulation leads to a drastic decrease of the computational effort a formula for the construction of ader schemes that are arbitrary high order accurate in space and time is given the accuracy for some selected schemes is shown numerically for the two dimensional linearized euler equations as a mathematical model for noise propagation in the time domain in aeroacoustics

fast decoding of algebraic geometric codes up to the designed minimum distance we present a decoding algorithm for algebraic geometric codes from regular plane curves in particular the hermitian curve which corrects all error patterns of weight less than d 2 with low complexity the algorithm is based on the majority scheme of feng and rao 1993 and uses a modified version of sakata s 1988 generalization of the berlekamp massey algorithm

decoding binary 2 d cyclic codes by the 2 d berlekamp massey algorithm a method of decoding two dimensional 2 d cyclic codes by applying the 2 d berlekamp massey algorithm is proposed to explain this decoding method the author introduces a subclass of 2 d cyclic codes which are called 2 d bch codes due to their similarity with bch codes it is shown that there are some short 2 d cyclic codes with a better cost parameter value the merit of the approach is verified by showing several simple examples of 2 d cyclic codes

a high order godunov type scheme for shock interactions in ideal magnetohydrodynamics a high order godunov type scheme is developed for the shock interactions in ideal magnetohydrodynamics mhd the scheme is based on a nonlinear riemann solver and follows the basic procedure in the piecewise parabolic method the scheme takes into account all the discontinuities in ideal mhd and is in a strict conservation form the scheme is applied to numerical examples which include shock tube problems in ideal mhd and various interactions between strong mhd shocks all the waves involved in the corresponding riemann problems are resolved and are correctly displayed in the simulation results the correctness of the scheme is shown by the comparison between the simulation results and the solutions of the riemann problems the robustness of the scheme is demonstrated through the numerical examples it is shown that the scheme offers the principle advantages of a high order godunov type scheme robust operation in the presence of very strong waves thin shock fronts and thin contact and slip surface discontinuities

lemma for linear feedback shift registers and dfts applied to affine variety codes in this paper we establish a lemma in algebraic coding theory that frequently appears in the encoding and decoding of e g reed solomon codes algebraic geometry codes and affine variety codes our lemma corresponds to the nonsystematic encoding of affine variety codes and can be stated by giving a canonical linear map as the composition of an extension through linear feedback shift registers from a grobner basis and a generalized inverse discrete fourier transform we clarify that our lemma yields the error value estimation in the fast erasure and error decoding of a class of dual affine variety codes moreover we show that systematic encoding corresponds to a special case of erasure only decoding the lemma enables us to reduce the computational complexity of error evaluation from o n3 using gaussian elimination to o qn2 with some mild conditions on n and q where n is the code length and q is the finite field size

ranking of fuzzy intervals seen through the imprecise probabilistic lens within the fuzzy literature the issue of ranking fuzzy intervals has been addressed by many authors who proposed various solutions to the problem most of these solutions intend to find a total order on a given collection of fuzzy intervals however if one sees fuzzy intervals as descriptions of uncertain quantities an alternative to rank them is to use ranking rules issued from the imprecise probabilistic literature in this paper we investigate ranking rules based on different statistical features mean median and orderings and relate the obtained partial orders to some classical proposals in particular we propose a generic expression of stochastic orderings and then use it to systematically investigate extensions of the most usual stochastic orderings to fuzzy intervals we also show some relations between those extensions and explore their relation with existing fuzzy ranking proposals

a generalized forney formula for algebraic geometric codes this correspondence contains a straightforward generalization of decoding of bch codes to the decoding of algebraic geometric codes couched in terms of varieties ideals and grobner bases this consists of 1 a berlekamp massey type lattice shifting row reduction algorithm with majority voting similar to algorithms in the current literature 2 a realization that it produces a minimal grobner basis b for the error locator ideal i v relative to a particular weighted total degree monomial ordering 3 a factoring of that basis into several minimal plex bases that facilitates finding the variety v of error positions and 4 a direct generalization of forney s formula to calculate error magnitudes using functions spl sigma p which are by products of this factoring

alpha trimmed means and their relationship to median filters suppose that x is a finite set of n numbers the trimmed mean of x is obtained by sorting x into ascending order removing trimming a fixed fraction alpha 0 leq alpha leq 0 5 from the high and low ends of the sorted set and computing the average of the remaining values when applied to a sliding window of length lw the trimming process is called trim filtering for 0 5 the trimmed mean of a set is the median of the set and the filtering operation is called median filtering repeated application of a median filter to the output of a previous median filter of the same length lw eventually produces a signal which is invariant to median filtering this final signal is called the root signal this paper explains the relationship between trimmed means and median filters derives a simple straightforward and fast algorithm for applying a median filter and provides a new explanation of the convergence of repeated median filtering to the root signal the latter result incorporates an approach which permits generalization of the associated concepts to a larger class of index map filters

a second order godunov type scheme for compressible fluid dynamics abstract a second order accurate scheme for the integration in time of the conservation laws of compressible fluid dynamics is presented two related versions are proposed one lagrangian and the second direct eulerian they both share the common ingredient which is a full analytic solution for the time derivatives of flow quantities at a jump discontinuity assuming initial nonvanishing slopes on both sides while this solution is an extension of the solution to the classical riemann problem the resulting schemes are second order extensions of godunov s methods in both cases they are very simple to implement in computer codes several numerical examples are shown where the only additional mechanism is a simple monotonicity algorithm

a conservative three dimensional eulerian method for coupled solid fluid shock capturing a new method is presented for the explicit eulerian finite difference computation of shock capturing problems involving multiple resolved material phases in three dimensions we solve separately for each phase the equations of fluid dynamics or solid mechanics using as interface boundary conditions artificially extended representations of the individual phases for fluids we use a new 3d spatially unsplit implementation of the piecewise parabolic ppm method of colella and woodward for solids we use the 3d spatially unsplit eulerian solid mechanics method of miller and colella vacuum and perfectly incompressible obstacles may also be employed as phases a separate problem is the time evolution of material interfaces which are represented by planar segments constructed with a volume of fluid method the volume fractions are advanced in time using a second order 3d spatially unsplit advection routine with a velocity field determined by solution of interface normal two phase riemann problems from the riemann problem solutions we also determine cross interface momentum and energy fluxes the volume fractions in mixed cells may be arbitrarily small which would ordinarily make the courant friedrichs lewy time step stability limit arbitrarily small as well we overcome this limitation using the mass redistribution formalism to conservatively redistribute generalized mass in the neighborhood of the split cells we present an application of this method to an explosion contained in a metal can a reactive fluid approximating pbx 9404 is encased within an elastic plastic solid approximating copper surrounded by vacuum our implementation is in parallel and with adaptive mesh refinement

on the number of correctable errors for some ag codes an algorithm that for codes from a regular plane curve corrects up to d 2 m sup 2 8 m 4 9 8 errors where d is the designed distance and m is the degree of the curve was presented in an earlier work see ibid vol 35 p 811 21 1989 it is now shown that this bound is the best possible for the algorithm considered

arbitrary order exactly divergence free central discontinuous galerkin methods for ideal mhd equations ideal magnetohydrodynamic mhd equations consist of a set of nonlinear hyperbolic conservation laws with a divergence free constraint on the magnetic field neglecting this constraint in the design of computational methods may lead to numerical instability or nonphysical features in solutions in our recent work f li l xu s yakovlev central discontinuous galerkin methods for ideal mhd equations with the exactly divergence free magnetic field journal of computational physics 230 2011 4828 4847 second and third order exactly divergence free central discontinuous galerkin methods were proposed for ideal mhd equations in this paper we further develop such methods with higher order accuracy the novelty here is that the well established h div conforming finite element spaces are used in the constrained transport type framework and the magnetic induction equations are extensively explored in order to extract sufficient information to uniquely reconstruct an exactly divergence free magnetic field the overall algorithm is local and it can be of arbitrary order of accuracy numerical examples are presented to demonstrate the performance of the proposed methods especially when they are fourth order accurate

finding recursions for multidimensional arrays we produce a concise description of sakata s algorithm for finding recursion relations that are valid for an n dimensional array the new analysis extends to limit points which are excluded by previous authors we show that under a natural hypothesis the algorithm becomes stationary below each limit point and in particular constructs a full set of recursion relations for a recursive array at some finite point the method used to justify the algorithm stresses the duality between the fundamental extension operation of sakata and the s polynomial operation of buchberger

roe matrices for ideal mhd and systematic construction of roe matrices for systems of conservation laws in this paper the construction of a roe s scheme for the conservative system of ideal magnetohydrodynamics mhd is presented as this method relies on the computation of a roe matrix the problem is to find a matrixa ul ur which satisfies the following properties it is required to be consistent with the jacobian of the fluxf to have real eigenvalues a complete set of eigenvectors and to satisfy the relation f a ul ur u whereulandurare two admissible states and utheir difference for the ideal mhd system using eulerian coordinates a roe matrix is obtained without any hypothesis on the specific heat ratio especially its construction relies on an original expression of the magnetic pressure jump moreover a roe matrix is computed for lagrangian ideal mhd by extending the results of munz who obtained such a matrix for the system of lagrangian gas dynamics so this second matrix involves arithmetic averages unlike the eulerian one which contains classical roe averages like in eulerian gas dynamics in this paper a systematic construction of lagrangian roe matrices in terms of eulerian roe matrices for a general system of conservation laws is also presented this result applied to the above eulerian and lagrangian matrices for ideal mhd gives two new matrices for this system in the same way by applying this construction to the gas dynamics equations new roe matrices are also obtained all these matrices allow the construction of roe type schemes some numerical examples on the shock tube problem show the applicability of this method

multidimensional upwind methods for hyperbolic conservation laws abstract we present a class of second order conservative finite difference algorithms for solving numerically time dependent problems for hyperbolic conservation laws in several space variables these methods are upwind and multidimensional in that the numerical fluxes are obtained by solving the characteristic form of the full multidimensional equations at the zone edge and that all fluxes are evaluated and differenced at the same time in particular operator splitting is not used correct behavior at discontinuities is obtained by the use of solutions to the riemann problem and by limiting some of the second order terms numerical results are presented which show that the methods described here yield the same high resolution as the corresponding operator split methods

fast decoding of multipoint codes from algebraic curves multipoint codes are a broad class of algebraic geometry codes derived from algebraic functions which have multiple poles and or zeros on an algebraic curve thus they are more general than one point codes which are an important class of algebraic geometry codes in the sense that they can be decoded efficiently using the berlekamp massey sakata algorithm we present a fast method for decoding multipoint codes from a plane curve particularly a hermitian curve our method with some adaptation can be applied to decode multipoint codes from a general algebraic curve embedded in the n dimensional affine space fqn over a finite field fq so that those algebraic geometry codes can be decoded efficiently if the dimension n of the affine space including the defining curve is small

decoding of codes defined by a single point on a curve a decoding algorithm for certain codes from algebraic curves is presented the dual code which is used for decoding is formed by evaluating rational functions having poles at a single point a theoretical foundation is developed from which an improved bound for the minimum distance and results on decoding up to that bound are derived the decoding is done by a computationally efficient berlekamp massey type algorithm which is intrinsic to the curve

a fourth order divergence free method for mhd flows this paper extends our previous third order method s li high order central scheme on overlapping cells for magneto hydrodynamic flows with and without constrained transport method j comput phys 227 2008 7368 7393 to the fourth order central finite volume schemes on overlapping grid are used for both the volume averaged variables and the face averaged magnetic field the magnetic field at the cell boundaries falls within the dual grid and is naturally continuous so that our method eliminates the instability triggered by the discontinuity in the normal component of the magnetic field our fourth order scheme has much smaller numerical dissipation than the third order scheme the divergence free condition of the magnetic field is preserved by our fourth order divergence free reconstruction and the constrained transport method numerical examples show that the divergence free condition is essential to the accuracy of the method when a limiter is used in the reconstruction the high order low dissipation and divergence free properties of this method make it an ideal tool for direct magneto hydrodynamic turbulence simulations

an unsplit cell centered godunov method for ideal mhd we present a second order godunov algorithm for multidimensional ideal mhd our algorithm is based on the unsplit formulation of colella j comput phys 87 1990 with all of the primary dependent variables centered at the same location to properly represent the divergence free condition of the magnetic fields we apply a discrete projection to the intermediate values of the field at cell faces and apply a filter to the primary dependent variables at the end of each time step we test the method against a suite of linear and nonlinear tests to ascertain accuracy and stability of the scheme under a variety of conditions the test suite includes rotated planar linear waves mhd shock tube problems low beta flux tubes and a magnetized rotor problem for all of these cases we observe that the algorithm is second order accurate for smooth solutions converges to the correct weak solution for problems involving shocks and exhibits no evidence of instability or loss of accuracy due to the possible presence of non solenoidal fields

higher order multilevel framework for ader scheme in computational aeroacoustics abstract the versatile arbitrary derivative ader scheme is cast in a multilevel framework ml ader for fast solution of system of linear hyperbolic partial differential equations the solution is cycled through spatial operators of varying accuracy while retaining highest order accuracy by the use of a forcing function accuracy analysis of the multilevel framework including in the ml ader form is carried out in time domain as well as frequency domain results are obtained for benchmark problems in computational aeroacoustics at a much reduced computational cost

divergence free preserving high order schemes for magnetohydrodynamics an artificial magnetic resistivity method abstract this paper proposes a new strategy that is very simple divergence free high order accurate yet has an effective discontinuous capturing capability for simulating compressible magnetohydrodynamics mhd the new strategy is to construct artificial diffusion terms in a physically consistent manner such that the artificial terms act as a diffusion term only in the curl of magnetic field to capture numerical discontinuities in the magnetic field while not affecting the divergence field thus maintaining divergence free constraint the physically consistent artificial diffusion terms are built into the induction equations in a conservation law form at a partial differential equation level the proposed method may be viewed as adding an artificial magnetic resistivity to the induction equations and is inherently divergence free both ideal and resistive mhd with and without shock waves and also both inviscid and viscous flows the method is based on finite difference method with co located variable arrangement and we show that any linear finite difference scheme in an arbitrary order of accuracy can be used to discretize the modified governing equations to ensures the divergence free and the global conservation constraints numerically at the discretization level the artificial magnetic resistivity is designed to localize automatically in regions of discontinuity in the curl of magnetic field and vanish wherever the flow is sufficiently smooth with respect to the grid scale thereby maintaining the desirable high order accuracy of the employed discretization scheme in smooth regions two dimensional smooth and non smooth ideal mhd problems are considered to validate the capability of the proposed method

the behavioral meaning of the median we extend the notion of statistical preference to the general framework of imprecise probabilities by proposing a new notion of desirability of gambles called sign desirability different from the usual desirability notion in walley s framework we axiomatically characterize coherent families of sign desirable gambles we furthermore prove that the pair of lower and upper previsions of a gamble according to this new desirability notion coincides with the pair of bounds infimum and supremum of the set of medians associated to a coherent family of linear previsions thus a general notion of median is naturally derived and provided with a behavioral meaning as a consequence of these results the connection between statistical preference in classical probability theory and the sign of the median of the difference of two random variables is laid bare

the generalized riemann problems for compressible fluid flows towards high order the generalized riemann problems grp for nonlinear hyperbolic systems of balance laws in one space dimension are now well known and can be formulated as follows given initial data which are smooth on two sides of a discontinuity determine the time evolution of the solution near the discontinuity in particular the grp of k 1 th order high resolution is based on an analytical evaluation of time derivatives up to kth order which turns out to be dependent only on the spatial derivatives up to kth order while the classical riemann problem serves as a primary building block in the construction of many numerical schemes most notably the godunov scheme the analytic study of grp will lead to an array of grp schemes which extend the godunov scheme currently there are extensive studies on the second order grp scheme which proves to be robust and is capable of resolving complex multidimensional fluid dynamic problems ben artzi and falcovitz 2003 4 in this paper we provide a new approach for solving the grp for the compressible flow system towards high order accuracy the derivation of second order grp solver is more concise compared to those in previous works and the third order grp or quadratic grp is resolved for the first time the latter is shown to be necessary through numerical experiments with strong discontinuities our method relies heavily on the new treatment of rarefaction waves indeed as a main technical step the propagation of singularities argument for the rarefaction fan is simplified by deriving the linear ode systems for the evolution of characteristic derivatives in the x t coordinates for generalized riemann invariants the case of sonic point is incorporated into a general treatment the accuracy of the derived grp solvers is justified and numerical examples are presented for the performance of the resulting schemes

multidimensional quasi cyclic and convolutional codes we introduce multidimensional analogues of quasi cyclic qc codes and study their algebraic structure we demonstrate a concatenated structure for multidimensional qc codes and use this to prove that this class of codes is asymptotically good we also relate the new family of codes to convolutional codes it is known that the minimum distance of qc codes provides a natural lower bound on the free distance of convolutional codes we show that the same relation also holds between certain rank one 2 d convolutional codes and the related multidimensional qc codes we provide examples which show that our bound is sharp in some cases we also present some optimal 2 d qc codes along the way we provide a condition on the encoders of rank one convolutional codes which are equivalent to noncatastrophicity for 1 d convolutional codes in the n text d case n 1 our condition is sufficient for the noncatastrophicity of the encoder

algebraic geometry codes the theory of error correcting codes derived from curves in an algebraic geometry was initiated by the work of goppa as generalizations of bose chaudhuri hocquenghem bch reed solomon rs and goppa codes the development of the theory has received intense consideration since that time and the purpose of the paper is to review this work elements of the theory of algebraic curves at a level sufficient to understand the code constructions and decoding algorithms are introduced code constructions from particular classes of curves including the klein quartic elliptic and hyperelliptic curves and hermitian curves are presented decoding algorithms for these classes of codes and others are considered the construction of classes of asymptotically good codes using modular curves is also discussed

efficient forney functions for decoding ag codes using a forney formula to solve for the error magnitudes in decoding algebraic geometric ag codes requires producing functions spl sigma sub p which are 0 at all but one point p of the variety of the error locator ideal the best such function is produced here in a reasonably efficient way from a lex grobner basis this lex basis is in turn produced efficiently from a weighted grevlex basis by using the fglm algorithm these two steps essentially complete the efficient decoding scheme based on a forney formula started in the author s previous work see ibid vol 42 p 1263 8 1996

a code decomposition approach for decoding cyclic and algebraic geometric codes an approach based on code decomposition and partial transform for constructing algorithms for decoding cyclic codes and algebraic geometric ag codes is introduced a general decoding procedure applicable to arbitrary linear codes and their subfield subcodes is then developed in particular we have developed algorithms for error and erasure decoding of cyclic codes up to their actual minimum distance error and erasure decoding of ag codes up to their designed minimum distance and decoding of subfield subcodes of ag codes geometric bch codes moreover a generalization of geometric bch codes is introduced it is shown by an example that for a simple class of ag codes the so called one point codes this generalization brings a better estimate of their minimum distance it is also shown that the algorithms developed in this paper can be applied to decode these codes up to their estimated minimum distance

algebraic geometric codes and multidimensional cyclic codes a unified theory and algorithms for decoding using grobner bases it is proved that any algebraic geometric ag code can be expressed as a cross section of an extended multidimensional cyclic code both ag codes and multidimensional cyclic codes are described by a unified theory of linear block codes defined over point sets ag codes are defined over the points of an algebraic curve and an m dimensional cyclic code is defined over the points in m dimensional space the power of the unified theory is in its description of decoding techniques using grobner bases in order to fit an ag code into this theory a change of coordinates must be applied to the curve over which the code is defined so that the curve is in special position for curves in special position all computations can be performed with polynomials and this also makes it possible to use the theory of grobner bases next a transform is defined for ag codes which generalizes the discrete fourier transform the transform is also related to a grobner basis and is useful in setting up the decoding problem in the decoding problem a key step is finding a grobner basis for an error locator ideal for ag codes multidimensional cyclic codes and indeed any cross section of an extended multidimensional cyclic code sakata s algorithm can be used to find linear recursion relations which hold on the syndrome array in this general context the authors give a self contained and simplified presentation of sakata s algorithm and present a general framework for decoding algorithms for this family of codes in which the use of sakata s algorithm is supplemented by a procedure for extending the syndrome array

a 3d cell centered lagrangian scheme for the ideal magnetohydrodynamics equations on unstructured meshes abstract we propose a cell centered lagrangian numerical scheme for solving the 3d ideal magnetohydrodynamics mhd equations on unstructured meshes all the variables are cell centered and the lagrangian conservative system of ideal mhd equations is compatibly discretized in this scheme the geometric conservation law gcl requirement is satisfied by using the discrete compatible lagrangian framework of polyhedral meshes a nodal solver for mhd equations is then constructed through the nodal pressure flux and magnetic field invoking total energy conservation and thermodynamic consistency besides the magnetic divergence free constraint is fulfilled by a projection method after each time step various numerical tests are presented to assert the robustness and accuracy of our scheme

extending stochastic ordering to belief functions on the real line in this paper the concept of stochastic ordering is extended to belief functions on the real line defined by random closed intervals in this context the usual stochastic ordering is shown to break down into four distinct ordering relations called credal orderings which correspond to the four basic ordering structures between intervals these orderings are characterized in terms of lower and upper expectations we then derive the expressions of the least committed least informative belief function credally less respectively greater than or equal to a given belief function in each case the solution is a consonant belief function that can be described by a possibility distribution a simple application to reliability analysis is used as an example throughout the paper

the art of signaling fifty years of coding theory in 1948 shannon developed fundamental limits on the efficiency of communication over noisy channels the coding theorem asserts that there are block codes with code rates arbitrarily close to channel capacity and probabilities of error arbitrarily close to zero fifty years later codes for the gaussian channel have been discovered that come close to these fundamental limits there is now a substantial algebraic theory of error correcting codes with as many connections to mathematics as to engineering practice and the last 20 years have seen the construction of algebraic geometry codes that can be encoded and decoded in polynomial time and that beat the gilbert varshamov bound given the size of coding theory as a subject this review is of necessity a personal perspective and the focus is reliable communication and not source coding or cryptography the emphasis is on connecting coding theories for hamming and euclidean space and on future challenges specifically in data networking wireless communication and quantum information theory

solution of the generalized riemann problem for advection reaction equations we present a method for solving the generalized riemann problem for partial differential equations of the advection reaction type the generalization of the riemann problem here is twofold firstly the governing equations include nonlinear advection as well as reaction terms and secondly the initial condition consists of two arbitrary but infinitely differentiable functions an assumption that is consistent with piecewise smooth solutions of hyperbolic conservation laws the solution procedure local and valid for sufficiently small times reduces the solution of the generalized riemann problem of the inhomogeneous nonlinear equations to that of solving a sequence of conventional riemann problems for homogeneous advection equations for spatial derivatives of the initial conditions we illustrate the approach via the model advection reaction equation the inhomogeneous burgers equation and the nonlinear shallow water equations with variable bed elevation

simplified understanding and efficient decoding of a class of algebraic geometric codes an efficient decoding algorithm for algebraic geometric codes is presented for codes from a large class of irreducible plane curves including hermitian curves it can correct up to d 1 2 errors where d is the designed minimum distance with it we also obtain a proof of d sub min spl ges d without directly using the riemann roch theorem the algorithm consists of gaussian elimination on a specially arranged syndrome matrix followed by a novel majority voting scheme a fast implementation incorporating block hankel matrix techniques is obtained whose worst case running time is o mn sup 2 where m is the degree of the curve applications of our techniques to decoding other algebraic geometric codes to decoding bch codes to actual minimum distance and to two dimensional shift register synthesis are also presented

on determining the independent point set for doubly periodic arrays and encoding two dimensional cyclic codes and their duals for the purpose of encoding two dimensional cyclic tdc codes an effective algorithm for finding the independent point set of an arbitrary module of doubly periodic dp arrays is proposed in addition a method for determining the characteristic ideal of a given set of dp arrays is exhibited with the aid of these methods it is possible to specify the structure of the generator and check ideals of tdc codes by applying this algorithm to nonsemisimple binary tdc codes with small areas several optimal linear codes have been found and their previously unknown tdc structures have been exhibited

on the divergence free condition in godunov type schemes for ideal magnetohydrodynamics the upwind constrained transport method we present a general framework to design godunov type schemes for multidimensional ideal magnetohydrodynamic mhd systems having the divergence free relation and the related properties of the magnetic field b as built in conditions our approach mostly relies on the constrained transport ct discretization technique for the magnetic field components originally developed for the linear induction equation which assures b num 0 and its preservation in time to within machine accuracy in a finite volume setting we show that the ct formalism when fully exploited can be used as a general guideline to design the reconstruction procedures of the b vector field to adapt standard upwind procedures for the momentum and energy equations avoiding the onset of numerical monopoles of o 1 size and to formulate approximate riemann solvers for the induction equation this general framework will be named here upwind constrained transport uct to demonstrate the versatility of our method we apply it to a variety of schemes which are finally validated numerically and compared a novel implementation for the mhd case of the second order roetype positive scheme by lin and lax j comput fluid dyn 5 1996 133 and both the second and third order versions of a central type mhd scheme presented by londrillo and del zanna astrophys j 530 2000 508 where the basic uct strategies have been first outlined

fast estimation from above of the maximum wave speed in the riemann problem for the euler equations this paper is concerned with the construction of a fast algorithm for computing the maximum speed of propagation in the riemann solution for the euler system of gas dynamics with the co volume equation of state the novelty in the algorithm is that it stops when a guaranteed upper bound for the maximum speed is reached with a prescribed accuracy the convergence rate of the algorithm is cubic and the bound is guaranteed for gasses with the co volume equation of state and the heat capacity ratio in the range 1 5 3

finding the defining functions for one point algebraic geometry codes an iterative algorithm is given for producing the parity check functions for one point algebraic geometry ag codes in particular but not limited to those related to the two towers of function fields introduced by garcia and stichtenoth 1995 this simple method based on the linearity of the qth power map over f sub q is an alternative to the method of using laurent series expansions examples are given for small values of m with characteristic p 2 for both towers

thermodynamical effects and high resolution methods for compressible fluid flows one of the fundamental differences of compressible fluid flows from incompressible fluid flows is the involvement of thermodynamics this difference should be manifested in the design of numerical schemes unfortunately the role of entropy expressing irreversibility is often neglected even though the entropy inequality as a conceptual derivative is verified for some first order schemes in this paper we refine the grp solver to illustrate how the thermodynamical variation is integrated into the design of high resolution methods for compressible fluid flows and demonstrate numerically the importance of thermodynamic effects in the resolution of strong waves as a by product we show that the grp solver works for generic equations of state and is independent of technical arguments

rational approximation of 2 d linear discrete systems in this paper we present an efficient procedure to obtain a rational model for a 2 d linear shift invariant discrete system using first and second order data from it this procedure is a modification of the nonlinear least squares approximation and it generalizes the pade approximants and the spectral estimation modeling procedures the parameters of the approximating filter are obtained by solving a system of linear equations by means of an efficient recursive algorithm which is developed using the relation of the approximation problem with the theory of orthogonal polynomials on the unit bidisk we discuss some of the algebraic properties of the solution and apply them to define cases for which the bibo stability of the approximating filters is ensured the proposed procedure finds applications in the design and stabilization of 2 d recursive digital filters and in the autoregressive moving average arma modeling of stationary random fields

a conserving discretization for the free boundary in a two dimensional stefan problem the dissolution of a disk likeal2cuparticle is considered a characteristic property is that initially the particle has a nonsmooth boundary the mathematical model of this dissolution process contains a description of the particle interface of which the position varies in time such a model is called a stefan problem it is impossible to obtain an analytical solution for a general two dimensional stefan problem so we use the finite element method to solve this problem numerically first we apply a classical moving mesh method computations show that after some time steps the predicted particle interface becomes very unrealistic therefore we derive a new method for the displacement of the free boundary based on the balance of atoms this method leads to good results also for nonsmooth boundaries some numerical experiments are given for the dissolution of anal2cuparticle in anal cualloy

on glm curl cleaning for a first order reduction of the ccz4 formulation of the einstein field equations abstract in this paper we propose an extension of the generalized lagrangian multiplier method glm of munz et al 52 30 which was originally conceived for the numerical solution of the maxwell and mhd equations with divergence type involutions to the case of hyperbolic pde systems with curl type involutions the key idea here is to solve an augmented pde system in which curl errors propagate away via a maxwell type evolution system the new approach is first presented on a simple model problem in order to explain the basic ideas subsequently we apply it to a strongly hyperbolic first order reduction of the ccz4 formulation fo ccz4 of the einstein field equations of general relativity which is endowed with 11 curl constraints several numerical examples including the long time evolution of a stable neutron star in anti cowling approximation are presented in order to show the obtained improvements with respect to the standard formulation without special treatment of the curl involution constraints the main advantages of the proposed glm approach are its complete independence of the underlying numerical scheme and grid topology and its easy implementation into existing computer codes however this flexibility comes at the price of needing to add for each curl involution one additional 3 vector plus another scalar in the augmented system for homogeneous curl constraints and even two additional scalars for non homogeneous curl involutions for the fo ccz4 system with 11 homogeneous curl involutions this means that additional 44 evolution quantities need to be added

derivative riemann solvers for systems of conservation laws and ader methods in this paper we first briefly review the semi analytical method e f toro v a titarev solution of the generalized riemann problem for advection reaction equations proc roy soc london 458 2018 2002 271 281 for solving the derivative riemann problem for systems of hyperbolic conservation laws with source terms next we generalize it to hyperbolic systems for which the riemann problem solution is not available as an application example we implement the new derivative riemann solver in the high order finite volume ader advection schemes we provide numerical examples for the compressible euler equations in two space dimensions which illustrate robustness and high accuracy of the resulting schemes

a statistical comparative study of different similarity measures of consensus in group decision making an essential aim in group decision making gdm problems is to achieve a high level of consensus among experts consensus is defined as general or widespread agreement and it is usually modelled mathematically via a similarity function measuring how close experts opinions or preferences are similarity functions are defined based on the use of a metric describing the distance between experts opinions or preferences in the literature different metrics or distance functions have been proposed to implement in consensus models but no study has been carried out to analyse the influence the use of different distance functions can have in the gdm process this paper presents a comparative study of the effect of the application of some different distance functions for measuring consensus in gdm by using the nonparametric wilcoxon matched pairs signed ranks test it is concluded that different distance functions can produce significantly different results moreover it is also shown that their application also has a significant effect on the speed of achieving consensus finally these results are analysed and used to derive decision support rules based on a convergent criterion that can be used to control the convergence speed of the consensus process using the compared distance functions

high order ader schemes for a unified first order hyperbolic formulation of newtonian continuum mechanics coupled with electro dynamics abstract in this paper we propose a new unified first order hyperbolic model of newtonian continuum mechanics coupled with electro dynamics the model is able to describe the behavior of moving elasto plastic dielectric solids as well as viscous and inviscid fluids in the presence of electro magnetic fields it is actually a very peculiar feature of the proposed pde system that viscous fluids are treated just as a special case of elasto plastic solids this is achieved by introducing a strain relaxation mechanism in the evolution equations of the distortion matrix a which in the case of purely elastic solids maps the current configuration to the reference configuration the model also contains a hyperbolic formulation of heat conduction as well as a dissipative source term in the evolution equations for the electric field given by ohm s law via formal asymptotic analysis we show that in the stiff limit the governing first order hyperbolic pde system with relaxation source terms tends asymptotically to the well known viscous and resistive magnetohydrodynamics mhd equations furthermore a rigorous derivation of the model from variational principles is presented together with the transformation of the euler lagrange differential equations associated with the underlying variational problem from lagrangian coordinates to eulerian coordinates in a fixed laboratory frame the present paper hence extends the unified first order hyperbolic model of newtonian continuum mechanics recently proposed in 110 42 to the more general case where the continuum is coupled with electro magnetic fields the governing pde system is symmetric hyperbolic and satisfies the first and second principle of thermodynamics hence it belongs to the so called class of symmetric hyperbolic thermodynamically compatible systems shtc which have been studied for the first time by godunov in 1961 61 and later in a series of papers by godunov and romenski 67 69 119 an important feature of the proposed model is that the propagation speeds of all physical processes including dissipative processes are finite the model is discretized using high order accurate ader discontinuous galerkin dg finite element schemes with a posteriori subcell finite volume limiter and using high order ader weno finite volume schemes we show numerical test problems that explore a rather large parameter space of the model ranging from ideal mhd viscous and resistive mhd over pure electro dynamics to moving dielectric elastic solids in a magnetic field

a staggered mesh algorithm using high order godunov fluxes to ensure solenoidal magnetic fields in magnetohydrodynamic simulations the equations of magnetohydrodynamics mhd have been formulated as a hyperbolic system of conservation laws in that form it becomes possible to use higher order godunov schemes for their solution this results in a robust and accurate solution strategy however the magnetic field also satisfies a constraint that requires its divergence to be zero at all times this is a property that cannot be guaranteed in the zone centered discretizations that are favored in godunov schemes without involving a divergence cleaning step in this paper we present a staggered mesh strategy which directly uses the properly upwinded fluxes that are provided by a godunov scheme the process of directly using the upwinded fluxes relies on a duality that exists between the fluxes obtained from a higher order godunov scheme and the electric fields in a plasma by exploiting this duality we have been able to construct a higher order godunov scheme that ensures that the magnetic field remains divergence free up to the computer s round off error we have even presented a variant of the basic algorithm that uses multidimensional features in the flow to design an upwinded strategy that aligns itself with the predominant upwinded direction in the flow we have devised several stringent test problems to show that the scheme works robustly and accurately in all situations in doing so we have shown that a scheme that involves a collocation of magnetic field variables that is different from the one traditionally favored in the design of higher order godunov schemes can nevertheless offer the same robust and accurate performance of higher order godunov schemes provided the properly upwinded fluxes from the godunov methodology are used in the scheme s construction

architectures for syndrome generation and error location search in the decoding of hermitian codes when a hermitian curve is put in a special position with respect to its infinite rational point the x y coordinates of all its finite rational points have regular algebraic properties based on these properties the use of horner s rule and the mechanism of chien search in the decoding of reed solomon codes can be extended to render architectures for syndrome generation and error location search in the decoding of codes constructed from the hermitian curve

qualitative decision theory with preference relations and comparative uncertainty an axiomatic approach this paper investigates a purely qualitative approach to decision making under uncertainty since the pioneering work of savage most models of decision under uncertainty rely on a numerical representation where utility and uncertainty are commensurate giving up this tradition we relax this assumption and introduce an axiom of ordinal invariance requiring that the decision maker s preference between two acts only depends on the relative position of their consequences for each state within this qualitative framework we determine the only possible form of the corresponding decision rule then assuming the transitivity of the strict preference the underlying partial confidence relations are those at work in non monotonic inference and thus satisfy one of the main properties of possibility theory the satisfaction of additional postulates of unanimity and anonymity enforces the use of a necessity measure unique up to a monotonic transformation for encoding the relative likelihood of events

geometric variational discretization of continuum theories this study derives geometric variational discretization of continuum theories arising in fluid dynamics magnetohydrodynamics mhd and the dynamics of complex fluids a central role in these discretizations is played by the geometric formulation of fluid dynamics which views solutions to the governing equations for perfect fluid flow as geodesics on the group of volume preserving diffeomorphisms of the fluid domain inspired by this framework we construct a finite dimensional approximation to the diffeomorphism group and its lie algebra thereby permitting a variational temporal discretization of geodesics on the spatially discretized diffeomorphism group the extension to mhd and complex fluid flow is then made through an appeal to the theory of euler poincare systems with advection which provides a generalization of the variational formulation of ideal fluid flow to fluids with one or more advected parameters upon deriving a family of structured integrators for these systems we test their performance via a numerical implementation of the update schemes on a cartesian grid among the hallmarks of these new numerical methods are exact preservation of momenta arising from symmetries automatic satisfaction of solenoidal constraints on vector fields good long term energy behavior robustness with respect to the spatial and temporal resolution of the discretization and applicability to irregular meshes

higher order time integration with a local lax wendroff procedure for a central scheme on an overlapping grid we have implemented a high order lax wendroff type time integration for a central scheme on an overlapping grid for conservation law problems using a local iterative approach presented by dumbser et al jcp 2008 12 we extend a local high order spatial reconstruction on each cell to a local higher order space time polynomial on the cell we rewrite the central scheme in a fully discrete form to avoid volume integration in the space time domain the fluxes at cell interfaces are calculated directly via integrating a higher order space time reconstruction of the flux we compare this approach with the corresponding multi stage runge kutta time integration rk numerical results show that the new time integration is more cost effective

von neumann stability analysis of globally divergence free rkdg schemes for the induction equation using multidimensional riemann solvers in this paper we focus on the numerical solution of the induction equation using rungekutta discontinuous galerkin rkdg like schemes that are globally divergence free the induction equation plays a role in numerical mhd and other systems like it it ensures that the magnetic field evolves in a divergence free fashion and that same property is shared by the numerical schemes presented here the algorithms presented here are based on a novel dg like method as it applies to the magnetic field components in the faces of a mesh i e this is not a conventional dg algorithm for conservation laws the other two novel building blocks of the method include divergence free reconstruction of the magnetic field and multidimensional riemann solvers both of which have been developed in recent years by the first author since the method is linear a von neumann stability analysis is carried out in two dimensions to understand its stability properties the von neumann stability analysis that we develop in this paper relies on transcribing from a modal to a nodal dg formulation in order to develop discrete evolutionary equations for the nodal values these are then coupled to a suitable rungekutta timestepping strategy so that one can analyze the stability of the entire scheme which is suitably high order in space and time we show that our scheme permits cfl numbers that are comparable to those of traditional rkdg schemes we also analyze the wave propagation characteristics of the method and show that with increasing order of accuracy the wave propagation becomes more isotropic and free of dissipation for a larger range of long wavelength modes this makes a strong case for investing in higher order methods we also use the von neumann stability analysis to show that the divergence free reconstruction and multidimensional riemann solvers are essential algorithmic ingredients of a globally divergence free rkdg like scheme numerical accuracy analyses of the rkdg like schemes are presented and compared with the accuracy of pnpm schemes it is found that pnpm retrieve much of the accuracy of the rkdg like schemes while permitting a larger cfl number

an efficient hyperbolic relaxation system for dispersive non hydrostatic water waves and its solution with high order discontinuous galerkin schemes abstract in this paper we propose a novel set of first order hyperbolic equations that can model dispersive non hydrostatic free surface flows the governing pde system is obtained via a hyperbolic approximation of the family of non hydrostatic free surface flow models recently derived by sainte marie et al in 1 our new hyperbolic reformulation is based on an augmented system in which the divergence constraint of the velocity is coupled with the other conservation laws via an evolution equation for the depth averaged non hydrostatic pressure similar to the hyperbolic divergence cleaning applied in generalized lagrangian multiplier methods glm for magnetohydrodynamics mhd we suggest a formulation in which the divergence errors of the velocity field are transported with a large but finite wave speed that is directly related to the maximal eigenvalue of the governing pde we then use arbitrary high order accurate ader discontinuous galerkin dg finite element schemes with an a posteriori subcell finite volume limiter in order to solve the proposed pde system numerically the final scheme is highly accurate in smooth regions of the flow and very robust and positive preserving for emerging topographies and wet dry fronts it is well balanced making use of a path conservative formulation of hll type riemann solvers based on the straight line segment path furthermore the proposed ader dg scheme with a posteriori subcell finite volume limiter adapts very well to modern gpu architectures resulting in a very accurate robust and computationally efficient computational method for non hydrostatic free surface flows the new model proposed in this paper has been applied to idealized academic benchmarks such as the propagation of solitary waves as well as to more challenging physical situations that involve wave runup on a shore including wave breaking in both one and two space dimensions in all cases the achieved agreement with analytical solutions or experimental data is very good thus showing the validity of both the proposed mathematical model and the numerical solution algorithm

least median of squares regression abstract classical least squares regression consists of minimizing the sum of the squared residuals many authors have produced more robust versions of this estimator by replacing the square by something else such as the absolute value in this article a different approach is introduced in which the sum is replaced by the median of the squared residuals the resulting estimator can resist the effect of nearly 50 of contamination in the data in the special case of simple regression it corresponds to finding the narrowest strip covering half of the observations generalizations are possible to multivariate location orthogonal regression and hypothesis testing in linear models

an unsplit 3d upwind method for hyperbolic conservation laws abstract an unsplit upwind method for solving hyperbolic conservation laws in three dimensions is developed this paper derives the algorithm by generalizing a two dimensional advection algorithm of van leer and colella to three dimensions and then making appropriate modifications the method is implemented using the equations of gas dynamics several test problems are computed to both verify and display the behavior of the method these test problems include a 1d blast wave a 2d shock reflection off a 30 ramp and a 3d astrophysical jet

impulse response arrays of discrete space systems over a finite field the main thrust of this paper is directed towards an analysis of the structure and properties of the impulse response array of two dimensional 2 d discrete space systems characterizable by rational functions having coefficients in a field z q it is shown that such an array exhibits a row column type of periodicity expressions for the period are derived arrays with a maximum of three levels in the auto correlation function are identified and explicit expressions for these levels are given

a method to simulate linear stability of impulsively accelerated density interfaces in ideal mhd and gas dynamics we present a numerical method to solve the linear stability of impulsively accelerated density interfaces in two dimensions such as those arising in the richtmyer meshkov instability the method uses an eulerian approach and is based on an upwind method to compute the temporally evolving base state and a flux vector splitting method for the perturbations the method is applicable to either gas dynamics or magnetohydrodynamics numerical examples are presented for cases in which a hydrodynamic shock interacts with a single or double density interface and a doubly shocked single density interface convergence tests show that the method is spatially second order accurate for smooth flows and between first and second order accurate for flows with shocks

decoding algebraic geometric codes up to the designed minimum distance a simple decoding procedure for algebraic geometric codes c sub omega d g is presented this decoding procedure is a generalization of peterson s decoding procedure for the bch codes it can be used to correct any d 1 2 or fewer errors with complexity o n sup 3 where d is the designed minimum distance of the algebraic geometric code and n is the codelength

multi moment ader taylor methods for systems of conservation laws with source terms in one dimension a new integration method combining the ader time discretization with a multi moment finite volume framework is introduced ader runtime is reduced by performing only one cauchy kowalewski c k procedure per cell per time step and by using the differential transform method for high order derivatives three methods are implemented 1 single moment weno weno 2 two moment hermite weno hweno and 3 entirely local multi moment mm loc mm loc evolves all moments sharing the locality of galerkin methods yet with a constant time step during p refinement five 1 d experiments validate the methods 1 linear advection 2 burger s equation shock 3 transient shallow water sw 4 steady state sw simulation and 5 sw shock weno and hweno methods showed expected polynomial h refinement convergence and successfully limited oscillations for shock experiments mm loc showed expected polynomial h refinement and exponential p refinement convergence for linear advection and showed sub exponential yet super polynomial convergence with p refinement in the sw case hweno accuracy was generally equal to or better than a five moment mm loc scheme mm loc was less accurate than rkdg at lower refinements but with greater h and p convergence rkdg accuracy is eventually surpassed the ader time integrator of mm loc also proved more accurate with p refinement at a cfl of unity than a semi discrete rk analog of mm loc being faster in serial and requiring less frequent inter node communication than galerkin methods the ader based mm loc and hweno schemes can be spatially refined and have the same runtime making them a competitive option for further investigation

genetic learning of fuzzy rules based on low quality data genetic fuzzy systems gfs are based on the use of genetic algorithms for designing fuzzy systems and for providing them with learning and adaptation capabilities in this context fuzzy sets represent linguistic granules of information contained in the antecedents and consequents of the rules whereas the data used in the genetic learning is assumed to be crisp gfs seldom deal with fuzzy valued data in this paper we address this problem and propose a set of techniques that can be incorporated to different gfs in order to learn a knowledge base kb from interval and fuzzy data for regression problems details will be given about the representation of non standard data with fuzzy sets about the needed changes in the reasoning method of the fuzzy rule based system and also about a new generalization of the mean squared error to vague data in addition we will show that the learning process requires a genetic algorithm that must be capable of optimizing a multicriteria fitness function containing both crisp and interval valued criteria lastly we benchmark our procedures with some machine learning related datasets and a real world problem of marketing and the techniques proposed here are shown to improve the generalization properties of other kbs obtained from crisp training data

an unsplit godunov method for ideal mhd via constrained transport we describe a single step second order accurate godunov scheme for ideal mhd based on combining the piecewise parabolic method ppm for performing spatial reconstruction the corner transport upwind ctu method of colella for multidimensional integration and the constrained transport ct algorithm for preserving the divergence free constraint on the magnetic field we adopt the most compact form of ct which requires the field be represented by area averages at cell faces we demonstrate that the fluxes of the area averaged field used by ct can be made consistent with the fluxes of the volume averaged field returned by a riemann solver if they obey certain simple relationships we use these relationships to derive new algorithms for constructing the ct fluxes at grid cell corners which reduce exactly to the equivalent one dimensional solver for plane parallel grid aligned flow we show that the ppm reconstruction algorithm must include multidimensional terms for mhd and we describe a number of important extensions that must be made to ctu in order for it to be used for mhd with ct we present the results of a variety of test problems to demonstrate the method is accurate and robust

on the decoding of algebraic geometric codes this paper provides a survey of the existing literature on the decoding of algebraic geometric codes definitions theorems and cross references will be given we show what has been done discuss what still has to be done and pose some open problems

provably positive high order schemes for ideal magnetohydrodynamics analysis on general meshes this paper proposes and analyzes arbitrarily high order discontinuous galerkin dg and finite volume methods which provably preserve the positivity of density and pressure for the ideal magnetohydrodynamics mhd on general meshes unified auxiliary theories are built for rigorously analyzing the positivity preserving pp property of numerical mhd schemes with a harten lax van leer hll type flux on polytopal meshes in any space dimension the main challenges overcome here include establishing certain relation between the pp property and a discrete divergence of magnetic field on general meshes and estimating proper wave speeds in the hll flux to ensure the pp property in the 1d case we prove that the standard dg and finite volume methods with the proposed hll flux are pp under a condition accessible by a pp limiter for the multidimensional conservative mhd system the standard dg methods with a pp limiter are not pp in general due to the effect of unavoidable divergence error in the magnetic field we construct provably pp high order dg and finite volume schemes by proper discretization of the symmetrizable mhd system with two divergence controlling techniques the locally divergence free elements and suitably discretized godunov powell source term the former technique leads to zero divergence within each cell while the latter controls the divergence error across cell interfaces our analysis reveals in theory that a coupling of these two techniques is very important for positivity preservation as they exactly contribute the discrete divergence terms which are absent in standard multidimensional dg schemes but crucial for ensuring the pp property several numerical tests further confirm the pp property and the effectiveness of the proposed pp schemes unlike the conservative mhd system the exact smooth solutions of the symmetrizable mhd system are proved to retain the positivity even if the divergence free condition is not satisfied our analysis and findings further the understanding at both discrete and continuous levels of the relation between the pp property and the divergence free constraint

kinematic dynamos using constrained transport with high order godunov schemes and adaptive mesh refinement we propose to extend the well known muscl hancock scheme for euler equations to the induction equation modeling the magnetic field evolution in kinematic dynamo problems the scheme is based on an integral form of the underlying conservation law which in our formulation results in a finite surface scheme for the induction equation this naturally leads to the well known constrained transport method with additional continuity requirement on the magnetic field representation the second ingredient in the muscl scheme is the predictor step that ensures second order accuracy both in space and time we explore specific constraints that the mathematical properties of the induction equations place on this predictor step showing that three possible variants can be considered we show that the most aggressive formulations referred to as c muscl and u muscl reach the same level of accuracy as the other one referred to as runge kutta at a lower computational cost more interestingly these two schemes are compatible with the adaptive mesh refinement amr framework it has been implemented in the amr code ramses it offers a novel and efficient implementation of a second order scheme for the induction equation we have tested it by solving two kinematic dynamo problems in the low diffusion limit the construction of this scheme for the induction equation constitutes a step towards solving the full mhd set of equations using an extension of our current methodology

operator based preconditioning of stiff hyperbolic systems we introduce an operator based scheme for preconditioning stiff components encountered in implicit methods for hyperbolic systems of pdes posed on regular grids the method is based on a directional splitting of the implicit operator followed by a characteristic decomposition of the resulting directional parts this approach allows for the solution of any number of characteristic components from the entire system to only the fastest stiffness inducing waves we apply the preconditioning method to stiff hyperbolic systems arising in magnetohydrodynamics and gas dynamics we then present numerical results showing that this preconditioning scheme works well on problems where the underlying stiffness results from the interaction of fast transient waves with slowly evolving dynamics scales well to large problem sizes and numbers of processors and allows for additional customization based on the specific problems under study

an unsplit godunov method for ideal mhd via constrained transport in three dimensions we present a single step second order accurate godunov scheme for ideal mhd which is an extension of the method described in t a gardiner j m stone an unsplit godunov method for ideal mhd via constrained transport j comput phys 205 2005 509 to three dimensions this algorithm combines the corner transport upwind ctu method of colella for multidimensional integration and the constrained transport ct algorithm for preserving the divergence free constraint on the magnetic field we describe the calculation of the ppm interface states for 3d ideal mhd which must include multidimensional mhd source terms and naturally respect the balance implicit in these terms by the b 0 condition we compare two different forms for the ctu integration algorithm which require either 6 or 12 solutions of the riemann problem per cell per time step and present a detailed description of the 6 solve algorithm finally we present solutions for test problems to demonstrate the accuracy and robustness of the algorithm

finding a basis for the characteristic ideal of an n dimensional linear recurring sequence an n dimensional linear recurring sequence sigma of elements from a field f for n or 1 is considered an algorithm chi base which determines a basis for the ideal characteristic polynomials of sigma under certain reasonable conditions is presented this analysis applied to doubly periodic arrays in particular

decoding geometric goppa codes using an extra place decoding geometric goppa codes can be reduced to solving the key congruence of a received word in an affine ring if the codelength is smaller than the number of rational points on the curve then this method can correct up to 1 2 d l 2 s errors where d is the designed minimum distance of the code and s is the clifford defect the affine ring with respect to a place p is the set of all rational functions which have no poles except at p and it is somehow similar to a polynomial ring for a special kind of geometric goppa code namely c sub omega d mp the decoding algorithm is reduced to solving the key equation in the affine ring which can be carried out by the subresultant sequence in the affine ring with complexity o n sup 3 where n is the length of codewords

solution of the riemann problem for irreversibly compressible media the riemann problem for an irreversibly compressible medium has been solved this solution introduces the maximum medium density that is attained in the process of active loading to close the system of equations an extra equation is required to describe the transfer of this parameter through the eulerian mesh the possible wave configurations have been analyzed and the corresponding equations for the evaluation of the contact pressure and velocity have been obtained the existence and uniqueness of the solution have been proven the technique of the riemann problem s solution for the arbitrary lagrange euler mesh was developed examples of the riemann problem solution for various wave configurations show that neglecting the bulk elastic plastic deformations yields significant errors in the results both quantitatively and qualitatively copyright 2009 john wiley sons ltd

on semigroups generated by two consecutive integers and improved hermitian codes analysis of the berlekamp massey sakata algorithm for decoding one point codes leads to two methods for improving code rate one method due to feng and rao removes parity checks that may be recovered by their majority voting algorithm the second method is to design the code to correct only those error vectors of a given weight that are also geometrically generic in this work formulae are given for the redundancies of hermitian codes optimized with respect to these criteria as well as the formula for the order bound on the minimum distance the results proceed from an analysis of numerical semigroups generated by two consecutive integers

a fully implicit numerical method for single fluid resistive magnetohydrodynamics we present a nonlinearly implicit conservative numerical method for integration of the single fluid resistive mhd equations the method uses a high order spatial discretization that preserves the solenoidal property of the magnetic field the fully coupled pde system is solved implicitly in time providing for increased interaction between physical processes as well as additional stability over explicit time methods a high order adaptive time integration is employed which in many cases enables time steps ranging from one to two orders of magnitude larger than those constrained by the explicit cfl condition we apply the solution method to illustrative examples relevant to stiff magnetic fusion processes which challenge the efficiency of explicit methods we provide computational evidence showing that for such problems the method is comparably accurate with explicit time simulations while providing a significant runtime improvement due to its increased temporal stability

correspondence between constrained transport and vector potential methods for magnetohydrodynamics we show that one can formulate second order field and flux interpolated constrained transport central difference ct cd type methods as cell centered magnetic vector potential schemes we introduce four vector potential cta cda schemes three of which correspond to ct cd methods of toth 2000 1 and one of which is a new simple flux ct like scheme where the centroidal vector potential is the primal update variable these algorithms conserve a discretization of the b 0 condition to machine precision and may be combined with shock capturing godunov type base schemes for magnetohydrodynamics recasting ct in terms of a centroidal vector potential allows for some simple generalizations of divergence preserving methods to unstructured meshes and potentially new directions to generalize ct schemes to higher order

machine learning models epistemic set valued data and generalized loss functions we study those problems where the goal is to find optimal models with respect to some specific criterion in regression and supervised classification problems alternatives to the usual expected loss minimization criterion are proposed and a general framework where this criterion can be seen as a particular instance of a general family of criteria is provided in the new setting each model is formally identified with a random variable that associates a loss value to each individual in the population based on this identification different stochastic orderings between random variables lead to different criteria to compare pairs of models our general setting encompasses the classical criterion based on the minimization of the expected loss but also other criteria where a numerical loss function is not available and therefore the computation of its expectation does not make sense the presentation of the new framework is divided into two stages first we consider the new framework under standard situations about the sample information where both the collection of attributes and the response variables are observed with precision then we assume that just incomplete information about them expressed in terms of set valued data sets is provided we cast some comparison criteria from the recent literature on learning methods from low quality data as particular instances of our general approach

a systolic array implementation of the feng rao algorithm an efficient implementation of a parallel version of the feng rao algorithm on a one dimensional systolic array is presented in this paper by adopting an extended syndrome matrix syndromes of the same order lying on a slant diagonal in the extended syndrome matrix are scheduled to be examined by a series of cells simultaneously and therefore a high degree of concurrency of the feng rao algorithm can be achieved the time complexity of the proposed architecture is m g 1 by using a series of t g 1 2 1 nonhomogeneous but regular effective processors called pe cells and g trivial processors called d cells where t is designed as the half of the feng rao bound each d cell contains only delay units while each pe cell contains one finite field inverter and except the first one one or more finite field multipliers cell functions of each pe cell are basically the same and the overall control circuit of the proposed array is quite simple the proposed architecture requires in total t g 1 1 finite field inverters and t g 1 2 t g 1 2 1 2 finite field multipliers for a practical design this hardware complexity is acceptable

ader schemes for the shallow water equations in channel with irregular bottom elevation this paper deals with the construction of high order ader numerical schemes for solving the one dimensional shallow water equations with variable bed elevation the non linear version of the schemes is based on eno reconstructions the governing equations are expressed in terms of total water height instead of total water depth and discharge the eno polynomial interpolation procedure is also applied to represent the variable bottom elevation ader schemes of up to fifth order of accuracy in space and time for the advection and source terms are implemented and systematically assessed with particular attention to their convergence rates non oscillatory results are obtained for discontinuous solutions both for the steady and unsteady cases the resulting schemes can be applied to solve realistic problems characterized by non uniform bottom geometries

high order central scheme on overlapping cells for magneto hydrodynamic flows with and without constrained transport method this paper extends the central finite volume schemes of liu et al y liu c w shu e tadmor m zhang non oscillatory hierarchical reconstruction for central and finite volume schemes commun comput phys 2 2007 933 963 on overlapping cells to the magneto hydrodynamic mhd equations in particular we propose a high order divergence free reconstruction for the magnetic field that uses the face centered values we also advance the magnetic field with a high order constrained transport ct scheme to preserve the divergence free condition to machine round off error the overlapping cells are natural to be used to calculate the electric field flux without an averaging procedure we have developed a third order scheme which is verified by the numerical experiments other higher order schemes can be constructed accordingly our central constrained transport schemes do not need characteristic decomposition and are easy to code and combine with un split discretization of the source and parabolic terms the overlapping cell representation of the solution is also used to develop more compact reconstruction and less dissipative schemes the high resolution is achieved by non oscillatory hierarchical reconstruction which does not require characteristic decomposition either the numerical comparisons show that the central schemes with non ct perform as well as with ct for most of problems numerical examples are given to demonstrate efficacy of the new schemes

fast decoding of codes from algebraic plane curves improvement to an earlier decoding algorithm for codes from algebraic geometry is presented for codes from an arbitrary regular plane curve the authors correct up to d 2 m sup 2 8 m 4 9 8 errors where d is the designed distance of the code and m is the degree of the curve the complexity of finding the error locator is o n sup 7 3 where n is the length of the code for codes from hermitian curves the complexity of finding the error values given the error locator is o n sup 2 and the same complexity can be obtained in the general case if only d 2 m sup 2 2 errors are corrected