the strong simplex conjecture is false the design of m average energy constrained signals in additive white gaussian noise is addressed the long standing strong simplex conjecture which postulates that the regular simplex signal set maximizes the probability of correct detection under an average energy constraint is disproven a signal set is presented that performs better than the regular simplex signal set at low signal to noise ratios for all m spl ges 7 this leads to the result that for all m spl ges 7 there is no signal set of m signals which is optimal at all signal to noise ratios furthermore the optimal signal set at low signal to noise ratios is not an equal energy set for any m spl ges 7 the regular simplex is shown to be the unique signal set which maximizes the minimum distance between signals it follows that a signal set which maximizes the minimum distance is not necessarily optimum however the regular simplex is shown to be globally optimum in the sense of uniquely maximizing the union bound on error probability at all signal to noise ratios

generalized means as model of compensative connectives abstract empirical investigations have shown that instead of strong logical and and or connectives there is often some degree of compensation in between in this paper the generalized means are proposed as connective operators for fuzzy set theory which easily allow for modelling the degree of compensation in a natural manner including the arithmetic and geometric means as well as the maximum and minimum operators as special cases numerical examples with empirical data form an illustration of this concept some aspects of applications to decision making are discussed

a new class of truly consistent splitting schemes for incompressible flows a new class of splitting schemes for incompressible flows is introduced the new schemes are based on a weak form of the pressure poisson equation and at each time step only require to solve a set of helmholtz type equations for the velocity and a poisson equation in the weak form for the pressure just as pressure correction and velocity correction schemes however unlike pressure correction and velocity correction schemes the new splitting schemes are free of splitting errors and deliver full accuracy on the vorticity and the pressure

spurious transients of projection methods in microflow simulations the temporal behavior of projection methods for viscous incompressible lowreynolds number ows is adressed the methods considered result from algebraically splitting the linear system corresponding to each time step in such a way that the computation of velocity is segregated from that of pressure each method is characterized by two possibly equal approximate inverses b1 and b2 of the momentum equation velocity matrix plus a parameter which renders the method non incremental if 0 or incremental if 1 the classical rst order projection method together with more sophisticated methods perot s second order method yosida method pseudoexact factorization method and their incremental variants are put into the same algebraic form and their accuracy numerically tested splitting errors of rst

computation of the exact bit error rate of coherent m ary psk with gray code bit mapping the problem of calculating the average bit error probability bep of coherent m ary phase shift keying psk over a gaussian channel has been studied previously in the literature a solution to the problem for systems using a binary reflected gray code brgc to map bits to symbols was first presented by p j lee see ibid vol com 34 p 488 91 1986 we show that the results obtained by lee are incorrect for m spl ges 16 we show that the reason for this is an invalid assumption that the bit error rate ber is independent of the transmitted symbols an assumption which has also propagated to textbooks we give a new expression for the ber of m psk systems using the brgc and compare this with lee s results

pressure stability in fractional step finite element methods for incompressible flows abstract the objective of this paper is to analyze the pressure stability of fractional step finite element methods for incompressible flows that use a pressure poisson equation for the classical first order projection method it is shown that there is a pressure control which depends on the time step size and therefore there is a lower bound for this time step for stability reasons the situation is much worse for a second order scheme in which part of the pressure gradient is kept in the momentum equation the pressure stability in this case is extremely weak to overcome these shortcomings a stabilized fractional step finite element method is also considered and its stability is analyzed some simple numerical examples are presented to support the theoretical results

on equivalence classes of fuzzy connectives the case of fuzzy integrals an equivalence relation between connectives or operators in the framework of multiple criteria decision making is introduced two operators are said to be equivalent if they lead to the same ranking of alternatives some general results to find equivalence classes of operators are given through the concept of level surfaces in a second part these results are applied to the case of discrete fuzzy integrals which are considered here as n place operators first some general results on the situation of fuzzy integrals among fuzzy operators are given and then the equivalence classes of fuzzy integrals

a stabilized implicit fractional step method for the time dependent navier stokes equations using equal order pairs abstract a stabilized implicit fractional step method for numerical solutions of the time dependent navier stokes equations is presented in this paper the time advancement is decomposed into a sequence of two steps the first step has the structure of the linear elliptic problem the second step can be seen as the generalized stokes problem the two problems satisfy the full homogeneous dirichlet boundary conditions on the velocity on the other hand a locally stabilized term is added in the second step of the schemes it allows one to enhance the numerical stability and efficiency by using the equal order pairs convergence analysis and error estimates for the velocity and pressure of the schemes are established via the energy method some numerical experiments are also used to demonstrate the efficiency of this new method

fuzzy measure of fuzzy events defined by fuzzy integrals abstract we define the concept of fuzzy measure of a fuzzy event by using a general form of fuzzy integral proposed by murofushi called fuzzy t conorm integral encompassing previous definitions zadeh defined the probability measure of a fuzzy event and later the possibility measure of fuzzy event using a duality property of fuzzy t conorm integral we propose a general definition of fuzzy measure of fuzzy events which is compatible with previous definitions of zadeh and possesses all properties of a fuzzy measure in particular the duality property using our definition we examine the case of decomposable measures and belief functions a comparison with previous works is provided

stabilized mixed methods for the stokes problem the solution of the stokes problem is approximated by three stabilized mixed methods one due to hughes balestra and franca and the other two being variants of this procedure in each case the bilinear form associated with the saddle point problem of the standard mixed formulation is modified to become coercive over the finite element space error estimates are derived for each procedure

high order ale schemes for incompressible capillary flows the spatial discretization of problems with moving boundaries is considered incorporating the temporal evolution of not just the mechanical variables but also of the nodal positions of the moving mesh the outcome is a system of differential algebraic equations dae of index 2 or in the case of inertialess flow just 1 from the dae formulation it its possible to define strategies to build schemes of arbitrary accuracy we introduce here several schemes of order 2 and 3 that avoid the solution of a nonlinear system involving simultaneously the mechanical variables and the geometrical ones this class of schemes has been the one adopted by the majority of practitioners of computational fluid dynamics up to now the proposed schemes indeed achieve the design accuracy and further show stability restrictions that are not significantly more severe than those of popular first order schemes the numerical experimentation is performed on capillary problems discretized by both div stable p 2 p 1 p 1 p 1 and equal order p 1 p 1 stabilized finite elements and incorporating surface tension and triple contact line effects

segregated runge kutta methods for the incompressible navier stokes equations in this work we propose runge kutta time integration schemes for the incompressible navier stokes equations with two salient properties first velocity and pressure computations are segregated at the time integration level without the need to perform additional fractional step techniques that spoil high orders of accuracy second the proposed methods keep the same order of accuracy for both velocities and pressures the segregated runge kutta methods are motivated as an implicit explicit runge kutta time integration of the projected navier stokes system onto the discrete divergence free space and its re statement in a velocity pressure setting using a discrete pressure poisson equation we have analysed the preservation of the discrete divergence constraint for segregated runge kutta methods and their relation in their fully explicit version with existing half explicit methods we have performed a detailed numerical experimentation for a wide set of schemes from first to third order including implicit and imex integration of viscous and convective terms for incompressible laminar and turbulent flows further segregated runge kutta schemes with adaptive time stepping are proposed

pictorial representations of fuzzy connectives part i cases of t norms t conorms and averaging operators part i of this paper shows a number of examples of existing t norms and t conorms which are known as good models of fuzzy set theoretic intersection and union and then the pictorial representations of t norms and t conorms are made with the aid of a computer several new examples of t norms and t conorms are also given averaging operators between min and max are summarized and their pictorial representations are also made

fuzzy systems as universal approximators an additive fuzzy system can uniformly approximate any real continuous function on a compact domain to any degree of accuracy an additive fuzzy system approximates the function by covering its graph with fuzzy patches in the input output state space and averaging patches that overlap the fuzzy system computes a conditional expectation e y x if we view the fuzzy sets as random sets each fuzzy rule defines a fuzzy patch and connects commonsense knowledge with state space geometry neural or statistical clustering systems can approximate the unknown fuzzy patches from training data these adaptive fuzzy systems approximate a function at two levels at the local level the neural system approximates and tunes the fuzzy rules at the global level the rules or patches approximate the function

connectives and quantifiers in fuzzy sets abstract we discuss some of the issues involved in the selection of appropriate operators for implementing the union and intersection of fuzzy subsets we discuss the extension principles used in extending operators to fuzzy subsets we provide a structure for aggregating linguistic variables in the theory of approximate reasoning we look at mean operators on fuzzy subsets as well as the inclusion of importances in aggregation we discuss non monotone set operators we introduce the concept of linguistic quantifiers and look at some applications of these structures we are particularly concerned with their application to linguistic summarizers syllogistic reasoning and multi criteria decision making

asymptotic comparison of ml and map detectors for multidimensional constellations a classical problem in digital communications is to evaluate the symbol error probability sep and bit error probability bep of a multidimensional constellation over an additive white gaussian noise channel in this paper we revisit this problem for nonequally likely symbols and study the behavior of the optimal maximum a posteriori map detector at asymptotically high signal to noise ratios exact closed form asymptotic expressions for sep and bep for arbitrary constellations and input distributions are presented the well known union bound is proven to be asymptotically tight under general conditions the performance of the practically relevant maximum likelihood ml detector is also analyzed although the decision regions with map detection converge to the ml regions at high signal to noise ratios the ratio between the map and ml detectors in terms of both sep and bep approaches a constant which depends on the constellation and a priori probabilities necessary and sufficient conditions for asymptotic equivalence between the map and ml detectors are also presented

a numerical method for incompressible viscous flow simulation we describe a numerical scheme for computing time dependent solutions of the incompressible navier stokes equations in the primitive variable formulation this scheme uses finite elements for the space discretization and operator splitting techniques for the time discretization the resulting discrete equations are solved using specialized nonlinear optimization algorithms that are computationally efficient and have modest storage requirements the basic numerical kernel is the preconditioned conjugate gradient method for symmetric positive definite sparse matrix systems which can be efficiently implemented on the architectures of vector and parallel processing supercomputers

approximation of the incompressible navier stokes equations using orthogonal subscale stabilization and pressure segregation on anisotropic finite element meshes abstract this paper describes a finite element model to solve the incompressible navier stokes equations based on the stabilization with orthogonal subscales and a pressure segregation the former consists of adding a least square form of the component orthogonal to the finite element space of the convective and pressure gradient terms this allows to deal with convection dominated flows and to use equal velocity pressure interpolation the pressure segregation is inspired in fractional step schemes although the converged solution corresponds to that of a monolithic time integration likewise we put special emphasis on the use of anisotropic grids in particular we describe some possible choices for the calculation of the element length that appears in the stabilization parameters and check their behavior in two classical numerical examples the preconditioning strategy used to solve the resulting algebraic system for very anisotropic meshes is also briefly described

optimal nonuniform signaling for gaussian channels variable rate data transmission schemes in which constellation points are selected according to a nonuniform probability distribution are studied when the criterion is one of minimizing the average transmitted energy for a given average bit rate the best possible distribution with which to select constellations points is a maxwell boltzmann distribution in principle when constellation points are selected according to a maxwell boltzmann distribution the ultimate shaping gain pi e 6 or 1 53 db can be achieved in any dimension nonuniform signaling schemes can be designed by mapping simple variable length prefix codes onto the constellation using the huffman procedure prefix codes can be designed that approach the optimal performance these schemes provide a fixed rate primary channel and a variable rate secondary channel and are easily incorporated into standard lattice type coded modulation schemes

factorization methods for the numerical approximation of navier stokes equations we investigate a general approach for the numerical approximation of incompressible navier stokes equations based on splitting the original problem into successive subproblems which are cheaper to solve the splitting is obtained through an algebraic approximate factorization of the matrix arising from space and time discretization of the original equations several schemes based on approximate factorization are investigated for some of these methods a formal analogy with well known time advancing schemes such as the projection chorin temam s can be pointed out features and limits of this analogy that was earlier introduced in b perot j comp phys 108 1993 51 8 are addressed other new methods can also be formulated starting from this approach in particular we introduce the so called yosida method which can be investigated in the framework of quasi compressibility schemes numerical results illustrating the different performances of the different methods addressed are presented for a couple of test cases

error analysis of some galerkin least squares methods for the elasticity equations the recent technique of stabilizing mixed finite element methods by augmenting the galerkin formulation with least squares terms calculated separately on each element is considered the error analysis is performed in a unified manner yielding improved results for some methods introduced earlier in addition a new formulation is introduced and analyzed method is used within two different contexts the first is in connection with the plain strain or three dimensional problems near the incompressible limit for which the poisson ratio equals one half it is well known that for these problems a standard lower order displacement finite element method will break down by now it is also well known how a working method can be obtained a new unknown the pressure is introduced and discretized with a finite element space different from that used for the displacements the finite element method obtained falls into the class of saddlepoint problems for which there is a general theory developed by brezzi and babuska 5 7 the application of this theory shows that the method converges optimally if the discrete spaces for the displacement and pressure satisfy a stability condition for a particular choice of displacement and pressure approximations it can be a difficult task to verify this babuska brezzi or inf sup condition during the last decade this problem has been intensively studied and the performances of many combinations are now known cf 18 and 23 26 for some recent extensions in addition there exists a general technique utilizing bubble functions by which a stable method can

owa operators on complete lattices considering some aggregation functions we define bf b a weighting vectors then a definition for ordered weighted average owa operators is given based on bf b a weighting vectors moreover we show that our proposed definition for owa operators over complete lattices is a generalization of the given definition by lizasoain and moreno finally a special case is studied

first second and third order fractional step methods for the three field viscoelastic flow problem in this paper three different fractional step methods are designed for the three field viscoelastic flow problem whose variables are velocity pressure and elastic stress the starting point of our methods is the same as for classical pressure segregation algorithms used in the newtonian incompressible navier stokes problem these methods can be understood as an inexact lu block factorization of the original system matrix of the fully discrete problem and are designed at the pure algebraic level the final schemes allow one to solve the problem in a fully decoupled form where each equation for velocity pressure and elastic stress is solved separately the first order scheme is obtained from a straightforward segregation of pressure and elastic stress in the momentum equation whereas the key point for the second order scheme is a first order extrapolation of these variables the third order fractional step method relies on yosida s scheme referring to the spatial discretization either the galerkin method or a stabilized finite element formulation can be used we describe the fractional step methods first assuming the former and then we explain the modifications introduced by the stabilized formulation we employ and that has been proposed in a previous work this discretization in space shows very good stability permitting in particular the use of equal interpolation for all variables

on some pressure segregation methods of fractional step type for the finite element approximation of incompressible flow problems abstract in this paper we treat several aspects related to time integration methods for the incompressible navier stokes equations that allow to uncouple the calculation of the velocities and the pressure the first family of schemes consists of classical fractional step methods of which we discuss several possibilities for the pressure extrapolation and the time integration of first and second order the second family consists of schemes based on an explicit treatment of the pressure in the momentum equation followed by a poisson equation for the pressure it turns out that this staggered treatment of the velocity and the pressure is stable finally we present predictor corrector methods based on the above schemes that aim to converge to the solution of the monolithic time integration method apart from presenting these schemes and check its numerical performance we also present a complete set of stability results for the fractional step methods that are independent of the space stability of the velocity pressure interpolation that is of the classical inf sup condition

an analysis of the fractional step method the fractional step method for solving the incompressible navier stokes equations in primitive variables is analyzed as a block lu decomposition in this formulation the issues involving boundary conditions for the intermediate velocity variables and the pressure are clearly resolved in addition it is shown that poor temporal accuracy first order is not due to boundary conditions but due to the method itself a generalized block lu decomposition that overcomes this difficulty is presented allowing arbitrarily high temporal order of accuracy the generalized decomposition is shown to be useful for a wide range of problems including steady problems technical issues such as stability and the appropriate pressure update scheme are also addressed numerical simulations of the steady incompressible navier stokes equations in a square domain confirm the theoretical results 18 refs 4 figs

unconditionally stable operator splitting algorithms for the incompressible magnetohydrodynamics system discretized by a stabilized finite element formulation based on projections summary in this article we propose different splitting procedures for the transient incompressible magnetohydrodynamics mhd system that are unconditionally stable we consider two levels of splitting on one side we perform the segregation of the fluid pressure and magnetic pseudo pressure from the vectorial fields computation at the second level the fluid velocity and induction fields are also decoupled this way we transform a fully coupled indefinite multi physics system into a set of smaller definite ones clearly reducing the cpu cost with regard to the finite element approximation we stick to an unconditionally convergent stabilized finite element formulation because it introduces convection stabilization allows to circumvent inf sup conditions clearly simplifying implementation issues and is able to capture non smooth solutions of the magnetic subproblem however residual based finite element formulations are not suitable for segregation because they lose the skew symmetry of the off diagonal blocks therefore in this work we have proposed a novel term by term stabilization of the mhd system based on projections that is still unconditionally convergent copyright 2012 john wiley sons ltd

analysis of a stabilized finite element approximation of the transient convection diffusion equation using an ale framework in this paper we analyze a stabilized finite element method to approximate the convection diffusion equation on moving domains using an arbitrary lagrangian eulerian ale framework as basic numerical strategy we discretize the equation in time using first and second order backward differencing bdf schemes whereas space is discretized using a stabilized finite element method the orthogonal subgrid scale formulation to deal with convection dominated flows the semidiscrete problem continuous in space is first analyzed in this situation it is easy to identify the error introduced by the ale approach after that the fully discrete method is considered we obtain optimal error estimates in both space and time in a mesh dependent norm the analysis reveals that the ale approach introduces an upper bound for the time step size for the results to hold the results obtained for the fully discretized second order scheme in time are associated to a weaker norm than the one used for the first order method nevertheless optimal convergence results have been proved for fixed domains we recover stability and convergence results with the strong norm for the second order scheme stressing the aspects that make the analysis of this method much more involved

splitting methods based on algebraic factorization for fluid structure interaction we discuss in this paper the numerical approximation of fluid structure interaction fsi problems dealing with strong added mass effect we propose new semi implicit algorithms based on inexact block lu factorization of the linear system obtained after the space time discretization and linearization of the fsi problem as a result the fluid velocity is computed separately from the coupled pressure structure velocity system at each iteration reducing the computational cost we investigate explicit implicit decomposition through algebraic splitting techniques originally designed for the fsi problem this approach leads to two different families of methods which extend to fsi the algebraic pressure correction method and the yosida method two schemes that were previously adopted for pure fluid problems furthermore we have considered the inexact factorization of the fluid structure system as a preconditioner the numerical properties of these methods have been tested on a model problem representing a blood vessel system

a characterization of the ordered weighted averaging functions based on the ordered bisymmetry property this paper deals with the characterization of a class of aggregation operators this class concerns operators that are symmetric increasing stable for the same positive linear transformations and present a property close to the bisymmetry property the ordered bisymmetry property it is proved that the class investigated contains exactly the ordered weighted averaging operators introduced by yager 1988

high snr asymptotics of mutual information for discrete constellations with applications to bicm asymptotic expressions of the mutual information between any discrete input and the corresponding output of the scalar additive white gaussian noise channel are presented in the limit as the signal to noise ratio snr tends to infinity asymptotic expressions of the symbol error probability sep and the minimum mean square error mmse achieved by estimating the channel input given the channel output are also developed it is shown that for any input distribution the conditional entropy of the channel input given the output mmse and sep have an asymptotic behavior proportional to the gaussian q function the argument of the q function depends only on the minimum euclidean distance med of the constellation and the snr and the proportionality constants are functions of the med and the probabilities of the pairs of constellation points at med the developed expressions are then generalized to study the high snr behavior of the generalized mutual information gmi for bit interleaved coded modulation bicm by means of these asymptotic expressions the long standing conjecture that gray codes are the binary labelings that maximize the bicm gmi at high snr is proven it is further shown that for any equally spaced constellation whose size is a power of two there always exists an anti gray code giving the lowest bicm gmi at high snr

aggregation functions means this two part state of the art overview on aggregation theory summarizes the essential information concerning aggregation issues an overview of aggregation properties is given including the basic classification on aggregation functions in this first part the stress is put on means i e averaging aggregation functions both with fixed arity n ary means and with multiple arities extended means

approximation of the inductionless mhd problem using a stabilized finite element method in this work we present a stabilized formulation to solve the inductionless magnetohydrodynamic mhd problem using the finite element fe method the mhd problem couples the navier stokes equations and a darcy type system for the electric potential via lorentz s force in the momentum equation of the navier stokes equations and the currents generated by the moving fluid in ohm s law the key feature of the fe formulation resides in the design of the stabilization terms which serve several purposes first the formulation is suitable for convection dominated flows second there is no need to use interpolation spaces constrained to a compatibility condition in both sub problems and therefore equal order interpolation spaces can be used for all the unknowns finally this formulation leads to a coupled linear system this monolithic approach is effective since the coupling can be dealt by effective preconditioning and iterative solvers that allows to deal with high hartmann numbers

stabilized finite element approximation of transient incompressible flows using orthogonal subscales abstract in this paper we present a stabilized finite element method to solve the transient navier stokes equations based on the decomposition of the unknowns into resolvable and subgrid scales the latter are approximately accounted for so as to end up with a stable finite element problem which in particular allows to deal with convection dominated flows and the use of equal velocity pressure interpolations three main issues are addressed the first is a method to estimate the behavior of the stabilization parameters based on a fourier analysis of the problem for the subscales secondly the way to deal with transient problems discretized using a finite difference scheme is discussed finally the treatment of the nonlinear term is also analyzed a very important feature of this work is that the subgrid scales are taken as orthogonal to the finite element space in the transient case this simplifies considerably the numerical scheme

characterization of some aggregation functions stable for positive linear transformations abstract this paper deals with the characterization of some classes of aggregation functions often used in multicriteria decision making problems the common properties involved in these characterizations are increasing monotonicity and stability for positive linear transformations additional algebraic properties related to associativity allow to completely specify the functions

an adaptive fixed mesh ale method for free surface flows in this work we present a fixed mesh ale method for the numerical simulation of free surface flows capable of using an adaptive finite element mesh covering a background domain this mesh is successively refined and unrefined at each time step in order to focus the computational effort on the spatial regions where it is required some of the main ingredients of the formulation are the use of an arbitrary lagrangian eulerian formulation for computing temporal derivatives the use of stabilization terms for stabilizing convection stabilizing the lack of compatibility between velocity and pressure interpolation spaces and stabilizing the ill conditioning introduced by the cuts on the background finite element mesh and the coupling of the algorithm with an adaptive mesh refinement procedure suitable for running on distributed memory environments algorithmic steps for the projection between meshes are presented together with the algebraic fractional step approach used for improving the condition number of the linear systems to be solved the method is tested in several numerical examples the expected convergence rates both in space and time are observed smooth solution fields for both velocity and pressure are obtained as a result of the contribution of the stabilization terms finally a good agreement between the numerical results and the reference experimental data is obtained

fuzzy t conorm integral with respect to fuzzy measures generalization of sugeno integral and choquet integral abstract this article discusses integrals with respect to sugeno s fuzzy measures sugeno integrals and choquet integrals with respect to general fuzzy measures are generalized in the setting of a t conorm algebraic system first t conorm integrals with respect to decomposable measures based on t conorm algebraic system are defined they are a modification of the weber integral secondly they are extended to fuzzy t conorm integrals with respect to general fuzzy measures the extension is made in the same way as the extension of the lebesgue integral to the choquet integral the class of fuzzy t conorm integrals includes choquet integrals and sugeno integrals properties of the integrals especially their representation are discussed

convergence analysis of the fem approximation of the first order projection method for incompressible flows with and without the inf sup condition in this paper we obtain convergence results for the fully discrete projection method for the numerical approximation of the incompressible navier stokes equations using a finite element approximation for the space discretization we consider two situations in the first one the analysis relies on the satisfaction of the inf sup condition for the velocity pressure finite element spaces after that we study a fully discrete fractional step method using a poisson equation for the pressure in this case the velocity pressure interpolations do not need to accomplish the inf sup condition and in fact we consider the case in which equal velocity pressure interpolation is used optimal convergence results in time and space have been obtained in both cases

on the optimality of the binary reflected gray code this paper concerns the problem of selecting a binary labeling for the signal constellation in m psk m pam and m qam communication systems gray labelings are discussed and the original work by frank gray is analyzed as is noted the number of distinct gray labelings that result in different bit error probability grows rapidly with increasing constellation size by introducing a recursive gray labeling construction method called expansion the paper answers the natural question of what labeling among all possible constellation labelings will give the lowest possible average probability of bit errors for the considered constellations under certain assumptions on the channel the answer is that the labeling proposed by gray the binary reflected gray code is the optimal labeling for all three constellations which has surprisingly never been proved before