a finite element method using singular functions for the poisson equation corner singularities consider the poisson equation with homogeneous dirichlet boundary conditions on a polygonal domain with one reentrant corner in this paper we develop a new finite element method for the accurate computation of the solution and stress intensity factors it is well known that the solution of such a problem has a singular function representation u w lambda eta s where w in h 2 omega cap h 1 0 omega lambda in cal r and eta are the stress intensity factor and cut off function respectively and s is a known singular function depending only on the reentrant angle by using the dual singular and an extra cut off function we are able to derive a new extraction formula for lambda in terms of w and hence deduce a well posed variational problem for w standard continuous piecewise linear finite element approximation yields o h optimal accuracy for w which in turn implies the same accuracy for u in the h 1 norm we are able only to prove o h 1 frac pi omega error bounds for w and u in the l 2 norm and for lambda in the absolute value where omega is the internal angle

fully discrete stabilized multiphysics finite element method for the polymer gel model abstract in this paper we propose a fully discrete stabilized multiphysics finite element method by the pressure projection method to solve the polymer gel model to reveal the multi physical process of the polymer gel model we reformulate the polymer gel model by introducing a new variable to get a new multi field problem then we propose the fully discrete stabilized multiphysics finite element method using the simplest equal order element of p 1 p 1 p 1 without the discrete inf sup condition to solve the new reformulated system and we prove that the new method not only has no locking phenomenon but also preserves some energy conservation laws also we prove that the stabilized multiphysics finite element method has optimal convergence order finally we give the numerical example to verify the theoretical results

a fast algorithm for determining the linear complexity of a sequence with period p sup n over gf q a fast algorithm is presented for determining the linear complexity of a sequence with period p sup n over gf q where p is an odd prime and where q is a prime and a primitive root mod p sup 2

on the linear complexity of nonlinearly filtered pn sequences binary sequences of period 2 sup n 1 generated by a linear feedback shift register lfsr whose stages are filtered by a nonlinear function f are studied new iterative formulas are derived for the calculation of the linear complexity of the output sequences it is shown that these tools provide an efficient mechanism for controlling the linear complexity of the nonlinearly filtered maximal length sequences

the complexity of gentzen systems for propositional logic abstract examples are given of valid sequents of classical propositional logic involving only the biconditional which require exponentially long proofs in a cut free gentzen system the sequents have polynomial size proofs if the cut rule is allowed

a modified streamline diffusion method for solving the stationary navier stokes equation recently hughes et al 11 12 proposed new finite element schemes of petrov galerkin type for solving the stokes problem which do not require the discrete version of the ladyshenskaya babuska brezzi condition lbb condition in this paper we derive a conforming finite element method for solving the stationary navier stokes equations which combines the advantages of arbitrary finite element spaces for velocity pressure with the favourable properties of the streamline diffusion method in the case of moderate and high reynolds number

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

error analysis of some finite element methods for the stokes problem we prove the optimal order of convergence for some two dimensional finite element methods for the stokes equations first we consider methods of the taylor hood type the triangular p3 p2 element and the qk qk 1 i k 2 family of quadrilateral elements then we introduce two new low order methods with piecewise constant approximations for the pressure the analysis is performed using our macroelement technique which is reviewed in a slightly altered form

an error analysis of the finite element method overcoming corner singularities for the stationary stokes problem in this paper we introduce a mixed finite element method to overcome corner singularities of the stationary stokes system on a non convex polygon the reference choi and kweon 2013 says that the velocity field and the pressure function are composed of singular parts and regular remainders near a non convex vertex and furthermore the regular parts are sufficiently smooth on the polygon we use the corner singularity expansion and propose new extraction formulae for coefficients of singularities for the proposed numerical method we first try to find finite element solutions for the regular parts and then calculate approximations of the coefficients by the derived formulae expressed by the remainders and given functions we show error estimates of the approximations for the regular parts and coefficients and give some numerical experiments to confirm the efficiency and reliability of the proposed method

on a multiscale approach to the transient stokes problem dynamic subscales and anisotropic space time discretization abstract in this article we analyze some residual based stabilization techniques for the transient stokes problem when considering anisotropic time space discretizations we define an anisotropic time space discretization as a family of time space partitions that does not satisfy the condition h 2 c t with c uniform with respect to h and t standard residual based stabilization techniques are motivated by a multiscale approach approximating the effect of the subscales onto the large scales one of the approximations is to consider the subscales quasi static neglecting their time derivative it is well known that these techniques are unstable for anisotropic time space discretizations we show that the use of dynamic subscales where the subscales time derivatives are not neglected solves the problem and prove optimal convergence and stability results that are valid for anisotropic time space discretizations also the improvements related to the use of orthogonal subscales are addressed

an anisotropic pressure stabilized finite element method for incompressible flow problems we consider a pressure stabilized finite element approximation of incompressible flow problems in primitive velocity pressure variables which is based on a projection of the gradient of the discrete pressure onto the space of discrete functions equal order interpolation for the velocity and the pressure can be employed with this formulation the method introduced here is specially developed to be used on anisotropic finite element meshes with large element aspect ratios

on the linear and nonlinear complexity profile of nonlinear pseudorandom number generators we obtain lower bounds on the linear and nonlinear complexity profile of a general nonlinear pseudorandom number generator of the inversive generator and of a new nonlinear generator called quadratic exponential generator the results are interesting for applications to cryptography and monte carlo methods

results on the nonlinear span of binary sequences the problem of finding the length of a shortest feedback shift register that generates a given finite length sequence is considered an efficient algorithm for the determination of the span is proposed that takes advantage of the special block structure of the associated system of linear equations the span distribution of finite length binary sequences is also studied

tractability of cut free gentzen type propositional calculus with permutation inference ii in arai 1996 we introduced a new inference rule called permutation to propositional calculus and showed that cut free gentzen system lk gcnf with permutation 1 satisfies the feasible subformula property and 2 proves pigeonhole principle and k equipartition polynomially in this paper we survey more properties of our system first we prove that cut free lk permutation has polynomial size proofs for nonunique endnode principle bondy s theorem second we remark the fact that permutation inference has an advantage over renaming inference in automated theorem proving since gcnf renaming does not always satisfy the feasible subformula property finally we discuss on the relative efficiency of our system vs frege systems and show that frege polynomially simulates gcnf renaming if and only if frege polynomially simulates extended frege

chaotic and stochastic functions abstract we study chaotic functions that are exact solutions to nonlinear maps a generalization of these functions which cannot be expressed as a recursive procedure anymore can produce truly random sequences even if the initial conditions are known exactly the next values are in principle unpredictable we present a mathematical formulation of an elementary stochastic process several applications are discussed

multigrid methods for the computation of singular solutions and stress intensity factors i corner singularities we consider the poisson equation u f with homogeneous dirichlet boundary condition on a two dimensional polygonal domain with cracks multigrid methods for the computation of singular solutions and stress intensity factors using piecewise linear functions are analyzed the convergence rate for the stress intensity factors is mathcal o h 3 2 in whenfel2 and mathcal o h 2 in whenfeh1 the convergence rate in the energy norm is mathcal o h 1 in in the first case and mathcal o h in the second case the costs of these multigrid methods are proportional to the number of elements in the triangulation the general case wherefehm is also discussed

viscous flow in domains with corners numerical artifacts their origin and removal abstract viscous flows in domains with boundaries forming two dimensional corners are considered we examine the case where on each side of the corner the boundary condition for the tangential velocity is formulated in terms of stress it is shown that computing such flows numerically by straightforwardly applying well tested algorithms and numerical codes based on their use such as comsol multiphysics can lead to spurious multivaluedness and mesh dependence in the distribution of the fluid s pressure the origin of this difficulty is that near a corner formed by smooth parts of the boundary in addition to the solution of the formulated inhomogeneous problem there also exists an eigensolution for obtuse corner angles this eigensolution a becomes dominant and b has a singular radial derivative of velocity at the corner despite the bulk pressure in the eigensolution being constant when the derivatives of the velocity are singular numerical errors in the velocities calculation near the corner give rise to pressure spikes whose magnitude increases as the mesh is refined a method is developed that uses the knowledge about the eigensolution to remove the artifacts in the pressure distribution the method is first explained in the simple case of a stokes flow in a corner region and then generalized for the navier stokes equations applied to describe steady and unsteady free surface flows encountered in problems of dynamic wetting

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

an absolutely stabilized finite element method for the stokes problem on presente une formulation a elements finis absolument stabilisee pour le probleme de stokes on etablit des estimations d erreurs optimales dans la norme l 2 pour l approximation des champs de vitesses et de pressions

a unified stabilized method for stokes and darcy s equations we use the lowest possible approximation order piecewise linear continuous velocities and piecewise constant pressures to compute solutions to stokes equation and darcy s equation applying an edge stabilization term to avoid locking we prove that the formulation satisfies the discrete inf sup condition we prove an optimal a priori error estimate for both problems the formulation is then extended to the coupled case using a nitsche type weak formulation allowing for different meshes in the two subdomains finally we present some numerical examples verifying the theoretical predictions and showing the flexibility of the coupled approach

chaotic frequency hopping sequences this letter describes a novel family of frequency hopping sequences generated by chaotic systems the sequences give a uniform spread over the entire frequency bandwidth in addition to having good hamming correlation properties they possess ideal linear span the sequences produce almost as good performance as random hopping patterns when used in frequency hopping code division multiple access fh cdma systems many numerical examples based on a digital chaos generator are presented

a fully discrete stabilized finite element method for the time dependent navier stokes equations in this article we consider a fully discrete stabilized finite element method based on two local gauss integrations for the two dimensional time dependent navier stokes equations it focuses on the lowest equal order velocity pressure pairs unlike the other stabilized method the present approach does not require specification of a stabilization parameter or calculation of higher order derivatives and always leads to a symmetric linear system the euler semi implicit scheme is used for the time discretization it is shown that the proposed fully discrete stabilized finite element method results in the optimal order bounds for the velocity and pressure

a finite element formulation for the stokes problem allowing equal velocity pressure interpolation abstract in this paper we study a variational formulation of the stokes problem that accommodates the use of equal velocity pressure finite element interpolations the motivation of this method relies on the analysis of a class of fractional step methods for the navier stokes equations for which it is known that equal interpolations yield good numerical results the reason for this turns out to be the difference between two discrete laplacian operators computed in a different manner the formulation of the stokes problem considered here aims to reproduce this effect from the analysis of the finite element approximation of the problem we obtain stability and optimal error estimates using velocity pressure interpolations satisfying a compatibility condition much weaker than the inf sup condition of the standard formulation in particular this condition is fulfilled by the most common equal order interpolations

analysis of a pressure stabilized finite element approximation of the stationary navier stokes equations the purpose of this paper is to analyze a finite element approximation of the stationary navier stokes equations that allows the use of equal velocity pressure interpolation the idea is to introduce as unknown of the discrete problem the projection of the pressure gradient multiplied by suitable algorithmic parameters onto the space of continuous vector fields the difference between these two vectors pressure gradient and projection is introduced in the continuity equation the resulting formulation is shown to be stable and optimally convergent both in a norm associated to the problem and in the l 2 norm for both velocities and pressure this is proved first for the stokes problem and then it is extended to the nonlinear case all the analysis relies on an inf sup condition that is much weaker than for the standard galerkin approximation in spite of the fact that the present method is only a minor modification of this

an anisotropic gls stabilized finite element method for incompressible flow problems abstract we consider a stabilized finite element approximation of incompressible flow problems in primitive velocity pressure variables which is based on a gls formulation equal order interpolation for the velocity and the pressure can be employed with this formulation the method introduced here is specially developed to be used on anisotropic finite element meshes with large element aspect ratios rather than using a single stabilization parameter within each element the jacobian matrix of the affine transformation from the reference element is employed for stabilization purposes stability and anisotropic error estimates in a suitable mesh dependent norm are proved for the linear stokes problem numerical results confirm the accuracy and robustness of the proposed method compared to similar previous stabilized schemes

a finite element method for singular solutions of the navier stokes equations on a non convex polygon it is shown in choi and kweon 2013 that a solution of the navier stokes equations with no slip boundary condition on a non convex polygon can be written as u p c 1 1 1 c 2 2 2 u r p r near each non convex vertex where u r p r h 2 h 1 i i are corner singularity functions for the stokes problem with no slip condition and c i r are coefficients which are called the stress intensity factors we design a finite element method to approximate the coefficients c i and the regular part u r p r show the unique existence of the approximations and derive their error estimates some numerical examples are given confirming convergence rates for the approximations

a posteriori error estimators for the stokes equations we present two a posteriori error estimators for the mini element discretization of the stokes equations one is based on a suitable evaluation of the residual of the finite element solution the other one is based on the solution of suitable local stokes problems involving the residual of the finite element solution both estimators are globally upper and locally lower bounds for the error of the finite element discretization numerical examples show their efficiency both in estimating the error and in controlling an automatic self adaptive mesh refinement process the methods presented here can easily be generalized to the navier stokes equations and to other discretization schemes

regularity of solutions for the navier stokes system of incompressible flows on a polygon abstract we are concerned with singularities and regularities of solutions for the navier stokes system of incompressible flows on a polygonal domain with a concave vertex we subtract the corner singularities by the stokes operator from the solution velocity and pressure functions of the system it is shown that the stress intensity factors are functions of time variable belong to a fractional sobolev space on the time interval and can be expressed in terms of given data an increased regularity for the remainder is obtained

on the linear complexity profile of the power generator we obtain a lower bound on the linear complexity profile of the power generator of pseudo random numbers modulo a blum integer a different method is also proposed to estimate the linear complexity profile of the blum blum shub 1986 generator in particular these results imply that lattice reduction attacks on such generators are not feasible

resolution proofs of generalized pigeonhole principles we extend results of haken to give an exponential lower bound on the size of resolution proofs for propositional formulas encoding a generalized pigeonhole principle these propositional formulas express the fact that there is no one one mapping from c n objects to n objects when c 1 as a corollary resolution proof systems do not p simulate constant formula depth frege proof systems

time dependent subscales in the stabilized finite element approximation of incompressible flow problems abstract in this paper we analyze a stabilized finite element approximation for the incompressible navier stokes equations based on the subgrid scale concept the essential point is that we explore the properties of the discrete formulation that results allowing the subgrid scales to depend on time this apparently natural idea avoids several inconsistencies of previous formulations and also opens the door to generalizations

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

pressure stabilization of finite element approximations of time dependent incompressible flow problems in this paper we develop and analyze pressure stabilized finite element methods for the solution of the transient stokes problem which is a linear model problem of transient incompressible flow a model for the bubble enrichment is proposed to stabilize the numerical solution and an implicit backward euler method is considered for the time approximation different methods are obtained depending on whether bubbles are allowed to evolve with time or they are considered quasi static stability estimates are provided for the two methods considered both for the velocity and the pressure solutions numerical results obtained on test cases are also given which confirm the theoretical stability results

lp theory for stokes and navier stokes equations with navier boundary condition abstract this work was intended as an attempt at studying stationary stokes and navier stokes problem with navier boundary conditions 1 3 we wish to investigate some results of existence uniqueness and regularity of solutions in hilbert case and in l p theory

continuous interior penalty finite element method for oseen s equations in this paper we present an extension of the continuous interior penalty method of douglas and dupont interior penalty procedures for elliptic and parabolic galerkin methods in computing methods in applied sciences lecture notes in phys 58 springer verlag berlin 1976 pp 207 216 to oseen s equations the method consists of a stabilized galerkin formulation using equal order interpolation for pressure and velocity to counter instabilities due to the pressure velocity coupling or due to a high local reynolds number we add a stabilization term giving l2 control of the jump of the gradient over element faces edges in two dimensions to the standard galerkin formulation boundary conditions are imposed in a weak sense using a consistent penalty formulation due to nitsche we prove energy type a priori error estimates independent of the local reynolds number and give some numerical examples recovering the theoretical results

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

solution methods for the poisson equation with corner singularities numerical results in z cai and s kim siam j numer anal 39 2001 pp 286 299 we developed a new finite element method using singular functions for the poisson equation on a polygonal domain with re entrant angles such a method first computes the regular part of the solution then the stress intensity factor and finally the solution itself this paper studies solution methods for solving the system of linear equations arising from the discretization and focuses on numerical results including the finite element accuracy and the multigrid performance

coefficients of the singularities for elliptic boundary value problems on domains with conical points iii finite element methods on polygonal domains in the two first parts of this work rairo model math anal numer 24 1990 pp 27e52 rairo model math anal numer 24 1990 pp 343 367 formulas giving the coefficients arising in the singular expansion of the solutions of elliptic boundary value problems on nonsmooth domains are investigated now for the case of homogeneous strongly elliptic operators with constant coefficients on polygonal domains the solution of such problems by the finite element method is considered in order to approximate the solution or the coefficients different methods are used based on the expressions of the coefficients that were obtained in the first two parts the dual singular function method is also generalized

a new family of stable elements for nearly incompressible elasticity based on a mixed petrov galerkin finite element formulation adding to the classical hellinger reissner formulation another residual form of the equilibrium equation a new petrov galerkin finite element method is derived it fits within the framework of a mixed finite element method and is proved to be stable for rather general combinations of stress and displacement interpolations including equal order discontinuous stress and continuous displacement interpolations which are unstable within the galerkin approach error estimates are presented using the babuska brezzi theory and numerical results confirm these estimates as well as the good accuracy and stability of the method

stabilization of low order cross grid pkql mixed finite elements abstract in this paper we analyze a low order family of mixed finite element methods for the numerical solution of the stokes problem and a second order elliptic problem in two space dimensions in these schemes the pressure is interpolated on a mesh of rectangular elements while the velocity is approximated on a triangular mesh obtained by dividing each rectangle into four triangles by its diagonals for the lowest order p 1 q 0 a global spurious pressure mode is shown to exist and so this element as p 1 q 1 case analyzed in armentano and blasco 2010 is unstable however following the ideas given in bochev et al 2006 a simple stabilization procedure can be applied when we approximate the solution of the stokes problem such that the new p 1 q 0 and p 1 q 1 methods are unconditionally stable and achieve optimal accuracy with respect to solution regularity with simple and straightforward implementations moreover we analyze the application of our p 1 q 1 element to the mixed formulation of the elliptic problem in this case by introducing the modified mixed weak form proposed in brezzi et al 1993 optimal order of accuracy can be obtained with our stabilized p 1 q 1 elements numerical results are also presented which confirm the existence of the spurious pressure mode for the p 1 q 0 element and the excellent stability and accuracy of the new stabilized methods

edge stabilization for the generalized stokes problem a continuous interior penalty method in this note we introduce and analyze a stabilized finite element method for the generalized stokes equation stability is obtained by adding a least squares penalization of the gradient jumps acro

the optimal convergence rate of a c1 finite element method for non smooth domains we establish optimal up to arbitrary e 0 convergence rates for a finite element formulation of a model second order elliptic boundary value problem in a weightedh 2 sobolev space with 5th degree argyris elements this formulation arises while generalizing to the case of non smooth domains an unconditionally stable scheme developed by liu et al j g liu j liu r l pego stability and convergence of efficient navier stokes solvers via a commutator estimate comm pure appl math 60 2007 pp 1443 1487 for the navier stokes equations we prove the optimality for both quasiuniform and graded mesh refinements and provide numerical results that agree with our theoretical predictions

penalty finite element method for the navier stokes equations abstract we present an analysis of a penalty formulation of the stationary navier stokes equations for an incompressible fluid subject to restrictions on the viscosity and prescribed body force it is shown that there exists a unique solution to this penalty problem the solution to the penalty problem is shown to converge to the solution of the navier stokes problem as o e where e 0 is the penalty parameter existence uniqueness and stability properties for the approximate problem are then developed and we derive estimates for finite element approximation of the penalized navier stokes problem presented here numerical studies are conducted to examine rates of convergence and sample numerical results presented for test cases

a nonconforming finite element method for the stationary navier stokes equations approximations to solutions of the inhomogeneous boundary value problem for the navier stokes equations are constructed via a nonstandard finite element method the velocity field is approximated using piecewise solenoidal functions that are totally discontinuous across interelement boundaries but which are pointwise divergence free on each element the pressure is approximated by c0 functions optimal rates of convergence results are obtained requiring only local quasi uniformity assumptions on the meshes

on conforming finite element methods for the inhomogeneous stationary navier stokes equations we consider the stationary navier stokes equations written in terms of the primitive variables in the case where both the partial differential equations and boundary conditions are inhomogeneous under certain conditions on the data the existence and uniqueness of the solution of a weak formulation of the equations can be guaranteed a conforming finite element method is presented and optimal estimates for the error of the approximate solution are proved in addition the convergence properties of iterative methods for the solution of the discrete nonlinear algebraic systems resulting from the finite element algorithm are given numerical examples using an efficient choice of finite element spaces are also provided

continuous interior penalty finite element method for the time dependent navier stokes equations space discretization and convergence this paper focuses on the numerical analysis of a finite element method with stabilization for the unsteady incompressible navier stokes equations incompressibility and convective effects are both stabilized adding an interior penalty term giving l 2 control of the jump of the gradient of the approximate solution over the internal faces using continuous equal order finite elements for both velocities and pressures in a space semi discretized formulation we prove convergence of the approximate solution the error estimates hold irrespective of the reynolds number and hence also for the incompressible euler equations provided the exact solution is smooth

the intractability of resolution abstract we prove that for infinitely many disjunctive normal form propositional calculus tautologies the length of the shortest resolution proof of cannot be bounded by any polynomial of the length of the tautologies we use were introduced by cook and reckhow 1979 and encode the pigeonhole principle extended resolution can furnish polynomial length proofs of these formulas

a finite volume method for stokes problems on quadrilateral meshes abstract we present a finite volume method for stokes problems using the isoparametric q 1 q 0 element pair on quadrilateral meshes to offset the lack of the i n f s u p condition a jump term of discrete pressure stabilizing term is added to the continuity approximation equation thus we establish a stabilized finite volume scheme on quadrilateral meshes then based on some superclose estimates we derive the optimal error estimates in the h 1 and l 2 norms for velocity and in the l 2 norm for pressure respectively numerical examples are provided to illustrate our theoretical analysis we emphasize that our work is the first time to propose and analyze a finite volume method for stoke problems using isoparametric elements on quadrilateral meshes

determining the complexity of fh ss sequence by approximate entropy high complexity of frequency hopping fh spreadspectrum ss sequence is of great importance to high security multiple access communication systems for it makes fh ss sequence difficult to be analyzed with the growing development in the design of fh ss sequence in much wider fields the wellknown complexity measuresiquestthe linear complexity lc the linear complexity profile lcp and the k error linear complexity k error lc iquestare widely used but not sufficient to evaluate the complexities of the sequences available such as the cryptographical sequence and the chaotic sequence families in this paper a new complexity metric to evaluate the unpredictability of fh ss sequence based on the approximate entropy apen is proposed in the view of the maximal randomness of the sequences with arbitrary length and the theoretical bounds of the apen are derived from a probabilistic point of view simulations and analysis results show that the proposed apen works effectively to discern the changing complexities of the fh ss sequences with small number of samples which provide superior performance over its candidates

stable and unstable cross grid pkql mixed finite elements for the stokes problem in this paper we develop and analyze a family of mixed finite element methods for the numerical solution of the stokes problem in two space dimensions in these schemes the pressure is interpolated on a mesh of rectangular elements while the velocity is approximated on a triangular mesh obtained by dividing each rectangle into four triangles by its diagonals continuous interpolations of degrees k for the velocity and l for the pressure are considered so the new finite elements are called cross grid p kq l a stability analysis of these approximations is provided based on the macroelement technique of stenberg the lowest order p 1q 1 and p 2q 1 cases are analyzed in detail in the first case a global spurious pressure mode is shown to exist so this element is unstable in the second case however stability is rigorously proved numerical results obtained in these two cases are also presented which confirm the existence of the spurious pressure mode for the p 1q 1 element and the stability of the p 2q 1 element

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

hard examples for resolution exponential lower bounds are proved for the length of resolution refutations of sets of disjunctions constructed from expander graphs using the method of tseitin since these sets of clauses encode biconditionals they have short polynomial length refutations in a standard axiomatic formulation of propositional calculus

stabilized finite element method for the transient navier stokes equations based on a pressure gradient projection abstract in this paper we present a stabilized finite element formulation for the transient incompressible navier stokes equations the main idea is to introduce as a new unknown of the problem the projection of the pressure gradient onto the velocity space and to add to the incompresibility equation the difference between the laplacian of the pressure and the divergence of this new vector field this leads to a pressure stabilization effect that allows the use of equal interpolation for both velocities and pressures in the case of the transient equations we consider the possibility of treating the pressure gradient projection either implicitly or explicity in the first case the number of unknowns of the problem is substantially increased with respect to the standard galerkin formulation nevertheless iterative techniques may be used in order to uncouple the calculation of the pressure gradient projection from the rest of unknowns velocity and pressure when this vector field is treated explicitly the increment of computational cost of the stabilized formulation with respect to the galerkin method is very low we provide a stability estimate for the case of the simple backward euler time integration scheme for both the implicit and the explicit treatment of the pressure gradient projection

a proper hierarchy of propositional sequent calculi abstract it is known that lk a system of propositional sequent calculus without a cut rule written in tree form does not p simulate lk with a full cut rule written in tree form 1 6 it is also known that lk with a full cut rule in tree form p simulates lk in dag form in this paper we show that lk in tree form with a cut rule where the complexity of cut formulas is bounded by k 1 has an exponential speed up over the one bounded by k we also show that lk in tree form with a bounded complexity cut rule does not polynomially simulate cut free lk in dag form

randomness and degrees of irregularity the fundamental question are sequential data random arises in myriad contexts often with severe data length constraints furthermore there is frequently a critical need to delineate nonrandom sequences in terms of closeness to randomness e g to evaluate the efficacy of therapy in medicine we address both these issues from a computable framework via a quantification of regularity apen approximate entropy defining maximal randomness for sequences of arbitrary length indicating the applicability to sequences as short as n 5 points an infinite sequence formulation of randomness is introduced that retains the operational and computable features of the finite case in the infinite sequence setting we indicate how the foundational definition of independence in probability theory and the definition of normality in number theory reduce to limit theorems without rates of convergence from which we utilize apen to address rates of convergence of a deficit from maximal randomness refining the aforementioned concepts in a computationally essential manner representative applications among many are indicated to assess i random number generation output ii well shuffled arrangements and iii the quality of bootstrap replicates

analysis of a streamline diffusion finite element method for the stokes and navier stokes equations for the stokes equations with convection and the incompressible navier stokes equations the authors analyze a streamline diffusion finite element method that is capable of balancing both the convection and the pressure thus allowing the use of arbitrary pairs of velocity pressure spaces for the linear problem the authors obtain for all mesh peclet numbers optimal error estimates in natural norms including in particular the l 2 norm of the pressure the same holds for the nonlinear problem which close to a regular branch of solutions i e the linearized operator is an isomorphism of the norm of the inverse of which still depends on the reynolds number consequently the dependence of the error constants on the reynolds number is not completely resolved in this case

how sampling reveals a process a series of observations xi 1 xi 2 xi 3 ldots is presented to us and at each time n when we have observed the first n of them we are called upon to give our guess for what stochastic process produced the data a universal scheme is given which for any bernoulli process not necessarily independent gives a sequence of processes that converges in a strong sense the bar d metric to the real process in addition to this main result many others are given which put it into proper perspective in particular it is shown that in a certain sense the class of bernoulli processes is the largest one for which such a universal scheme is possible

accurate solution of the thomasfermi equation using the fractional order of rational chebyshev functions in this paper the nonlinear singular thomasfermi differential equation for neutral atoms is solved using the fractional order of rational chebyshev orthogonal functions frcs of the first kind ftn t l on a semi infinite domain where l is an arbitrary numerical parameter first using the quasilinearization method the equation be converted into a sequence of linear ordinary differential equations ldes and then these ldes are solved using the frcs collocation method using 300 collocation points we have obtained a very good approximation solution and the value of the initial slope y 0 1 5880710226113753127186845094239501095 highly accurate to 37 decimal places

stabilization of low order mixed finite elements for the stokes equations we present a new family of stabilized methods for the stokes problem the focus of the paper is on the lowest order velocity pressure pairs while not lbb compliant their simplicity and attractive computational properties make these pairs a popular choice in engineering practice our stabilization approach is motivated by terms that characterize the lbb deficiency of the unstable spaces the stabilized methods are defined by using these terms to modify the saddle point lagrangian associated with the stokes equations the new stabilized methods offer a number of attractive computational properties in contrast to other stabilization procedures they are parameter free do not require calculation of higher order derivatives or edge based data structures and always lead to symmetric linear systems furthermore the new methods are unconditionally stable achieve optimal accuracy with respect to solution regularity and have simple and straightforward implementations we present numerical results in two and three dimensions that showcase the excellent stability and accuracy of the new methods

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

determining lyapunov exponents from a time series we present the first algorithms that allow the estimation of non negative lyapunov exponents from an experimental time series lyapunov exponents which provide a qualitative and quantitative characterization of dynamical behavior are related to the exponentially fast divergence or convergence of nearby orbits in phase space a system with one or more positive lyapunov exponents is defined to be chaotic our method is rooted conceptually in a previously developed technique that could only be applied to analytically defined model systems we monitor the long term growth rate of small volume elements in an attractor the method is tested on model systems with known lyapunov spectra and applied to data for the belousov zhabotinskii reaction and couette taylor flow

analysis of velocity flux first order system least squares principles for the navier stokes equations part i this paper develops a least squares approach to the solution of the incompressible navier stokes equations in primitive variables as with our earlier work on stokes equations we recast the navier stokes equations as a first order system by introducing a velocity flux variable and associated curl and trace equations we show that a least squares principle based on l2 norms applied to this system yields optimal discretization error estimates in the h1 norm in each variable including the velocity flux an analogous principle based on the use of an h 1 norm for the reduced system with no curl or trace constraints is shown to yield similar estimates but now in the l2 norm for velocity flux and pressure although the h 1 least squares principle does not allow practical implementation these results are critical to the analysis of a practical least squares method for the reduced system based on a discrete equivalent of the negative norm a practical method of this type is the subject of a companion paper finally we establish optimal multigrid convergence estimates for the algebraic system resulting from the l2 norm approach