the consistent value of fuzzy games in the framework of fuzzy games we offer an extension of the reduced game introduced by hart and mas colell which we name the self reduced game according to consistency which related to the self reduced game we provide a definition of the consistent value which is a generalization of the shapley value of fuzzy games we adopt three existing concepts from coalitional game theory and reinterpret them in the framework of fuzzy games the first one is that there exists a unique potential function and the resulting payoff vector coincides with the consistent value second based on the properties of balanced contributions and consistency we offer several axiomatizations of the consistent value finally we propose a dynamic process to illustrate that the consistent value can be reached by players who start from an arbitrary efficient payoff vector and make successive adjustments

on frechet differentiability of lipschitz maps between banach spaces a well known open question is whether every countable collection of lipschitz functions on a banach space x with separable dual has a common point of frechet differentiability we show that the answer is positive for some infinite dimensional x previously even for collections consisting of two functions this has been known for finite dimensional x only although for one function the answer is known to be affirmative in full generality our aims are achieved by introducing a new class of null sets in banach spaces called f null sets whose definition involves both the notions of category and measure and showing that the required differentiability holds almost everywhere with respect to it we even obtain existence of frechet derivatives of lipschitz functions between certain infinite dimensional banach spaces no such results have been known previously our main result states that a lipschitz map between separable banach spaces is frechet differentiable f almost everywhere provided that it is regularly gateaux differentiable f almost everywhere and the gateaux derivatives stay within a norm separable space of operators it is easy to see that lipschitz maps of x to spaces with the radon nikodym property are gateaux differentiable f almost everywhere moreover gateaux differentiability implies regular gateaux differentiability with exception of another kind of negligible sets so called a porous sets the answer to the question is therefore positive in every space in which every r porous set is f null we show that this holds for c k with k countable compact the tsirelson space and for all subspaces of co but that it fails for hilbert spaces

fuzzy interval cooperative games we introduce a core like concept called f core for games in which the worth of any coalition is given by means of a fuzzy interval such a class of cooperative games was introduced by mares in 1999 different from mares approach the f core generalizes the interval core introduced by alparslan branzei and tijs in 2008 for games where the worth of any coalition is a compact interval of the real line moreover we introduce a balanced like condition and prove that this condition is necessary but not sufficient to guarantee the f core to be non empty

typical differentiability within an exceptionally small set abstract we verify the existence of a purely unrectifiable set in which the typical lipschitz function has a large set of differentiability points the example arises from a construction due to csornyei preiss and tiser of a universal differentiability set in which a certain lipschitz function has only a purely unrectifiable set of differentiability points

a measure zero universal differentiability set in the heisenberg group we show that the heisenberg group mathbb h n contains a measure zero set n such that every lipschitz function f mathbb h n rightarrow mathbb r is pansu differentiable at a point of n the proof adapts the construction of small universal differentiability sets in the euclidean setting we find a point of n and a horizontal direction where the directional derivative in horizontal directions is almost locally maximal then deduce pansu differentiability at such a point

attractors and error estimates for discretizations of incompressible navier stokes equations by embedding sets of nodal values to function spaces variational arguments are applied to the finite difference approximations to the two dimensional incompressible navier stokes equations the error estimates for trajectories and the it time free error estimates with tolerance for attractors are proved the upper semicontinuity of the attractors with respect to the finite difference discretizations are also proved arguments of applying the techniques to the finite element approximations are also given

numerical simulation of a generalized zakharov system in this paper we propose and study two time splitting spectral methods for the generalized zakharov system these methods are spectrally accurate in space second order in time and unconditionally stable the unconditional stability of the methods offers greater numerical efficiency than those given in previous papers especially in the subsonic regime our numerical experiments confirm the accuracy and stability in particular we analyze their behavior in the subsonic regime the first method using the exact time integration in phase space for the wave equation for the nondispersive field converges unformly with respect to the sound speed for the dispersive wave field while the second method using the crank nicolson method in the same step with an initial layer fix by an l stable time discretization converges uniformly with respect to the sound speed for both dispersive and nondispersive fields using these new methods we also study the collision behavior of two solitons in the subsonic region as well as the transsonic region we obtain numerical results which are quantitatively different from those reported in previous papers using lower resolution numerical techniques

taylor vortex flow a dynamical system taylor vortex flows have been studied over a period of more than sixty years they occur between two concentric circular cylinders for example when the inner cylinder rotates and the outer is at rest and the flow takes on a toroidal vortex form with periodicity or quasi periodicity along the axis complex variations on this simple description occur when the angular speed is raised or when the length of the apparatus is reduced a rather special form of turbulence can occur and there may be some relation to chaos in the sense of ordinary differential equations as a dynamical system the experimental and theoretical evidence concerned with these phenomena is discussed

studies of phase turbulence in the one dimensional complex ginzburg landau equation the phase turbulent pt regime for the one dimensional complex ginzburg landau equation cgle is carefully studied in the limit of large systems and long integration times using an efficient integration scheme particular attention is paid to solutions with a nonzero phase gradient for fixed control parameters solutions with conserved average phase gradient ensuremath nu exist only for ensuremath nu less than some upper limit the transition from phase to defect turbulence happens when this limit becomes zero a lyapunov analysis shows that the system becomes less and less chaotic for increasing values of the phase gradient for high values of the phase gradient a family of nonchaotic solutions of the cgle is found these solutions consist of spatially periodic or aperiodic waves traveling with constant velocity they typically have incommensurate velocities for phase and amplitude propagation showing thereby a type of quasiperiodic behavior the main features of these traveling wave solutions can be explained through a modified kuramoto sivashinsky equation that rules the phase dynamics of the cgle in the pt phase the latter explains also the behavior of the maximal lyapunov exponents of chaotic solutions

stability of oscillating hexagons in rotating convection abstract breaking the chiral symmetry rotation induces a secondary hopf bifurcation in weakly nonlinear hexagon patterns which gives rise to oscillating hexagons we study the stability of the oscillating hexagons using three coupled ginzburg landau equations close to the bifurcation point we derive reduced equations for the amplitude of the oscillation coupled to the phase of the underlying hexagons within these equations we identify two types of long wave instabilities and study the ensuing dynamics using numerical simulations of the three coupled ginzburg landau equations

on cores and stable sets for fuzzy games in this paper cores and stable sets for games with fuzzy coalitions are introduced and their relations studied for convex fuzzy games it turns out that all cores coincide and that the core is the unique stable set also relations between cores and stable sets of fuzzy clan games are discussed

numerical computation of e entropy for parabolic equations with analytic solutions abstract we report on numerical experiments computing the e entropy for parabolic partial differential equations the e entropy is a measure of the spatial density of complexity for the dynamics on an invariant set in function space and has been studied analytically by a number of authors the e entropy only requires solutions of the equation to the accuracy of the parameter e and the resulting number is asymptotically independent of domain size we consider the complex ginzburg landau equation as an example where a number of analytic results exist and the kuramoto sivashinsky equation where the accompanying theory has yet to be fully developed our numerical results for the kuramoto sivashinsky equation do not contradict the conjectured linear scaling of the dimension with domain size

superconvergence analysis of a two grid finite element method for ginzburg landau equation abstract in this paper a two grid method tgm is presented for the complex ginzburg landau equation in which the original nonlinear system is analyzed on the coarse grid based on the newton iteration method for the backward euler fully discrete scheme and then a simple linearized problem developed through taylor s expansion on the fine grid is solved by use of the character of the element and some special techniques the superclose estimation in the h1 norm is deduced for the tgm scheme furthermore the global superconvergent result is derived through interpolation postprocessing skill numerical results illustrate that the proposed tgm is very effective and its computing cost is much less than that of the traditional galerkin finite element method fem without loss of accuracy

boldmath topological and epsilon entropy for large volume limits of discretized parabolic equations we consider semidiscrete and fully discrete approximations of nonlinear parabolic equations in the limit of unbounded domains which by a scaling argument is equivalent to the limit of vanishing viscosity we define the spatial density of varepsilon entropy topological entropy and dimension for the attractors and show that these quantities are bounded we also provide practical means of computing lower bounds on them the proof uses the property that solutions lie in gevrey classes of analyticity which we define in a way that does not depend on the size of the spatial domain as a specific example we discuss the complex ginzburg landau equation

a nonstiff euler discretization of the complex ginzburg landau equation in one space dimension a nonstiff discretization method is applied to the complex ginzburg landau cgl equation with periodic boundary conditions begin eqnarray partial t u 1 i nu partial xx 2 u ru 1 i mu u 2 u u t geq 0 end eqnarray this parabolic equation is discretized first in space by a truncated fourier series that is a finite fourier sum and then in time by an explicit euler method the exponential decay of fourier modes in both the original cgl equation and the resulting equation for the truncated fourier series independently from the number of fourier modes in the truncation is used in an essential way to prove the nonstiffness also dissipativity of the discretized equation is established and numerical results are discussed

a lexicographical solution concept in an n person cooperative fuzzy game abstract in this paper a new solution concept in an n person cooperative fuzzy game with sidepayment is proposed we first define an excess with respect to a player in a fuzzy game with sidepayment usually the concept of an excess is defined for each coalition in contrast however we define an excess of a player by summing up all the excess of a coalition to which he belongs by considering a payoff vector which minimizes the excess of a player in the lexicographical order we proposed a new solution concept in a fuzzy game as well as in a nonfuzzy game then we further consider the problem to extend a nonfuzzy game into a fuzzy game such an extension can be described by the mappings from a characteristic function in a nonfuzzy game into a characteristic function in a fuzzy game an illustrative numerical example of the proposed solution concept to some extended fuzzy games is also presented

on the incompressible fluid limit and the vortex motion law of the nonlinear schrodinger equation the nonlinear schrodinger equation nls has been a fundamental model for understanding vortex motion in superfluids the vortex motion law has been formally derived on various physical grounds and has been around for almost half a century we study the nonlinear schrodinger equation in the incompressible fluid limit on a bounded domain with dirichlet or neumann boundary condition the initial condition contains any finite number of degree 1 vortices we prove that the nls linear momentum weakly converges to a solution of the incompressible euler equation away from the vortices if the initial nls energy is almost minimizing we show that the vortex motion obeys the classical kirchhoff law for fluid point vortices similar results hold for the entire plane and periodic cases and a related complex ginzburg landau equation we treat as well the semi classical wkb limit of nls in the presence of vortices in this limit sound waves propagate through steady vortices

vortices in complex scalar fields abstract consider a spatially extended field which evolves in time according to a pde the solutions contain particle like defects whose motions are parts of the full dynamics we inquire into the formulation of an asymptotic particle field defect dynamics which derives from the full pde we carry out this program for two complex scalar field equations in two space dimensions the nonlinear schrodinger equation and the nonlinear heat equation the topological defects are zeros of the complex scalar field with nonzero integer winding numbers called vortices vortices evolving under the nonlinear schrodinger equation behave like point vortices in ideal fluid pairs of vortices evolving under the nonlinear heat equation with like opposite winding numbers undergo a repulsive attractive interaction

an asymptotic preserving scheme for the euler equations in a strong magnetic field this paper is concerned with the numerical approximation of the isothermal euler equations for charged particles subject to the lorentz force the euler lorentz system when the magnetic field is large or equivalently when the parameter e representing the non dimensional ion cyclotron frequency tends to zero the so called drift fluid or gyro fluid approximation is obtained in this limit the parallel motion relative to the magnetic field direction splits from perpendicular motion and is given implicitly by the constraint of zero total force along the magnetic field lines in this paper we provide a well posed elliptic equation for the parallel velocity which in turn allows us to construct an asymptotic preserving ap scheme for the euler lorentz system this scheme gives rise to both a consistent approximation of the euler lorentz model when e is finite and a consistent approximation of the drift limit when e 0 above all it does not require any constraint on the space and time steps related to the small value of e numerical results are presented which confirm the ap character of the scheme and its asymptotic stability

on the time splitting spectral method for the complex ginzburg landau equation in the large time and space scale limit we are interested in the numerical approximation of the complex ginzburg landau equation in the large time and space limit there are two interesting regimes in this problem one being the large space time limit and one being the nonlinear schrodinger limit these limits have been studied analytically in for example t colin and a soyeur asymptot anal 13 1996 pp 361 372 f h lin comm pure appl math 51 1998 pp 385 441 f h lin and j x xin comm math phys 200 1999 pp 249 274 we study a time splitting spectral method for this problem in particular we are interested in whether such a scheme is asymptotic preserving ap with respect to these two limits our results show that the scheme is ap for the first limit but not the second one for the large space time limit our numerical experiments show that the scheme can capture the correct physical behavior without resolving the small scale dynamics even for transitional problems where small and large scales coexist

modulated amplitude waves and defect formation in the one dimensional complex ginzburg landau equation the transition from phase chaos to defect chaos in the complex ginzburg landau equation cgle is related to saddle node bifurcations of modulated amplitude waves maws first the spatial period p of maws is shown to be limited by a maximum psn which depends on the cgle coefficients maw like structures with period larger than psn evolve to defects second slowly evolving near maws with average phase gradients 0 and various periods occur naturally in phase chaotic states of the cgle as a measure for these periods we study the distributions of spacings p between neighbouring peaks of the phase gradient a systematic comparison of p and psn as a function of coefficients of the cgle shows that defects are generated at locations where p becomes larger than psn in other words maws with period psn represent critical nuclei for the formation of defects in phase chaos and may trigger the transition to defect chaos since rare events where p becomes sufficiently large to lead to defect formation may only occur after a long transient the coefficients where the transition to defect chaos seems to occur depend on system size and integration time we conjecture that in the regime where the maximum period psn has diverged phase chaos persists in the thermodynamic limit 2001 published by elsevier science b v

convex fuzzy games and participation monotonic allocation schemes in this paper the cone of convex cooperative fuzzy games is studied as in the classical case of convex crisp games these games have a large core and the fuzzy shapley value is the barycenter of the core surprisingly the core and the weber set coincide as in the classical case but the coincidence of these sets for a fuzzy game does not imply automatically convexity as in the crisp case participation monotonic allocation schemes pamas are introduced and it turns out that each core element of a convex fuzzy game is pamas extendable

efficient asymptotic preserving ap schemes for some multiscale kinetic equations many kinetic models of the boltzmann equation have a diffusive scaling that leads to the navier stokes type parabolic equations as the small scaling parameter approaches zero in practical applications it is desirable to develop a class of numerical schemes that can work uniformly with respect to this relaxation parameter from the rarefied kinetic regimes to the hydrodynamic diffusive regimes an earlier approach in s jin l pareschi and g toscani siam j numer anal 35 1998 pp 2405 2439 reformulates such systems into the common hyperbolic relaxation system by jin and xin for hyperbolic conservation laws used to construct the relaxation schemes and then uses a multistep time splitting method to solve the relaxation system here we observe that the combination of the two time split steps may yield hyperbolic parabolic systems that are more advantageous in both stability and efficiency for numerical computations we show that such an approach yields a class of asymptotic preserving ap schemes which are suitable for the computation of multiscale kinetic problems we use the goldstein taylor and carleman models to illustrate this approach

pseudo spectral solution of nonlinear schro dinger equations abstract we compare four pseudo spectral split step methods for solving a class of nonlinear schrodinger nls equations the importance of observing the l 2 invariance of the continuous problem is demonstrated through numerical experiments the best performance is obtained by transforming the given equation to an nls equation where two of the coefficients satisfy a simple algebraic relationship the problem can be solved efficiently in terms of the new variables and the l 2 norm of the computed solution is time invariant

c1approximations of inertial manifolds for dissipative nonlinear equations abstract in this paper we study a class of nonlinear dissipative partial differential equations that have inertial manifolds this means that the long time behavior is equivalent to a certain finite system of ordinary differential equations we investigate ways in which these finite systems can be approximated in thec1sense geometrically this may be interpreted as constructing manifolds in phase space that arec1close to the inertial manifold of the partial differential equation under such approximations the invariant hyperbolic sets of the global attractor persist

linear production games with fuzzy control the aim of this paper is to analyse linear production with committee control situations arising when controllers face the possibility of graduating their options in order to model these situations we consider several kinds of fuzzy controls which can be modelled as different simple fuzzy games an lp game which is an extension of lp games with committee control introduced in curiel et al on balanced games and games with committee control or spectrum 11 1989 83 88 is obtained and its core is studied

a new shapley value for games with fuzzy coalitions abstract this paper deals with cooperative games over fuzzy coalitions in these situations there is a continuous set of fuzzy coalitions instead of a finite set of them as in the classical case the unit square in an n dimensional space there exist in the literature two different extensions of the known shapley value for crisp games to games with fuzzy coalitions the crisp shapley value and the diagonal value the first value only uses a finite information in the set of fuzzy coalitions the vertices of the square while the second one uses a neighbourhood of the diagonal of the square we propose a new extension of the shapley value improving the crisp shapley value for games with fuzzy coalitions this new version uses the faces of the square namely an infinity quantity of information we analyze several properties of the new value we endow it with an axiomatization and we study the behavior when it is applied to known fuzziness of crisp games

weak and strong solutions of the complex ginzburg landau equation abstract the generalized complex ginzburg landau equation t a ra 1 iv a 1 i a 2 a has been proposed and studied as a model for turbulent dynamics in nonlinear partial differential equations it is a particularly interesting model in this respect because it is a dissipative version of the hamiltonian nonlinear schrodinger equation possessing solutions that form localized singularities in finite time in this paper we investigate existence and regularity of solutions to this equation subject to periodic boundary conditions in various spatial dimensions appropriately defined weak solutions are established globally in time and unique strong solutions are found locally a new collection of a priori estimates are presented and we discuss the relationship of our results for the complex ginzburg landau equation to analogous issues for fluid turbulence described by the incompressible navier stokes equations

enlarged cores and bargaining schemes in games with fuzzy coalitions in this paper we introduce a new concept of solution for games with fuzzy coalitions which we call an enlarged core the enlarged core captures an idea that various groups of fuzzy coalitions can have different bargaining power or influence on the final distribution of wealth resulting from the cooperation process we study a bargaining scheme for the enlarged core which is an iterative procedure for generating sequences converging to elements of the enlarged core it is shown that the enlarged core coincides with aubin s core for a specific class of games with fuzzy coalitions

a compact null set containing a differentiability point of every lipschitz function we prove that in a euclidean space of dimension at least two there exists a compact set of lebesgue measure zero such that any real valued lipschitz function defined on the space is differentiable at some point in the set such a set is constructed explicitly

numerical study of time splitting spectral discretizations of nonlinear schrodinger equations in the semiclassical regimes in this paper we study the performance of time splitting spectral approximations for general nonlinear schrodinger equations nls in the semiclassical regimes where the planck constant varepsilon is small the time splitting spectral approximation under study is explicit unconditionally stable and conserves the position density in l 1 moreover it is time transverse invariant and time reversible when the corresponding nls is extensive numerical tests are presented for weak strong focusing defocusing nonlinearities for the gross pitaevskii equation and for current relaxed quantum hydrodynamics the tests are geared towards the understanding of admissible meshing strategies for obtaining correct physical observables in the semiclassical regimes furthermore comparisons between the solutions of the nls and its hydrodynamic semiclassical limit are presented

order estimates in time of splitting methods for the nonlinear schrodinger equation in this paper we consider the nonlinear schrodinger equation u t i delta u f u 0 in two dimensions we show by an operator theoretic proof that the well known lie and strang formulae which are splitting methods are approximations of the exact solution of order 1 and 2 in time

a universal differentiability set in banach spaces with separable dual abstract we show that any non zero banach space with a separable dual contains a totally disconnected closed and bounded subset s of hausdorff dimension 1 such that every lipschitz function on the space is frechet differentiable somewhere in s

cores and weber sets for fuzzy extensions of cooperative games this paper investigates fuzzy extensions of cooperative games and the coincidence of the solutions for fuzzy and crisp games we show that an exact game has an exact fuzzy extension such that its fuzzy core coincides with the core for games with empty cores we exploit lovasz extensions to establish the coincidence of weber sets for fuzzy and crisp games

a note on the core minimal conversely consistent enlargement abstract the moulin reduction is extended by reducing the number of the players to the framework of fuzzy games based on this extended moulin reduction the axiomatic result of the core in tadenuma s 25 case does not hold in the context of fuzzy games and the core also violates the converse consistency therefore we propose the minimal core which possesses the converse consistency and is also the smallest solution satisfying the core

an asymptotic preserving scheme for the two fluid euler poisson model in the quasineutral limit this paper deals with the modeling of a plasma in the quasineutral limit using the two fluid euler poisson system in this limit explicit numerical schemes suffer from severe numerical constraints related to the small debye length and large plasma frequency here we propose an implicit scheme which reduces to a scheme for the quasineutral euler model in the quasineutral limit such a property is referred to as asymptotic preservation one of the distinctive features of this scheme is that it has a comparable numerical cost to that of an explicit scheme simply the poisson equation is replaced by a different but formally equivalent elliptic problem we present numerical simulations for two different one dimensional test cases they confirm the expected stability of the scheme in the quasineutral limit they also show that this scheme has some accuracy problems in the limit of small electron to ion mass ratio in reproducing the correct electron velocity but this problem is already present in the results of the classical algorithm numerical simulations are also performed for a two dimensional problem of a plasma expansion in vacuum between two electrodes

the measure of interaction among players in games with fuzzy coalitions in this paper the derivative among participation levels of players in games with fuzzy coalitions which measures the simultaneous interaction among players with certain participation levels is defined some properties of the derivative of fuzzy game with k monotonicity are studied furthermore the interaction index among participation levels is established based on the assumption that fuzzy characteristic functions are continuous the integral index of absolute interaction among levels is proposed and the integral index of absolute interaction among players is defined as well at last the shapley total integral index of interaction among players is constructed and a series of properties relative to the index are proved

on time splitting spectral approximations for the schrodinger equation in the semiclassical regime in this paper we study time splitting spectral approximations for the linear schrodinger equation in the semiclassical regime where the planck constant e is small in this regime the equation propagates oscillations with a wavelength of o e and finite difference approximations require the spatial mesh size h o e and the time step k o e in order to obtain physically correct observables much sharper mesh size constraints are necessary for a uniform l2 approximation of the wave function the spectral time splitting approximation under study will be proved to be unconditionally stable time reversible and gauge invariant it conserves the position density and gives uniform l2 approximation of the wave function for k o e and h o e extensive numerical examples in both one and two space dimensions and analytical considerations based on the wigner transform even show that weaker constraints e g k independent of e and h o e are admissible for obtaining correct observables finally we address the application to nonlinear schrodinger equations and conduct some numerical experiments to predict the corresponding admissible meshing strategies

low dimensional dynamics for the complex ginzburg landau equation abstract a method is presented which results in low dimensional dynamical systems for situations in which low dimensional attractors are known to exist the method is based on the use of the karhunen loeve procedure for the determination of an optimal basis and the subsequent use of the galerkin procedure to generate the dynamical system the method is applied to two problems for the ginzburg landau equation for which large databases have been obtained in each instance a dynamical system is generated which has roughly twice the number of degrees of freedom as the hausdorff dimension of the exact case it is also demonstrated that the approximations are robust in that they are accurate over a wide range of parameter space

a shapley function on a class of cooperative fuzzy games abstract in this paper we make a study of the shapley values for cooperative fuzzy games games with fuzzy coalitions which admit the representation of rates of players participation to each coalition a shapley function has been introduced by another author as a function which derives the shapley value from a given pair of a fuzzy game and a fuzzy coalition however the previously proposed axioms of the shapley function can be considered unnatural furthermore the explicit form of the function has been given only on an unnatural class of fuzzy games we introduce and investigate a more natural class of fuzzy games axioms of the shapley function are renewed and an explicit form of the shapley function on the natural class is given we make sure that the obtained shapley value for a fuzzy game in the natural class has several rational properties finally an illustrative example is given

dimension of the attractors associated to the ginzburg landau partial differential equation abstract we study the long time behavior of solutions to the ginzburg landau partial differential equation it is shown that a finite dimensional attractor captures all the solutions an upper bound on this dimension is given in terms of physical quantities by estimating the lyapunov exponents on the trajectories finally using the well known side band instabilities of an exact time dependent solution stokes solution we derive lower bounds on the dimension of the universal attractor moreover the lower and upper bounds agree

the global dynamics of discrete semilinear parabolic equations a class of scalar semilinear parabolic equations possessing absorbing sets a lyapunov functional and a global attractor are considered the gradient structure of the problem implies that provided all steady states are isolated solutions approach a steady state as t to infty the dynamical properties of various finite difference and finite element schemes for the equations are analysed the existence of absorbing sets bounded independently of the mesh size is proved for the numerical methods discrete lyapunov functions are constructed to show that under appropriate conditions on the mesh parameters numerical orbits approach steady state solutions as discrete time increases however it is shown that insufficient spatial resolution can introduce deceptively smooth spurious steady solutions and cause the stability properties of the true steady solutions to be incorrectly represented furthermore it is also shown that the explicit euler scheme introduces spurious solutions with period 2 in the timestep as a result the absorbing set is destroyed and there is initial data leading to blow up of the scheme however small the mesh parameters are taken to obtain stabilization to a steady state for this scheme it is necessary to restrict the timestep in terms of the initial data and the space step implicit schemes are constructed for which absorbing sets and lyapunov functions exist under restrictions on the timestep that are independent of initial data and of the space step both one step and multistep bdf methods are studied

max consistency complement consistency and the core of fuzzy games recently hwang introduced two extensions of the max reduced game to fuzzy games by reducing the number of the players based on these reduced games he offered analogous axiomatizations of the core related to serrano and volij in the context of fuzzy games here we continue and develop hwang s work on similar topics however we turn to a different definition of the reduced game by simultaneously reducing both the number of the players and the participation levels we propose such extensions of the complement reduced game and of the max reduced game to fuzzy games and define the related properties of consistency and converse consistency based on these properties we offer several analogous characterizations of the core related to peleg serrano and volij and tadenuma respectively

a new compact finite difference scheme for solving the complex ginzburg landau equation the complex ginzburg landau equation is often encountered in physics and engineering applications such as nonlinear transmission lines solitons and superconductivity however it remains a challenge to develop simple stable and accurate finite difference schemes for solving the equation because of the nonlinear term most of the existing schemes are obtained based on the crank nicolson method which is fully implicit and must be solved iteratively for each time step in this article we present a fourth order accurate iterative scheme which leads to a tri diagonal linear system in 1d cases we prove that the present scheme is unconditionally stable the scheme is then extended to 2d cases numerical errors and convergence rates of the solutions are tested by several examples

on the possibility of soft and hard turbulence in the complex ginzburg landau equation abstract we present analytical methods which predict the occurrence of both soft weak and hard strong turbulence in the complex ginzburg landau cgl equation a t ra 1 i a 1 i a a 2 on a periodic domain 0 1 d in d spatial dimensions hard turbulence is characterised by large fluctuations away from spatial and temporal averages with a cascade of energy to small scales this form of hard turbulence appears to occur not in 1d but only in 2d and 3d in parameter regions which are bounded by hyperbolic curves in the second and fourth quadrants of the planes where the system is modulationally unstable 1 2n f n n 1 a 2 n a 2n dx for n 0 for large times and large r upper bounds exist for the infinite set of fn s constructed from the hierarchy of differential inequalities fn 2nr cn a 2 fn bnf2n fn 1 for cn bn 0 f0 1 estimates for the bottom rung f2 give upper bounds for the whole ladder long time upper bounds on f2 and a 2 and hence all fn are well controlled in the soft region but become much larger in the hard region whereas spati al and temporal averages remain comparatively small when the nonlinearity is a a 2q the critical case qd 2 gives parallel results

runge kutta methods for parabolic equations and convolution quadrature we study the approximation properties of runge kutta time discretizations of linear and semilinear parabolic equations including incompressible navier stokes equations we derive asymptotically sharp error bounds and relate the temporal order of convergence which is generally noninteger to spatial regularity and the type of boundary conditions the analysis relies on an interpretation of runge kutta methods as convolution quadratures in a different context these can be used as efficient computational methods for the approximation of convolution integrals and integral equations they use the laplace transform of the confolution kernal via a discrete operational calculus 23 refs 2 tabs

the convergence of numerical transfer schemes in diffusive regimes i discrete ordinate method in highly diffusive regimes the transfer equation with anisotropic boundary conditions has an asymptotic behavior as the mean free path epsilon tends to zero that is governed by a diffusion equation and boundary conditions obtained through a matched asymptotic boundary layer analysis a numerical scheme for solving this problem has an epsilon 1 contribution to the truncation error that generally gives rise to a nonuniform consistency with the transfer equation for small epsilon thus degrading its performance in diffusive regimes in this paper we show that whenever the discrete ordinate method has the correct diffusion limit both in the interior and at the boundaries its solutions converge to the solution of the transport equation uniformly in epsilon our proof of the convergence is based on an asymptotic diffusion expansion and requires error estimates on a matched boundary layer approximation to the solution of the discrete ordinate method

on the rate of convergence of the nonlinear galerkin methods in this paper we provide estimates to the rate of convergence of the nonlinear galerkin approximation method in particular and by means of an illustrative example we show that the nonlinear galerkin method converges faster than the usual galerkin method

directional upper derivatives and the chain rule formula for locally lipschitz functions on banach spaces motivated by an attempt to find a general chain rule formula for differentiating the composition f g of lipschitz functions f and g that would be as close as possible to the standard formula f g x f g x g x we show that this formula holds without any artificial assumptions provided derivatives are replaced by complete derivative assignments the idea behind these assignments is that the derivative of f at y is understood as defined only in the direction of a suitable tangent space u f y and so it exists at every point but these tangent spaces are chosen in such a way that for any g they contain the range of g x for almost every x showing the existence of such assignments leads us to detailed study of derived sets and the ways in which they describe pointwise behavior of lipschitz functions

cooperative fuzzy games we derive versions of known results dealing with core equilibria and shapley values of cooperative games in the case of cooperative fuzzy games i e games defined on fuzzy subsets of the set of n players a fuzzy coalition is an n vector i associating with each player i his rate of participation i 0 1 in the fuzzy coalition and the real number v is the coalition worth assumed to be positively homogeneous if also v is superadditive or equivalently concave the fuzzy game with side payments has a nonempty core associated with the coalition worth function for any ordinary game with side payments is a fuzzy extension thereof viz the fuzzy game whose coalition worth function is the least positively homogeneous superadditive function majorizing the coalition worth function of the original game the fuzzy extension always has a nonempty core moreover if the original game has a nonempty core it coincides with that of its fuzzy extension analogous results are established for games without side payments an axiomatization of values of fuzzy games with side payments is also given the results are applied to show that the set of walras equilibria coincides with the fuzzy core of an economy

differentiability of lipschitz functions on banach spaces abstract the main result of this note says that if the norm of a banach space e is differentiable frechet gateaux or in some intermediate sense away from the origin then every locally lipschitz function defined on an open subset g of e is differentiable in the same sense at every point of some subset of g dense in g as the main corollary we prove that every lipschitz function on an asplund space is frechet differentiable on a dense set moreover in all these results the mean value theorem for the points of differentiability which is equivalent to the possibility of computing the clarke subdifferential from the points of differentiability is shown to hold

attractors and inertial manifolds for finite difference approximations of the complex ginzburg landau equation a semidiscrete spatial finite difference approximation and two fully discrete finite difference approximations to the complex ginzburg landau equation are considered in this paper the existence of an inertial manifold is proved inside a discrete h1 absorbing ball for the semi discrete approximation by showing that certain spectral properties hold for the linear operator and certain lipschitz properties hold for the nonlinear term convergence of the true and discrete inertial manifolds is then shown by considering the contraction mappings used to construct the inertial manifolds a fully implicit scheme is shown to form a continuous semigroup in a discrete l2 space and absorbing balls of radii independent of the spatial and temporal mesh sizes in discrete l2 and h1 spaces are constructed existence of a global attractor follows furthermore the existence of an inertial manifold is proved by showing that certain spectral and lipschitz properties hold for a semi implicit scheme existence of absorbing balls in the discrete space l2 of radii independent of the spatial and temporal mesh is proved existence of a global attractor follows

a time splitting spectral scheme for the maxwell dirac system we present a time splitting spectral scheme for the maxwell dirac system and similar time splitting methods for the corresponding asymptotic problems in the semi classical and the non relativistic regimes the scheme for the maxwell dirac system conserves the lorentz gauge condition is unconditionally stable and highly efficient as our numerical examples show in particular we focus in our examples on the creation of positronic modes in the semi classical regime and on the electron positron interaction in the non relativistic regime furthermore in the non relativistic regime our numerical method exhibits uniform convergence in the small parameter d which is the ratio of the characteristic speed and the speed of light

the equal allocation of nonseparable costs an extension under fuzzy behavior by considering the players and the activity levels simultaneously we propose a consistent solution which is a generalization of the equal allocation of nonseparable costs eansc on fuzzy games we also adopt two pre existing concepts from traditional game theory and reinterpret them in the framework of fuzzy games first based on the consistency which related to an extended reduced game we offer two axiomatizations of the extended eansc second by applying the excess function we propose a dynamic process to illustrate that the extended eansc can be reached by players who start from an arbitrary efficient solution and make consecutive amendments

the equalizer and the lexicographical solutions for cooperative fuzzy games characterization and properties in this paper we analyze the lexicographical solution for fuzzy tu games we study its properties and obtain a characterization the lexicographical solution was introduced by sakawa and nishizaki fuzzy sets and systems 61 1994 265 275 as a solution for crisp tu games and then extended as a value for fuzzy tu games we approach the problem by means of the close relationship that exists between the lexicographical solution for crisp tu games and the least square nucleolus a crisp value defined by ruiz et al internat j game theory 25 1996 113 134 previously and also based on this relationship we axiomatically characterize the equalizer solution for fuzzy tu games both values the equalizer and the lexicographical solutions are based on the consideration of a measure of dissatisfaction of players rather than coalitions

nonlinear analysis of the eckhaus instability modulated amplitude waves and phase chaos with nonzero average phase gradient abstract we analyze the eckhaus instability of plane waves in the one dimensional complex ginzburg landau equation cgle and describe the nonlinear effects arising in the eckhaus unstable regime modulated amplitude waves maws are quasi periodic solutions of the cgle that emerge near the eckhaus instability of plane waves and cease to exist due to saddle node sn bifurcations these maws can be characterized by their average phase gradient and by the spatial period p of the periodic amplitude modulation a numerical bifurcation analysis reveals the existence and stability properties of maws with arbitrary and p maws are found to be stable for large enough and intermediate values of p for different parameter values they are unstable to splitting and attractive interaction between subsequent extrema of the amplitude defects form from perturbed plane waves for parameter values above the sn of the corresponding maws the break down of phase chaos with average phase gradient 0 wound up phase chaos is thus related to these sns a lower bound for the break down of wound up phase chaos is given by the necessary presence of sns and an upper bound by the absence of the splitting instability of maws

the general prenucleolus of n person cooperative fuzzy games abstract in this paper we define the concept of the general prenucleolus minimizing the player complaint vector in the lexicographic order over the preimputation set for the cooperative games with fuzzy coalitions for the general prenucleolus we get a sufficient condition that the complaints of all players are in equal amount under the case of linear complaint functions concluding the proposed player excess sakawa and nishizaki 1994 15 as a result we can obtain the proposed fuzzy solutions with the corresponding linear complaint functions such as the equalizer solution molina and tejada 2002 5 and shapley function etc we prove that the least square general prenucleolus minimizing the variance of the resulting player complaints is the general prenucleolus thus an optimal solution considered from two aspects of the lexicographic order and the least square criterion is obtained in addition several general prenucleoli are proposed in terms of specific situations

bifurcations to invariant 2 tori for the complex ginzburg landau equation we present a numerical study of the large time asymptotic behavior of solutions to the one dimensional complex ginzburg landau equation with periodic boundary conditions our parameters belong to the benjamin feir unstable region our solutions start near a pure mode rotating wave that is stable under sideband perturbations for the reynolds number r ranging over an interval r s u b r s u p we find sub and supercritical bifurcations from this stable rotating wave to a stable 2 torus as the parameter r is decreased or increased past the critical value r s u b or r s u p as r r s u p further increases we observe additional stable 2 tori together with a variety of other dynamical phenomena we compare our numerical simulations to both rigorous mathematical results and experimental observations for binary fluid mixtures

runge kutta approximation of quasi linear parabolic equations we study the convergence properties of implicit runge kutta meth ods applied to time discretization of parabolic equations with time or solution dependent operator error bounds are derived in the energy norm the con vergence analysis uses two different approaches the first technically simpler approach relies on energy estimates and requires algebraic stability of the runge kutta method the second one is based on estimates for linear time invariant equations and uses fourier and perturbation techniques it applies to a 9 stable runge kutta methods and yields the precise temporal order of conver gence this order is noninteger in general and depends on the type of boundary conditions

fuzzy games a characterization of the core in this paper we extend to the cooperative fuzzy games case the reduced game introduced by davis and maschler the kernel of a cooperative game naval res logist quart 12 1965 223 259 we shall introduce two types of such a reduced game to cooperative fuzzy games and define the related properties of consistency and converse consistency we further offer two axiomatizations of the core on the domain of all cooperative fuzzy games by means of consistency and its converse