length of optimal path in random networks with strong disorder abstract we study the optimal distance l opt in random networks in the presence of disorder implemented by assigning random weights to the links the optimal distance between two nodes is the length of the path for which the sum of weights along the path cost is a minimum we study the case of strong disorder for which the distribution of weights is so broad that its sum along any path is dominated by the largest link weight in the path we find that in random graphs l opt scales as n 1 3 where n is the number of nodes in the network thus l opt increases dramatically compared to the known small world result for the minimum distance l min which scales as log n we also study theoretically and by simulations scale free networks characterized by a power law distribution for the number of links p k k and find that l opt scales as n 1 3 for 4 and as n 3 1 for 3 opt scales logarithmically with n

a note on rationality conditions of fuzzy choice functions this note investigates the rationality conditions of fuzzy choice functions for studying the rationality of fuzzy choice functions banerjee introduced many regularity conditions that are defined for revealed preference relations however in the standard framework of economics and decision making theory researchers usually assume people s choice behavior is observable while the preference behind the choice behavior is unobservable it is worthwhile to study rationality conditions that are defined for fuzzy choice functions instead that for revealed preference relations for this purpose we propose a set of new rationality conditions depending only on the fuzzy choice function we study the connection among these rationality conditions and give a relatively complete description for them we also find that banerjee rationality is too weak to capture some kind of consistency of the fuzzy choice function this motivates us to introduce two notions on strong rationality the relationships between our new consistency conditions and the rationality banerjee rationality and strong rationality of the fuzzy choice function are discussed

the equation for time like extremal surfaces in minkowski space r2 n in this paper we investigate the equation for time like extremal surfaces in the minkowski space r2 n and show that this kind of equation enjoys many interesting properties nonstrict hyperbolicity constant multiplicity of eigenvalues boundedness of characteristic propagation speeds linear degeneracy of all characteristic fields richness etc without any smallness assumption of initial data we give the necessary and sufficient condition on the global existence of classical solutions of the cauchy problem based on this we prove some global existence theorems on classical solutions of the dirichlet problem and neumann problem for this kind of equation finally we present an explicit exact representation involving two independent arbitrary functions of general solution

two a posteriori error estimates for one dimensional scalar conservation laws in this paper we propose a posteriori local error estimates for numerical schemes in the context of one dimensional scalar conservation laws we first consider the schemes for which a consistent in cell entropy inequality can be derived then we extend this result to second order schemes written in viscous form satisfying weak entropy inequalities as an illustration we show several numerical tests on the burgers equation and we propose an adaptive algorithm for the selection of the mesh

rational choice under fuzzy preferences the orlovsky choice function abstract there have been many different suggestions in the literature as to how to generate exact choices on the basis of fuzzy preferences this paper seeks to provide axiomatic support to one of these choice functions due to orlovsky it is shown that under a transitivity restriction independent of max min transitivity this choice function implies and is implied by a set of simple conditions

a priori error estimates for numerical methods for scalar conservation laws part ii flux splitting monotone schemes on irregular cartesian grids this paper is the second of a series in which a general theory of a priori error estimates for scalar conservation laws is constructed in this paper we focus on how the lack of consistency introduced by the nonuniformity of the grids influences the convergence of flux splitting monotone schemes to the entropy solution we obtain the optimal rate of convergence of x 1 2 in l l 1 for consistent schemes in arbitrary grids without the use of any regularity property of the approximate solution we then extend this result to less consistent schemes called p consistent schemes and prove that they converge to the entropy solution with the rate of x min 1 2 p in l l 1 again no regularity property of the approximate solution is used finally we propose a new explanation of the fact that even inconsistent schemes converge with the rate of x 1 2 in l l 1 we show that this well known supraconvergence phenomenon takes place because the consistency of the numerical flux and the fact that the scheme is written in conservation form allows the regularity properties of its approximate solution total variation boundedness to compensate for its lack of consistency the nonlinear nature of the problem does not play any role in this mechanism all the above results hold in the multidimensional case provided the grids are cartesian products of one dimensional nonuniform grids

acyclic fuzzy preferences and the orlovsky choice function a note abstract this note corrects and extends a recent axiomatic characterization of the orlovsky choice function for a particular class of transitive fuzzy relations the interest of characterizing choice functions for well behaved fuzzy relations is then discussed

equivalence of the euler and lagrangian equations of gas dynamics for weak solutions abstract this paper demonstrates the equivalence of the euler and the lagrangian equations of gas dynamics in one space dimension for weak solutions which are bounded and measurable in eulerian coordinates the precise hypotheses include all known global solutions on r r in particular solutions containing vacuum states zero mass density are included furthermore there is a one to one correspondence between the convex extensions of the two systems and the corresponding admissibility criteria are equivalent in the presence of a vacuum the definition of weak solution for the lagrangian equations must be strengthened to admit test functions which are discontinuous at the vacuum as an application we translate a large data existence result of diperna for the euler equations for isentropic gas dynamics into a similar theorem for the lagrangian equations

convergence of an upstream finite volume scheme for a nonlinear hyperbolic equation on a triangular mesh we study here the discretisation of the nonlinear hyperbolic equationu t div vf u 0 in 3 with given initial conditionu 0 u 0 in 2 wherev is a function from 2 to 2 such that divv 0 andf is a given nondecreasing function from to an explicit euler scheme is used for the time discretisation of the equation and a triangular mesh for the spatial discretisation under a usual stability condition we prove the convergence of the solution given by an upstream finite volume scheme towards the unique entropy weak solution to the equation

convergence of a shock capturing streamline diffusion finite element method for a scalar conservation law in two space dimensions convergence of a shock capturing streamline diffusion nite element method for a conservation law in two space dimensions

error estimates for finite element methods for scalar conservation laws in this paper new a posteriors error estimates for the shock capturing streamline diffusion scsd method and the shock capturing discontinuous galerkin scdg method for scalar conservation laws are obtained these estimates are then used to prove that the scsd method and the scdg method converge to the entropy solution with a rate of at least h 1 8 and h 1 8 respectively in the l infty l 1 norm the triangulations are made of general acute simplices and the approximate solution is taken to be piecewise a polynomial of degree k the result is independent of the dimension of the space

probabilistic analysis of the upwind scheme for transport equations we provide a probabilistic analysis of the upwind scheme for d dimensional transport equations we associate a markov chain with the numerical scheme and then obtain a backward representation formula of kolmogorov type for the numerical solution we then understand that the error induced by the scheme is governed by the fluctuations of the markov chain around the characteristics of the flow we show in various situations that the fluctuations are of diffusive type as a by product we recover recent results due to merlet and vovelle numer math 106 129 155 2007 and merlet siam j numer anal 46 1 124 150 2007 we prove that the scheme is of order 1 2 in l infty 0 t l 1 mathbb r d for an integrable initial datum of bounded variation and of order 1 2 e for all e 0 in l infty 0 t times mathbb r d for an initial datum of lipschitz regularity our analysis provides a new interpretation of the numerical diffusion phenomenon

l 1 framework for continuous dependence and error estimates for quasilinear anisotropic degenerate parabolic equations we develop a general l 1 framework for deriving continuous de pendence and error estimates for quasilinear anisotropic degenerate parabolic equations with the aid of the chen perthame kinetic approach 9 we ap ply our l 1 framework to establish an explicit estimate for continuous depen dence on the nonlinearities and an optimal error estimate for the vanishing anisotropic viscosity method without imposition of bounded variation of the approximate solutions finally as an example of a direct application of this framework to numerical methods we focus on a linear convection diusi on model equation and derive an l 1 error estimate for an upwind central finite dierence scheme

biased and greedy random walks on two dimensional lattices with quenched randomness the greedy ant within a disordered environment the main characteristics of biased greedy random walks bgrws on two dimensional lattices with real valued quenched disorder on the lattice edges are studied here the disorder allows for negative edge weights in previous studies considering the negative weight percolation nwp problem this was shown to change the universality class of the existing static percolation transition in the presented study four different types of bgrws and an algorithm based on the ant colony optimization heuristic were considered regarding the bgrws the precise configurations of the lattice walks constructed during the numerical simulations were influenced by two parameters a disorder parameter ensuremath rho that controls the amount of negative edge weights on the lattice and a bias strength b that governs the drift of the walkers along a certain lattice direction the random walks are greedy in the sense that the local optimal choice of the walker is to preferentially traverse edges with a negative weight associated with a net gain of energy for the walker here the pivotal observable is the probability that after termination a lattice walk exhibits a total negative weight which is here considered as percolating the behavior of this observable as function of ensuremath rho for different bias strengths b is put under scrutiny upon tuning ensuremath rho the probability to find such a feasible lattice walk increases from zero to 1 this is the key feature of the percolation transition in the nwp model here we address the question how well the transition point ensuremath rho mathrm c resulting from numerically exact and static simulations in terms of the nwp model can be resolved using simple dynamic algorithms that have only local information available one of the basic questions in the physics of glassy systems

exact enumeration of self avoiding walks on lattices with random site energies the self avoiding random walk on lattices with quenched random site energies is studied using exact enumeration in d 2 and 3 for each configuration we compute the size r and energy e of the minimum energy self avoiding walk saw configuration averages yield the exponents ensuremath nu and ensuremath chi defined by mathit r 2 ifmmode bar else textasciimacron fi ensuremath sim mathit n 2 ensuremath nu and ensuremath delta mathit e 2 ifmmode bar else textasciimacron fi ensuremath sim mathit n 2 mathrm ensuremath chi these calculations indicate that ensuremath nu is significantly larger than its value in the pure system finite temperature studies support the notion that the system is controlled by a zero temperature fixed point consequently exponents obtained from minimum energy saw s characterize the properties of finite temperature saw s on disordered lattices

well posedness and long time behavior of lipschitz solutions to generalized extremal surface equations we show that in one space dimension lipschitz solutions of generalized extremal surface equations are equivalent to entropy solutions in l r of a non strictly hyperbolic system of conservation laws we obtain an explicit representation formula and the uniqueness of the entropy solutions to the cauchy problem of the system by using this formula we also obtain the convergence and convergence rates as t of the entropy solutions to explicit traveling waves in the l1 r norm moreover when initial data are constants outside of a finite space interval the entropy solutions become the explicit traveling waves after a finite time finally we prove l1 stabilities of the entropy solutions

fuzzy choice functions revealed preference and rationality abstract this paper investigates the conditions under which a fuzzy set valued choice function is rationalisable by a fuzzy revealed preference relation satisfying certain regularity conditions attention is confined to the case where the domain of the choice function consists of all crisp finite subsets of the universal set of alternatives two sets of weak and strong axioms of fuzzy revealed preference wafrp and safrp are stated in both cases it turns out that wafrp is not equivalent to safrp and that safrp does not characterise rationality in the special case where every set of avialable alternatives has at least one element which is unambiguously chosen wafrp is equivalent to safrp but safrp still does not characterise rationality a fuzzy congruence condition stronger than safrp is proposed and is shown to be necessary and sufficient for rationality

most probable paths in homogeneous and disordered lattices at finite temperature we determine the geometrical properties of the most probable paths at nite temperatures t between two points separated by a distance r in one dimensional lattices with positive energies of interactioni associated with bond i the most probable path length tmp in a homogeneous medium i for all i is found to undergo a phase transition from an optimal like form tmp r at low temperatures to a random walk form tmp r 2 near the critical temperature tc ln 2 at t t c the most probable path length diverges discontinuously for all nite endpoint separations greater than a particular value r t in disordered lattices withi ho mogeneously distributed between 2 and 2 the random walk phase is absent but a phase transition to diverging tmp still takes place di3erent disorder con gurations have di3erent transition points a way to characterize the whole ensemble of disorder for a given distribution is suggested c 2001 elsevier science b v all rights reserved

equilibrium schemes for scalar conservation laws with stiff sources we consider a simple model case of stiff source terms in hyperbolic conservation laws namely the case of scalar conservation laws with a zeroth order source with low regularity it is well known that a direct treatment of the source term by finite volume schemes gives unsatisfactory results for both the reduced cfl condition and refined meshes required because of the lack of accuracy on equilibrium states the source term should be taken into account in the upwinding and discretized at the nodes of the grid in order to solve numerically the problem we introduce a so called equilibrium schemes with the properties that i the maximum principle holds true ii discrete entropy inequalities are satisfied iii steady state solutions of the problem are maintained one of the difficulties in studying the convergence is that there are no bv estimates for this problem we therefore introduce a kinetic interpretation of upwinding taking into account the source terms based on the kinetic formulation we give a new convergence proof that only uses property ii in order to ensure desired compactness framework for a family of approximate solutions and that relies on minimal assumptions the computational efficiency of our equilibrium schemes is demonstrated by numerical tests that show that in comparison with an usual upwind scheme the corresponding equilibrium version is far more accurate furthermore numerical computations show that equilibrium schemes enable us to treat efficiently the sources with singularities and oscillating coefficients

invariant domains and second order continuous finite element approximation for scalar conservation equations we propose a technique for approximating nonlinear scalar conservation equations that uses continuous finite elements and is formally at least second order accurate in space and maximum principle preserving the method is explicit in time uses unstructured continuous finite elements in space and works in any space dimension the stability and accuracy of the method are achieved by adapting the artificial viscosity

an error estimate for finite volume methods for multidimensional conservation laws in this paper an l ll error estimate for a class of finite volume methods for the approximation of scalar multidimensional conservation laws is obtained these methods can be formally high order accurate and are defined on general triangulations the error is proven to be of order ft 4 where h represents the size of the mesh via an extension of kuznetsov approximation theory for which no estimate of the total variation and of the modulus of con tinuity in time are needed the result is new even for the finite volume method constructed from monotone numerical flux functions

a geometric approach to error estimates for conservation laws posed on a spacetime abstract we consider a hyperbolic conservation law posed on an n 1 dimensional spacetime whose flux is a field of differential forms of degree n generalizing the classical kuznetsov s method we derive an l 1 error estimate which applies to a large class of approximate solutions in particular we apply our main theorem and deal with two entropy solutions associated with distinct flux fields as well as with an entropy solution and an approximate solution our framework encompasses for instance equations posed on a globally hyperbolic lorentzian manifold

convergence of the finite volume method for multidimensional conservation laws we establish the convergence of the finite volume method applied to multidimensional hyperbolic conservation laws and based on monotone numerical flux functions our technique applies with a fairly unrestrictive assumption on the triangulations flat elements are allowed and to lipschitz continuous flux functions we treat the initial and boundary value problem and obtain the strong convergence of the scheme to the unique entropy discontinuous solution in the sense of kruzkov the proof of convergence is based on a convergence framework coquel and lefloch math comp 57 1991 pp 169 210 and j numer anal 30 1993 pp 675 700 from a convex decomposition of the scheme we derive a new estimate for the rate of entropy dissipation and a new formulation of the discrete entropy inequalities these estimates are shown to be sufficient for the passage to the limit in the discrete equation convergence follows from diperna s uniqueness result in the class of entropy measure valued solutions

error control for a class of runge kutta discontinuous galerkin methods for nonlinear conservation laws we propose an a posteriori error estimate for the runge kutta discontinuous galerkin method rk dg of arbitrary order in arbitrary space dimensions for stabilization of the scheme a general framework of projections is introduced finally it is demonstrated numerically how the a posteriori error estimate is used to design both an efficient grid adaption and gradient limiting strategy numerical experiments show the stability of the scheme and the gain in efficiency in comparison with computations on uniform grids

a moving mesh numerical method for hyperbolic conservation laws we show that the possibly discontinuous solution of a scalar conservation law in one space dimension may be approximated in l1 r to within o n 2 by a piecewise linear function with o fn nodes the nodes are moved according to the method of characteristics we also show that a previous method of dafermos which uses piecewise constant approxima tions is accurate to o n 1 these numerical methods for conservation laws are the first to have proven convergence rates of greater than o fn 1 2 1 introduction it is well known that the solution of the hyperbolic conservation law

transient l1 error estimates for well balanced schemes on non resonant scalar balance laws abstract the ability of well balanced wb schemes to capture very accurately steady state regimes of non resonant hyperbolic systems of balance laws has been thoroughly illustrated since its introduction by greenberg and leroux 1996 15 see also the anterior wb glimm scheme in e 1992 8 this paper aims at showing by means of rigorous c t 0 l x 1 estimates that these schemes deliver an increased accuracy in transient regimes too namely after explaining that for the vast majority of non resonant scalar balance laws the c t 0 l x 1 error of conventional fractional step tang and teng 1995 45 numerical approximations grows exponentially in time like exp max g t x as a consequence of the use of gronwall s lemma it is shown that wb schemes involving an exact riemann solver suffer from a much smaller error amplification thanks to strict hyperbolicity their error grows at most only linearly in time see also layton 1984 30 numerical results on several test cases of increasing difficulty including the classical leveque yee s benchmark problem leveque and yee 1990 34 in the non stiff case confirm the analysis

global existence for small initial data in the born infeld equations we prove global existence of a classical solution for small initial in the cauchy problem of the born infeld system describing nonlinear electromagnetism for the proof we crucially use the null form structure of the the nonlinear terms under the lorentz gauge condition

optimal path in random networks with disorder a mini review abstract we review the analysis of the length of the optimal path l opt in random networks with disorder i e random weights on the links in the case of strong disorder in which the maximal weight along the path dominates the sum we find that l opt increases dramatically compared to the known small world result for the minimum distance l min for erd s renyi er networks l opt n 1 3 while for scale free sf networks with degree distribution p k k we find that l opt scales as n 3 1 for 3 4 and as n 1 3 for 4 thus for these networks the small world nature is destroyed for 2 3 our numerical results suggest that l opt scales as ln 1 n we also find numerically that for weak disorder l opt ln n for er models as well as for sf networks we also study the transition between the strong and weak disorder regimes in the scaling properties of the average optimal path l opt in er and sf networks

on nonlinear stochastic balance laws we are concerned with multidimensional stochastic balance laws we identify a class of nonlinear balance laws for which uniform spatial bv bound for vanishing viscosity approximations can be achieved moreover we establish temporal equicontinuity in l1 of the approximations uniformly in the viscosity coefficient using these estimates we supply a multidimensional existence theory of stochastic entropy solutions in addition we establish an error estimate for the stochastic viscosity method as well as an explicit estimate for the continuous dependence of stochastic entropy solutions on the flux and random source functions various further generalizations of the results are discussed

dynamics of linear polymers in random media we study phenomenological scaling theories of the polymer dynamics in random media employing the existing scaling theories of polymer chains and the percolation statistics we investigate both the rouse and the zimm model for brownian dynamics and estimate the diffusion constant of the center of mass of the chain in such disordered media for internal dynamics of the chain we estimate the dynamic exponents we propose similar scaling theory for the reptation dynamics of the chain in the framework of flory theory for the disordered medium the modifications in the case of correlated disorders are also discussed

continuous dependence on the nonlinearities of solutions of degenerate parabolic equations explicit estimates for the continuous dependence inl 0 t l1 rd of solutions of the equation lv v v in 0 rdwith initial conditionv 0 h with respect to the nonlinear continuously differential functions and are established

validity of nonlinear geometric optics for entropy solutions of multidimensional scalar conservation laws nonlinear geometric optics with various frequencies for entropy so lutions only in l 1 of multidimensional scalar conservation laws is analyzed a new approach to validate nonlinear geometric optics is developed via entropy dissipation through scaling compactness homogenization and l 1 stability new multidimensional features are recognized especially including nonlinear propagations of oscillations with high frequencies the validity of nonlinear geometric optics for entropy solutions in l 1 of multidimensional scalar con servation laws is justified

the initial boundary value problem for general non local scalar conservation laws in one space dimension we prove global well posedness results for weak entropy solutions of bounded variation bv of scalar conservation laws with non local flux on bounded domains under suitable regularity assumptions on the flux function in particular existence is obtained by proving the convergence of an adapted lax friedrichs algorithm lipschitz continuos dependence from initial and boundary data is derived applying kru hkov s doubling of variable technique

convergence rates for relaxation schemes approximating conservation laws in this paper we prove a global error estimate for a relaxation scheme approximating scalar conservation laws to this end we decompose the error into a relaxation error and a discretization error including an initial error omega ep we obtain the rate of convergence of sqrt ep in l1 for the relaxation step the estimate here is independent of the type of nonlinearity in the discretization step a convergence rate of sqrt del x in l1 is obtained these rates are independent of the choice of initial error omega ep thereby we obtain the order 1 2 for the total error

error estimate for godunov approximation of locally constrained conservation laws we consider a model of traffic flow with unilateral constraint on the flux introduced by colombo and goatin j differential equations 234 2007 pp 654 675 for which the convergence of numerical approximation using monotone finite volume schemes has been performed by andreianov goatin and seguin numer math 115 2010 pp 609 645 we derive for this problem a new rm bv estimate and make use of it to provide an error estimate for the godunov approximation of the problem of order h 1 3 that is improved into the optimal order h 1 2 under a reasonable assumption numerical experiments are then provided to illustrate the optimality of the result

finite volume relaxation schemes for multidimensional conservation laws we consider finite volume relaxation schemes for multidimensional scalar conservation laws these schemes are constructed by appropriate discretization of a relaxation system and it is shown to converge to the entropy solution of the conservation law with a rate of h 1 4 in l 0 t l loc 1 r d

energy momentum wave velocities and characteristic shocks in euler s variational equations with application to the born infeld theory we consider the euler s variational equations deriving from a general lagrangian l qr qs under the assumption of convexity of energy we write down some inequalities for the energy momentum tensor including hawking ellis energy conditions we show that there exists the same number of positive and negative wave velocities and no velocity can change sign finally we study the structure of the characteristic shocks with particular attention to the generalized born infeld lagrangian describing the electron with spin

on convergence of minmod type schemes a class of nonoscillatory numerical methods for solving nonlinear scalar conservation laws in one space dimension is considered this class of methods contains the classical lax friedrichs and the second order nessyahu tadmor schemes in the case of linear flux new l2 stability results and error estimates for the methods are proved numerical experiments confirm that these methods are one sided l2 stable for convex flux instead of the usual lip stability

source solutions and asymptotic behavior in conservation laws abstract we study the uniqueness of the solutions to the scalar conservation law u t u x 0 when the initial datum is a finite measure the case of a dirac mass is particularly emphasized it is shown how it provides a description of the asymptotic behavior of the solutions initiated by an arbitrary integrable function this behavior is proved to depend on one parameter in the case when is odd while it depends on two when is convex

convergence of a staggered lax friedrichs scheme for nonlinear conservation laws on unstructured two dimensional grids based on nessyahu and tadmor s nonoscillatory central difference schemes for one dimensional hyperbolic conservation laws 16 for higher dimensions several finite volume extensions and numerical results on structured and unstructured grids have been presented the experiments show the wide applicability of these multidimensional schemes the theoretical arguments which support this are some maximum principles and a convergence proof in the scalar linear case a general proof of convergence as obtained for the original one dimensional nt schemes does not exist for any of the extensions to multidimensional nonlinear problems for the finite volume extension on two dimensional unstructured grids introduced by arminjon and viallon 3 4 we present a proof of convergence for the first order scheme in case of a nonlinear scalar hyperbolic conservation law

a necessary and sufficient condition for the existence of orlovsky s choice set abstract in a previous paper 2 the authors proved that a property of acyclity in fuzzy preference relations was a necessary and sufficient condition for the existence of unfuzzy nondominated alternatives when such a set of alternatives is finite in this paper a general property of foundation is proved to be a necessary and sufficient condition without requiring finiteness on the set of alternatives both concepts are based on classical results in crisp binary relations

a further study on rationality conditions of fuzzy choice functions the investigation of rationality plays a central role in the study of fuzzy choice functions in this paper we deal with some important rationality conditions of fuzzy choice functions including weak strong fuzzy congruence axiom weak strong axiom of fuzzy revealed preference fuzzy versions of famous crisp conditions a b c and d etc in the framework of the banerjee choice function we systematically investigate the relationships between these conditions under the assumption that every involved choice set is normal and verify some equivalence results for arbitrary t norms as a result a fuzzy version of the arrow sen theorem is presented the research makes a significant difference compared with the current investigation in the framework of the georgescu choice function

hyperbolicity of the nonlinear models of maxwell s equations we consider the class of nonlinear models of electromagnetism that has been described by coleman dill 7 a model is completely determined by its energy density w b d viewing the electromagnetic field b d as a 3 2 matrix we show that polyconvexity of w implies the local well posedness of the cauchy problem within smooth functions of class hs with s 1 d 2

fuzzy preference and orlovsky choice procedure abstract this paper provides an axiomatic characterization of the orlovsky choice procedure for a decision maker whose preference are fuzzy in contrast to the result in banerjee 1993 our characterization does not require that in a pairwise choice the choice coincides with the orlovsky set moreover our characterization result holds for a larger domain of preferences than that in banerjee 1993

stochastic nonlocal conservation laws on whole space abstract after introducing an entropy formulation for stochastic nonlocal conservation laws via an integral formula we develop a uniqueness theory by using a doubling variables technique and an existence theory by using a vanishing viscosity method we further consider the continuous dependence of the entropy solution on initial data

weakly nonoscillatory schemes for scalar conservation laws a new class of godunov type numerical methods called here weakly nonoscillatory or wno for solving nonlinear scalar conservation laws in one space dimension is introduced this new class generalizes the classical nonoscillatory schemes in particular it contains modified versions of min mod and uno under certain conditions convergence and error estimates for wno methods are proved

continuous dependence estimate for conservation laws with levy noise abstract we are concerned with multidimensional stochastic balance laws driven by levy processes using bounded variation bv estimates for vanishing viscosity approximations we derive an explicit continuous dependence estimate on the nonlinearities of the entropy solutions under the assumption that levy noise only depends on the solution this result is used to show the error estimate for the stochastic vanishing viscosity method in addition we establish fractional bv estimate for vanishing viscosity approximations in case the noise coefficient depends on both the solution and spatial variable

a priori error estimates for numerical methods for scalar conservation laws part i the general approach we construct a general theory of a priori error estimates for scalar conservation laws by suitably modifying the original kuznetsov approximation theory as a first application of this general technique we show that error estimates for conservation laws can be obtained without having to use explicitly any regularity properties of the approximate solution thus we obtain optimal error estimates for the engquist osher scheme without using the fact i that the solution is uniformly bounded ii that the scheme is total variation diminishing and iii that the discrete semigroup associated with the scheme has the l 1 contraction property which guarantees an upper bound for the modulus of continuity in time of the approximate solution

a note on congruence conditions of fuzzy choice functions in order to reflect the fuzziness existing in a choice problem banerjee introduces the concept of fuzzy choice function meanwhile banerjee proposes three congruence conditions in assessing the rationality of a fuzzy choice function in this paper we prove some dependencies among these conditions although banerjee asserts that they are independent

modified equation for adaptive monotone difference schemes and its convergent analysis a modified parabolic equation for adaptive monotone difference schemes based on equal arclength mesh applied to the linear convection equation is derived and its convergence analysis shows that solutions of the modified equation approach a discontinuous piecewise smooth solution of the linear convection equation at order one rate in the l 1 norm it is well known that solutions of the monotone schemes with uniform meshes and their modified equation approach the same discontinuous solution at a half order rate in the l 1 norm therefore the convergence analysis for the modified equation provided in this work demonstrates theoretically that the monotone schemes with adaptive grids can improve the solution accuracy numerical experiments also confirm the theoretical conclusions