a non local elliptic hyperbolic system related to the short pulse equation abstract in this paper we prove the well posedness of a non local elliptic hyperbolic system related to the short pulse equation it is a model which describes the evolution of the electrical field of linearly polarized continuum spectrum pulses in optical waveguides including fused silica telecommunication type or photonic crystal fibers as well as hollow capillaries filled with transparent gases

on the local bump friedberg l function let f be a p adic field with residue field of cardinality q to each irreducible representation of gl n f we attach a local euler factor l bf q s q t pi via the rankin selberg method and show that it is equal to the expected factor l s t 1 2 phi pi l 2s lambda 2 circ phi pi of the langlands parameter phi pi of pi the corresponding local integrals were introduced in bump and friedberg the exterior square automorphic l functions on mathrm gl n 47 65 1990 and studied in matringe j reine angew math doi 10 1515 crelle 2013 0083 this work is in fact the continuation of matringe j reine angew math doi 10 1515 crelle 2013 0083 the result is a consequence of the fact that if delta is a discrete series representation of gl 2m f and chi is a character of levi subgroup l gl m f times gl m f which is trivial on gl m f embedded diagonally then delta is l chi distinguished if an only if it admits a shalika model this result was only established for chi mathbf 1 before

fixed points for fuzzy mappings in this paper the problem of the existence and computation of fixed points for fuzzy mappings is approached a fuzzy mapping r over a set x is defined to be a function attaching to each x in x a fuzzy subset r of x an element x of x is called fixed point of r iff its membership degree to r is at least equal to the membership degree to r of any y x i e r r y y x two existence theorems for fixed points of a fuzzy mapping are proved and an algorithm for computing approximations of such a fixed point is described the convergence theorem of our algorithm is proved under the restrictive assumption that for any x in x the membership function of r has a complementary function examples of fuzzy mappings having this property are given but the problem of proving general criteria for a function to have a complementary remain open

erosion profile by a global model for granular flow in this paper we study an integro differential equation that models the erosion of a mountain profile caused by small avalanches the equation is in conservative form with a non local flux involving an integral of the mountain slope under suitable assumptions on the erosion rate the mountain profile develops several types of singularities which we call kinks shocks and hyper kinks we study the formation of these singularities and derive admissibility conditions furthermore entropy weak solutions to the cauchy problem are constructed globally in time taking limits of piecewise affine approximate solutions entropy and entropy flux functions are introduced and a lax entropy condition is established for the weak solutions

a note on fixed point theorems of hadzci c abstract in this paper we give a fixed point theorem for multi valued probabilistic contraction mappings on a menger space as a special case a fixed point theorem for multi valued contraction mappings on a fuzzy metric space is obtained the results presented improve and generalize in a sense some recent fixed point theorems proved by had ic

common fixed point theorems in fuzzy metric spaces in this paper we prove common fixed point theorems for six mappings in fuzzy metric space our main results extend generalize and fuzzify some known results in fuzzy metric spaces probabilistic metric spaces and uniform spaces

conservative solutions to a system of variational wave equations abstract we investigate a system of variational wave equations which is the euler lagrange equations of a variational principle arising in the theory of nematic liquid crystals and a few other physical contexts we establish the global existence of an energy conservative weak solution to its cauchy problem for initial data of finite energy the main difficulty arises from the possible concentration of energy we construct the solution by introducing a new set of variables depending on the energy whereby all singularities are resolved

coincidence theorems and variational inequalities for fuzzy mappings abstract in this paper some coincidence theorems and existence theorems of solutions of variational inequalities for fuzzy mappings are established

coincidence degree and coincidence theorems for fuzzy mappings abstract in this paper the concept of coincidence degree and some coincidence theorems for fuzzy mappings have been introduced and established the results presented in this paper generalize and unify some results of 2 3 4 5 8 and give a fuzzy generalization of the famous kakutani ky fan theorem

fixed degree for fuzzy mappings and a generalization of ky fan s theorem abstract in this paper the concept of some properties of fixed degree for fuzzy mappings are introduced and studied the results presented generalize and unify some recent results

conservative solutions to a system of asymptotic variational wave equations abstract this paper is concerned with an asymptotic variational wave system which models weakly nonlinear waves for a system of variational wave equations arising in the theory of nematic liquid crystals and a few other physical contexts by constructing a global semigroup we establish the well posedness of the initial boundary value problem within the class of energy conservative solutions for initial data of finite energy

energy conservative solutions to the system of full variational sine gordon equations in a unit sphere we establish the global existence of a conservative weak solution to the cauchy problem for a complete system of variational sine gordon equations which models the motion of long waves on a neutral dipole chain in the continuum limit in a unit sphere although singularities may develop in finite time the energy of the solution is conserved across singular times we also obtain the continuous dependence of solutions on the given initial data

weak solutions to a nonlinear variational sine gordon equation abstract this paper considers a nonlinear variational sine gordon equation u t t c u c u u x x 2 2 sin 2 u 0 which describes the motion of long waves on a neutral dipole chain in the continuum limit and a few other physical phenomena we establish the global existence of dissipative weak solutions to its cauchy problem for initial data in the space h 1 l 2 by using the young measure theory in the setting of l p spaces

a fixed point theorem for contractive type fuzzy mappings abstract in this paper we define a contractive type fuzzy mapping and show that a contractive type fuzzy mapping has a fixed point on a complete metric linear space

the slow erosion limit in a model of granular flow we study a 2 2 system of balance laws that describes the evolution of a granular material avalanche flowing downhill the original model was proposed by hadeler and kuttler granul matter 2 9 18 1999 the cauchy problem for this system has been studied by the authors in recent papers amadori and shen in commun partial differ equ 34 1003 1040 2009 shen in j math anal appl 339 828 838 2008 in this paper we first consider an initial boundary value problem the boundary condition is given by the flow of the incoming material for this problem we prove the global existence of bv solutions for a suitable class of data with bounded but possibly large total variations we then study the slow erosion or deposition limit we show that if the thickness of the moving layer remains small then the profile of the standing layer depends only on the total mass of the avalanche flowing downhill not on the time law describing the rate at which the material slides down more precisely in the limit as the thickness of the moving layer tends to zero the slope of the mountain is provided by an entropy solution to a scalar integro differential conservation law

on a nonlinear hyperbolic variational equation i global existence of weak solutions we study the nonlinear hyperbolic partial differential equation u t uux x 1 2u x 2 this partial differential equation is the canonical asymptotic equation for weakly nonlinear solutions of a class of hyperbolic equations derived from variational principles in particular it describes waves in a massive director field of a nematic liquid crystal global smooth solutions of the partial differential equation do not exist since their derivatives blow up in finite time while weak solutions are not unique we therefore define two distinct classes of admissible weak solutions which we call dissipative and conservative solutions we prove the global existence of each type of admissible weak solution provided that the derivative of the initial data has bounded variation and compact support these solutions remain continuous despite the fact that their derivatives blow up there are no a priori estimates on the second derivatives in any l p space so the existence of weak solutions cannot be deduced by using sobolev type arguments instead we prove existence by establishing detailed estimates on the blowup singularity for explicit approximate solutions of the partial differential equation we also describe the qualitative properties of the partial differential equation including a comparison with the burgers equation for inviscid fluids and a number of illustrative examples of explicit solutions we show that conservative weak solutions are obtained as a limit of solutions obtained by the regularized method of characteristics and we prove that the large time asymptotic behavior of dissipative solutions is a special piecewise linear solution which we call a kink wave

new general solutions to linear fredholm integro differential equations and their applications on solving the boundary value problems abstract this paper introduces the n general solution to linear fredholm integro differential equations and sets its properties the conditions for existence of classical general solution and solvability criteria for the equation are provided necessary and sufficient conditions for solvability of linear boundary value problems are established algorithms for construction of the n general solutions are obtained this paper also proposes approximate and numerical methods to solve the boundary value problems

fuzzy mappings and fixed point theorems abstract we extend heilpern s fixed point theorem for fuzzy contraction mappings to a pair of generalized fuzzy contraction mappings also we prove a fixed point theorem for nonexpansive fuzzy mappings on a compact star shaped subset of a banach space

a semigroup approach to an integro differential equation modeling slow erosion abstract the paper is concerned with a scalar conservation law with nonlocal flux providing a model for granular flow with slow erosion and deposition while the solution u u t x can have jumps the inverse function x x t u is always lipschitz continuous its derivative has bounded variation and satisfies a balance law with measure valued sources using a backward euler approximation scheme combined with a nonlinear projection operator we construct a continuous semigroup whose trajectories are the unique entropy weak solutions to this balance law going back to the original variables this yields the global well posedness of the cauchy problem for the granular flow model

une preuve simple des conjectures de langlands pour gl n sur un corps p adique let f be a finite extension of p for each integer n 1 we construct a bijection from the set f 0 n of isomorphism classes of irreducible degree n representations of the absolute weil group of f onto the set f 0 n of isomorphism classes of smooth irreducible supercuspidal representations of gl n f those bijections preserve epsilon factors for pairs and hence we obtain a proof of the langlands conjectures for gl n over f which is more direct than harris and taylor s our approach is global and analogous to the derivation of local class field theory from global class field theory we start with a result of kottwitz and clozel on the good reduction of some shimura varieties and we use a trick of harris who constructs non galois automorphic induction in certain cases

an alternative characterization of probabilistic menger spaces with h type triangular norms abstract the class of h type triangular norms was introduced for the first time by had ic in 1978 in this paper a new characteristic property of the h type triangular norm is presented by virtue of this alternative characterization the continuity of quasi metrics and quasi norms is studied and some properties of the probabilistic menger spaces with this triangular norm are considered as applications new fixed point and fixed degree theorems for probabilistic nonlinear contractions and fuzzy mappings are given

on the shape of avalanches in this paper we study a dimensionless model of granular matter the model can be rewritten into a system of balance laws we prove that every sufficiently small compactly supported perturbation of a lipschitz continuous decoupled initial data gives decoupled solution in finite time moreover no gradient catastrophe occurs i e the solution does not develop discontinuities

fixed degree and fixed point theorems for fuzzy mappings in probabilistic metric spaces abstract this paper introduces the concept and properties of fixed degrees for fuzzy mappings in probabilistic metric spaces by virtue of this concept some theorems about common fixed degree of a sequence of fuzzy mappings in probabilistic metric spaces are obtained these new results are a unified approach to generalize several fixed point theorems for fuzzy mappings

dynamics of director fields an asymptotic equation for weakly nonlinear hyperbolic waves governed by variational principles is derived and analyzed the equation is used to study a nonlinear instability in the director field of a nematic liquid crystal it is shown that smooth solutions of the asymptotic equation break down in finite time also constructed are weak solutions of the equation that are continuous despite the fact that their spatial derivative blows up

existence and uniqueness of solutions of an asymptotic equation arising from a variational wave equation with general data we establish here the global existence and uniqueness of admissible both dissipative and conservative weak solutions to a canonical asymptotic equation for weakly nonlinear solutions of a class of nonlinear variational wave equations with any l 2 initial datum we use the method of young measures and mollification techniques

fixed point theorems for multivalued mappings in some classes of fuzzy metic spaces abstract using the probabilistic function of noncompactness a fixed point theorem for multivalued mappings in probabilistic metric spaces is proved as an application a fixed point theorem for multivalued mappings in fuzzy metric spaces is obtained

weak solutions to a nonlinear variational wave equation we establish the global existence of weak solutions to the cauchy problem for a nonlinear variational wave equation where the wave speed is a given monotone function of the wave amplitude the equation arises in modeling wave motions of nematic liquid crystals long waves on a dipole chain and a few other fields we use the young measure method in the setting of lp spaces we overcome the difficulty that oscillations get amplified by the growth terms of the equation

on fuzzy metric spaces abstract in this paper we introduce the concept of a fuzzy metric space the distance between two points in a fuzzy metric space is a non negative upper semicontinuous normal and convex fuzzy number properties of fuzzy metric spaces are studied and some fixed point theorems are proved

fixed point theorems for multivalued mappings in probabilistic metric spaces abstract in this paper we prove a fixed point theorem for multivalued mappings in probabilistic metric spaces some applications in fuzzy metric and random normed spaces are given

unique conservative solutions to a variational wave equation relying on the analysis of characteristics we prove the uniqueness of conservative solutions to the variational wave equation u tt c u c u u x x 0 given a solution u t x even if the wave speed c u is only hor continuous in the t x plane one can still define forward and backward characteristics in a unique way using a new set of independent variables x y constant along characteristics we prove that t x u together with other variables satisfy a semilinear system with smooth coefficients from the uniqueness of the solution to this semilinear system one obtains the uniqueness of conservative solutions to the cauchy problem for the wave equation with general initial data u 0 cdot in h 1 i r u t 0 cdot in l 2 i r

conservative solutions to a nonlinear variational wave equation we establish the existence of a conservative weak solution to the cauchy problem for the nonlinear variational wave equation utt c u c u ux x 0 for initial data of finite energy here c is any smooth function with uniformly positive bounded values

global energy conservative solutions to a system of variational wave equations abstract this paper is concerned with a system of variational wave equations which is the euler lagrange equations of a variational principle arising in the theory of nematic liquid crystals and a few other physical contexts the global existence of an energy conservative weak solution to its cauchy problem for initial data of finite energy is established by using the method of energy dependent coordinates and the young measure theory

global conservative solutions of the camassa holm equation this paper develops a new approach in the analysis of the camassa holm equation by introducing a new set of independent and dependent variables the equation is transformed into a semilinear system whose solutions are obtained as fixed points of a contractive transformation these new variables resolve all singularities due to possible wave breaking returning to the original variables we obtain a semigroup of global solutions depending continuously on the initial data our solutions are conservative in the sense that the total energy equals a constant for almost every time

generalized vector complementarity problem in fuzzy environment abstract this paper is devoted to introduce and study a new class of generalized vector complementarity problems gvcp for short and generalized vector variational inequalities gvvi for short in fuzzy environment under suitable conditions we prove the equivalence between gvcp and gvvi in banach spaces then without any monotonicity assumption we apply kkm technique to establish an existence theorem of solutions for gvvi finally we show that the solution set of gvcp is nonempty and closed

on a nonlinear hyperbolic variational equation ii the zero viscosity and dispersion limits we consider viscosity and dispersion regularizations of the nonlinear hyperbolic partial differential equation u t uux x 1 2u x 2 with the simplest initial data such that u x blows up in finite time we prove that the zero viscosity limit selects a unique global weak solution of the partial differential equation without viscosity we also present numerical experiments which indicate that the zero dispersion limit selects a different global weak solution of the same initial value problem

fixed point theorems for fuzzy mappings abstract this paper presents some new fixed point theorems for fuzzy mappings the results given in this paper improve and extend some recent results

probabilistic fractals and attractors in menger spaces abstract probabilistic fractals are considered as self similar sets for contraction mappings in hyperspaces of the menger probabilistic metric spaces the completeness of hyperspaces of all closed or closed and bounded or compact nonempty subsets with respect to the probabilistic hausdorff metric is studied in some general conditions of triangular norm using the properties of hyperspaces and triangular norms of h type several existence results of attractors are obtained for a finite family and a countable family of probabilistic nonlinear contractions respectively our results are generalizations in many aspects

archimedean non vanishing cohomological test vectors and standard l functions of gl2n complex case abstract the purpose of this paper is to study the local zeta integrals of friedberg jacquet at complex place and to establish similar results to the recent work 4 joint with c chen and d jiang in this paper we will 1 give a necessary and sufficient condition on an irreducible essentially tempered cohomological representation of gl 2 n c with a non zero shalika model 2 construct a new twisted linear period s and give a different expression of the linear model for 3 give a necessary and sufficient condition on the character such that there exists a uniform cohomological test vector v v which we construct explicitly for s as a consequence we obtain the non vanishing of local friedberg jacquet integral at complex place all of the above are essential preparations for attacking a global period relation problem in the forthcoming paper 11

on fixed degree theorems for fuzzy mappings in menger pm spaces in this paper we establish a new common fixed degree theorem for a sequence of fuzzy mappings in menger pm spaces as an immediate consequence of this theorem we obtain an improvement of a corresponding result of chang et al fuzzy sets and systems 87 1997 325 334 in addition we also obtain some fixed degree and fixed point theorems for fuzzy mappings in fuzzy metric spaces our results unify and generalize the results of heilpern j math anal appl 83 1981 566 569 butnariu fuzzy sets and systems 7 1982 191 207 hadzic fuzzy sets and systems 29 1989 115 125 fang fuzzy sets and systems 48 1992 391 395 lee et al fuzzy sets and systems 61 1994 309 312 j fuzzy math 2 1994 859 870 and chang et al math japon 40 1994 289 293 fuzzy sets and systems 87 1997 325 334

on the weak solutions to a shallow water equation we obtain the existence of global in time weak solutions to the cauchy problem for a one dimensional shallow water equation that is formally integrable and can be obtained by approximating directly the hamiltonian for euler s equation in the shallow water regime the solution is obtained as a limit of viscous approximation the key elements in our analysis are some new a priori one sided supernorm and space time higher norm estimates on the first order derivatives 2000 john wiley sons inc

energy conservative solutions to a one dimensional full variational wave system we establish the existence of a conservative weak solution to the initial value problem for a complete system of variational wave equations modeling liquid crystals in one space dimension in which the director has two degrees of freedom the solutions exist globally in time and singularities may develop in finite time but the energy of the solutions is conserved across singular times the method for existence also yields continuous dependence of solutions on the initial data 2011 wiley periodicals inc

existence and stability of traveling waves for an integro differential equation for slow erosion abstract we study an integro differential equation that describes the slow erosion of granular flow the equation is a first order nonlinear conservation law where the flux function includes an integral term we show that there exist unique traveling wave solutions that connect profiles with equilibrium slope at such traveling waves take very different forms from those in standard conservation laws furthermore we prove that the traveling wave profiles are locally stable i e solutions with monotone initial data approach the traveling waves asymptotically as t

convergent difference schemes for the hunter saxton equation we propose and analyze several finite difference schemes for the hunter saxton equation hs u t uu x 1 2 x 0 u x 2 d x x 0 t 0 this equation has been suggested as a simple model for nematic liquid crystals we prove that the numerical approximations converge to the unique dissipative solution of hs as identified by zhang and zheng a main aspect of the analysis in addition to the derivation of several a priori estimates that yield some basic convergence results is to prove strong convergence of the discrete spatial derivative of the numerical approximations of u which is achieved by analyzing various renormalizations in the sense of diperna and lions of the numerical schemes finally we demonstrate through several numerical examples the proposed schemes as well as some other schemes for which we have no rigorous convergence results

asymptotic variational wave equations we investigate the equation ut f u x x f u ux 2 2 where f u is a given smooth function typically f u u 2 2 or u 3 3 this equation models unidirectional and weakly nonlinear waves for the variational wave equation utt c u c u ux x 0 which models some liquid crystals with a natural sinusoidal c the equation itself is also the euler lagrange equation of a variational problem two natural classes of solutions can be associated with this equation a conservative solution will preserve its energy in time while a dissipative weak solution loses energy at the time when singularities appear conservative solutions are globally defined forward and backward in time and preserve interesting geometric features such as the hamiltonian structure on the other hand dissipative solutions appear to be more natural from the physical point of view we establish the well posedness of the cauchy problem within the class of conservative solutions for initial data having finite energy and assuming that the flux function f has lipschitz continuous second order derivative in the case where f is convex the cauchy problem is well posed also within the class of dissipative solutions however when f is not convex we show that the dissipative solutions do not depend continuously on the initial data

conservative solutions to a one dimensional nonlinear variational wave equation abstract this paper is focused on a nonlinear variational wave equation which is the euler lagrange equation of a variational principle whose action is a quadratic function of the derivatives of the field we establish the global existence of an energy conservative weak solution to its cauchy problem for initial data of finite energy the approach follows very closely the method of energy dependent coordinates proposed by bressan zhang and zheng 6 7 by introducing a new set of variables which resolve all singularities due to the possible concentration of energy the equation can be rewritten as a semilinear system we construct the global weak solution by expressing the solution of the semilinear system in terms of the original variables

well posedness for a slow erosion model abstract we improve in two ways the well posedness results of 2 for a slow erosion model proposed in 11 firstly we study the asymptotic profile when u 0 1 u 0 l where u 0 is the initial datum moreover using a compensated compactness based argument we prove the existence of solutions when u 0 1 u 0 l 3

conservative solutions to a system of variational wave equations of nematic liquid crystals in this paper we solve a system of hyperbolic equations by modelling nematic liquid crystals

a finite difference approximation of a two layer system for growing sandpiles we study from a numerical point of view a system of partial differential equations recently proposed in k p hadeler and c kuttler granular matter 2 1999 pp 9 18 to model the dynamics of growing sandpiles generated by a vertical source on a flat bounded table in such a system an eikonal equation for the standing layer of the pile is coupled to an advection equation for the rolling layer we analyze a suitable explicit finite difference scheme in one dimension and discuss its properties a comparison is made with respect to the variational approach of l prigozhin european j appl math 7 1996 pp 225 235 particularly in terms of steady state solutions since the effective equilibrium configuration reached by the growing process is not completely clear for this model we show experiments in one and two dimensions which characterize the steady state solutions for different source terms

constant term of smooth h_psi spherical functions on a reductive p adic group let be a smooth character of a closed subgroup h of a reductive p adic group g if p is a parabolic subgroup of g such that ph is open in g we define the constant term of every smooth function on g which transforms by under the right action of g the example of mixed models is given it includes symmetric spaces and whittaker models in this case a notion of cuspidal function is defined and studied it leads to finiteness theorems

a fixed point theorem for multivalued mappings in probabilistic metric spaces and an application in fuzzy metric spaces in this paper we shall generalize a fixed point theorem for multivalued mappings in probabilistic metric spaces proved in j math anal appl 202 1996 433 449 as a corollary a fixed point result in menger spaces s f t where t is a strict t norm is obtained some special cases where t is a member of dombi schweizer sklar and aczel alsina families of t norms are investigated an application in fuzzy metric spaces is presented

derivatives and exceptional poles of the local exterior square l function for gl_m let pi be an irreducible admissible representation of gl m f where f is a non archimedean local field of characteristic zero in 1990 s jacquet and shalika established an integral representation for the exterior square l function we complete following the method developed by cogdell and piatetski shapiro the computation of the local exterior square l function l s pi wedge 2 via the integral representation in terms of l functions of supercuspidal representations by a purely local argument with this result we show the equality of the local analytic l functions l s pi wedge 2 via the integral representation for the irreducible admissible representation pi for gl m f and the local arithmetic l functions l s wedge 2 phi pi of its langlands parameter phi pi through local langlands correspondence

conservative solutions to a nonlinear variational sine gordon equation abstract this paper is concerned with a nonlinear variational sine gordon equation u t t c u c u u x x 2 2 s i n 2 u 0 which describes the motion of long waves on a neutral dipole chain in the continuum limit and a few other physical phenomena we establish the global existence of an energy conservative weak solution to its cauchy problem for initial data of finite energy to deal with the possible blowup of solutions we introduce a new set of variables depending on the energy whereby all singularities are resolved

generic regularity and lipschitz metric for the hunter saxton type equations abstract the hunter saxton equation determines a flow of conservative solutions taking values in the space h 1 r however the solution typically includes finite time gradient blowups which make the solution flow not continuous w r t the natural h 1 distance the aim of this paper is to first study the generic properties of conservative solutions of some initial boundary value problems to the hunter saxton type equations then using these properties we give a new way to construct a finsler type metric which renders the flow uniformly lipschitz continuous on bounded subsets of h 1 r

on fixed point theorems in fuzzy metric spaces abstract the purpose of this paper is to give some new fixed point theorems for contractive type mappings in fuzzy metric spaces the results presented improve and generalize some recent results

fixed points in fuzzy metric spaces abstract in this note the well known fixed point theorems of banach and edelstein are extended to fuzzy metric spaces in the settle of kramosil and michalek