time dependent differential inclusions cocycle attractors and fuzzy differential equations traditional formulations of fuzzy differential equations do not reproduce the rich and varied behavior of crisp differential equations des a recent interpretation in terms of differential inclusions expressed level setwise overcomes this deficiency and opens up for profitable investigation such properties as stability attraction periodicity and the like this is especially important for investigating continuous systems which are uncertain or incompletely specified this paper studies attractors of fuzzy des in terms of cocycles and encompasses both the time dependent and autonomous cases

brief note on the variation of constants formula for fuzzy differential equations this note gives a theory of state transition matrices for linear systems of fuzzy differential equations this is used to give a fuzzy version of the classical variation of constants formula a simple example of a time independent control system is used to illustrate the methods while similar problems to the crisp case arise for time dependent systems in time independent cases the calculations are elementary solutions of eigenvalue eigenvector problems in particular for nonnegative or nonpositive matrices the problems at each level set can easily be solved in matlab to give the level sets of the fuzzy solution

fuzzy differential equations and the extension principle we study the cauchy problem for differential equations considering its parameters and or initial conditions given by fuzzy sets these fuzzy differential equations are approached in two different ways a by using a family of differential inclusions and b the zadeh extension principle for the solution of the model we conclude that the solutions of the cauchy problem obtained by both are the same we also provide some illustrative examples

zeroes of zeta functions and symmetry hilbert and polya suggested that there might be a natural spectral interpretation of the zeroes of the riemann zeta function while at the time there was little evidence for this today the evidence is quite convincing firstly there are the function field analogues that is zeta functions of curves over finite fields and their generalizations for these a spectral interpretation for their zeroes exists in terms of eigenvalues of frobenius on cohomology secondly the developments both theoretical and numerical on the local spacing distributions between the high zeroes of the zeta function and its generalizations give striking evidence for such a spectral connection moreover the low lying zeroes of various families of zeta functions follow laws for the eigenvalue distributions of members of the classical groups in this paper we review these developments in order to present the material fluently we do not proceed in chronological order of discovery also in concentrating entirely on the subject matter of the title we are ignoring the standard body of important work that has been done on the zeta function and l functions 1 the montgomery odlyzko law we begin with the riemann zeta function and some phenomenology associated with it

random matrix ensembles associated to compact symmetric spaces we introduce random matrix ensembles that correspond to the infinite families of irreducible riemannian symmetric spaces of type i in particular we recover the circular orthogonal and symplectic ensembles of dyson and find other families of unitary orthogonal and symplectic ensembles of jacobi type we discuss the universal and weakly universal features of the global and local correlations of the levels in the bulk and at the hard edge of the spectrum i e at the central points 1 on the unit circle previously known results are extended and we find new simple formulas for the bessel kernels that describe the local correlations at a hard edge

stable trace formula cuspidal tempered terms consider a connected reductive group g over a number field f for technical reasons we assume that the derived group of g is simply connected see l1 in l3 langlands partially stabilizes the trace formula for g after making certain assumptions he writes the elliptic regular part of the trace formula for g as a linear combination of the elliptic g regular parts of the stable trace formulas for the elliptic endoscopic groups h of g the function f used in the stable trace formula forh is obtained from the function f used in the trace formula for g by transferring orbital integrals

open fuzzy cubature rule with application to nonlinear fuzzy volterra integral equations in two dimensions abstract in this paper we propose an open fuzzy cubature formula and as application we construct an iterative numerical method for solving nonlinear fuzzy volterra integral equations in two dimensions the convergence of the method is proved by providing the error estimate and it is tested on two numerical experiments

special l values of drinfeld modules we state and prove a formula for a certain value of the goss l function of a drinfeld module this gives characteristic p valued function eld analogues of the class number formula and of the birch and swinnerton dyer conjecture the formula and its proof are presented in an entirely selfcontained fashion

determination of the algebraic relations among special γ values in positive characteristic we devise a new criterion for linear independence over function fields using this tool in the setting of dual t motives we find that all algebraic relations among special values of the geometric r function over f q t are explained by the standard functional equations

counting and equidistribution for quaternion algebras we aim at studying automorphic forms of bounded analytic conductor in the totally definite quaternion algebra setting we prove the equidistribution of the universal family with respect to an explicit and geometrically meaningful measure it leads to answering the sato tate conjectures in this case and contains the counting law of the universal family with a power savings error term

endoscopic transfer of orbital integrals in large residual characteristic this article constructs shalika germs in the context of motivic integration both for ordinary orbital integrals and kappa orbital integrals based on transfer principles in motivic integration and on waldspurger s endoscopic transfer of smooth functions in characteristic zero we deduce the endoscopic transfer of smooth functions in sufficiently large residual characteristic

on differential equations with interactive fuzzy parameter via t norms abstract in this paper we study fuzzy differential equations with uncertain parameters modeled by interactive fuzzy numbers the interactivity is formalized with the help of upper semicontinuous t norms to obtain solutions to fuzzy differential equations we use two different approaches the first uses a family of differential inclusions while the second is the fuzzification of the deterministic problem using the zadeh extension principle we show that the solutions obtained by the two methods are equal interactivity among the parameters and variable of the problem are studies with respect two methods we show that a hierarchy in uncertainties of the solutions arises when we chose one of the basic t norm the minimum the t norm of the product the t norm of lukasiewicz and t norm of the drastic product to model the interaction between parameters finally to illustrate the concepts introduced in the paper we study the malthusian model with interactive parameters

constructible exponential functions motivic fourier transform and transfer principle we introduce spaces of exponential constructible functions in the motivic setting for which we construct direct image functors in the absolute and relative settings this allows us to define a motivic fourier transformation for which we get various inversion statements we also define spaces of motivic schwartz bruhat functions on which motivic fourier transformation induces isomorphisms our motivic integrals specialize to nonarchimedean integrals we give a general transfer principle comparing identities between functions defined by exponential integrals over local fields of characteristic zero resp of positive characteristic having the same residue field we also prove new results about p adic integrals of exponential functions and stability of this class of functions under p adic integration

fuzzy differential equation with completely correlated parameters abstract in this paper we study fuzzy differential equations with parameters and initial conditions interactive the interactivity is given by means of the concept of completely correlated fuzzy numbers we consider the problem in two different ways the first by using a family of differential inclusions in the second the extension principle for completely correlated fuzzy numbers is employed to obtain the solution of the model we conclude that the solutions of the fuzzy differential equations obtained by these two approaches are the same the solutions are illustrated with the radioactive decay model where the initial condition and the decay rate are completely correlated fuzzy numbers we also present an extension principle for completely correlated fuzzy numbers and we show that nguyen s theorem remains valid in this environment in addition we compare the solution via extension principle of the fuzzy differential equation when the parameters are non interactive fuzzy numbers and when the parameters are completely correlated fuzzy numbers finally we study the si epidemiological model in two forms first considering that the susceptible and infected individuals are completely correlated and then assuming that the transfer rate and the initial conditions are completely correlated

integrability of oscillatory functions on local fields transfer principles for oscillatory functions on local fields coming from motivic exponential functions we show that integrability over q n p implies integrability over f p t n for large p and vice versa more generally the integrability only depends on the isomorphism class of the residue field of the local field once the characteristic of the residue field is large enough this principle yields general local integrability results for harish chandra characters in positive characteristic as we show in other work transfer principles for related conditions such as boundedness and local integrability are also obtained the proofs rely on a thorough study of loci of integrability to which we give a geometric meaning by relating them to zero loci of functions of a specific kind

generalized differentiability of fuzzy valued functions in the present paper using novel generalizations of the hukuhara difference for fuzzy sets we introduce and study new generalized differentiability concepts for fuzzy valued functions several properties of the new concepts are investigated and they are compared to similar fuzzy differentiabilities finding connections between them characterization and relatively simple expressions are provided for the new derivatives

algebraic relations among periods and logarithms of rank 2 drinfeld modules for any rank 2 drinfeld module rho defined over an algebraic function field we consider its period matrix p rho which is analogous to the period matrix of an elliptic curve defined over a number field suppose that the characteristic of the finite field bbb f q is odd and that rho does not have complex multiplication we show that the transcendence degree of the field generated by the entries of p rho over bbb f q theta is 4 as a consequence we show also the algebraic independence of drinfeld logarithms of algebraic functions which are linearly independent over bbb f q theta

a continuous time dynamic fuzzy system ii fuzzy potentials abstract this paper is a sequel of yoshida 9 fuzzy potentials are introduced in a continuous time dynamic fuzzy system and a fuzzy relational differential equation is given to characterize the fuzzy potentials

low lying zeros of l functions and random matrix theory by looking at the average behavior n level density of the low lying zeros of certain families of l functions we find evidence as predicted by function field analogs in favor of a spectral interpretation of the nontrivial zeros in terms of the classical compact groups

existence and uniqueness for solutions to fuzzy stochastic differential equations driven by local martingales under the non lipschitzian condition abstract this paper makes a research into a class of fuzzy stochastic differential equations fsdes driven by a continuous local martingale under the non lipschitzian condition such equations can be useful in modelling of hybrid systems where the phenomena are subjected to two kinds of uncertainties randomness and fuzziness simultaneously the solutions of fsdes are the fuzzy stochastic processes and their uniqueness is considered to be in a strong sense thus the existence and uniqueness of solutions to fsdes under the non lipschitzian condition is first proven and the continuity of solutions to fsdes with respect to the initial data or the coefficients of the equations is investigated

initial and boundary value problems for fuzzy differential equations we prove a wintner type result for fuzzy ivps and a superlinear type result for fuzzy bvps both results rely on a generalized schauder theorem in metric spaces

the sato tate conjecture for hilbert modular forms we prove the sato tate conjecture for hilbert modular forms more precisely we prove the natural generalisation of the sato tate conjecture for regular algebraic cuspidal automorphic representations of gl2 af f a totally real field which are not of cm type the argument is based on the potential automorphy techniques developed by taylor et al but makes use of automorphy lifting theorems over ramified fields together with a topological argument with local deformation rings in particular we give a new proof of the conjecture for modular forms which does not make use of potential automorphy theorems for non ordinary n dimensional galois representations

the de rham isomorphism for drinfeld modules over tate algebras abstract introduced by angles pellarin and tavares ribeiro drinfeld modules over tate algebras are closely connected to anderson log algebraicity identities pellarin l series and taelman class modules in the present paper we define the de rham map for drinfeld modules over tate algebras and we prove that it is an isomorphism under natural hypotheses as part of this investigation we determine further criteria for the uniformizability and rigid analytic triviality of drinfeld modules over tate algebras

corps de nombres peu ramifies et formes automorphes autoduales let s be a finite set of primes p in s and q s a maximal algebraic extension of q unramified outside s and infinity assume that s 2 we show that the natural maps gal q p bar q p gal q s q are injective much of the paper is devoted to the problem of constructing selfdual automorphic cuspidal representations of gl 2n a q with prescribed properties at all places that we study via the twisted trace formula of j arthur the techniques we develop shed also some lights on the orthogonal symplectic alternative for selfdual representations of gl 2n

on some haar measures on reductive groups we give a characteristic free proof of a theorem of b h gross comparing two haar measures on a reductive group over a local field as a consequence of this theorem we obtain an integration formula for adele groups over global function fields

almost periodic solutions of fuzzy systems we prove the existence of almost periodic solutions and asymptotically almost periodic solutions for the fuzzy functional differential equations moreover we consider uniform stable and uniformly asymptotically stable of almost periodic solutions for the fuzzy system

towards fuzzy differential calculus part 1 integration of fuzzy mappings abstract this paper deals with fuzzy set valued mappings of the real line and more particularly focuses on mappings from the real line to the set of convex normal fuzzy sets of the real line these mappings can also be viewed as fuzzy relations using zadeh s extension principle the integral of such fuzzy mappings over a crisp interval is defined provided a special analytical representation of the fuzzy mapping the practical computation of such an integral is shown to be easy practically speaking it yields the fuzzy surface of a fuzzily bounded area

on generalization on nguyen s theorem abstract the goal of this paper is to generalize certain results of nguyen 1 concerning the cuts of two place functions defined by the zadeh s extension principle to the case of extended two place functions defined via a sup t norm convolution

a proof of langland s conjecture on plancherel measures complementary series of p adic groups analysis of p adic reductive groups our first result theorem 7 9 proves a conjecture of langlands on normalization of intertwining operators by means of local langlands root numbers and l functions at least when the group is quasi split and the inducing representation is generic assuming two natural conjectures in harmonic analysis of p adic groups we also prove the validity of the conjecture in general theorem 9 5 as our second result we obtain all the complementary series and special representations of quasi split p adic groups coming from rank one parabolic subgroups and generic supercuspidal represen

differentials of fuzzy functions abstract in this paper the radstrom embedding theorem proc amer math soc 3 1952 165 is generalized and is used to define the concept of the differential of a fuzzy function

a new bernoulli wavelet method for accurate solutions of nonlinear fuzzy hammerstein volterra delay integral equations in this article bernoulli wavelet method has been developed to solve nonlinear fuzzy hammerstein volterra integral equations with constant delay this type of integral equation has a particular case the fuzzy variant of a mathematical model from epidemiology bernoulli wavelets have been generated by dilation and translation of bernoulli polynomials the properties of bernoulli wavelets and bernoulli polynomials are first presented the present wavelet method reduces these integral equations to a system of nonlinear algebraic equations and again these algebraic systems have been solved numerically by newton s method convergence analysis of the present method has been discussed in this article also the results obtained by present wavelet method have been compared with that of by b spline wavelet method some illustrative examples have been demonstrated to show the applicability and accuracy of the present method

linear independence of gamma values in positive characteristic we investigate the arithmetic nature of special values of thakur s func tion field gamma function at rational points our main result is that all linear dependence relations over the field of algebraic functions are consequences of the anderson deligne thakur bracket relations

stability in possibilistic linear programming with continuous fuzzy number parameters abstract we prove that possibilistic linear programming problems introduced by buckley in 2 with continuous fuzzy number parameters are well posed i e small changes of the membership function of the parameters may cause only a small deviation in the possibilistic distribution of the objective function

on finite group actions on reductive groups and buildings let h be a connected reductive group over a non archimedean local field k and let f autk h be a finite group of order not divisible by p the residual characteristic of k let g h f be the identity component of the subgroup of h consisting of points fixed by f the main theorem of this paper asserts that the bruhat tits building b g of g can be identified with the set of f fixed points of b h several special cases of this theorem have been known previously when e k is a finite totally ramified galois extension h rese k g and f gal e k the condition p f is simply that e k is tamely ramified in this case our main theorem is a well known but unpublished theorem of g rousseau recently one of us g p found a simple proof of this theorem p when g is a classical group realized in the standard way as the identity component of the group of fixed points of an involution of a general linear group h bruhat and tits bt4 have given a description of b g as a subset of b h in particular it follows from their description that b g b h when p 2 recently this fact has been rediscovered by j kim and a moy km and independently a simple proof has been given by gy let h be the split form of spin 8 then one can choose an outer automorphism aut h of order 3 such that g h is of type g2 from a joint work gy by w t gan and one of us j y it is known that b g b h is true for arbitrary p

discrete series characters and the lefschetz formula for hecke operators this paper consists of three independent but related parts in the rst part xx1 6 we give a combinatorial formula for the constants appearing in the numerators of characters of stable discrete series representations of real groups see x3 as well as an analogous formula for individual discrete series representations see x6 moreover we give an explicit formula theorem 5 1 for certain stable virtual characters on real groups by theorem 5 2 these include the stable discrete series characters and thus we recover the results of x3 in a more natural way in the second part x7 we use the character formula given in theorem 5 1 to rewrite the lefschetz formula of gm for the local contribution at a single xed point component to the trace of a hecke operator on weighted cohomology in the same spirit as that of arthur s lefschetz formula a in terms of stable virtual characters on real groups see theorem 7 14 b we then sum the contributions of the various xed point components and show that in the case of middle weighted cohomology the resulting global lefschetz xed point formula agrees with arthur s lefschetz formula this gives a topological proof of arthur s formula

on the convergence of fuzzy sets three kind of convergences are defined on a space of fuzzy sets relationships between these convergences are studied some comments on the fixed point property are represented

tannakian duality for anderson drinfeld motives and algebraic independence of carlitz logarithms we develop a theory of tannakian galois groups for t motives and relate this to the theory of frobenius semilinear difference equations we show that the transcendence degree of the period matrix associated to a given t motive is equal to the dimension of its galois group using this result we prove that carlitz logarithms of algebraic functions that are linearly independent over the rational function field are algebraically independent

special values of drinfeld modular forms and algebraic independence let a be a polynomial ring in one variable over a finite field and k be its fraction field let f be a drinfeld modular form of nonzero weight for a congruence subgroup of gl2 a so that the coefficients of the q expansion of f are algebraic over k we consider n cm points 1 n on the drinfeld upper half plane for which the quadratic fields k 1 k n are pairwise distinct suppose that f is non vanishing at these n points then we prove that f 1 f n are algebraically independent over k

transcendence and drinfeld modules it has been ten years since v g drinfeld introduced in 3 the concept of elliptic a module which we now call drinfeld a module these modules are analogues of elliptic curves for global function field k and we have witnessed a beautiful algebraic theory gradually taking shape in 13 we have asked a few natural t ranscendence questions conjectures concerning these modules having in mind the analogue of the classical work of siegel schneider about elliptic integrals and based on evidences provided by the old papers of carlitz and wade cf 1 11 here in this article we will prove those conjectures we will show that indeed there is an interesting transcendence theory for each algebraic curve over a finite field fol lowing drinfeld we let m be a lattice in i e a finitely generated discrete a module in k and form

low lying zeros of l functions with orthogonal symmetry we investigate the moments of a smooth counting function of the zeros near the central point of l functions of weight k cuspidal newforms of prime level n we split by the sign of the functional equations and show that for test functions whose fourier transform is supported in 1 n 1 n as n the first n centered moments are gaussian by extending the support to 1 n 1 1 n 1 we see non gaussian behavior in particular the odd centered moments are nonzero for such test functions if we do not split by sign we obtain gaussian behavior for support in 2 n 2 n if 2k n the nth centered moments agree with random matrix theory in this extended range providing additional support for the katz sarnak conjectures the proof requires calculating multidimensional integrals of the nondiagonal terms in the bessel kloosterman expansion of the petersson formula we convert these multidimensional integrals to one dimensional integrals already considered in the work of iwaniec luo and sarnak ils and derive a new and more tractable expression for the nth centered moments for such test functions this new formula facilitates comparisons between number theory and random matrix theory for test functions supported in 1 n 1 1 n 1 by simplifying the combinatorial arguments as an application we obtain bounds for the percentage of such cusp forms with a given order of vanishing at the central point

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

homology of affine springer fibers in the unramified case assuming a certain purity conjecture we derive a formula for the complex cohomology groups of the affine springer fiber corresponding to any unramified regular semisimple element we use this calculation to present a complex analog of the fundamental lemma for function fields we show that the kappa orbital integral that arises in the fundamental lemma is equal to the lefschetz trace of the frobenius acting on the etale cohomology of a related variety

periodic boundary value problems for impulsive fuzzy differential equations the peculiarity of the hukuhara derivative makes it impossible to find periodic solutions for fuzzy differential equations with the exception of very restrictive situations in this work we consider a boundary value problem associated with an impulsive fuzzy differential equation and approximate the extremal solutions in a fuzzy functional interval using the monotone method fuzzy comparison results are useful in our procedure and the expression of the solution for some impulsive periodic linear differential problems is also provided

membership induced on manifolds by vector fields and flows abstract in many engineering and scientific applications the need arises to perform differential calculations on manifolds if such calculations involve imprecise data methods for computing with such data must be determined definitions and results are given for memberships on manifolds induced by differentiation along vector fields and by flows of vector fields with uncertain parameters examples are presented which illustrate the concepts

on possibilistic mean value and variance of fuzzy numbers dubois and prade introduced the mean value of a fuzzy number as a closed interval bounded by the expectations calculated from its upper and lower distribution functions in this paper introducing the notations of lower possibilistic and upper possibilistic mean values we definine the interval valued possibilistic mean and investigate its relationship to the interval valued probabilistic mean we also introduce the notation of crisp possibilistic mean value and crisp possibilistic variance of continuous possibility distributions which are consistent with the extension principle we also show that the variance of linear combination of fuzzy numbers can be computed in a similar manner as in probability theory

on limit multiplicites of discrete series representations in spaces of automorphic forms of course the groups f are then arithmetic subgroups of g in this situation it seems natural to assume that as n the spectral decomposition of l2 f g will approximate that of g in particular let 3 be a discrete series representation of g if f is a subgroup of g let re f 6 be the multiplicity of 3 in the representation of g by right translations on l2 f g choose a haar measure dg on g if f is arithmetic let v f g be the finite volume of f g for the measure induced by dg let d 3 be the formal degree of 3 for the measure dg

sato tate theorem for families and low lying zeros of automorphic l functions we consider certain families of automorphic representations over number fields arising from the principle of functoriality of langlands let g be a reductive group over a number field f which admits discrete series representations at infinity let l g widehat g rtimes mathrm gal bar f f be the associated l group and r l g rightarrow mathrm gl d mathbb c a continuous homomorphism which is irreducible and does not factor through mathrm gal bar f f the families under consideration consist of discrete automorphic representations of g mathbb a f of given weight and level and we let either the weight or the level grow to infinity we establish a quantitative plancherel and a quantitative sato tate equidistribution theorem for the satake parameters of these families this generalizes earlier results in the subject notably of sarnak prog math 70 321 331 1987 and serre j am math soc 10 1 75 102 1997 as an application we study the distribution of the low lying zeros of the associated family of l functions l s pi r assuming from the principle of functoriality that these l functions are automorphic we find that the distribution of the 1 level densities coincides with the distribution of the 1 level densities of eigenvalues of one of the unitary symplectic and orthogonal ensembles in accordance with the katz sarnak heuristics we provide a criterion based on the frobenius schur indicator to determine this symmetry type if r is not isomorphic to its dual r vee then the symmetry type is unitary otherwise there is a bilinear form on mathbb c d which realizes the isomorphism between r and r vee if the bilinear form is symmetric resp alternating then r is real resp quaternionic and the symmetry type is symplectic resp orthogonal

constructible motivic functions and motivic integration 1 1 in this paper intended to be the first in a series we lay new general foundations for motivic integration and give answers to some important issues in the subject since its creation by maxim kontsevich 23 motivic integration developed quickly and has spread out in many directions in a nutshell in motivic integration numbers are replaced by geometric objects like virtual varieties or motives but classicaly not only numbers are defined using integrals but also interesting classes of functions the previous constructions of motivic integration were all quite geometric and it was quite unclear how they could be generalized to handle integrals depending on parameters the new approach we present here based on cell decomposition allows us to develop a very general theory of motivic integration taking parameters into account more precisely we define a natural class of functions constructible motivic functions which is stable under integration the basic idea underlying our approach is to construct more generally push forward morphisms f which are functorial they satisfy f g f g so that performing motivic integration corresponds to taking the push forward to the point this strategy has many technical advantages in essence it allows to reduce the construction of f to the case of closed immersions and projections and in the latter case we can perform induction on the relative dimension the basic case being that of relative dimension 1

variation of constant formula for first order fuzzy differential equations in this paper we study first order linear fuzzy differential equations by using the generalized differentiability concept and we present the general form of their solutions we also correct and complete some previous results finally some examples are given to illustrate our results

numerical solutions of the nonlinear fuzzy hammerstein volterra delay integral equations in this paper an iterative numerical method that solves nonlinear fuzzy hammerstein volterra integral equations with constant delay is developed by using the error estimates a practical stopping criterion of the algorithm is obtained the convergence and the numerical stability of the method is proved and its accuracy is illustrated on three numerical examples the study of this integral equation is important because it has as a particular case the fuzzy variant of a mathematical model from epidemiology

asymptotic behavior of supercuspidal representations and sato tate equidistribution for families abstract we establish properties of families of automorphic representations as we vary prescribed supercuspidal representations at a given finite set of primes for the tame supercuspidals constructed by j k yu we prove the limit multiplicity property with error terms thereby we obtain a sato tate equidistribution for the hecke eigenvalues of these families the main new ingredient is to show that the orbital integrals of matrix coefficients of tame supercuspidal representations with increasing formal degree on a connected reductive p adic group tend to zero uniformly for every noncentral semisimple element

equidistribution theorems for holomorphic siegel modular forms for gsp_4 hecke fields and n level density this paper is a continuation of kim et al j inst math jussieu 2018 we supplement four results on a family of holomorphic siegel cusp forms for gsp 4 mathbb q first we improve the result on hecke fields namely we prove that the degree of hecke fields is unbounded on the subspace of genuine forms which do not come from functorial lift of smaller subgroups of gsp 4 second we prove simultaneous vertical sato tate theorem namely we prove simultaneous equidistribution of hecke eigenvalues at finitely many primes third we compute the n level density of degree 4 spinor l functions and thus we can distinguish the symmetry type depending on the root numbers this is conditional on certain conjecture on root numbers fourth we consider equidistribution of paramodular forms in this case we can prove the conjecture on root numbers main tools are the equidistribution theorem in our previous work and shin templier s compos math 150 12 2003 2053 2014 work

on periods of the third kind for rank 2 drinfeld module in analogy with the periods of abelian integrals of differentials of the third kind for an elliptic curve defined over a number field we introduce a notion of periods of the third kind for a rank 2 drinfeld mathbb f q t module defined over an algebraic function field in this paper we establish explicit formulae for these periods of the third kind for combining with the main result in chang and papanikolas j am math soc 25 123 150 2012 we show the algebraic independence of the periods of first second and third kinds for

fuzzy differential equations abstract this paper deals with fuzzy set valued mappings of a real variable whose values are normal convex upper semicontinuous and compactly supported fuzzy sets in rn we study differentiability and integrability properties of such functions and give an existence and uniqueness theorem for a solution to a fuzzy differential equation

additions of interactive fuzzy numbers this paper provides an account of an approach to modeling unknown data by means of fuzzy set theory and addresses the problem of deriving the uncertainty on a sum of variables whose values lie within fuzzy intervals the first part is an extensive presentation of the theoretical background of the approach the extension principle is stated in terms of possibility of an event the concept of variable interaction is investigated at length section ii gives new results regarding the effective practical computation of additions of fuzzy numbers its originality lies in the introduction of interaction which enables to control the growth of uncertainty in calculations moreover the problem of computing mathematical expectations with fuzzy probabilities is solved the results derived in this paper can easily be used in decision problems where values of parameters or decision variables are not yet precisely fixed or assessed typical applications could be multicriteria optimization and decision making under uncertainty where fuzzy expected utilities can be obtained out of uncompletely assessed probabilities more generally fuzzy arithmetic can be an important tool for sophisticated computationally tractable sensitivity analysis in systems modeling computer aided design and operations research

nonabelian cohomology with coefficients in lie groups in this paper we prove some properties of the nonabelian cohomology h 1 a g of a group a with coefficients in a connected lie group g when a is finite we show that for every a submodule k of g which is a maximal compact subgroup of g the canonical map h1 a k h 1 a g is bijective in this case we also show that h 1 a g is always finite when a z and g is compact we show that for every maximal torus t of the identity component g z 0 of the group of invariants g z h 1 z t h 1 z g is surjective if and only if the z action on g is 1 semisimple which is also equivalent to the fact that all fibers of h 1 z t h 1 z g are finite when a z nz we show that h 1 z nz t h 1 z nz g is always surjective where t is a maximal compact torus of the identity component g z nz of g z nz when a is cyclic we also interpret some properties of h 1 a g in terms of twisted conjugate actions of g

estimating the order of vanishing at infinity of drinfeld quasi modular forms we introduce and study certain deformations of drinfeld quasi modular forms by using rigid analytic trivialisations of corresponding anderson s t motives we show that a sub algebra of these deformations has a natural graduation by the group z 2 x z q 1 z and an homogeneous automorphism and we deduce from this and other properties multiplicity estimates

towards fuzzy differential calculus part 2 integration on fuzzy intervals abstract the problem of integrating mappings over fuzzy domains has already received some attention in the literature however there is not a unique approach but several definitions have been proposed each carrying its own meaning this paper tries to emphasize the relationships and the differences between the various points of view

towards fuzzy differential calculus part 3 differentiation this paper deals successively with differentiation of ordinary functions at a fuzzy point and with differentiation of fuzzy valued functions at a nonfuzzy point in both cases the concept of differentiation is extended and the problem of the linearity is addressed in the second case practical methods of computation are presented in practical situations the available knowledge about mappings may be fuzzy it is the motivation of this work

a possibilistic argument for irreversibility abstract our aim is to explicate the idea of irreversibility by a mathematical representation of irreversible processes occurring in possibilistic dynamical systems with this in mind solutions of the cauchy problem in the space of fuzzy points are examined to meet the correspondence argument solutions of the cauchy problem in the space of concentrated points are examined too

fuzzy random variables abstract in this paper we define the concepts of fuzzy random variable and the expectation of a fuzzy random variable the new definition of expectation generalizes the integral of a set valued function we derive some properties of these new concepts by considering a suitable generalization of the hausdorff metric we derive the lebesgue dominated convergence type theorem

hukuhara derivative of the fuzzy expected value in this paper we establish sufficient conditions to guarantee the exchange of the fuzzy expected value for a fuzzy random variable depending on certain parameter and its hukuhara derivative with respect to the parameter main results are obtained for two different sets of general conditions one of them requiring measurability conditions with respect to the product space the fuzzy random variable is defined from and the second one just requiring conditions over the projections of the fuzzy random variables

the l2 lefschetz numbers of hecke operators introduction 5 1 hecke operators and l2 cohomology 52 the spectral decomposition of cohomology 6 3 application of the trace formula 54 the functions pa t 5 5 proof of theorem 5 1 6 the main formula appendix bibliography

new approach for studying nonlocal problems related to differential systems and partial differential equations in generalized fuzzy metric spaces abstract this study considers the solvability of nonlocal problems for fuzzy differential systems under gh differentiability using some linear transforms we convert partial differential equations into fuzzy integral systems before some similar results are obtained for fuzzy wave equations with nonlocal conditions as a consequence we give some further estimates of the convergence rates of approximation schemes to exact solutions the main tool used in our proofs is based on perov s fixed point principle which is applied to vector valued integral operators these operators appear as the sum of two integral operators where one is fredholm type and the other is of a volterra type that depends on the restriction of the domain the novel feature of this study is that we combine the matrix convergent to zero technique with calculations of fuzzy valued functions in generalized fuzzy metric spaces some examples are presented to demonstrate our theoretical results