structure arising from induction and jacquet modules of representations of classical p adic groups jacquet modules are very useful in the study of parabolically induced representations of reductive groups over a p adic field f we shall assume char f 2 in this paper it is very hard to describe explicitly the structure of jacquet modules of parabolically induced representations particularly in the most interesting cases there exists a description of factors of certain filtrations on them that description was done by j bernstein and a v zelevinsky in bz2 and by w casselman in c in the case of general linear groups the functor of parabolic induction and the jacquet functor induce a structure of z graded hopf algebra on the sum r of grothendieck groups of categories of smooth representations of gl n f s of finite length n 0 z1 the multiplication m r r r is defined using parabolic induction while the comultiplication m r r r is defined in terms of jacquet modules the most interesting part of the structure is the property that m r r r is a ring homomorphism hopf axiom this enables one to compute composition series of parabolically induced representations in a very simple way it is interesting to note that the existence of this strong structure did not have serious impact on the development of the representation theory of gl n f one of the reasons for that may lay in the fact that for gl n f there existed a very powerful theory of gelfandkazhdan derivatives and the main results of z1 were obtained using them nevertheless a v zelevinsky showed in z2 that some interesting parts of the representation theory of gl n over a finite field can be obtained as a structure theory of such hopf algebra defined in this setting besides that one of the main tools for the study of representation theory of gl n over a central division f algebra in t1 is such hopf algebra structure in this situation are not available gelfand kazhdan derivatives it is natural to ask does some structure of this kind exist for other simple split classical p adic groups since levi factors of classical groups are isomorphic to direct products of general linear groups and smaller groups from the same series one can expect for such structure to have some relation with r if it exists in the third section we define the direct sum of grothendieck groups r s which corresponds either to the series sp n f n 0 or so 2n 1 f n 0 in a similar way as r was defined for general linear groups the action of r on r s is defined using the parabolic induction in this way r s becomes z graded r module we can make r s a z graded comodule over r the comodule structure map r s r r s is again defined using the jacquet modules similarly as in the case of gl n f it is not hard to see that r s is not a hopf module over r see remark 7 3 in this paper we

an asymptotic limit law with a singularly perturbed drift and a random noise an asymptotic stochastic initial value problem with a random microscale superposed upon a deterministic macroscale is considered in this article we derive and prove a limit theorem for the random problem with a rapidly varying deterministic component the asymptotic character of the stochastic initial value problem with a small parameter is realized by solving a final value problem of which the infinitesimal generator consists of a singularly perturbed deterministic component and a random fluctuation intensity component we also give an estimate for the error in the asymptotic approximation in terms of the small parameter this abstract limit theorem is reduced to a limit theorem for the stochastic processes solving a system of stochastic differential equations the corresponding infinitesimal generator of the kolmogorov fokker planck equation is obtained in an asymptotic form and demonstrates how an effective driving force couples with a zero mean random perturbation in both drift and diffusion coefficients our theorem provides a characterization of random noise for evanescent waves in a layered random medium

fuzzy inference in a formal theory of semantic equivalence abstract this work shows how ten different fuzzy implication operators together with appropriately corresponding versions of four different rules of inference can be represented within a formal axiomatization of the theory of approximate reasoning the same formalization methods can also be applied to zadeh s notion of semantic entailment as well as to all of the familiar linguistic hedges

membership function as an evaluation abstract after giving an overview of the different kinds of mathematical forms of the membership functions we extract the different demands and determine the rational class of the membership functions from the generalisation of our result we can determine it giving four parameters the internal a b the sharpness and the decision level we show the correspondence of this membership function to the zimmermann zysno model and using their empirical data we also test our mathematical model we also show the connections between the operators of the evaluation and membership functions which gives the generalisation of this concept in a more general form as a special case we can get a linear form

reflection from a one dimensional totally refracting random multilayer ii internal field statistics the modeling of acoustic scattering by ocean sediments has led to the formulation of an idealized one dimensional problem involving the interplay of random scattering and total internal reflection the behavior of the reflection coefficient in the lossless case was discussed in w e kohler reflection from a one dimensional totally refracting multilayer siam j appl math 46 1986 pp 464 482 using the ideas of invariant embedding expressions for the mean field intensities and intensity fluctuations as functions of depth within the sediment layer are now derived

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

on supports of induced representations for symplectic and odd orthogonal groups let g be sp 2 n f resp so 2 n 1 f where f is a p adic field of characteristic zero in this paper we give a correspondence which associates to an irreducible representation of g an m tuple of irreducible representations of lower rank symplectic resp orthogonal groups based on the supercuspidal support of we show that this correspondence respects the induction and jacquet module functors in a sense to be made precise as well as verifying a number of other useful properties in essence this correspondence allows one to isolate the effects of the different families of supercuspidal representations of general linear groups which appear in the support of

strongly positive representations of gspin_ 2n 1 and the jacquet module method we explicitly construct the structure of jacquet modules of parabolically induced representations of gspin 2n 1 over a p adic field f of any characteristic using this construction of the jacquet module we obtain a classification of strongly positive representations of gspin 2n 1 over f and describe the general discrete series representations of gspin 2n 1 over f assuming the half integer conjecture one application of this paper is the proof of the equality of l functions from the langlands shahidi method and artin l functions through the local langlands correspondence kim in langlands shahidi l functions for gspin groups and the generic arthur packet conjecture preprint

on the ramanujan conjecture and finiteness of poles for certain l functions in this paper we prove a number of general results about automorphic l functions which appear in the constant terms of eisenstein series for an arbitrary quasi split connected reductive algebraic group over a number field these l functions were first introduced by langlands for chevalley groups 20 and through them he was led to make some of his deep conjectures 21 one significance of these l functions is that all the automorphic l functions studied so far are among them there are three general results first we obtain a uniform line of absolute convergence for all of these l functions theorem 5 1 a uniform estimate for the hecke eigenvalues of generic cusp forms on many absolutely simple quasi split connected reductive algebraic groups over number fields corollary 5 4 and an improvement on the best available estimate for the fourier coefficients of maass wave forms corollary 5 5 also follow next we establish a meromorphic continuation and functional equation for each of these l functions theorem 6 1 finally in theorem 6 2 we prove finiteness of poles on the whole complex plane for an important class of these l functions corollaries 6 6 through 6 10 more precisely let g be a quasi split connected reductive algebraic group over a number field f set g g a f where a f is the ring of adeles of f fix a borel subgroup b of g over f and let u be its unipotent radical let p be a maximal f parabolic subgroup of g with p d b in the context of the problems studied here nothing new will be obtained if one drops the maximality condition on p write p mn a levi decomposition n c u and let b u p m and n be the corresponding groups of adelic points for every place v of f let gv g fj similarly we have bv us pv me and nv let x xv be a generic character of u f u cf section 3 then each xv is generic let r ov 7tv be a cusp form on m we shall say 7t is

a multiple criteria linguistic decision model mcldm for human decision making abstract this paper presents a human nature like decision model which makes the decision making process easier for human beings the model which is called the multiple criteria linguistic decision model mcldm can be used to evaluate a set of alternatives over various criteria by using linguistic variables and then produces a linguistic decision output for selecting the best alternative the mcldm uses fuzzy set theory fst to deal with the imprecision measurement of decision makers dms subjective opinions which usually exist in the decision making process the decision model is originally designed for the screening of research projects however it can also be applied to problems such as program evaluation project performance evaluation and many other management decisions

on the generic local langlands correspondence for gspin groups in the case of split gspin groups we prove an equality of l functions between automorphic local l functions defined by the langlands shahidi method and local artin l functions our method of proof is based on previous results of the first author which allow to reduce the problem to supercuspidal representations of levi subgroups of gspin by constructing langlands parameters for general generic irreducible admissible representations of gspin from the one for generic irreducible supercuspidal representations of its levi subgroups

caracterisation de la correspondance de langlands locale par les facteurs e de paires soitf un corps local non archimedien a corps residuel fini la conjecture de langlands locale prouvee par laumon rapoport et stuhler quandf est de caracteristique non nulle associe a une classe d isomorphisme de representations irreductibles du groupe de weil def une classe d isomorphisme de representations admissibles irreductibles supercuspidales d un groupe lineaire surf le groupe gl n f si est de dimensionn nous prouvons dans cet appendice qu il existe au plus une telle correspondance qui preserve les facteurs e de paires et coincide en dimension 1 avec l application donnee par la theorie du corps de classes

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

axioms for a theory of semantic equivalence abstract godel type semantic completeness theorems are established for a formal theory of semantic equivalence based on l a zadeh s concept of a linguistic variable the linguistics that is employed allows for the expression of propositions such as it is not the case that young is semantically equivalent with not old or in symbols young x old x the result is a two leveled semantics which at the lower level is a multivalent interpretation of fuzzy assertions e g old x in terms of fuzzy subsets of a given universe and at the upper level is a two valued classical interpretation based on the fact that two closed fuzzy assertions either do or do not have the same truth value the main proof is of the henkin variety employing adaptations of the algebraic methods found in rasiowa 9 and rasiowa and sikorski 10

on an algebraic approach to the zelevinsky classification for classical p adic groups abstract in this paper we classify irreducible admissible representations of p adic classical groups in a purely algebraic way we present a new and simple algorithm for constructing the classifying data which is also useful in other contexts where the computation with jacquet modules or constant terms of eisenstein series appears we construct and study non standard intertwining operators they are defined in a purely algebraic way although their rationality follows from g muic a geometric construction of intertwining operators for reductive p adic groups manuscripta math 125 2008 241 272

on regular square integrable representations of p adic groups we study the problem of construction of noncuspidal irreducible square integrable representations of classical p adic groups and questions related to it starting from cuspidal reducibilities in the generalized rank one case we give a construction of regular irreducible square integrable representations of p adic gsp n sp n and so 2 n 1 under an assumption expected to hold in general we show that all such representations should come from this construction further we obtain a number of general results about places where square integrable representations can appear in parabolically induced representation among others we show that in irreducible cuspidal representations of general linear groups only the self contragredient ones play a role in the construction of square integrable representations of the above groups at the end we use our regular square integrable representations to study some basic properties of whittaker models we also show that there exists nondegenerate standard modules of classical groups which contain degenerate irreducible subrepresentations

applications of langlands functorial lift of odd orthogonal groups together with cogdell piatetski shapiro and shahidi we proved earlier the existence of a weak functorial lift of a generic cuspidal representation of so 2n 1 to gl 2n recently ginzburg rallis and soudry obtained a more precise form of the lift using their integral representation technique namely the lift is an isobaric sum of cuspidal representations of gln i more precisely cuspidal representations of gl2n i such that the exterior square l functions have a pole at s 1 one purpose of this paper is to give a simpler proof of this fact in the case that a cuspidal representation has one supercuspidal component in a separate paper we prove it without any condition using a result on spherical unitary dual due to barbasch and moy we give several applications of the functorial lift first we parametrize square integrable representations with generic supercuspidal support which have been classified by moeglin and tadic second we give a criterion for cuspidal reducibility of supercuspidal representations of gl m x so 2n 1 third we obtain a functorial lift from generic cuspidal representations of so 5 to automorphic representations of gl 5 corresponding to the l group homomorphism sp 4 c gl 5 c given by the second fundamental weight

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

layman s probability theory a calculus for reasoning with linguistic likelihood abstract this paper distinguishes between the task of modeling chance occurrences in the physical world and that of modeling natural human reasoning about such occurrences it is proposed that everyday common sense often prescribes that the probabilistic and which corresponds to the joint probability of physical events should be expressed in terms of the arithmetic min operation and that it is dual the or should be couched in terms of the arithmetic max thus in effect it is proposed that the logic normally associated with the theory of fuzzy sets can be adapted as a kind of layman s probability theory the rationale for such an erroneous model of probability is that such seems to underly natural human decision making in the face of uncertainty in the interests of modeling and to whatever extent possible replicating such decision processes it is of interest to properly encode the underlying logics the crux of the article it to present such an encoding as a new kind of formal logical system for reasoning with linguistic likelihood i e with fuzzy terms such as likely very likely somewhat unlikely etc it is verified that the system allows for semantically coherent expression of the desired probablistic arguments

stochastic turning point problem in a one dimensional refractive random multilayer a one dimensional model of random scattering is considered for a totally refracting random multilayer that has two separated spatial scales i e deterministic macroscale and random microscale the interplay of internal refraction and random multiple scattering for a turning point problem is analyzed with an intermediate scale of the wavelength two extended limit theorems for stochastic differential equations with a small parameter provide the characterization of the diffusion processes above and below the turning point both results are combined and a global limit law for the phenomenon of the random phase is obtained

local coefficients as artin factors for real groups introduction the purpose of this paper is to prove the equality of certain local coefficients of arithmetic significance which were attached to representations of quasi split real reductive algebraic groups in 27 with their corresponding artin factors attached by local class field theory 21 as a consequence we establish an identity satisfied by certain normalized intertwining operators it seems to be useful in applications of the trace formula 1 29 more precisely let g be the group of real points of a quasi split reductive algebraic group over r let a be the set of simple roots defined by a fixed minimal parabolic subgroup po m0a0u of g fix 6 c a and let p p9 be the corresponding standard parabolic subgroup of g and write p man for its langlands decomposition fix a nondegenerate character x f u i a h o be an irreducible admissible x gic banach in particular x generic unitary representation of m cf section 1 given v g a the complex dual of the lie algebra of a let i v o 0 be the continuously quasi unitarily if o is unitary induced representation indp ga e v 9 and let v v o 0 be its space section 0 then f a vfoo o now let w be the weyl group of ao in g choose w g w such that w 0 c a let n be the unipotent group opposite to n define n u c wn w where w is a representative of w in g for g f a 00 define

an asymptotic diffusion limit for electromagnetic wave reflection from a random medium we consider a temporally pulsed electromagnetic wave obliquely incident upon a weakly dispersive and dissipative random multilayer the incident pulse width is chosen to be intermediate to two spatial scales with a deterministic macroscale and a random microscale an asymptotic diffusion limit theory of stochastic differential equations is extended to a noncentered system and applied to analyze the asymptotic interplay of random scattering and total internal reflection the perturbation analysis of the kolmogorov fokker planck equation is performed for the random reflection coefficient and the pseudodifferential operator theory is used to represent the transition probability density of it

on the non unitary unramified dual for classical p adic groups in this paper we give a zelevinsky type classification of unramified irreducible representations of split classical groups

construction of discrete series for classical p adic groups in this paper the authors complete the classification of irreducible square integrable representations of classical p adic groups assuming a natural assumption which is expected to hold in general this classification implies a parameterization of irreducible tempered representations of these groups and it implies a classification of the non unitary duals of these groups modulo cuspidal data

generic transfer for general spin groups we prove langlands functoriality for the generic spectrum of general spin groups both odd and even contrary to other recent instances of functoriality our resulting automorphic representations on the general linear group are not self dual together with cases of classical groups this completes the list of cases of split reductive groups whose l groups have classical derived groups the important transfer from gsp4 to gl4 follows from our result as a special case

strongly positive representations of metaplectic groups abstract in this paper we obtain a classification of irreducible strongly positive square integrable genuine representations of metaplectic groups over p adic fields using a purely algebraic approach our results parallel those of m glin and tadic for classical groups but their work relies on certain conjectures on the other hand our results are complete and there are no additional conditions or hypotheses the important point to note here is that our results and techniques can be used in the case of classical p adic groups in a completely analogous manner