unicity of types for supercuspidal representations of gln let f be a non archimedean local field with the ring of integers mathfrak o f let g mathrm gl n f k mathrm gl n mathfrak o f and pi be a supercuspidal representation of g we show that there exists a unique irreducible smooth representation tau of k such that the restriction to k of a smooth irreducible representation pi of g contains tau if and only if pi is isomorphic to pi otimes chi circ det where chi is an unramified quasicharacter of f times moreover we show that pi contains tau with the multiplicity 1 as a corollary we obtain a kind of inertial local langlands correspondence

a theory of independent fuzzy probability for system reliability fuzzy fault trees provide a powerful and computationally efficient technique for developing fuzzy probabilities based on independent inputs the probability of any event that can be described in terms of a sequence of independent unions intersections and complements may be calculated by a fuzzy fault tree unfortunately fuzzy fault trees do not provide a complete theory many events of substantial practical interest cannot be described only by independent operations thus the standard fuzzy extension based on fuzzy fault trees is not complete since not all events are assigned a fuzzy probability other complete extensions have been proposed but these extensions are not consistent with the calculations from fuzzy fault trees we propose a new extension of crisp probability theory our model is based on n independent inputs each with a fuzzy probability the elements of our sample space describe exactly which of the n input events did and did not occur our extension is complete since a fuzzy probability is assigned to every subset of the sample space our extension is also consistent with all calculations that can be arranged as a fault tree our approach allows the reliability analyst to develop complete and consistent fuzzy reliability models from existing crisp reliability models this allows a comprehensive analysis of the system computational algorithms are provided both to extend existing models and develop new models the technique is demonstrated on a reliability model of a three stage industrial process

fuzzy system reliability analysis based on level λ 1 interval valued fuzzy numbers this study uses level 1 interval valued fuzzy numbers to examine the fuzzy reliability of a serial system and a parallel system and obtain the estimated reliability of both systems in the fuzzy sense

extended deligne lusztig varieties for general and special linear groups abstract we give a generalisation of deligne lusztig varieties for general and special linear groups over finite quotients of the ring of integers in a non archimedean local field previously a generalisation was given by lusztig by attaching certain varieties to unramified maximal tori inside borel subgroups in this paper we associate a family of so called extended deligne lusztig varieties to all tamely ramified maximal tori of the group moreover we analyse the structure of various generalised deligne lusztig varieties and show that the unramified varieties including a certain natural generalisation do not produce all the irreducible representations in general on the other hand we prove results which together with some computations of lusztig show that for sl 2 f q 2 with odd q the extended deligne lusztig varieties do indeed afford all the irreducible representations

the fuzzy decision problem an approach to the problem of testing statistical hypotheses with fuzzy information abstract this paper is devoted to the problems of testing statistical hypotheses about an experiment when the available information from its sampling is vague when the information supplied by the experimental sampling is exact the problems of testing statistical hypotheses about the experiment can be regarded as a particular statistical decision problem in addition decision procedures may be used in problems of testing hypotheses in a similar manner the problem of testing statistical hypotheses about an experiment when the available sample information is vague is approached in this paper as a particular fuzzy decision problem as defined by tanaka okuda and asai this approach assumes that the previous information about the experiment can be expressed by means of certain conditional probabilistic information whereas the present information about it can be expressed by means of fuzzy information the preceding framework allows us to extend the notion of risk function and some nonfuzzy decision procedures to the fuzzy case and particularize them to the problem of testing finally several illustrative examples are presented

a convex concave problem with a nonlinear boundary condition in this paper we study the existence of nontrivial solutions of the problem u u u p 2uin u u q 2uon with 1 q 2 n 1 n 2 and 1 p 2n n 2 in the concave convex case i e 1 q 2 p if is small there exist two positive solutions while for large there is no positive solution when p is critical and q subcritical we obtain existence results using the concentration compactness method finally we apply the implicit function theorem to obtain solutions for small near u0 1

fuzzy system reliability analysis by interval of confidence abstract the use of fuzzy number over interval of confidence instead of probability and possibilitic considerations for evaluating the range value and interval of the fuzzy reliability is proposed this approach of evaluating fuzzy system reliability by interval arithmetic and cuts has a considerable advantage we can calculate reliability problems easily by the use of derive and mathcad packages through theoretical analysis an illustrative example and computational results we show that the proposed approach is more general and simplified

ramified automorphic induction and zero dimensional affine deligne lusztig varieties to any connected reductive group g over a non archimedean local field f and to any maximal torus t of g we attach a family of extended affine deligne lusztig varieties and families of torsors over them over the residue field of f this construction generalizes affine deligne lusztig varieties of rapoport which are attached only to unramified tori of g via this construction we can attach to any maximal torus t of g and any character of t a representation of g this procedure should conjecturally realize the automorphic induction from t to g for g mathrm gl 2 in the equal characteristic case we prove that our construction indeed realizes the automorphic induction from at most tamely ramified tori moreover if the torus is purely tamely ramified then the varieties realizing this correspondence turn out to be quite complicate combinatorial objects they are zero dimensional and reduced i e just disjoint unions of points

existence of infinitely many weak solutions for the p laplacian with nonlinear boundary conditions abstract in this paper we deal with the existence of weak solutions for quasilinear elliptic problem involving a p laplacian of the form p u x u p 2 u f x u in u p 2 u u p 2 u on we consider the above problem under several conditions on f for f superlinear and subcritical with respect to u we prove the existence of infinitely many solutions of the above problem by using the fountain theorem and the dual fountain theorem respectively for the case where f is critical with a subcritical perturbation namely f x u u p 2 u u r 2 u we show that there exists at least a nontrivial solution when p r p and there exist infinitely many solutions when 1 r p by using the mountain pass theorem and the concentration compactness principle respectively

on fuzzy bayesian inference abstract the paper combines methods from bayesian statistics with ideas from fuzzy set theory to generalize bayesian methods both for samples of fuzzy data and for prior distributions with non precise parameters applying the principle of propagation of fuzziness we introduce a fuzzy valued likelihood function bayes theorem for both fuzzy data and fuzzy priors a fuzzy bayes estimator fuzzy predictive densities and distributions and fuzzy h p d regions

bayesian reliability analysis for fuzzy lifetime data lifetime data are important in reliability analysis classical reliability estimation is based on precise lifetime data it is usually assumed that observed lifetime data are precise real numbers however some collected lifetime data might be imprecise and are represented in the form of fuzzy numbers thus it is necessary to generalize classical statistical estimation methods for real numbers to fuzzy numbers bayesian methods have proved to be very useful when the sample size is small there is little study on bayesian reliability estimation based on fuzzy lifetime data most of the reported works in this area is limited to single parameter lifetime distributions in this paper we propose a new method to determine the membership function of the estimates of the parameters and the reliability function of multi parameter lifetime distributions an artificial neural network is used to approximate the calculation process of parameter estimation and reliability prediction the genetic algorithm is used to find the boundary values of the membership function of the estimate of interest at any cut level this method can be used to determine the membership functions of the bayesian estimates of multi parameter distributions the effectiveness of the proposed method is illustrated with normal and weibull distributions

the fuzzy estimators of fuzzy parameters based on fuzzy random variables abstract the concept for fuzzy estimators of fuzzy parameters in fuzzy random variables is proposed in this paper due to the resolution identity the construction of a fuzzy number from a family of closed intervals is developed the construction of the fuzzy estimators of fuzzy parameters from the known conventional estimators inherits evidently from the aforementioned technique in the meantime we prove that the fuzzy estimator is a fuzzy random variable in order to provide the notion of fuzzy expectation and variance of fuzzy estimator the computational procedure is also provided by solving the related nonlinear programming problems that are transformed from the original problem for the purpose of evaluation of the membership values of the fuzzy estimates

representation growth of compact linear groups we study the representation growth of simple compact lie groups and of sln o where o is a compact discrete valuation ring as well as the twist representation growth of gln o this amounts to a study of the abscissae of convergence of the corresponding twist representation zeta functions we determine the abscissae for a class of mellin zeta functions which include the witten zeta functions as a special case we obtain a new proof of the theorem of larsen and lubotzky that the abscissa of witten zeta functions is r where r is the rank and the number of positive roots we then show that the twist zeta function of gln o exists and has the same abscissa of convergence as the zeta function of sln o provided n does not divide char o we compute the twist zeta function of gl2 o when the residue characteristic p of o is odd and approximate the zeta function when p 2 to deduce that the abscissa is 1 finally we construct a large part of the representations of sl2 fq t q even and deduce that its abscissa lies in the interval 1 5 2

multiplicites modulaires et representations de rm gl sb 2 mathbf z sb p et de rm gal overline mathbf q sb p mathbf q sb p en ell p appendice par guy henniart sur l unicite des types pour rm gl sb 2

fuzzy system reliability analysis using fuzzy number arithmetic operations abstract this paper presents a new method to analyze fuzzy system reliability using fuzzy number arithmetic operations where the reliability of each system component is represented by a triangular fuzzy number because the proposed method uses simplified fuzzy arithmetic operations of fuzzy numbers rather than the complicated interval arithmetic operations of fuzzy numbers mentioned by cheng and mon in fuzzy sets and systems 56 1993 29 35 or the complicated extended algebraic operations of fuzzy numbers mentioned by singer in fuzzy sets and systems 34 1990 145 155 its execution is faster than the ones presented by cheng and mon and singer

multiplicity of positive solutions for some quasilinear elliptic equation in rnwith critical sobolev exponent consider the equation pu g x u p 2u f x u p 2u 1 in rn where 1 0 be the principal eigenvalue of pu g x u p 2uinrn rng x u p 0 2 withu 1 0 the associated eigenfunction we prove i equation 1 has at least one positive solution if 0 1 ii suppose rn f x u 1 p 1such that 1 has at least one positive solution for 1 0 moreover ifp 2 there exists 0 1such that 1 has at least two positive solutions for 1 0

a fuzzy set approach to fault tree and reliability analysis abstract conventional fault tree and reliability analysis does not give a picture concerning the tolerances of the probability values of hazards to overcome this shortcoming the relative frequencies of the basic envents are considered as fuzzy numbers using standard approximations for the membership functions n ary possibilistic and or and neg operators are derived allowing a straightforward evaluation of the frequencies of hazard events in complex systems simultaneously with their tolerances the paper shows the use of these operators for constructing possibilistic fault trees the use of the method for numerical calculation is demonstrated on a real like safety problem

combined effects of concave and convex nonlinearities in some elliptic problems abstract this paper deals with a class of semilinear elliptic dirichlet boundary value problems where the combined effects of a sublinear and a superlinear term allow us to establish some existence and multiplicity results

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

multiple positive solutions for a class of concave convex elliptic problems in rn involving sign changing weight in this paper we study the multiplicity of positive solutions for the following concave convex elliptic equation u u f x uq 1 g x up 1in rn u 0in rn u h1 rn where 1 q 2 p 2 2 2nn 2 if n 3 2 if n 1 2 and the parameters 0 we assume that f x f x f x is sign changing and g x a x b x where the functions f a and b satisfy suitable conditions

nehari manifold and existence of positive solutions to a class of quasilinear problems abstract in this paper existence and multiplicity results to the following nonlinear elliptic equation p u u q 2 u u p 2 u u 0 in r n together with mixed dirichlet neumann or neumann boundary conditions are established here p u denotes the p laplacian operator 1 q p n p np n p and is a positive real parameter the study is based on the extraction of palais smale sequences in the nehari manifold

flags and orbits of connected reductive groups over local rings we prove that generic higher deligne lusztig representations over truncated formal power series are non nilpotent when the parameters are non trivial on the biggest reduction kernel of the centre we also establish a relation between the orbits of higher deligne lusztig representations of mathrm sl n and of mathrm gl n then we introduce a combinatorial analogue of deligne lusztig construction for general and special linear groups over local rings this construction generalises the higher deligne lusztig representations and affords all the nilpotent orbit representations and for mathrm gl n it also affords all the regular orbit representations as well as the invariant characters of the lie algebra

system failure engineering and fuzzy methodology an introductory overview abstract system failure engineering may encompass reliability safety security maintainability risk and quality control in this paper we pay a unified view i e a failure oriented view to system failure engineering the notion of failure can be represented in terms of fuzzy sets and widely interpreted we then discuss various application aspects of fuzzy methodology in system failure engineering which include fuzzy methodology in fault diagnosis in probist systems in structural reliability in software reliability in human reliability in safety engineering in security engineering in risk engineering and in quality control as well as profust posbist and posfust reliability theories engineering case studies and mathematical problems raised by applications of fuzzy methodology in system failure engineering are also addressed in this paper

action du groupe des tresses sur une categorie we describe how to define by generators and relations an action of the braid group on a category more generally how to define a functor from a generalized positive braids monoid corresponding to a finite coxeter group to a monoidal category applications to constructions of bondal exceptional systems and of broue michel correspondences on flag manifolds are given

fuzzy universal generating functions for multi state system reliability assessment the paper considers a multi state system mss where performance rates or and corresponding state probabilities are presented as fuzzy values in many real world msss it is difficult to estimate precise values of performance rates and their probabilities because of two main reasons the first reason is inaccuracy and insufficiency of data the second one is based on the fact that msss are often used as the approximation for continuous state systems in order to simplify computational burden to overcome these deficiencies performance rates levels or and corresponding probabilities are considered as fuzzy values in this paper the fuzzy universal generating function fugf is developed to extend the universal generating function with crisp sets the composition operators are extended for fugfs and introduced in more general forms based on this a special technique for reliability assessment of such msss is developed illustrative examples are presented to demonstrate the technique

on the nonlinear neumann problem involving the critical sobolev exponent on the boundary in this paper we investigate the solvability of the neumann problem 1 1 involving the critical sobolev exponents on the right hand side of the equation and in the boundary condition it is assumed that the coefficients q and p are smooth we examine the common effect of the mean curvature of the boundary and the shape of the graph of the coefficients q and p on the existence of solutions of problem 1 1

the nehari manifold for a semilinear elliptic equation with a sign changing weight function abstract the nehari manifold for the equation u x a x u x b x u x 1u x for x together with dirichlet boundary conditions is investigated exploiting the relationship between the nehari manifold and fibrering maps i e maps of the form t j tu where j is the euler functional associated with the equation we discuss how the nehari manifold changes as changes and show how existence and non existence results for positive solutions of the equation are linked to properties of the manifold

a bayesian approach to fuzzy hypotheses testing in statistical decisions we may come across imprecise fuzzy concepts one important case is a situation where we are interested in testing the hypotheses that are fuzzy rather than crisp in this paper we consider and analyze the testing of fuzzy hypotheses on the basis of a bayesian approach we illustrate our method by some examples and compare it with previous works on this topic

existence results for the p laplacian with nonlinear boundary conditions in this paper we study the existence of nontrivial solutions for the problem pu u p 2u in a bounded smooth domain rn with a nonlinear boundary condition given by u p 2 u f u on the boundary of the domain the proofs are based on variational and topological arguments

computer assisted reliability analysis an application of possibilistic reliability theory to a subsystem of a nuclear power plant abstract since the late 1970s multistate structure functions have been introduced to overcome the shortcomings of the classical and binary approach to the structural aspects of systems and their components the uncertainty about the state of a system and its components classically is described by probability theory recently several new models are proposed that are based upon fuzzy set theory and possibility theory the spread and success of these models however highly depend upon the development of computer tools that allow the reliability engineer to apply these new methods rather easily in this paper we present such tool cara computer assisted reliability analysis which is able to represent and study the multistate aspects of systems and their components when only incomplete information is available

reliability and mean time to failure of unrepairable systems with fuzzy random lifetimes in practice the lifetimes of unrepairable systems contain both randomness and fuzziness so it is appropriate to assume the lifetimes of systems to be fuzzy random variables in this paper the definitions of reliability and mean time to failure mttf of unrepairable systems with fuzzy random lifetimes are given respectively then basic mathematical models of unrepairable systems with fuzzy random lifetimes are established furthermore the reliability and mttf of series systems parallel systems series parallel systems parallel series systems and cold standby systems are discussed respectively finally some numerical examples are presented to illustrate how to calculate the reliability and mttf of unrepairable systems with fuzzy random lifetimes

on statistically inference for fuzzy data with applications to descriptive statistics abstract the object of this paper is to discuss how fuzziness of data is propagated when statistical inference for samples of non precise data is carried out first fuzzy data and fuzzy samples are defined subsequently the method of propagation of fuzziness as used in previous work for specific stochastic models is formulated in rather general terms this method may be applied to any statistical method which leads to a result that may be expressed as a function f x 1 x n of the data x 1 x n it is proved that this method is equal to determining the images of a family of compact subsets of the sample space under the function f this equivalence is utilized in order to perform propagation of fuzziness in practice finally this approach is applied to some concepts of descriptive statistics such as fuzzy sample mean fuzzy sample variance and to the empirical distribution function of a fuzzy sample

the nehari manifold for a semilinear elliptic problem with the nonlinear boundary condition abstract using the nehari manifold and fibering maps we prove the existence theorem of the nonlinear boundary problem u u u p 2 u for x u n u q 2 u for x on a bounded domain r n we discuss how the nehari manifold changes as changes and show how the existence of solutions depends on the properties of the nehari manifold

representations of automorphism groups of finite o modules of rank two abstract let o be a complete discrete valuation domain with finite residue field in this paper we describe the irreducible representations of the groups aut m for any finite o module m of rank two the main emphasis is on the interaction between the different groups and their representations an induction scheme is developed in order to study the whole family of these groups coherently the results obtained depend on the ring o in a very weak manner mainly through the degree of the residue field in particular a uniform description of the irreducible representations of gl 2 o p l is obtained where p is the maximal ideal of o

multiple positive solutions for a dirichlet problem involving critical sobolev exponent abstract in this paper we study the decomposition of the nehari manifold via the combination of concave and convex nonlinearities furthermore we use this result and the ljusternik schnirelmann category to prove that the existence of multiple positive solutions for a dirichlet problem involving critical sobolev exponent

on the use of zadeh s probabilistic definition for testing statistical hypotheses from fuzzy information abstract a statistical hypothesis is an assertion about the distribution of an experiment we consider the study of the problem of testing a statistical hypothesis that is the problem of concluding whether or not the hypothesis is correct on the basis of data from the experiment when its outcomes do not provide exact but rather fuzzy information for establishing optimality criteria of testing we will use the definition of probability of a fuzzy event given by zadeh in order to extend both neyman pearson and bayes theories to the fuzzy framework then we will analyze several properties for the new criteria particularly the goodness of optimal procedures in both the fuzzy and the nonfuzzy situation will be compared for each criterion finally we will apply the extended criteria for testing simple hypotheses this application leads us to prefer bayesian procedures to neyman pearson procedures in the fuzzy context

fuzzy variables as a basis for a theory of fuzzy reliability in the possibility context abstract conventional reliability theory is based on the binary state assumption and the probability assumption namely 1 the systems are precisely defined as functioning or failed 2 the system behavior is fully characterized in the context of probability measures however the probability assumption is no longer reasonable in the case of small size of samples since the term probability stems from the sample generality in this way possibility measures should be used to characterize the sample particularity in this paper the binary state assumption is reserved and the possibility assumption is taken in place of the probability assumption thus a concept of fuzzy reliability i e posbist reliability is introduced and a theory of fuzzy reliability i e posbist reliability theory is established various conclusions which are contrary to statements in conventional reliability theory i e probist reliability theory are then drawn

a general formal approach for fuzzy reliability analysis in the possibility context abstract in this paper we focus on the fuzzy reliability analysis in the posbist reliability theory in accordance with this theory the system failure state is defined precisely and the system failure and repair behaviour is fully characterized in the context of possibility measures to formalize the reliability analysis in the posbist theory we propose a general approach on the basis of a system of functional equations the solution of the system allows us to obtain fuzzy reliability characteristics of the arbitrary repairable and unrepairable systems to illustrate the construction and application of the system of functional equations various examples are given

affine deligne lusztig varieties of higher level and the local langlands correspondence for gl2 abstract in the present article we define coverings of affine deligne lusztig varieties attached to a connected reductive group over a non archimedean local field in the case of gl 2 and positive characteristic the unramified cuspidal part of the local langlands correspondence is realized in the l adic cohomology of these varieties we show this by giving a detailed comparison with the realization of local langlands via cuspidal types by bushnell henniart all proofs are purely local

a fuzzy set approach for event tree analysis the traditional event tree analysis uses a single probability to represent each top event however it is unrealistic to evaluate the occurrence of each event by using a crisp value without considering the inherent uncertainty and imprecision a state has the fuzzy set theory is universally applied to deal with this kind of phenomena the main purpose of this study is to construct an easy method to evaluate human errors and integrate them into event tree analysis by using fuzzy concepts a systematic fuzzy event tree analysis algorithm is developed to evaluate the risk of a large scale system a practical example in a nuclear power plant is used to demonstrate this procedure

an extension of bruhat s lemma abstract in recent work of lusztig and he g lusztig parabolic character sheaves i mosc math j 4 2004 153 179 g lusztig parabolic character sheaves ii mosc math j 4 2004 869 896 x he unipotent variety in the group compactification adv math 203 2006 109 131 x he the g stable pieces of the wonderful compactification trans amer math soc in press certain decompositions are introduced in the wonderful compactification of an adjoint group g to establish them a combinatorial machinery introduced by bedard is used the present note gives another approach to these results we derive them in section 3 from a result about g an analogue of bruhat s lemma proved in section 2 see theorem 2 6 basic in our approach is the elementary lemma 1 6 the approach can also be used to deal with properties of lusztig s parabolic character sheaves we do not go into this here

three positive solutions for dirichlet problems involving critical sobolev exponent and sign changing weight abstract in this paper we study the decomposition of the nehari manifold via the combination of concave and convex nonlinearities furthermore we use this result and the lusternik schnirelman category to prove that a semilinear elliptic equation involving a sign changing weight function has at least three positive solutions

an approach to human reliability on man machine systems using error possibility abstract this paper is concerned with proposing the concept error possibility instead of the error rate and presenting a method of fault tree analysis of human errors based on this concept the dependence between consecutive human tasks is considered as a fuzzy causal relation human reliability is defined as the evaluation of the error possibility from several points of view 1 the likelihood of error which gives the maximal grade of membership 2 potentiality for error 3 fuzziness of error possibility and 4 importance of a basic event as an illustrative example the emergency tasks in blackout at a pwr plant are shown and the fault tree concerning the error of these tasks is analyzed it is shown that the proposed method gives us information as well