eigenvalues of an elliptic system we describe the spectrum of a non self adjoint elliptic system on a finite interval under certain conditions we find that the eigenvalues form a discrete set and converge asymptotically at infinity to one of several straight lines the eigenfunctions need not generate a basis of the relevant hilbert space and the larger eigenvalues are extremely sensitive to small perturbations of the operator we show that the leading term in the spectral asymptotics is closely related to a certain convex polygon and that the spectrum does not determine the operator up to similarity two elliptic systems which only differ in their boundary conditions may have entirely different spectral asymptotics while our study makes no claim to generality the results obtained will have to be incorporated into any future general theory

cuspidal ell modular representations of p adic classical groups for a classical group over a non archimedean local field of odd residual characteristic p we construct all cuspidal representations over an arbitrary algebraically closed field of characteristic different from p as representations induced from a cuspidal type we also give a fundamental step towards the classification of cuspidal representations identifying when certain cuspidal types induce to equivalent representations this result is new even in the case of complex representations finally we prove that the representations induced from more general types are quasi projective a crucial tool for extending the results here to arbitrary irreducible representations

intertwining and supercuspidal types for p adic classical groups let f be a non archimedean local field of residual characteristic different from 2 and let g be a unitary symplectic or orthogonal group considered as the fixed point subgroup in gl n f of an involution s we generalize the notion of a simple character for which was introduced by bushnell and kutzko annals of mathematics studies 129 princeton university press 1993 to define semisimple characters given a semisimple character for fixed by s we transfer it to a character for g and calculate its intertwining if the torus associated to is maximal compact we obtain supercuspidal representations of g which are new if the torus is split only over a wildly ramified extension

hecke algebras of classical groups over p adic fields and supercuspidal representations let k be a p adic field with involution 0 and let k 0 be its fixed subfield of k let v be a finite dimensional vector space defined over k equipped with e hermitian form v k 0 is large

an interactive possibilistic programming approach for multiple objective supply chain master planning providing an efficient production plan that integrates the procurement and distribution plans into a unified framework is critical to achieving competitive advantage in this paper we consider a supply chain master planning model consisting of multiple suppliers one manufacturer and multiple distribution centers we first propose a new multi objective possibilistic mixed integer linear programming model mopmilp for integrating procurement production and distribution planning considering various conflicting objectives simultaneously as well as the imprecise nature of some critical parameters such as market demands cost time coefficients and capacity levels then after applying appropriate strategies for converting this possibilistic model into an auxiliary crisp multi objective linear model molp we propose a novel interactive fuzzy approach to solve this molp and finding a preferred compromise solution the proposed model and solution method are validated through numerical tests computational results indicate that the proposed fuzzy method outperforms other fuzzy approaches and is very promising not only for solving our problem but also for any molp model especially multi objective mixed integer models

spectral properties of matrices associated with some directed graphs we study the spectral properties of certain non self adjoint matrices associated with large directed graphs asymptotically the eigenvalues converge to certain curves apart from a finite number that have limits not on these curves

inverse eigenvalue problems on directed graphs the differential operators id and d2 p are constructed on certain finite directed weighted graphs two types of inverse spectral problems are considered first information about the graph weights and boundary conditions is extracted from the spectrum of d2 second the compactness of isospectral sets for d2 p is established by computation of the residues of the zeta function

vendor selection problem by using an interactive fuzzy multi objective approach with modified s curve membership functions in this paper the vendor selection vs problem with fuzzy goals is considered an interactive method is developed for solving multi objective vs problems where fuzzy data are represented by using s curve membership functions the proposed method attempts simultaneously to minimize the total order costs the number of rejected items and the number of late delivered items with reference to several constraints such as meeting buyers demand vendors capacity vendors quota flexibility vendors allocated budget etc an interactive solution methodology is proposed to solve the multi objective vs problem and to find a preferred compromise solution moreover the performance of s curve membership functions that represent uncertainty goals and constraints in vs problems with linear membership functions in an industrial case is compared

possibilistic linear programming for managing interest rate risk abstract in this study we consider the linear programming problem with the objective of the investment discounted value where the interest rate is imprecise and has a triangular possibilistic distribution an crisp auxiliary bi objective linear programming model is proposed to resolve this possibilistic nature furthermore we develop an extended zimmermann approach called augmented max min approach for solving this auxiliary bi objective linear programming problem and other multiple objective linear programming problems finally a numerical bank balance sheet problem where interest rates price of futures contract loan demand deposit supply and ratio of desired loan to deposit are assumed to be fuzzy is solved for illustrating the new approach

a two phase possibilistic linear programming methodology for multi objective supplier evaluation and order allocation problems in this study an integration of the analytic hierarchy process ahp and a multi objective possibilistic linear programming moplp technique is developed to account for all tangible intangible quantitative and qualitative factors which are used to evaluate and select suppliers and to define the optimum order quantities assigned to each a multi objective linear programming technique is first employed to solve the problem to model the uncertainties encountered in the integrated supplier evaluation and order allocation methodology fuzzy theory is adopted hence possibilistic linear programming plp is proposed for solving the problem as it is believed to be the best approach for absorbing the imprecise nature of the real world in the supplier evaluation phase environmental criteria are also considered

construction of tame supercuspidal representations the notion of depth is defined by moy prasad mp2 the notion of a generic character will be defined in 9 when g gln or g is the multiplicative group of a central division algebra of dimension n with n p 1 our generic characters are just the generic characters in my where the definition is due to kutzko moreover in these cases our construction literally specializes to howe s construction as formulated in my and it is known that the construction yields all supercuspidal representations my hm notice that the initial datum in our construction consists of very simple objects linear characters and supercuspidal representations of depth zero the latter are well understood by the work of moy prasad and morris see 3 by the work of howe irreducible supercuspidal representations of gln f with n p 1 are parametrized by certain characters of e as e varies through

spectra of a class of non self adjoint matrices we consider a new class of non self adjoint matrices that arise from an indefinite self adjoint linear pencil of matrices and obtain the spectral asymptotics of the spectra as the size of the matrices diverges to infinity we prove that the spectrum is qualitatively different when a certain parameter c equals 0 and when it is non zero and that certain features of the spectrum depend on diophantine properties of c

an interactive fuzzy satisficing method for multiobjective linear fractional programming problems abstract we present a new interactive fuzzy decision making method for solving multiobjective linear fractional programming problems by assuming that the decision maker dm has fuzzy goals for each of the objective functions through the interaction with the dm the fuzzy goals of the dm are quantified by eliciting the corresponding membership functions including nonlinear functions after determining the membership functions if the dm specifies reference membership values the minimax problem is solved by combined use of the bisection method and the linear programming method and the dm is supplied with the corresponding pareto optimal solution together with the trade off rates between the membership functions then by considering the current values of the membership functions as well as the trade off rates the dm responds by updating his her reference membership values in this way the compromise or satisficing solution for the dm can be derived efficiently from among a pareto optimal solution set by updating his her reference membership values on the basis of the proposed method a time sharing computer program is written and an illustrative numerical example is demonstrated along with the computer outputs

semisimple types for p adic classical groups we construct for any symplectic unitary or special orthogonal group over a locally compact nonarchimedean local field of odd residual characteristic a type for each bernstein component of the category of smooth representations using bushnell kutzko s theory of covers moreover for a component corresponding to a cuspidal representation of a maximal levi subgroup we prove that the hecke algebra is either abelian or a generic hecke algebra on an infinite dihedral group with parameters which are at least in principle computable via results of lusztig in an appendix we make a correction to the proof of a result of the second author that every irreducible cuspidal representation of a classical group as considered here is irreducibly compactly induced from a type

the supercuspidal representations of p adic classical groups let g be a unitary symplectic or special orthogonal group over a locally compact non archimedean local field of odd residual characteristic we construct many new supercuspidal representations of g and bushnell kutzko types for these representations moreover we prove that every irreducible supercuspidal representation of g arises from our constructions

supercuspidal representations an exhaustion theorem let be a reductive adic group we prove that all supercuspidal representations of arise through yu s construction subject to certain hypotheses on depending on as a corollary under the same hypotheses we see that any supercuspidal representation is compactly induced from a representation of an open subgroup which is compact modulo the center

soft sensing of level of satisfaction in toc product mix decision heuristic using robust fuzzy lp product mix decision through theory of constraints toc should take into account considerations like the decision maker s dm level of satisfaction in order to make product mix decision a robust one sensitivity of the decision made needs to be focused for a bottle neck free optimal product mix solution of toc problem a membership function mf has been suitably designed in the present work first in finding out the degree of imprecision in the product mix decision and thereafter to sense the level of satisfaction of the dm inefficiency of traditional linear programming lp in handling multiple bottleneck problem through toc has been discussed through an illustrative example comparison of traditional lp over fully fuzzified lp flp model has also been addressed to elucidate the advantages of flp in toc key objective of this work is to guide dms in finding out the optimal product mix with higher degree of satisfaction with lesser degree of fuzziness under tripartite fuzzy environment

semisimple characters for p adic classical groups let g be a unitary symplectic or orthogonal group over a non archimedean local field of residual characteristic different from 2 considered as the fixed point subgroup in a general linear group of an involution following previous work of bushnell and kutzko and of the author we generalize the notion of a semisimple character for and for g in particular following the formalism of bushnell and henniart we show that these semisimple characters have certain functorial properties finally we show that any positive level supercuspidal representation of g contains a semisimple character

on the hecke algebra of a type for unramified p adic unitary groups abstract let f be a non archimedean local field of odd residue characteristic equipped with a galois involution with fixed field f 0 and let g be a symplectic group over f or an unramified unitary group over f 0 for a simple type j p p in g which is a g cover associated to a certain simple stratum we show that the corresponding hecke algebra h g p is generic

a construction of the supercuspidal representations of _ adic let f be a nondiscrete locally compact non archimedean field in this paper we construct all irreducible supercuspidal representations of g gl n f for each such representation which we may as well assume is unitary we give a subgroup j of g that is compact mod the center z of g and a finite dimensional representation of j such that inducing to g gives the proof that all supercuspidals have been constructed appeals to a theorem the matching theorem that has been proved by global methods

non l r type fuzzy parameters in mathematical programming problems the triangular norm based operations in fuzzy logic usually lead to non l r type fuzzy sets this study considers mathematical programming problems with non l r type fuzzy parameters it shows that the fuzzy solutions to such problems can be obtained by solving an optimization problem on a mixed domain the necessary and sufficient conditions for solving the resulting optimization problems are investigated by employing the theory of convex optimization on mixed domains this is the first attempt to solve the fuzzy optimization problem with non l r type membership functions in view of optimization problems on a mixed domain

linear programming with multiple fuzzy goals abstract this paper describes the use of fuzzy set theory in goal programming gp problems in particular it is demonstrated how fuzzy or imprecise aspirations of the decision maker dm can be quantified through the use of piecewise linear and continuous functions models are then presented for the use of fuzzy goal programming with preemptive priorities with archimedean weights and with the maximization of the membership function corresponding to the minimum goal examples are also provided

unrefined minimal k types for p adic groups via their restriction to compact open subgroups was begun by mautner shalika and tanaka for groups of type ai in contrast to real reductive groups where the representation theory of a maximal compact subgroup k is given in terms of slight modifications to cartan s theory of the highest weight the representation theory of a compact parahoric subgroup is quite complicated there is still no comprehensive theory for classifying the irreducible representa tions in the case of