induction of fuzzy rules and membership functions from training examples abstract most fuzzy controllers and fuzzy expert systems must predefine membership functions and fuzzy inference rules to map numeric data into linguistic variable terms and to make fuzzy reasoning work in this paper we propose a general learning method as a framework for automatically deriving membership functions and fuzzy if then rules from a set of given training examples to rapidly build a prototype fuzzy expert system based on the membership functions and the fuzzy rules derived a corresponding fuzzy inference procedure to process inputs is also developed

learning rules for a fuzzy inference model abstract the problem of learning rules for a fuzzy inference model directly from empirical observations without resorting to assessments from experts is considered we develop a method that builds uncertain rules from a set of examples these rules match the following pattern if x then y is b is where a and b are fuzzy sets representing fuzzy restrictions on the variables x and y and are real numbers expressing lower and upper degrees of certainty in the truth of the rule the method is based on the minimization of a distance measure between the real output associated to a given input and the output predicted by the inference model using a parameterized version of the same rule to be learnt our approach is computationally efficient in running time as well as in storage requirements moreover it can be used in both training batch processing and adaptation iterative processing modes of learning

philos type oscillation criteria for linear differential equations with impulsive effects abstract the present paper deals with the problem of oscillation for a second order linear differential equation in which an impulsive effect is considered this equation can be regarded as an equation of motion in which the moving speed of a mass point changes sharply by some influence it is proved that there is a case that the mass point may oscillate due to the influence of the impulsive effect even if the mass point does not oscillate in the model removing the impulsive effect it is also shown that the obtained results extend some previous ones through the use of an example

fuzzy transform and least squares approximation analogies differences and generalizations investigating the relations between the least squares approximation techniques and the fuzzy transform in this paper we show that the discrete fuzzy transform is invariant with respect to the interpolating and least squares approximation additionally the fuzzy transform is evaluated at any point by simply resampling the continuous approximation underlying the input data using numerical linear algebra we also derive new properties e g stability to noise additivity with respect to the input data and characterizations e g radial and dual membership maps of the discrete fuzzy transform finally we define the geometry and confidence driven discrete fuzzy transforms which take into account the intrinsic geometry and the confidence weights associated to the data

variations of mass formulas for definite division algebras abstract the aim of this paper is to organize some known mass formulas arising from a definite central division algebra over a global field and to deduce some more new ones

nonlinear functionals and a theorem of sun we use a recently developed theory of nonlinear functionals in the study of oscillations of second order symmetric vector differential systems to extend a number of theorems of sun new kamenev type theorems for second order linear matrix differential systems appl math lett 2004 in press under a common theme the criteria presented here are of the form the integral of the coefficient matrix is bounded at infinity in a sense to be made explicit in the paper and bounded away from a positive absolute constant implies oscillation at infinity

data mining by attribute generalization with fuzzy hierarchies in fuzzy databases in this paper we examine the soft computing issues involving data generalization on fuzzy information the attribute induction process is formalized for these three cases crisp hierarchy fuzzy data fuzzy hierarchy crisp data fuzzy hierarchy fuzzy data each case is exemplified by applications of the algorithm to a prototype database

on kamenev type oscillation theorems for second order differential equations with damping abstract oscillation criteria for the nonlinear second order ordinary differential equation with damping x p t x f x 0 are given the results are extensions of integral averaging technique of kamenev and include earlier results of yeh yan and chen

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

integral inequalities and second order linear oscillation on the interval 0 a u 0 below by a solution we mean a non trivial solution a solution is oscillatory if it has an infinite number of zeros numerous oscillation criteria are known and diversified approaches have proved fruitful among these is the use of the associated riccati equation although the theory of differential and integral inequalities has been used by some investigators see e g hartman 4 71 the authors believe that it has not been fully exploited the non oscillation of 1 1 is equivalent to the existence of a solution of the associated riccati equation on a half line thus one technique of proving oscillation is to show that any solution of the riccati equation diverges to i co at a finite point the theory of differential and integral inequalities comes in handy in the estimation of the growth of such a solution below we describe some known results that are relevant to results established in this paper although these are stated here for the case i co in the rest of the paper we consider both cases a 0 and a 00 it is well known that if q is large in the mean then 1 1 is oscillatory a typical example of such a criterion is due to fite leighton and wintner if

mining association rules from imprecise ordinal data categorical data can generally be classified into ordinal data and nominal data although there have been numerous studies on finding association rules from nominal data few have tried to do so from ordinal data additionally previous mining algorithms usually assume that the input data is precise and clean which is unrealistic in practical situations real world data tends to be imprecise due to human errors instrument errors recording errors and so on therefore this paper proposes a new approach to discovering association rules from imprecise ordinal data experimental results from the survey data show the feasibility of the proposed mining algorithm performance analyses of the algorithms also show that the proposed approach can discover interesting and valuable rules that could never be found using the conventional approach the apriori algorithm

on some properties of solution of second order nonlinear differential equations on etudie le comportement oscillatoire des solutions de l equation differentielle non lineaire d ordre 2 sur t 0 a t x x q t f x t

interval criteria for oscillation of second order linear ordinary differential equations abstract new oscillation criteria are established for the equation py qy 0 that are different from most known ones in the sense that they are based on the information only on a sequence of subintervals of t 0 rather than on the whole half line our results are more natural according to the sturm separation theorem and sharper than some previous results and can be applied to extreme cases such as t 0 q t dt

weighted means and oscillation conditions for second order matrix differential equations on considere le systeme d equations differentielles d ordre 2 p t y t q t y t 0 pour t 0 ou p et q sont des matrices symetriques n n reelles sur 0 et y un vecteur colonne on suppose que p t est definie positive pour tout t tel que p t 1 on donne des conditions d oscillations

group schemes and local densities the subject matter of this paper is an old one with a rich history beginning with the work of gauss and eisenstein maturing at the hands of smith and minkowski and culminating in the fundamental results of siegel more precisely if l is a lattice over z for simplicity equipped with an integral quadratic form q the celebrated smith minkowski siegel mass formula expresses the total mass of l q which is a weighted class number of the genus of l q as a product of local factors these local factors are known as the local densities of l q subsequent work of kneser tamagawa and weil resulted in an elegant formulation of the subject in terms of tamagawa measures in particular the local density at a non archimedean place p can be expressed as the integral of a certain volume form ld over autzp l q which is an open compact subgroup of autqp l q the question that remains is whether one can find an explicit formula for the local density through the work of pall for p 6 2 and watson for p 2 such an explicit formula for the local density is in fact known for an arbitrary lattice over zp see p and wa the formula is obviously structured though cs seems to be the first to comment on this unfortunately the known proof as given in p and k does not explain this structure and involves complicated recursions on the other hand conway and sloane cs 13 have given a heuristic explanation of the formula in this paper we will give a simple and conceptual proof of the local density formula for p 6 2 the view point taken here is similar to that of our earlier work ghy and the proof is based on the observation that there exists a smooth affine group scheme g over zp with generic fiber autqp l q which satisfies g zp autzp l q this follows from general results of smoothening blr as we explain in section 3 for the purpose of obtaining an explicit formula it is necessary to have an explicit construction of g the main contribution of this paper is to give such an explicit construction of g in section 5 and to determine its special fiber in section 6 finally by comparing ld and the canonical volume form can of g we obtain the explicit formula for the local density in section 7 the smooth group schemes constructed in this paper should also be of independent interest

finding relevant attributes and membership functions fuzzy systems that automatically derive fuzzy if then rules from numeric data have been developed most have to predefine membership functions in order to learn hong and lee proposed a general learning method that automatically derives fuzzy if then rules and membership functions from a set of given training examples using a decision table all available attributes were included in the decision table and the initial membership functions for each attribute were built according to the predefined smallest unit although hong and lee s method accurately derives the fuzzy if then rules and final membership functions the decision table and the initial membership functions are complex if there are many attributes or if the predefined unit is small we improve hong and lee s method by first selecting relevant attributes and building appropriate initial membership functions these attributes and membership functions are then used in a decision table to derive final fuzzy if then rules and membership functions experimental results on iris data show that the proposed method effectively induces membership functions and fuzzy if then rules

a fuzzy inductive learning strategy for modular rules abstract in real applications data provided to a learning system usually contain linguistic information which greatly influences concept descriptions derived by conventional inductive learning methods the design of learning methods to learn concept descriptions in working with vague data is thus very important in this paper we apply fuzzy set concepts to machine learning to solve this problem a fuzzy learning algorithm based on the maximum information gain is proposed to manage linguistic information the proposed learning algorithm generates fuzzy rules from soft instances which differ from conventional instances in that they have class membership values experiments on the sports and the iris flower classification problems are presented to compare the accuracy of the proposed algorithm with those of some other learning algorithms experimental results show that the rules derived from our approach are simpler and yield higher accuracy than those from some other learning algorithms

a note on the continuity of solutions of parametric linear programs this note shows that if a parametric linear program min cx ax b1 b2 x 0 has optimal solutions in an interval left underset raise0 3em hbox smash scriptscriptstyle theta bar theta right for then depending on degeneracy the solutions is a continuous vector function or a continuous point to set mapping in the latter case an algorithm is introduced to solve the problem and generate a continuous vector solution in left underset raise0 3em hbox smash scriptscriptstyle theta bar theta right

oscillation results for selfadjoint differential systems abstract we consider the second order differential system 1 r t y q t y 0 where r q y are n n matrices with r t q t symmetric and r t positive definite for t a r t 0 t a we establish sufficient conditions in order that all prepared solutions y t of 1 are oscillatory that is det y t vanishes infinitely often on a the conditions involve the smallest and largest eigen values n r 1 t and 1 a t q s ds respectively the results obtained can be regarded as generalizing well known results of leighton and others in the scalar case

linearization of second order nonlinear oscillation theorems the problem of oscillation of super and sublinear emden fowler equations is studied established are a number of oscillation theorems involving comparison with related linear equations recent results on linear oscillation can thus be used to obtain interesting oscillation criteria for nonlinear equations 25 references

an inductive learning procedure to identify fuzzy systems abstract in many real cases a system may not be described by a functional input output description and the only way to describe it is through a finite set of fuzzy rules even in some cases where exact identification is possible looking for that rule description may be useful for the sake of ease and effectiveness the automatic identification of a system through the analysis of an input output data set is the aim of this work in order to identify a system from raw data obtained in repeated instances of its own system the frequency of appearance of some kind of patterns may be particularly interesting nevertheless when the base domain is fuzzy and the data can be crisp statistical methods are not very appropriate and it is necessary to study a new model for frequencies on fuzzy domains the proposed model for identifying systems is based on this definition

oscillation criteria of second order nonlinear matrix differential systems in this paper the second order nonlinear matrix differential systems p t y t f t y t y t 0 t t 0is considered where p t y t and f t y t y t are nxn real continuous matrix functions and p t 0 are positive definite and symmetric one some new oscillation criteria for the systems are established and some known results in the literature are improved and generalized

fuzzy data mining for interesting generalized association rules due to the increasing use of very large databases and data warehouses mining useful information and helpful knowledge from transactions is evolving into an important research area most conventional data mining algorithms identify the relationships among transactions using binary values and find rules at a single concept level transactions with quantitative values and items with hierarchy relation are however commonly seen in real world applications in this paper we thus introduce the problem of mining fuzzy generalized association rules from quantitative data a fuzzy mining algorithm based on srikant and agrawal s method is proposed for extracting implicit generalized knowledge from transactions stored as quantitative values it integrates fuzzy set concepts and generalized data mining technologies to achieve this purpose items in rules may be from any level of the given taxonomy the effect of numbers of fuzzy regions on the performance of the proposed algorithm is also discussed

an application of integral inequality to second order nonlinear oscillation abstract a simple result concerning integral inequalities enables us to give an alternative proof of waltman s theorem lim t t 0 a s ds implies oscillation of the second order nonlinear equation y t a t f y t 0 to prove an analog of wintner s theorem that relates the nonoscillation of the second order nonlinear equations to the existence of solutions of some integral equations assuming that lim t t 0 a s ds exists and to give an alternative proof and to extend a result of butler an often used condition on the coefficient a t is given a more familiar equivalent form and an oscillation criterion involving this condition is established

processing individual fuzzy attributes for fuzzy rule induction fuzzy systems that can automatically derive fuzzy if then rules and membership functions from numeric data have recently been developed in this paper we propose two new fuzzy learning methods for automatically deriving membership functions and fuzzy if then rules from a set of given training examples the proposed methods first select relevant attributes and build appropriate initial membership functions they then simplify the intervals and the membership functions of each attribute before forming a decision table these attributes and membership functions are then used in a decision table to derive the final fuzzy if then rules and membership functions experimental results for the iris data show that our methods can achieve a high degree of accuracy the proposed methods are thus useful in constructing membership functions and in managing uncertainty and vagueness they can also reduce the time and effort needed to develop a fuzzy knowledge base

from crispness to fuzziness three algorithms for soft sequential pattern mining most real world databases consist of historical and numerical data such as sensor scientific or even demographic data in this context classical algorithms extracting sequential patterns which are well adapted to the temporal aspect of data do not allow numerical information processing therefore the data are pre processed to be transformed into a binary representation which leads to a loss of information fuzzy algorithms have been proposed to process numerical data using intervals particularly fuzzy intervals but none of these methods is satisfactory therefore this paper completely defines the concepts linked to fuzzy sequential pattern mining using different fuzzification levels we propose three methods to mine fuzzy sequential patterns and detail the resulting algorithms speedyfuzzy minifuzzy and totallyfuzzy finally we assess them through different experiments thus revealing the robustness and the relevancy of this work

induction of fuzzy decision trees abstract most decision tree induction methods used for extracting knowledge in classification problems do not deal with cognitive uncertainties such as vagueness and ambiguity associated with human thinking and perception in this paper cognitive uncertainties involved in classification problems are explicitly represented measured and incorporated into the knowledge induction process a fuzzy decision tree induction method which is based on the reduction of classification ambiguity with fuzzy evidence is developed fuzzy decision trees represent classification knowledge more naturally to the way of human thinking and are more robust in tolerating imprecise conflict and missing information

haar measure and the artin conductor let g be a connected reductive group defined over a local non archimedean field k the group g k is locally compact and unimodular in gr a haar measure g was defined on g k using the theory of bruhat and tits in this note we give another construction of the measure g using the artin conductor of the motive m of g over k the equivalence of the two constructions is deduced from a result of prasad p 1 the root datum and motive of g in this section k is an arbitrary field and g is a connected reductive group over k we let k be an algebraic closure of k ks the separable closure of k in k and gal ks k let t b g be a maximal torus contained in a borel subgroup defined over ks let g b t be the based root datum defined by this choice we recall cf sp pg3 12 that x t t b x t t b 1 1 with x t and x t the character and cocharacter groups of t respectively and and the simple roots and coroots determined by b respectively let w ng t t be the weyl group of the finite group w acts as automorphisms of x t and is generated by the reflections s x x x 1 2 for the galois group acts as automorphisms of ie as automorphisms of the group x t preserving the finite set as follows if then we can find g g ks such that int g t g t g t and int g b g b g b with g well defined up to left multiplication by t ks hence it induces a well defined automorphism x t x t date 14th january 1997 1 2 benedict h gross and wee teck gan preserving hence we get a group homomorphism aut via acts on aut by inner automorphisms similarly if f g g is any automorphism of g over ks it induces an automorphism f of which depends only on the image of f in the quotient group outks g of outer automorphisms the resulting map outks g aut is an isomorphism which respects the respective galois actions on the two groups cf sp pg10 the galois group also acts on w via the formula s s 1 3 and the semi direct product w acts on the rational vector space e x t q 1 4 let r sym e w which is a graded q module let r be the ideal of elements of positive degree in r and define v r r 2 d 1vd 1 5 this is a graded q module and chevalley proved that dim v dim e cf ch steinberg extended the proof to show that e and v are isomorphic modules cf st pg22 we sketch a proof of this result that does not involve the classification of irreducible root systems proposition 1 6 the q modules e and v are isomorphic proof by the criterion in se pg 104 it suffices to show that for all the fixed spaces e and v have the same dimension for any graded module a am we define the poincare series of by p a t tr am t then p a b p a p b steinberg showed that there is an isomorphism of graded modules s e s vd a here a is finite dimensional with basis bw w w and action given by bw b w the degree of bw is the length l w of w with respect to the generators s furnished by this isomorphism yields the following identity of poincare series det 1 t e d 1 det 1 t vd

a fuzzy rule based approach for screening international distribution centres in practical situations a decision maker often has to deal with numerous alternatives in evaluating and selecting the most suitable international distribution centre idc location for enhancing the organizational competitiveness to improve the effectiveness of the decision making process it is critical to reduce the number of alternatives through screening so that the decision maker can focus on the most attractive alternatives for further consideration this paper presents a fuzzy rule based approach to effectively screen decision alternatives in adequately solving the problem of evaluating and selecting idc locations case based reasoning with the use of fuzzy production rules is adopted to screen out unattractive alternatives based on past experience in a specific decision making situation a decision support system based on the proposed approach is presented to improve the effectiveness of the screening process an example is given to demonstrate the applicability of the proposed approach in improving the effectiveness of the decision making process in multicriteria decision making

riccati techniques and variational principles in oscillation theory for linear systems on etablit des conditions suffisantes pour que toutes les solutions soient oscillatoires on utilise les techniques de riccati et les principes variationnels

epipelagic l packets and rectifying characters we provide an explicit construction of the local langlands correspondence for general tamely ramified reductive p adic groups and a class of wildly ramified langlands parameters furthermore we verify that our construction satisfies many expected properties of such a correspondence more precisely we show that each l packet we construct admits a parameterization in terms of the langlands dual group contains a unique generic element for a fixed whittaker datum satisfies the formal degree conjecture is compatible with central and cocentral characters provides a stable virtual character and satisfies the expected endoscopic character identities moreover we show that in the case of mathrm gl n our construction coincides with the established local langlands correspondence our techniques provide a general approach to the construction of the local langlands correspondence for tamely ramified groups and regular supercuspidal parameters

oscillation of two dimensional linear second order differential systems abstract this article is concerned with the oscillatory behavior at infinity of the solution y a r 2 of a system of two second order differential equations y t q t y t 0 t a q is a continuous matrix valued function on a whose values are real symmetric matrices of order 2 it is shown that the solution is oscillatory at infinity if the largest eigenvalue of the matrix at q s ds tends to infinity as t this proves a conjecture of d hinton and r t lewis rocky mountain j math 10 1980 751 766 for the two dimensional case furthermore it is shown that considerably weaker forms of the condition still suffice for oscillatory behavior at infinity

oscillation criteria for second order linear differential equations abstract some oscillation criteria are given for the second order linear differential equation r t u t c t u t 0 where r t c 1 t 0 0 and c t c t 0 r these results improve oscillation criteria of wintner hartman kamenev yan and philos by using a generalized riccati transformation t a t r t u t u t f t where f c 1 is a given function on t 0 and a t exp 2 t f s ds

interval oscillation of a general class of second order nonlinear differential equations with nonlinear damping abstract the paper is concerned with the oscillation of a class of general type second order differential equations with nonlinear damping terms several new interval oscillation criteria are established for such a class of differential equations under quite general assumptions examples are also given to illustrate the results in particular it is shown that under some very mild conditions on k 1 k 2 and f the equation k 1 x x cos tk 2 x x x sin tf x 0 is oscillatory which extends the result obtained by kwong and wong j math anal appl 288 2003 15

developing an efficient knowledge discovering model for mining fuzzy multi level sequential patterns in sequence databases sequential pattern mining from sequence databases has been recognized as an important data mining problem with various applications items in a sequence database can be organized into a concept hierarchy according to taxonomy based on the hierarchy sequential patterns can be found not only at the leaf nodes individual items of the hierarchy but also at higher levels of the hierarchy this is called multiple level sequential pattern mining in previous research taxonomies based on crisp relationships between any two disjointed levels however cannot handle the uncertainties and fuzziness in real life for example tomatoes could be classified into the fruit category but could be also regarded as the vegetable category to deal with the fuzzy nature of taxonomy chen and huang developed a novel knowledge discovering model to mine fuzzy multi level sequential patterns where the relationships from one level to another can be represented by a value between 0 and 1 in their work a generalized sequential patterns gsp like algorithm was developed to find fuzzy multi level sequential patterns this algorithm however faces a difficult problem since the mining process may have to generate and examine a huge set of combinatorial subsequences and requires multiple scans of the database in this paper we propose a new efficient algorithm to mine this type of pattern based on the divide and conquer strategy in addition another efficient algorithm is developed to discover fuzzy cross level sequential patterns since the proposed algorithm greatly reduces the candidate subsequence generation efforts the performance is improved significantly experiments show that the proposed algorithm is much more efficient and scalable than the previous one in mining real life databases our works enhance the model s practicability and could promote more applications in business

averaging techniques for self adjoint matrix equations on a measure chain abstract we apply averaging techniques to establish oscillation and nonoscillation criteria for the self adjoint matrix dynamic equation lx t p t x t q t x t 0 on a measure chain t these results extend and unify earlier results for the differential and difference equation case

sign changes in harmonic analysis on reductive groups let g be a connected reductive group over a field f in this note the author constructs an element e g of the brauer group of f the square of this element is trivial for a local field e g may be regarded as an element of i and is needed for harmonic analysis on reductive groups over that field for a global field there is a product formula the purpose of this note is to provide a cohomological interpretation of the sign changes in harmonic analysis on reductive groups over local fields that are caused by inner twistings the best understood example occurs in the work of shelstad 8 on inner twistings of real groups theorem 6 3 of that paper gives the following character identity 1 q g q g x here g is a connected reductive group over r g is its quasi split inner form x and x are stabilized characters of matched tempered l packets of g r and g r and y and y are matched regular semisimple elements of g r and g r the sign change in the character identity is q g q g where q g is one half of the dimension of the symmetric space attached to g more precisely attached to the simply connected cover of the derived group of g although q g may be only half integral the difference q g q g is always integral it is reasonable to expect an analogous character identity for groups g over a nonarchimedean local field f we can determine what the sign change must be by considering the steinberg characters of g f and g f since these should be related by the character identity let r g denote the f rank of the derived group of g the steinberg character of g f has value i r g on the elliptic regular set of g f and hence the sign change in the character identity must be l r g r g there are two groups for which the character identity has been proved the multiplicative group of a central division algebra of dimension d2 over f for d 2 see proposition 15 5 on p 484 of 4 and d 3 see theorem 1 of 1 later in this paper we will use a cohomological construction to define a sign e g 1 for any connected reductive group g over a local field let g denote a quasi split inner form of g we will show that e g l r g r g when the base received by the editors may 10 1982 1980 mathematics subject classification primary 22e50 partially supported by the national science foundation under grant mcs 78 02331 1983 american mathematical society 0002 9947 82 0000 11 93 03 25

on an exact mass formula of shimura in a series of recent papers g shimura obtained an exact formula for the mass of a maximal lattice in a quadratic or hermitian space over a totally real number field using bruhat tits theory we obtain a quick and more conceptual proof of his formula when the form is totally definite

on certain riccati integral equations and second order linear oscillation are closely related is well known many important results in the oscillation theory of 1 1 are in fact established by studying either 1 2 or 1 3 recent studies suggest that a great deal can still be said about 1 2 and l 3 thus leading to new results on 1 1 see 7 91 particularly useful in these studies is the theory of differential and integral inequalities the present work further supports this view point in this paper we first give a comparison theorem section 2 theorem 1 for riccati integral equations of the form 1 3 involving monotonic rearrangements of the function q t ji q s ds as a corollary we establish an extension of the well known oscillation criteria of hille s 6 to more general potentials section 3 theorem 4 in section 4 we elaborate on a method of hartman to derive a comparison type result involving the square of the integral j h q s ds and then deduce a lyapunov type inequality for disfocality the preliminaries will be introduced in the appropriate sections 315 0022 247x 82 020315 16 02 00 o

linear transformation and oscillation criteria for hamiltonian systems abstract using a linear transformation similar to the kummer transformation some new oscillation criteria for linear hamiltonian systems are established these results generalize and improve the oscillation criteria due to i s kumari and s umanaheswaram i sowjaya kumari s umanaheswaram oscillation criteria for linear matrix hamiltonian systems j differential equations 165 2000 174 198 q yang et al q yang r mathsen s zhu oscillation theorems for self adjoint matrix hamiltonian systems j differential equations 190 2003 306 329 and s chen and z zheng shaozhu chen zhaowen zheng oscillation criteria of yan type for linear hamiltonian systems comput math appl 46 2003 855 862 these criteria also unify many of known criteria in literature and simplify the proofs

arithmetic invariants of discrete langlands parameters the local langlands correspondence can be used as a tool for making verifiable predictions about irreducible complex representations of p adic groups and their langlands parameters which are homomorphisms from the local weil deligne group to the l group in this article we refine a conjecture of hiraga ichino and ikeda which relates the formal degree of a discrete series representation to the value of the local gamma factor of its parameter we attach a rational function in x with rational coefficients to each discrete parameter which specializes at x q the cardinality of the residue field to the quotient of this local gamma factor by the gamma factor of the steinberg parameter the order of this rational function at x 0 is also an important invariant of the parameter it leads to a conjectural inequality for the swan conductor of a discrete parameter acting on the adjoint representation of the l group we verify this conjecture in many cases when we impose equality we obtain a prediction for the existence of simple wild parameters and simple supercuspidal representations both of which are found and described in this article

evolutionary fuzzy rule induction process for subgroup discovery a case study in marketing this paper presents a genetic fuzzy system for the data mining task of subgroup discovery the subgroup discovery iterative genetic algorithm sdiga which obtains fuzzy rules for subgroup discovery in disjunctive normal form this kind of fuzzy rule allows us to represent knowledge about patterns of interest in an explanatory and understandable form that can be used by the expert experimental evaluation of the algorithm and a comparison with other subgroup discovery algorithms show the validity of the proposal sdiga is applied to a market problem studied in the university of mondragon spain in which it is necessary to extract automatically relevant and interesting information that helps to improve fair planning policies the application of sdiga to this problem allows us to obtain novel and valuable knowledge for experts

oscillation theorems for linear matrix hamiltonian systems using a matrix linear transformation which preserves oscillatory property some new oscillation criteria for the following linear matrix hamiltonian system u a t t i u b t v v c t u t i a t v t t 0 are obtained which improve and generalize some recent results in literature

oscillation of linear hamiltonian systems abstract in this paper sufficient conditions have been obtained for the oscillation of a class of linear hamiltonian systems