joint torsion of several commuting operators abstract we introduce the notion of joint torsion for several commuting operators satisfying a fredholm condition this new secondary invariant takes values in the group of invertibles of a field it is constructed by comparing determinants associated with different filtrations of a koszul complex our notion of joint torsion generalize the carey pincus joint torsion of a pair of commuting fredholm operators as an example under more restrictive invertibility assumptions we show that the joint torsion recovers the multiplicative lefschetz numbers furthermore in the case of toeplitz operators over the polydisc we provide a link between the joint torsion and the cauchy integral formula we will also consider the algebraic properties of the joint torsion they include a cocycle property a triviality property and a multiplicativity property the proof of these results relies on a quite general comparison theorem for vertical and horizontal torsion isomorphisms associated with certain diagrams of chain complexes

hilbert schmidtness of some finitely generated submodules in h2 d2 abstract a closed subspace m of the hardy space h 2 d 2 over the bidisk is called a submodule if it is invariant under multiplication by coordinate functions z 1 and z 2 whether every finitely generated submodule is hilbert schmidt is an unsolved problem this paper proves that every finitely generated submodule m containing z 1 z 2 is hilbert schmidt where is any finite blaschke product some other related topics such as fringe operator and fredholm index are also discussed

an aggregation disaggregation approach to obtain robust conclusions with electre tri electre tri is a well known method to assign a set of alternatives to a set of predefined categories considering multiple criteria using this method requires setting many parameters which is often a difficult task we consider the case where the decision makers dms in the decision process are unsure of which values should each parameter take which may result from uncertain imprecise or inaccurately determined information as well as from lack of consensus among them this paper discusses the synergy between two approaches developed independently to deal with this difficulty the first approach infers the value of parameters from assignment examples provided by the dms as an elicitation aid each assignment example originates mathematical constraints that the parameter values should satisfy the second approach considers a set of constraints on the parameter values reflecting the imprecise information that the dms are able to provide then it computes the best and worst categories for each alternative compatible with constraints in order to present robust conclusions both approaches avoid asking for precise values for the parameters rather they proceed to solve the problem in a way that requires from the dms much less effort by integrating these two approaches this paper proposes a new interactive approach where the insight obtained during robustness analyses guides the dms during the elicitation phase

operator theory in the hardy space over the bidisk iii this paper is a continuation of a project of developing a systematic operator theory inh2 d2 a large part of it is devoted to a study ofevaluation operator which is a very useful tool in the theory a number of elementary properties of the evaluation operator are exhibited and these properties are used to derive results in other topics such as interpretation of characteristic opertor function inh2 d2 spectral equivalence compactness compressions of shift operators etc even though some results reflect the two variable nature ofh2 d2 the goal of this paper is to manifest a close tie between the operator theory inh2 d2 and classical single operator theory the unilateral shift of a finite multiplicity and the bergman shift will be used as examples to illustrate some of the results

the resultant on compact riemann surfaces we introduce a notion of the resultant of two meromorphic functions on a compact riemann surface and demonstrate its usefulness in several respects for example we exhibit several integral formulas for the resultant relate it to potential theory and give explicit formulas for the algebraic dependence between two meromorphic functions on a compact riemann surface as a particular application the exponential transform of a quadrature domain in the complex plane is expressed in terms of the resultant of two meromorphic functions on the schottky double of the domain

multicriteria assignment method proaftn methodology and medical application abstract this paper presents a new fuzzy multicriteria classification method called proaftn for assigning alternatives to predefined categories this method belongs to the class of supervised learning algorithms and enables to determine the fuzzy indifference relations by generalising the indices concordance and discordance used in the electre iii method then it assigns the fuzzy belonging degree of the alternatives to the categories we also present a clinical application of the proposed method in the cytopathological diagnosis of acute leukaemia

existence of positive solutions for second order functional differential equations we afford a existence criterion of positive solutions of a boundary value problem concerning a second order functional differential equation by using the krasnoselskii fixed point theorem on cones in banach spaces moreover we also apply our results to establish several existence theorems of multiple positive solutions for some functional differential equations

reference based preferences aggregation procedures in multi criteria decision making this paper aims at introducing and investigating a new family of merely qualitative models for multicriteria decision making such models do not require any numerical representation within this family we will focus on decision rules using reference levels in order to help comparing several alternatives we will investigate both the descriptive potential of such rules and their axiomatic foundations after recalling the descriptive and prescriptive limitations of merely ordinal rules that do not use reference points we will introduce a new axiom requiring that the decision maker s preference between two alternatives depends on the respective positions of their consequences relatively to reference levels under this assumption we will determine the only possible form for the decision rule and characterize some particular instances of this rule under transitivity constraints our results show that introducing reference points overcomes the usual limitations of purely ordinal aggregation methods by moving the application point of arrow s theorem

a new approach to multi criteria sorting based on fuzzy outranking relations the theseus method abstract in this paper we propose the theseus method a new approach based on fuzzy outranking relations to multi criteria sorting problems compared with other outranking based methods theseus is inspired by another view of multi criteria classification problems it utilizes a new way of evaluating the assignment of an object to an element of the set of ordered categories that were previously defined this way is based on comparing every possible assignment with the information from various preference relations that are derived from a fuzzy outranking relation defined on the universe of objects the appropriate assignment is determined by solving a simple selection problem the capacity of a reference set for making appropriate assignments is related to a good characterization of the categories a single reference action characterizing a category may be insufficient to achieve well determined assignments in this paper the reference set capacity to perform appropriate assignments is characterized by some new concepts this capacity may be increased when more objects are added to the reference set theseus is a method for handling the preference information contained in such larger reference sets

samuel multiplicity and fredholm theory in this note we combine methods from commutative algebra and complex analytic geometry to calculate the generic values of the cohomology dimensions of a commuting multioperator on its fredholm domain more precisely we prove that for a given fredholm tuple t t 1 t n of commuting bounded operators on a complex banach space x the limits c p t rm lim k rightarrow infty rm dim h p t k x k n exist and calculate the generic dimension of the cohomology groups h p z t x of the koszul complex of t near z 0 to deduce this result we show that the above limits coincide with the samuel multiplicities of the stalks of the cohomology sheaves h p z t mathcal o x mathbb c n of the associated complex of analytic sheaves at z 0

an evolutionary approach to construction of outranking models for multicriteria classification the case of the electre tri method outranking methods constitute an important class of multicriteria classification models often however their implementation is cumbersome due to the large number of parameters that the decision maker must specify past studies tried to address this issue using linear and nonlinear programming to elicit the necessary preferential information from assignment examples in this study an evolutionary approach based on the differential evolution algorithm is proposed in the context of the electre tri method computational results are given to test the effectiveness of the methodology and the quality of the obtained models

neighborhoods of certain p valently analytic functions with negative coefficients in this investigation by making use of the familiar concept of neighborhoods of p valently analytic functions the authors prove coefficient bounds distortion inequalities associated inclusion relations for the n neighborhoods of a family of p valently analytic functions and its certain derivatives which is defined by means of a certain non homogenous differential equation

spectral permanence for joint spectra for a c subalgebra a of a c algebra b and a commuting tuple a a a of elements of a we prove that sp a a sp a b where sp denotes taylor spectrum as a consequence we prove that 0 g sp a a if and only if

neighborhoods of a new class of harmonic multivalent functions abstract we introduce and investigate a new subclass of harmonic multivalent functions defined by using a differential operator we obtain coefficient conditions distortion bounds extreme points convex combination for the above class of harmonic multivalent functions we also derive inclusion relationships involving the neighborhoods of harmonic multivalent functions

the dirac operator of a commuting d tuple abstract given a commuting d tuple t t1 td of otherwise arbitrary operators on a hilbert space there is an associated dirac operator dt significant attributes of the d tuple are best expressed in terms of dt including the taylor spectrum and the notion of fredholmness in fact all properties of t derive from its dirac operator we introduce a general notion of dirac operator in dimension d 1 2 that is appropriate for multivariable operator theory we show that every abstract dirac operator is associated with a commuting d tuple and that two dirac operators are isomorphic iff their associated operator d tuples are unitarily equivalent by relating the curvature invariant introduced in a previous paper to the index of a dirac operator we establish a stability result for the curvature invariant for pure d contractions of finite rank it is shown that for the subcategory of all such t that are a fredholm and and b graded the curvature invariant k t is stable under compact perturbations we do not know if this stability persists when t is fredholm but ungraded although there is concrete evidence that it does

increasing selective pressure towards the best compromise in evolutionary multiobjective optimization the extended nosga method most current approaches in the evolutionary multiobjective optimization literature concentrate on adapting an evolutionary algorithm to generate an approximation of the pareto frontier however finding this set does not solve the problem the decision maker still has to choose the best compromise solution out of that set here we introduce a new characterization of the best compromise solution of a multiobjective optimization problem by using a relational system of preferences based on a multicriteria decision aid way of thinking and an outranked based dominance generalization we derive some necessary and sufficient conditions which describe satisfactory approximations to the best compromise such conditions define a lexicographic minimum of a bi objective optimization problem which is a map of the original one the nosga ii method is a nsga ii inspired efficient way of solving the resulting mapped problem

weyl s theorem in several variables in this note we consider weyl s theorem and browder s theorem in several variables the main result is as follows let t be a doubly commuting n tuple of hyponormal operators acting on a complex hilbert space if t has the quasitriangular property i e the dimension of the left cohomology for the koszul complex t is greater than or equal to the dimension of the right cohomology for t for all cn then weyl s theorem holds for t i e the complement in the taylor spectrum of the taylor weyl spectrum coincides with the isolated joint eigenvalues of finite multiplicity

an interactive approach for placing alternatives in preference classes abstract in this paper we consider the multiple criteria decision making problem of partitioning alternatives into preference classes we develop an interactive procedure based on the assumption that the decision maker dm has a linear utility function the approach requires the dm to place an alternative in a preference class from time to time based on the preference information derived from the dm s placement as well as from dominance and linearity we try to place other alternatives we present results on the performance of the algorithm applied to four different sets of alternatives

fredholm and invertible tuples of operators the deformation problem using j l taylor s definition of joint spectrum we study fredholm and invertible tuples of operators on a hilbert space we give the foundations for a several variables theory including a natural generalization of atkinson s theorem and an index which well behaves we obtain a characterization of joint invertibility in terms of a single operator and study the main examples at length we then consider the deformation problem and solve it for the class of almost doubly commuting fredholm pairs with a semi fredholm coordinate 1 introduction 1 let t be a bounded linear operator on a banach space t is said to be invertible if there exists an operator s on such that ts st 1 the identity operator on 9c by the open mapping theorem this is equivalent to ker t 0 and r t range of t the last formulation does not rely upon the existence of an inverse for t but rather on the action of the operator t when t is replaced by an tuple of commuting operators several definitions of nonsingular ity exist j l taylor 19 has obtained one which reflects the actions of the operators by considering the koszul complex associated with the tuple 2 in this paper we develop a general several variables theory on the basis of taylor s work and study commuting and almost commuting commuting mod ulo the compacts tuples of operators on a hilbert space we obtain a characterization of joint invertibility in terms of the invertibility of a single operator which is essential for our approach from that we get a number of corollaries which generalize nicely the known elementary results in one variable at the same time the referred characterization allows us to define a continuous invariant under compact perturbations integer valued index on the class of fred holm tuples those almost commuting tuples which are invertible in the calkin algebra this index extends the classical one for fredholm operators we prove that an almost commuting tuple of essentially normal operators with all commu tators in trace class has index zero 2 and that a natural generalization of atkinson s theorem holds for tuples

electre tri nb a new multiple criteria ordinal classification method abstract this paper presents a new method for multiple criteria ordinal classification sorting problems in an ordinal classification problem the categories also called classes in related literature are pre defined and ordered from the best to the worst or from the worst to the best the actions not necessarily known a priori are assigned to the different ordered categories several electre type methods were designed to deal with this kind of problem however none of them proposes a characterization of the categories through a set of limiting profiles this is the novelty of the current method which may be considered as an extension of electre tri b it fulfills a set of structural requirements uniqueness of the assignments independence monotonicity homogeneity conformity and stability with respect to merging and splitting operations all these features will be presented in the current paper and illustrated through three examples

estimates for hilbertian koszul homology abstract the objective of this paper is to give new kind of estimates for hilbertian koszul homology inspired by commutative algebra in multivariable fredholm theory

electre tri c a multiple criteria sorting method based on characteristic reference actions in this paper a new sorting method following a decision aiding constructive approach is proposed this method is called electre tri c as a sorting method a set of categories must be defined to represent the way in which the actions that are going to be assigned to each of them should further be processed this method is appropriate to deal with decision aiding contexts where the categories are completely ordered and each of them is defined through a single characteristic reference action the set of characteristic actions should be co constructed through an interactive process between the analyst and the decision maker electre tri c has been conceived to verify a set of natural structural requirements conformity homogeneity monotonicity and stability which can be viewed as its fundamental properties this method is composed of two joint rules called descending rule and ascending rule which must be used conjointly and not separately each one of these rules selects only one category or a range of possible categories for a possible assignment of an action this assignment depends on the comparison of such an action to the characteristic actions according to a chosen credibility level numerical examples are also presented in order to illustrate the main theoretical results provided by the method

commuting partial differential operators and vector bundles over abelian varieties since then the case of rings of rank r were studied by several people 14 25 34 then the complete determination of geometrical object which classifies commutative rings of rank r for r 2 was accomplished by mulase 22 in 1989 it is thus natural to ask what happens if we replace ordinary differential operators by partial differential operators there are a few results on this problem 4 14 3 in these papers all operators are of scalar coefficients and spectral varieties are singular varieties curves or their products in 26 we have constructed commuting partial differential operators from line bundles on abelian varieties the particular feature of these operators is that they are of matrix coefficients the main purpose of this paper is to construct commuting partial differential operators with matrix coefficients from a class of vector bundles on abelian varieties in studying commuting operators their common eigenfunctions play a central role krichever 13 characterized such eigenfunctions as baker akhiezer ba functions in the case of ordinary differential operators the concept of ba functions are generalized to higher dimensions 26 7 ba functions are constructed from x d ri where x is a projective variety d an ample divisor on x and ri is a base of differentials of the second kind with poles on d modulo exact forms in this paper we introduce ba functions of coherent sheaves on abelian varieties which are our main objects of study in this paper

using assignment examples to infer weights for electre tri method some experimental results given a finite set of alternatives a the sorting or assignment problem consists in the assignment of each alternative to one of the pre defined categories in this paper we are interested in multiple criteria sorting problems and more precisely in the existing method electre tri this method requires the elicitation of preferential parameters weights thresholds category limits in order to construct a preference model which the decision maker dm accepts as a working hypothesis in the decision aid study a direct elicitation of these parameters requiring a high cognitive effort from the dm v mosseau r slowinski journal of global optimization 12 2 1998 174 proposed an interactive aggregation disaggregation approach that infers electre tri parameters indirectly from holistic information i e assignment examples in this approach the determination of electre tri parameters that best restore the assignment examples is formulated through a nonlinear optimization program in this paper we consider the subproblem of the determination of the weights only the thresholds and category limits being fixed this subproblem leads to solve a linear program rather than nonlinear in the global inference model numerical experiments were conducted so as to check the behaviour of this disaggregation tool results showed that this tool is able to infer weights that restores in a stable way the assignment examples and that it is able to identify inconsistencies in the assignment examples

neighborhoods of certain multivalent functions with negative coefficients by means of a differential operator we introduce and investigate two new subclasses of p valently analytic functions of complex order the various results obtained here for each of these function classes include coefficient inequalities and the consequent inclusion relationships involving the neighborhoods of the p valently analytic functions

neighborhoods of a certain family of multivalent functions with negative coefficients abstract by making use of the familiar concept of neighborhoods of analytic and p valent functions the authors prove coefficient bounds and distortion inequalities and associated inclusion relations for the n neighborhoods of a family of multivalent functions with negative coefficients which is defined by means of a certain nonhomogeneous cauchy euler differential equation relevant connections of the various function classes investigated in this paper with those considered by earlier workers on the subject are also mentioned

inferring electre s veto related parameters from outranking examples when considering electre s valued outranking relations aggregation disaggregation methodologies have difficulties in taking discordance veto into account we present a partial inference procedure to compute the value of the veto related parameters that best restore a set of outranking statements i e examples that an electre model should restore provided by a decision maker given fixed values for the remaining parameters of the model this paper complements previous work on the inference of other preference related parameters weights cutting level category limits advancing toward an integrated framework of inference problems in electre iii and tri methods we propose mathematical programs to infer veto related parameters first considering only one criterion then all criteria simultaneously using the original version of electre outranking relation and two variants this paper shows that these inference procedures lead to linear programming 0 1 linear programming or separable programming problems depending on the case

application of the non outranked sorting genetic algorithm to public project portfolio selection this paper proposes the application of multi criteria analysis to the problem of allocating public funds to competing programs projects or policies with a subjective approach applied to define the concept of highest portfolio social return this portfolio corresponds to an attainable non strictly outranked state of the social object under consideration its existence requires a decision maker dm to establish a relational preference system of minimal consistency as the number of feasible portfolios increases exponentially the dm s asymmetric preference relation should be computable to perform an exploration of the portfolio space the complexity of many real situations requires evolutionary algorithms but in presence of many objectives evolutionary algorithms are inefficient we overcome this problem by using the extended non outranked sorting genetic algorithm nosga ii which handles multi criteria preferences through a robust model based on a binary fuzzy outranking relation expressing the truth value of the predicate portfolio x is at least as good as portfolio y the dm is assumed to be capable of assigning the parameters for constructing the outranking relation in case of collective decision making we first assume that the possible differing values of the group members are not strongly conflicting so that a consensus can be achieved on the model s parameters otherwise we propose a method in which each member of the heterogeneous group gets his her own best portfolio these individual solutions are then aggregated in a group s best acceptable portfolio which maximizes a measure of group satisfaction and minimizes regret the proposal is examined through two real size problems in which good solutions are reached the first example is useful to illustrate the case of social action program selection the second illustrates the case of basic research project portfolios

rough sets theory for multicriteria decision analysis the original rough set approach proved to be very useful in dealing with inconsistency problems following from information granulation it operates on a data table composed of a set u of objects actions described by a set q of attributes its basic notions are indiscernibility relation on u lower and upper approximation of either a subset or a partition of u dependence and reduction of attributes from q and decision rules derived from lower approximations and boundaries of subsets identified with decision classes the original rough set idea is failing however when preference orders of attribute domains criteria are to be taken into account precisely it cannot handle inconsistencies following from violation of the dominance principle this inconsistency is characteristic for preferential information used in multicriteria decision analysis mcda problems like sorting choice or ranking in order to deal with this kind of inconsistency a number of methodological changes to the original rough sets theory is necessary the main change is the substitution of the indiscernibility relation by a dominance relation which permits approximation of ordered sets in multicriteria sorting to approximate preference relations in multicriteria choice and ranking problems another change is necessary substitution of the data table by a pairwise comparison table where each row corresponds to a pair of objects described by binary relations on particular criteria in all those mcda problems the new rough set approach ends with a set of decision rules playing the role of a comprehensive preference model it is more general than the classical functional or relational model and it is more understandable for the users because of its natural syntax in order to workout a recommendation in one of the mcda problems we propose exploitation procedures of the set of decision rules finally some other recently obtained results are given rough approximations by means of similarity relations rough set handling of missing data comparison of the rough set model with sugeno and choquet integrals and results on equivalence of a decision rule preference model and a conjoint measurement model which is neither additive nor transitive

a multicriteria classification approach based on pairwise comparisons abstract classification refers to the assignment of a set of alternatives into predefined homogenous classes most of the existing classification methodologies are based on absolute comparisons among the alternatives and some reference profiles cut off points that discriminate the classes this paper proposes a new approach that involves pairwise comparisons based on the multicriteria decision aid mcda paradigm the basis of the methodology is a preference relation that is used to perform pairwise comparisons among the alternatives the criteria weights used to construct the preference relation are specified using a reference set of alternatives training sample on the basis of linear programming techniques

multiplication operators on the bergman space via the hardy space of the bidisk in this paper we develop a machinery to study multiplication operators on the bergman space via the hardy space of the bidisk we show that only a multiplication operator by a finite blaschke product has a unique reducing subspace on which its restriction is unitarily equivalent to the bergman shift using the machinery we study the structure of reducing subspaces unitary equivalence of a multiplication operator on the bergman space as a consequence we completely classify reducing subspaces of the multiplication operator by a blaschke product with order three on the bergman space to solve a conjecture of zhu 38 and obtain that the number of minimal reducing subspaces of the multiplication operator equals the number of connected components of the riemann surface of 1 over d