discrete and continuous recursive forms of owa operators abstract we firstly present an evaluation problem for online shop based on gradually increasing number of inputs then we propose a model using recursive owa operator with constant orness andness grade involved next we analyze properties of discrete recursive owa operators show their relationship with pascal triangle and further generalize this relationship to function for the continuous case we propose a concept of self similar ordered weighting functions owf and analyze some properties of owf using these concepts we present the recursive aggregation method of continuous arguments under continuous owf we show a relationship of owf with the regular increasing rim quantifier furthermore based on an isomorphism relation between discrete and continuous recursive owa operators left recursive owa can be seen as the discrete form of continuous owf

p moment stability of solutions to stochastic differential equations driven by g brownian motion abstract this paper is concerned with p moment stability of solutions to stochastic differential equations driven by g brownian motion gsdes by means of the lyapunov function and the ito formula an example is given to illustrate the effectiveness of the obtained results

preference voting and project ranking using dea and cross evaluation cook and kress 1990 using data envelopment analysis dea as their starting point proposed a procedure to rank order the candidates in a preferential election notionally each candidate is permitted to choose the most favourable weights to be applied to his her standings first place second place etc votes in the usual dea manner with the additional assurance region restriction that the weight for a j place vote should be more than that for a j 1 amount we consider that this freedom to choose weights is essentially illusory when maximum discrimination between the candidates is sought in which case the weights used to evaluate and rank the candidates are as if imposed externally at the outset to avoid this we present an alternative procedure which retains cook and kress central idea but where as well as using each candidate s rating of him herself we now make use of each candidate s ratings of all the candidates we regard the so called cross evaluation matrix as the summary of a self and peer rating process in which the candidates seek to interpret the voters preferences as favourably for themselves relative to the other candidates as possible the problem then becomes one of establishing an overall rating for each candidate from these individual ratings for this for each candidate we use a weighted average of all the candidates ratings of that candidate where the weights themselves are in proportion to each candidate s overall rating the overall ratings are therefore proportional to the components of the principal left hand eigenvector of the cross evaluation matrix these ideas are then applied to the selection of r d projects to comprise an r d program thus indicating thier wider applicability

polyhedral cone ratio dea models with an illustrative application to large commercial banks abstract polyhedral cone ratio data envelopment analysis models generalizing the ccr ratio model are developed for situations with a finite number of dmus and employing polyhedral cones of virtual multipliers they provide improved definitions of efficiency over ccr models whose input output data and or numbers of dmus are inadequate to capture aspects or restrictions which should be involved the focus here is on the sum form for cones which easily provides for capturing exogenous expert opinion as well as mathematical reduction to the old form with its very powerful software transformation from the usual intersection form to it and vice versa is explicitly given thereby the advantages of either or both are available the theory is illustrated with two dimensional examples and by real banking examples for motivation

an analytic approach for obtaining maximal entropy owa operator weights one important issue in the theory of ordered weighted averaging owa operators is the determination of the associated weights one of the first approaches suggested by o hagan determines a special class of owa operators having maximal entropy of the owa weights for a given level of orness algorithmically it is based on the solution of a constrained optimization problem in this paper using the method of lagrange multipliers we shall solve this constrained optimization problem analytically and derive a polynomial equation which is then solved to determine the optimal weighting vector

stability of solutions for stochastic impulsive systems via comparison approach this note studies stability problem of solutions for stochastic impulsive systems by employing lyapunov like function method and it s formula comparison principles of existence and uniqueness and stability of solutions for stochastic impulsive systems are established based on these comparison principles the stability properties of stochastic impulsive systems are derived by the corresponding stability properties of a deterministic impulsive system as the application the stability results are used to design impulsive control for the stabilization of unstable stochastic systems finally one example is given to illustrate the obtained results

owa generation function and some adjustment methods for owa operators with application we propose the concept of ordered weighted averaging owa generation function with some properties illustrative examples and usages a number of new properties of owa operators and relations between some well known owa operators are proposed and proved using owa generation functions we discuss some orness andness adjustment methods for a predetermined owa operator a practical application about investment prediction problem is given with detailed illustration and analysis which can show the advantages of the adjustment methods proposed in this paper in particular the concept consistent adjustment matrix is proposed and the interests and advantages of it can be shown by its special properties

achievement and benchmarking of countries at the summer olympics using cross efficiency evaluation method in this paper an extension tool of data envelopment analysis dea namely cross efficiency evaluation method is used to measure the performance of the nations participating in the last six summer olympic games the model in the paper considers two inputs gdp per capita and population and three outputs number of gold silver and bronze medals won and the weight restrictions are included to guarantee that a unit of silver medal corresponds to a higher valuation than a unit of bronze medal and the highest for gold medal the results for the last six summer olympic games are analyzed and a unique ordering of the participants based on average cross efficiency is provided also cluster analysis technique is used to select the more appropriate targets for poorly performing countries to use as benchmarks

on the issue of obtaining owa operator weights we first investigate the issue of obtaining the weights associated with the owa aggregation in the situation when we have observed data on the arguments and the aggregated value we next introduce a family of owa operators called exponential owa operators finally we look at a simple procedure for generating the weights given a required degree of orness

on obtaining minimal variability owa operator weights one important issue in the theory of ordered weighted averaging owa operators is the determination of the associated weights one of the first approaches suggested by o hagan determines a special class of owa operators having maximal entropy of the owa weights for a given level of orness algorithmically it is based on the solution of a constrained optimization problem another consideration that may be of interest to a decision maker involves the variability associated with a weighting vector in particular a decision maker may desire low variability associated with a chosen weighting vector in this paper using the kuhn tucker second order sufficiency conditions for optimality we shall analytically derive the minimal variability weighting vector for any level of orness

weighted aggregation operators based on minimization minimization based aggregation operators a g d are discussed special attention is paid to weighting function g based cases related to some fixed dissimilarity function d when d 2 x y x y 2 we recognize mixture operators and we recall some sufficient conditions for g ensuring the monotonicity of a g d for d 1 x y x y and non decreasing non increasing g a g d is shown to be the upper lower median whenever a g d is an aggregation operator

preference aggregation and dea an analysis of the methods proposed to discriminate efficient candidates abstract there are different ways to allow the voters to express their preferences on a set of candidates in ranked voting systems each voter selects a subset of the candidates and ranks them in order of preference a well known class of these voting systems are scoring rules where fixed scores are assigned to the different ranks and the candidates with the highest score are the winners one of the most important issues in this context is the choice of the scoring vector since the winning candidate can vary according to the scores used to avoid this problem cook and kress w d cook m kress a data envelopment model for aggregating preference rankings management science 36 11 1990 1302 1310 using a dea ar model proposed to assess each candidate with the most favorable scoring vector for him her however the use of this procedure often causes several candidates to be efficient i e they achieve the maximum score for this reason several methods to discriminate among efficient candidates have been proposed the aim of this paper is to analyze and show some drawbacks of these methods

the golden number and fibonacci sequences in the design of voting structures abstract some distinguished types of voters as vetoes passers or nulls as well as some others play a significant role in voting systems because they are either the most powerful or the least powerful voters in the game independently of the measure used to evaluate power in this paper we are concerned with the design of voting systems with at least one type of these extreme voters and with few types of equivalent voters with this purpose in mind we enumerate these special classes of games and find out that its number always follows a fibonacci sequence with smooth polynomial variations as a consequence we find several families of games with the same asymptotic exponential behavior except for a multiplicative factor which is the golden number or its square from a more general point of view our studies are related with the design of voting structures with a predetermined importance ranking

properties of ladder tournaments abstract ladder tournaments use work trials to screen workers for positions in organizations despite being common in many industries their properties remain poorly understood especially in organizations characterized by complex complementarities and externalities in their production process in this study we formalize the ranking rule generated by a ladder tournament and derive measures of relative performance that can be used to compare workers when their true inputs cannot be observed we show that this rule is reflexive but not generally transitive unless the organization has fewer than three layers of hierarchy or is complete it follows that complete organizations have an embedded merit based hierarchical structure we also study the relationship between a worker s tournament rank and his utility or usefulness as measured by the frequency with which he plays a pivotal role we show that a worker s likelihood of being pivotal is a weakly increasing function of his rank this finding implies that in complete organizations ladder tournaments discriminate more effectively between workers than do mechanisms based on pivotability or marginal productivity

strict vs weak ordinal relations for multipliers in data envelopment analysis in a recent paper golany 1988 proposes an interesting extension of data envelopment analysis to the situation where ordinal relations among weights corresponding to certain dimensions exist however the development of the extended model contains mathematical errors and the proposed equivalence is incorrect we establish the correct model equivalence and prove that weak ordinal relations require a nonstandard dea model we also show that the case of strict ordinal relations can be handled with the standard dea model these results hold for the ccr bcc additive and multiplicative models and for relations involving both input and output multipliers

aggregating preference rankings using owa operator weights one important issue of aggregating preference rankings is to determine the weights of different ranking places this paper proposes the use of ordered weighted averaging owa operator weights to aggregate preference rankings which allows the weights associated with different ranking places to be determined in terms of a decision maker dm s optimism level characterized by an orness degree by adjusting the dm s optimism level ties can be avoided and winner can be selected two numerical examples are examined using owa operator weights to show their applications simplicity and flexibility in aggregating preference rankings

a procedure for ranking efficient units in data envelopment analysis data envelopment analysis dea evaluates the relative efficiency of decision making units dmus but does not allow for a ranking of the efficient units themselves a modified version of dea based upon comparison of efficient dmus relative to a reference technology spanned by all other units is developed the procedure provides a framework for ranking efficient units and facilitates comparison with rankings based on parametric methods

some properties and representation methods for ordered weighted averaging operators this study demonstrates or proposes some new properties and representation methods for ordered weighted averaging owa operators the interweaving representation allows some well known owa operators to be decomposed into two other well known owa operators a theorem is proposed for determining the relations between owa operators with respect to their degree of orness andness we also provide a complex iteration method for well known owa operators as well as some new generation methods and possible adjustment methods for well known centered owa operators furthermore we investigate some new methods for generating step owa and orlike andlike window owa operators where these methods are accurate in terms of their orness andness degree we also demonstrate two interesting and useful properties of owa operators i e stage owa and dew owa and one of their applications

improved minimax disparity model for obtaining owa operator weights the determination of weights vector is one of the key issues in the theory of ordered weighted averaging owa operators for this reason many weight generating models have been proposed in the literature the main purpose of this note is to point out that the improved minimax disparity model which is suggested by emrouznejad and amin 2010 has infinite solutions as a consequence this model is not reliable

discrete repulsive oscillator wavefunctions for the study of infinite discrete systems on phase space the three dimensional lorentz algebra and group so 2 1 and so 2 1 provide a discrete model of the repulsive oscillator its eigenfunctions are found in the principal irreducible representation series where the compact generator that we identify with the position operator has the infinite discrete spectrum of the integers z while the spectrum of energies is a double continuum the right and left moving wavefunctions are given by hypergeometric functions that form a dirac basis for 2 z under contraction the discrete system limits to the well known quantum repulsive oscillator numerical computations of finite approximations raise further questions on the use of dirac bases for infinite discrete systems

models to determine parameterized ordered weighted averaging operators using optimization criteria this paper proposes a general optimization model for determining ordered weighted averaging owa operators and three specific models for generating monotonic and symmetric owa operators as well as those with any function shape in these models entropy and variance concepts are generalized as general dispersion indices for use in the objective functions while the ordinary orness level constraints are used in the constraint equations as a special case we define an orness function for monotonic owa operators which measures the closeness of the aggregation value to the maximum value and a medianness function for symmetric owa operators which measures the closeness of the aggregation value to the median value we also extend the commonly used models for determining owa operators under given orness values to determine monotonic owa operators with given orness function values and symmetric owa operators with given medianness function values analytical solutions and properties of these models are discussed we also provide analytical solutions of the maximum entropy and minimum variance problems with given linear medianness values by setting different forms of the objective function and constraints the parameterized owa operator family elements can achieve various distributions in any desired shape two examples are given to show the owa operator elements distributed in quadratic and gaussian distribution function shapes

aggregating preferences rankings with variable weights abstract one of the most important issues for aggregating preferences rankings is the determination of the weights associated with the different ranking places to avoid the subjectivity in determining the weights cook and kress 1990 5 suggested evaluating each candidate with the most favorable scoring vector for him her with this purpose various models based on data envelopment analysis have appeared in the literature although these methods do not require predetermine the weights subjectively some of them have a serious drawback the relative order between two candidates may be altered when the number of first second k th ranks obtained by other candidates changes although there is not any variation in the number of first second k th ranks obtained by both candidates in this paper we propose a model that allows each candidate to be evaluated with the most favorable weighting vector for him her and avoids the previous drawback moreover in some cases we give a closed expression for the score assigned with our model to each candidate

a selection method for a preferential election this paper deals with a recently proposed method for a ranked voting system it is based on a data envelopment analysis model it is shown that the number of problems to be solved and the number of constraints in the model can be decreased in addition the winner can be selected with a fewer efforts and in some cases without solving any problems the obtained results also illustrate the importance of selecting a proper norm in the model

achievable hierarchies in voting games with abstention abstract it is well known that he influence relation orders the voters the same way as the classical banzhaf and shapley shubik indices do when they are extended to the voting games with abstention vga in the class of complete games moreover all hierarchies for the influence relation are achievable in the class of complete vga the aim of this paper is twofold firstly we show that all hierarchies are achievable in a subclass of weighted vga the class of weighted games for which a single weight is assigned to voters secondly we conduct a partial study of achievable hierarchies within the subclass of h complete games that is complete games under stronger versions of influence relation

lyapunov type conditions and stochastic differential equations driven by g brownian motion abstract this paper studies the solvability and the stability of stochastic differential equations driven by g brownian motion gsdes in particular the existence and uniqueness of the solution for locally lipschitz gsdes are obtained by localization methods also the stability of such gsdes is discussed with lyapunov type conditions

suitability and redundancy of non homogeneous weight restrictions for measuring the relative efficiency in dea abstract weight restrictions are non homogeneous if they are formulated as linear less than or equal to inequalities with a non zero constant on the right hand side absolute weight bounds are typical examples it has recently been shown that in the presence of such restrictions the fractional linear data envelopment analysis dea model and its linear forms may incorrectly evaluate the maximum relative efficiency of the assessed unit this paper investigates the problem further and identifies certain types of non homogeneous restrictions that do not cause the observed error thus the relative efficiency is always assessed correctly if in the same ccr model no positive lower bounds are imposed on any of the input weights and no upper bounds are imposed on any of the output weights the redundancy of certain types of weight restrictions in dea models is also considered based on this the traditional use of small positive constants to separate weights from zero in dea models is questioned

median value and median interval of a fuzzy number median value and median interval of a fuzzy number are investigated effects of concentration and dilation of a trapezoidal fuzzy number on the location of the median value and the median interval are studied relationship between the median interval and the mean interval is explored central value and central interval of a fuzzy number are proposed

parameterized defuzzification with continuous weighted quasi arithmetic means an extension parameterized aggregation becomes an attractive idea in many applications by applying the quasi arithmetic mean based defuzzification method and its orness measure we extend the properties of discrete quasi arithmetic mean with an orness measure to the case of continuous weighted quasi arithmetic means and apply them to the parameterized estimation of fuzzy or random variables when facing the uncertainty of these variables the decision maker can obtain the crisp value estimation which is always consistent with his her preference information two families of continuous weighted quasi arithmetic means with exponential and power function generators are discussed combining these conclusions with that of the discrete case we can understand better the properties of quasi arithmetic means and extend their possible applications

a method for discriminating efficient candidates with ranked voting data abstract ranked voting data arise when voters select and rank more than one candidate with order of preference cook and kress management science 36 11 1990 1302 introduced data envelopment analysis dea to analyze ranked voting data by using dea each candidate may use the most favorable weights for him her to estimate his her own preference score however dea often suggests that more than one unit are equally efficient so a method to discriminate these efficient candidates is needed some methods of such purpose are proposed however these methods have a weak point that the order of efficient candidates may be changed by existence of an inefficient candidate in this paper we propose a new method our method does not use information about inefficient candidates to discriminate efficient candidates it is based on a very simple idea and is realizable visually so we hope that it is acceptable to election officials

a preemptive goal programming method for aggregating owa operator weights in group decision making this paper reveals that owa operator weights cannot be aggregated by the weighted arithmetic or geometric average method in group decision making a preemptive goal programming method pgpm is proposed for aggregating owa operator weights which is an extension of the minimax disparity approach developed earlier by the same authors the effectiveness of pgpm is illustrated with a numerical example

discriminating dea efficient candidates by considering their least relative total scores data envelopment analysis very often identifies more than one candidate in a voting system to be dea efficient in order to choose a winner from among the dea efficient candidates this paper proposes a new method that discriminates the dea efficient candidates by considering their least relative total scores the proposed method is illustrated with two numerical examples and proves to be effective and practical

the dea game cross efficiency model and its nash equilibrium in this paper we examine the cross efficiency concept in data envelopment analysis dea cross efficiency links one decision making unit s dmu performance with others and has the appeal that scores arise from peer evaluation however a number of the current cross efficiency approaches are flawed because they use scores that are arbitrary in that they depend on a particular set of optimal dea weights generated by the computer code in use at the time one set of optimal dea weights possibly out of many alternate optima may improve the cross efficiency of some dmus but at the expense of others while models have been developed that incorporate secondary goals aimed at being more selective in the choice of optimal multipliers the alternate optima issue remains in cases where there is competition among dmus this situation may be seen as undesirable and unfair to address this issue this paper generalizes the original dea cross efficiency concept to game cross efficiency specifically each dmu is v

a minimax disparity approach for obtaining owa operator weights one of the key issues in the theory of ordered weighted averaging owa operators is the determination of owa operator weights in this paper a minimax disparity approach for obtaining owa operator weights is proposed this involves the formulation and solution of a linear programming lp model for a given degree of orness the proposed approach generates the owa operator weights by minimizing the maximum difference between any two adjacent weights a numerical example is provided to illustrate the application of the proposed approach in generating viable owa operator weights in a simple and effective way

p moment stability of stochastic differential equations with jumps in the paper p moment stability of stochastic differential equations with jumps is considered first some preliminary notes are given then several theorems on p moment stability of these equations are established using liapunov function at last an example is present to show application of the obtained results

a solution method to the problem proposed by wang in voting systems this paper proposes a method to rank multiple efficient candidates which often happens in dea method by comparing the least relative total scores for each efficient candidate with the best and the least relative total scores measured in the same range by a numerical example our model is used to identify efficient candidate and the model can get less efficient candidates too than that can be identified by the model given by wang and chin y m wang k s chin discriminating dea efficient candidates by considering their least relative total scores j comput appl math 206 2007 209 215 this paper also points out that there is a drawback in the theorem about e given by wang and chin y m wang k s chin discriminating dea efficient candidates by considering their least relative total scores j comput appl math 206 2007 209 215

on the analytic representation of the leximin ordering and its application to flexible constraint propagation we discuss the basic formulation of constraint propagation problems and extend it to the flexible constraint propagation environment where constraints are represented as fuzzy subsets some methods for ordering alternative solutions with respect to a collection of flexible constraints are discussed along with their drawbacks among the methods introduced is the leximin method where we note its lack of an analytic formulation with the aid of the ordered weighted averaging owa operator we suggest an analytic formulation for the leximin method some properties of this formulation are provided we then describe the application of this new formulation for the leximin method to situations in which the constraints are describable in a linear fashion we show how we can use mixed integer programming techniques to find an optimal solution

generalized ordered weighted utility proportional averaging hyperbolic absolute risk aversion operators and their applications to group decision making under the general utility we provide a new operator called gowupa operator under hara utility we present a new operator called the gowupa hara operator we put forward an orness measure of the gowupa hara operator we construct a new model for determining the weight of the gowupa hara operator we develop a new approach for multiple attributes group decision making this paper develops a new class of aggregation operator based on utility function which introduces the risk attitude of decision makers dms in the aggregation process first under the general framework of utility function we provide a new operator called the generalized ordered weighted utility proportional averaging gowupa operator and study its properties which are suitable for any utility function then under the hyperbolic absolute risk aversion hara utility function we propose another new operator named as the generalized ordered weighted utility proportional averaging hyperbolic absolute risk aversion gowupa hara operator and further investigate its families including a wide range of aggregation operators to determine the gowupa hara operator weights we put forward an orness measure of the gowupa hara operator and analyze its properties considering that different dms may have different opinions towards decision making and their opinions can be characterized by different orness measures we construct a new nonlinear optimization model to determine the optimal weights which can aggregate all the individual sets of weights into an overall set of weights furthermore based on the gowupa hara operator a method for multiple attribute group decision making magdm is developed finally an example is given to illustrate the application of the gowupa hara operator to the magdm

improving minimax disparity model to determine the owa operator weights determining the ordered weighted averaging owa operator weights is important in decision making applications several approaches have been proposed in the literature to obtain the associated weights this paper provides an alternative disparity model to identify the owa operator weights the proposed mathematical model extends the existing disparity approaches by minimizing the sum of the deviation between two distinct owa weights the proposed disparity model can be used for a preference ranking aggregation a numerical example in preference ranking and an application in search engines prove the usefulness of the generated owa weights

square mean almost automorphic mild solutions to non autonomous stochastic differential equations in hilbert spaces in this paper we first refine the definition of square mean almost automorphic functions introduced in fu and liu 2010 11 then we prove the existence and uniqueness of square mean almost automorphic mild solutions for a class of non autonomous stochastic differential equations in a real separable hilbert space some additional properties of square mean almost automorphic functions are also provided to prove our main result we use the banach contraction mapping principle

a multiple criteria approach to data envelopment analysis in this paper we present a multiple criteria data envelopment analysis mcdea model which can be used to improve discriminating power of dea methods and also effectively yield more reasonable input and output weights without a priori information about the weights in the proposed model several different efficiency measures including classical dea efficiency are defined under the same constraints each measure serves as a criterion to be optimized efficiencies are then evaluated under the framework of multiple objective linear programming molp the method is illustrated through three examples in which data sets are taken from previous research on dea s discriminating power and weight restriction

highlights and critical points in the theory and application of the analytic hierarchy process abstract this paper provides a detailed discussion with references on the fundamentals of the analytic hierarchy process and in particular of relative measurement the points discussed are grouped under the following categories structure in the ahp hierarchies and networks scales of measurement judgments consistency and the eigenvector synthesis and normative vs descriptive the paper also includes a discussion of rank and a number of citations of rank reversals attributed to a variety of factors ranging from intransitivity to procedure invariance that are thought to be unexplained by utility theory with its underlying principle to always preserve rank it is shown that when there is synergy due to the number of elements the ahp can be used to both preserve rank when it is desired to preserve it and allow it to reverse when it should reverse

a note on including ordinal relations among multipliers in data envelopment analysis data envelopment analysis dea evaluates the efficiency of decision making units without imposing a priori weights on the input and output dimensions involved this note extends dea to situations where ordinal relations among weights corresponding to certain dimensions exist the extended model is reduced to the original dea formulation where some of the input and output factors are accumulated an illustrative example is provided and potential areas of applications are pointed out

quantum tunnelling effect for the inverted caldirola kanai hamiltonian in order to study the behaviour of the inverted caldirola kanai hamiltonian in the quantum tunnelling effect the authors consider a wavepacket as the initial state and they calculate exactly the probability density they also obtain the transmission and reflection probability the expectation value of the particle s energy and the sojourn time which appears to be an increasing function of the dissipation parameter gamma a similar result is also obtained by considering a normalized plane wave as the initial state

non hermitian harmonic oscillator with discrete complex or real spectrum for non unitary squeeze operators in the present paper we enlarge the method of debergh beckers and szafraniec for non hermitian hamiltonians with complex parameters and obtain real eigenvalues for the case of non unitary squeeze operators with two complex parameters of non hermitian harmonic oscillator we obtain discrete complex spectrum and for special values of the complex parameters the spectrum is discrete real and positive even though the corresponding operators are not pt symmetric

on some methods for performance ranking and correspondence analysis in the dea context two novel methods named performance baseline and performance correspondence matrices are proposed to evaluate the performance of decision making units dmus based on the techniques of singular value decomposition svd the performance baseline matrix can be used to rank all the dmus because it provides a common basis for performance comparison the performance correspondence matrix can be used to conduct performance cluster analysis with which to explore the structure of input output variables that are associated with dmus the analysis can reveal the performance difference of the dmus and the key input output variables determining the efficiency of a certain dmu and provides valuable quantitative information for adjusting variables to improve efficiency of the dmu three case studies are presented to demonstrate that the proposed methods in this work are effective and easy to use and can provide insights into proper selection of input output variables for performance comparison to avoid over manipulating dea models in practice

equivalent formulations of nonlinear integer problems for efficient optimization the linearization technique of glover which seems to be the most efficient one appearing in the literature requires the addition of n new continuous variables unconstrained in sign and 4n new linear constraints to equivalently represent a 0 1 quadratic integer problem with n variables this paper shows that it is still possible to improve such a procedure in fact the number of new continuous variables can be kept at n but constrained in sign while further reducing the number of new linear constraints from 4n to 2n

p moment stability of stochastic differential equations with impulsive jump and markovian switching this paper introduces some new concepts of p moment stability for stochastic differential equations with impulsive jump and markovian switching some stability criteria of p moment stability for stochastic differential equations with impulsive jump and markovian switching are obtained by using liapunov function method an example is also discussed to illustrate the efficiency of the obtained results

tunnelling process for non hermitian systems the complex frequency inverted oscillator the authors study the tunnel effect for an inverted oscillator with complex frequency the solution of the corresponding non hermitian nh schrodinger equation is found by the evolution operator method based on the su 1 1 structure of the hamiltonian and the wei norman theorem 1963 the authors put forward a generalization of dwell time for nh systems built up from their biorthonormal states the resulting tunnelling time turns out to be complex

on the ordinal equivalence of the johnston banzhaf and shapley power indices abstract in this paper we characterize the games in which johnston shapley shubik and penrose banzhaf coleman indices are ordinally equivalent meaning that they rank players in the same way we prove that these three indices are ordinally equivalent in semicomplete simple games which is a newly defined class that contains complete games and includes most of the real world examples of binary voting systems this result constitutes a twofold extension of diffo lambo and moulen s result diffo lambo and moulen 2002 in the sense that ordinal equivalence emerges for three power indices not just for the shapley shubik and penrose banzhaf coleman indices and it holds for a class of games strictly larger than the class of complete games

stability of square mean almost automorphic mild solutions to impulsive stochastic differential equations driven by g brownian motion in this paper we consider a class of impulsive stochastic differential equations driven by g brownian motion igsdes in short in particular we study the exponentially and quasi sure exponentia

the appropriate total ranking method using dea for multiple categorized purposes when one expects to figure out the total ranking of objects from collected data it is a familiar method to compare the weighted sum of the selection number of rank vote after determining the weights in a selected rank green et al european j oper res 90 3 1996 461 using data envelopment analysis and cross evaluation proposed a procedure to order the objects from the ranking of one categorized data but they have not taken care of about making the weight of a certain rank 0 and the value of the difference between ranks becomes 0 in actual applications making the weight of a certain rank 0 means that we throw away the corresponding part of the obtained rank voting data further giving the same weight to different ranks destroys its original ranking character and then in this paper we show that the total ordinal rank of objects may produce a different result according to the difference of the weights between ranks consequently we explain that their ordering is not appropriate to applications and we propose a new ordering to solve the weights of ranks by considering feasible solutions region of the constraint set in lp also we would like to propose such a method that if extended it can be applied more widely not only when the selected category is for a single purpose but also when it is for multiple purposes especially with an example taken from the personal development issue at a corporation