poisson cohomology of plane poisson structures with isolated singularities revisited continuing the work of monnier israel j math 129 189 207 2002 we determine the gerstenhaber algebra structure over the poisson cohomology groups for a large class of poisson structures with isolated singularities over the plane it reveals that there exists a gaga type phenomenon we give an explicit description via generators and relations for the case of simple singularities

topsis for modm abstract in this study we extend topsis to solve a multiple objective decision making problem the principle of compromise of topsis for multiple criteria decision making is that the chosen solution should have the shortest distance from the positive ideal solution as well as the longest distance from the negative ideal solution thus we reduce a k dimensional objective space to a two dimensional objective space by a first order compromise procedure we then use membership functions of fuzzy set theory to represent the satisfaction level for both criteria we obtain a single objective programming problem by using the max min operator for the second order compromise operation to illustrate the procedure the bow river valley water quality management problem is solved by use of topsis

a differential complex for poisson manifolds construction du complexe canonique d une variete de poisson homologie canonique des varietes symplectiques application a l homologie de hochschild des algebres non commutatives

a modified topsis with a different ranking index abstract as a tool for decision analysis the topsis technique for order preference by similarity to ideal solution attempts to choose alternative that should simultaneously have the closest distance from the positive ideal solution pis and the farthest distance from the negative ideal solution nis although the ranking index of topsis is reasonable it contains a flaw that is this ranking index is irrespective of the weights of separations of an alternative from the pis and the nis in other words no matter what weights the decision maker assigns to these two separations the ranking results would not differ as if he has no preference for these two separations this flaw will certainly limit the applicability of topsis by treating the separations of an alternative from the pis and the nis as a cost criterion and a benefit criterion respectively we reduced the original mcdm multi criteria decision making problem to a new mcdm problem with these two criteria only by proposing w and w as the weights of the cost criterion and the benefit criterion respectively we defined a new ranking index experimental results showed that if the number of alternatives exceeds two or if the relative importance of the two separations should be considered the proposed ranking index would be a better choice finally two numerical examples of a real life case are given for illustration in summary the proposed ranking index is intelligible and intrinsically superior to the original ranking index in seeking compromised solutions

nonequilibrium lattice models series analysis of steady states a perturbation theory for steady states of interacting particle systems is developed and applied to several lattice models with nonequilibrium critical points near an absorbing state the expansion is expressed directly in terms of the kinetic parameter creation rate rather than in powers of the interaction an algorithm for generating series expansions for local properties is described order parameter series 16 terms and precise estimates of critical properties are presented for the one dimensional contact process and several related models

twisted poincare duality between poisson homology and poisson cohomology abstract a version of the twisted poincare duality is proved between the poisson homology and cohomology of a polynomial poisson algebra with values in an arbitrary poisson module the duality is achieved by twisting the poisson module structure in a canonical way which is constructed from the modular derivation in the case that the poisson structure is unimodular the twisted poincare duality reduces to the poincare duality in usual sense the main result generalizes the work of launois and richard 8 for the quadratic poisson structures and zhu 25 for the linear poisson structures

solving multi period project selection problems with fuzzy goal programming based on topsis and a fuzzy preference relation project portfolio managers are multi objective decision makers dms who are expected to select the best mix of projects by maximizing profits and minimizing risks over a multi period planning horizon however project portfolio decisions are complex multi objective problems with a high number of projects from which a subset has to be chosen subject to various constraints and a multitude of priorities and preferences we propose a goal programming gp approach for project portfolio selection that embraces conflicting fuzzy goals with imprecise priorities a fuzzy goal with an aspiration level and a predefined membership function is defined for each objective the impreciseness in the priorities of the membership values of the fuzzy goals is modeled with fuzzy relations this leads to type ii fuzzy sets since fuzzy relations are organized between the membership values of the fuzzy goals which are themselves fuzzy sets the proposed model is based on the technique for order preference by similarity to ideal solution topsis and fuzzy preference relations topsis is used to reduce the multi objective problem into a bi objective problem the resulting bi objective problem is solved with fuzzy gp fgp the fuzzy preference relations are used to help dms express their preferences with respect to the membership values of the fuzzy goals the proposed approach is used to solve a real life problem characterized as a fuzzy multi objective project selection with multi period planning horizon mops mpph the performance of the proposed approach is compared with a competing method in the literature we show that our approach generates high quality solutions with minimal computational efforts

minimum energy point charge configurations on a circular disk stochastic global optimization methods are used together with problem specific heuristics to find configurations of n equal point charges on a circular disk such that the potential energy is minimized previous such optimal or conjecturally optimal configurations have been published only for and n 29 30 50 earlier results are examined and the best currently known configurations most of them new for are presented

phase transitions on fractals iii infinitely ramified lattices for pt ii see ibid vol 17 p 435 1984 in the first two papers of this series the authors considered self similar fractal lattices with a finite order of ramification r in the present paper they study physical models defined on a family of fractals with r infinity in order to characterise the geometry of these systems they need the connectivity q and the lacunarity l in addition to the fractal dimensionality d it is found that discrete symmetry spin models on these lattices undergo a phase transition at tc 0 an approximate renormalisation group scheme is constructed and used to find the dependence of tc and the critical exponents on the geometrical factors they also solve the problem of resistor networks on these fractals and discuss its consequences concerning spin models with continuous symmetry

multi attribute decision making a simulation comparison of select methods abstract several methods have been proposed for solving multi attribute decision making problems madm a major criticism of madm is that different techniques may yield different results when applied to the same problem the problem considered in this study consists of a decision matrix input of n criteria weights and ratings of l alternatives on each criterion the comparative performance of some methods has been investigated in a few mostly field studies in this simulation experiment we investigate the performance of eight methods electre topsis multiplicative exponential weighting mew simple additive weighting saw and four versions of ahp original vs geometric scale and right eigenvector vs mean transformation solution simulation parameters are the number of alternatives criteria and their distribution the solutions are analyzed using twelve measures of similarity of performance similarities and differences in the behavior of these methods are investigated dissimilarities in weights produced by these methods become stronger in problems with few alternatives however the corresponding final rankings of the alternatives vary across methods more in problems with many alternatives although less significant the distribution of criterion weights affects the methods differently in general all ahp versions behave similarly and closer to saw than the other methods electre is the least similar to saw except for closer matching the top ranked alternative followed by mew topsis behaves closer to ahp and differently from electre and mew except for problems with few criteria a similar rank reversal experiment produced the following performance order of methods saw and mew best followed by topsis ahps and electre it should be noted that the electre version used was adapted to the common madm problem and therefore it did not take advantage of the method s capabilities in handling problems with ordinal or imprecise information

poisson cohomology of the affine plane abstract we compute the poisson cohomology of homogeneous poisson structures on the plane the singular locus of such a poisson structure consists of a family of lines passing through o and we show how the dimensions of the first and second cohomology groups are related to the weight of o as a singular point of

double poisson cohomology of path algebras of quivers abstract in this note we give a description of the graded lie algebra of double derivations of a path algebra as a graded version of the necklace lie algebra equipped with the kontsevich bracket furthermore we formally introduce the notion of double poisson lichnerowicz cohomology for double poisson algebras and give some elementary properties we introduce the notion of a linear double poisson tensor on a quiver and show that it induces the structure of a finite dimensional algebra on the vector spaces v v generated by the loops in the vertex v we show that the hochschild cohomology of the associative algebra can be recovered from the double poisson cohomology then we use the description of the graded necklace lie algebra to determine the low dimensional double poisson lichnerowicz cohomology groups for three types of linear and nonlinear double poisson brackets on the free algebra c x y this allows us to develop some useful techniques for the computation of the double poisson lichnerowicz cohomology

a modified weighted topsis to identify influential nodes in complex networks abstract identifying influential nodes in complex networks is still an open issue although various centrality measures have been proposed to address this problem such as degree betweenness and closeness centralities they all have some limitations recently technique for order performance by similarity to ideal solution topsis as a tradeoff between the existing metrics has been proposed to rank nodes effectively and efficiently it regards the centrality measures as the multi attribute of the complex network and connects the multi attribute to synthesize the evaluation of node importance of each node however each attribute plays an equally important part in this method which is not reasonable in this paper we improve the method to ranking the node s spreading ability a new method named as weighted technique for order performance by similarity to ideal solution weighted topsis is proposed in our method we not only consider different centrality measures as the multi attribute to the network but also propose a new algorithm to calculate the weight of each attribute to evaluate the performance of our method we use the susceptible infected recovered sir model to do the simulation on four real networks the experiments on four real networks show that the proposed method can rank the spreading ability of nodes more accurately than the original method

non equilibrium critical behaviour on fractal lattices a simple one component surface reaction model exhibiting a critical point has been studied on deterministic fractal lattices with fractal dimension 1 df 2 results from time dependent simulations show a change in the value of the critical exponents with df two of the exponents interpolate very nicely between the values in one and two dimensions

poisson co homology and isolated singularities abstract to each polynomial f x y z is associated a poisson structure on f 3 a surface and a poisson structure on this surface when is weight homogeneous with an isolated singularity we determine the poisson cohomology and homology of the two poisson varieties obtained

on the oscillatory dynamical behaviour of epidemic spreading in fractal media we present numerical evidence that dynamical physical processes that develop a time dependent characteristic length and take place in fractal media exhibiting spatial discrete scale invariance dsi with fundamental scaling ratio b may become coupled to the topology of the fractal leading to the observation of time dsi the hallmark of time dsi is the observation of a log periodic modulation of the dynamic or kinetic observables which is characterized by a well defined fundamental time scaling ratio both fundamental scaling ratios are linked according to b 1 z where z is the dynamic exponent characteristic of the physical process specifically we have studied the epidemic behaviour of the contact process cp in sierpinski carpets the cp exhibits second order irreversible phase transitions between an active regime and an absorbing state where the system is trapped without any escape possibility we observed that relevant dynamic observables such as the number of active sites the survival probability of the epidemics and the mean square displacement of the epidemic from the origin r2 t exhibit log periodic modulations by fitting the data we evaluate the fundamental time scaling ratio for various fractals and the corresponding dynamic exponents since at criticality one has that r2 t t2 z an independent estimation of the dynamic exponent can be performed in excellent agreement with results obtained by using the conjectured relationship for the fundamental scaling ratios b and

the method of images and green s function for spherical domains motivated by problems in electrostatics and vortex dynamics we develop two general methods for constructing green s function for simply connected domains on the surface of the unit sphere we prove a riemann mapping theorem showing that such domains can be conformally mapped to the upper hemisphere we then categorize all domains on the sphere for which green s function can be constructed by an extension of the classical method of images we illustrate our methods by several examples such as the upper hemisphere geodesic triangles and latitudinal rectangles we describe the point vortex motion in these domains which is governed by a hamiltonian determined by the dirichlet green s function

compromise solution by mcdm methods a comparative analysis of vikor and topsis the multiple criteria decision making mcdm methods vikor and topsis are based on an aggregating function representing closeness to the ideal which originated in the compromise programming method in vikor linear normalization and in topsis vector normalization is used to eliminate the units of criterion functions the vikor method of compromise ranking determines a compromise solution providing a maximum group utility for the majority and a minimum of an individual regret for the opponent the topsis method determines a solution with the shortest distance to the ideal solution and the greatest distance from the negative ideal solution but it does not consider the relative importance of these distances a comparative analysis of these two methods is illustrated with a numerical example showing their similarity and some differences 2003 elsevier b v all rights reserved

critical behaviour of the irreversible phase transitions of a dimer monomer process on fractal media the dynamic critical behaviour of a dimer monomer surface reaction process the zgb model of the type 1 2 a2 b to ab is studied on two different fractals namely a sierpinski carpet and percolating clusters which have almost the same fractal dimension df equivalent to 1 89 in both surfaces the model exhibits two continuous irreversible phase transitions for the sierpinski carpet the values of the critical exponents interpolate between those of directed percolation in 1 1 and 1 2 dimensions results corresponding to percolating clusters are not conclusive enough to assign the universality class of the model

a new method of identifying influential nodes in complex networks based on topsis abstract in complex networks identifying influential nodes is the very important part of reliability analysis which has been a key issue in analyzing the structural organization of a network in this paper a new evaluation method of node importance in complex networks based on technique for order performance by similarity to ideal solution topsis approach is proposed topsis as a multiple attribute decision making madm technique has been an important branch of decision making since then in addition topsis is first applied to identify influential nodes in a complex network in this open issue in different types of networks in which the information goes by different ways we consider several different centrality measures as the multi attribute of complex network in topsis application topsis is utilized to aggregate the multi attribute to obtain the evaluation of node importance of each node it is not limited to only one centrality measure but considers different centrality measures because every centrality measure has its own disadvantage and limitation then we use the susceptible infected si model to evaluate the performance numerical examples are given to show the efficiency and practicability of the proposed method

extension of the topsis method for decision making problems with fuzzy data decision making problem is the process of finding the best option from all of the feasible alternatives in this paper from among multicriteria models in making complex decisions and multiple attribute models for the most preferable choice technique for order preference by similarity to ideal solution topsis approach has been dealt with in real word situation because of incomplete or non obtainable information the data attributes are often not so deterministic there for they usually are fuzzy imprecise therefore the aim of this paper is to extend the topsis method to decision making problems with fuzzy data in this paper the rating of each alternative and the weight of each criterion are expressed in triangular fuzzy numbers the normalized fuzzy numbers is calculated by using the concept of a cuts finally a numerical experiment is used to illustrate the procedure of the proposed approach at the end of this paper

directed percolation in 2 1 dimensions the author presents results of monte carlo simulations for directed percolation in 2 1 dimensions very close to the percolation threshold his values for pc for bond and site percolation on the bcc and simple cubic lattices are more precise than previous estimates by one to two orders of magnitude the improvement on the critical exponents describing the behaviour at pc is less impressive but they are also substantially more precise than previous ones

an approach to generalization of fuzzy topsis method the topsis method is a technique for establishing order preference by similarity to the ideal solution and was primarily developed for dealing with real valued data this technique is currently one of most popular methods for multiple criteria decision making mcdm in many cases it is hard to present precisely exact ratings of alternatives with respect to local criteria and as a result these ratings are seen as fuzzy values a number of papers have been devoted to fuzzy extensions of the topsis method in the literature but these extensions are not complete since the ideal solutions are usually presented as real values not by fuzzy values or as fuzzy values which are not attainable in the decision matrix in most of these papers a defuzzification of elements of the fuzzy decision matrix is used which leads inevitably to a loss of important information and may even produce the wrong results in this paper we propose a new direct approach to the fuzzy extension of the topsis method which is free of the limitations of other known approaches we show that the distances of the alternatives from the ideal solutions may be treated in some sense as modified weighted sums of local criteria it is known that using weighted sums is not the best approach to the aggregation of local criteria in many real world situations therefore here we propose the use in addition to weighted sums some other types of local criteria aggregation in the topsis method and we develop a method for the generalization of different aggregation modes providing compromised final results