the consistent value of fuzzy games in the framework of fuzzy games we offer an extension of the reduced game introduced by hart and mas colell which we name the self reduced game according to consistency which related to the self reduced game we provide a definition of the consistent value which is a generalization of the shapley value of fuzzy games we adopt three existing concepts from coalitional game theory and reinterpret them in the framework of fuzzy games the first one is that there exists a unique potential function and the resulting payoff vector coincides with the consistent value second based on the properties of balanced contributions and consistency we offer several axiomatizations of the consistent value finally we propose a dynamic process to illustrate that the consistent value can be reached by players who start from an arbitrary efficient payoff vector and make successive adjustments

the green rings of the 2 rank taft algebra and its two relatives twisted abstract in the paper the representation rings or the green rings for a family of hopf algebras of tame type the 2 rank taft algebra at q 1 and its two relatives twisted by 2 cocycles are explicitly described via a representation theoretic analysis it turns out that the green rings can serve to detect effectively the twist equivalent hopf algebras here

the consistent coalitional value we describe a value for nontransferable utility games with coalition structure this value coincides with the consistent value for trivial coalition structures and with the owen value for transferable utility games with coalition structure furthermore we present two characterizations the first one using properties of balanced contributions and the second one using a consistency property

quantum divided power algebra q derivatives and some new quantum groups abstract the discussions in the present paper arise from exploring intrinsically the structural nature of the quantum n space a kind of braided category g b of graded commutative associative algebras over a field k is established the quantum divided power algebra over k related to the quantum n space is introduced and described as a braided hopf algebra in g b in terms of its 2 cocycle structure over which the so called special q derivatives are defined so that several new interesting quantum groups especially the quantized polynomial algebra in n variables as the quantized universal enveloping algebra of the abelian lie algebra of dimension n and the quantum group associated to the quantum n space are derived from our approach independently of using the r matrix as a verification of its validity for our discussion the quantum divided power algebra is equipped with the structure of a uq s l n module algebra via certain q differential operators realization particularly one of the four kinds of root vectors of uq s l n in the sense of lusztig can be specified precisely under the realization

percolation parameter and percolation threshold estimates for three dimensional random ellipses with widely scattered distributions of eccentricity and size in fractured materials of very low matrix permeability fracture connectivity is the first order determinant of the occurrence of flow for systems having a narrow distribution of object sizes short range percolation a first order percolation criterion is given by the total excluded volume which is almost constant at threshold in the case of fractured media recent observations have demonstrated that the fracture length distribution is extremely large because of this widely scattered fracture length distribution the classical expression of the total excluded volume is no longer scale invariant at the percolation threshold and has no finite limit for infinitely large systems thus the classical estimation method of the percolation threshold established in short range percolation becomes useless for the connectivity determination of fractured media in this study we derive an expression for the total excluded volume that remains scale invariant at the percolation threshold and that can thus be used as the proper control parameter called the parameter of percolation in percolation theory we show that the scale invariant expression of the total excluded volume is the geometrical union normalized by the system volume rather than the summation of the mutual excluded volumes normalized by the system volume the summation of the mutual excluded volume classical expression remains linked to the number of intersections between fractures whereas the normalized geometrical union of the mutual excluded volume our expression can be essentially identified with the percolation parameter moreover fluctuations of this percolation parameter at threshold with length and eccentricity distributions remain limited within a range of less than one order of magnitude giving in turn a rough percolation criterion we finally show that the scale dependence of the percolation parameter causes the connectivity of fractured media to increase with scale meaning especially that the hydraulic properties of fractured media can dramatically change with scale

a banzhaf function for a fuzzy game in this paper another important solution for fuzzy games called the banzhaf function is investigated first a sim plified expression for the banzhaf function for games with fuzzy coalition is proposed the relationship between this simplified ex pression and two kinds of particular banzhaf functions are dis cussed in detail furthermore in the framework of games with fuzzy coalitions we give a definition of the potential function of fuzzy games and prove that the marginal values of the potential function are the components of the banzhaf function further more a new axiomatic characterization of the banzhaf function for games with fuzzy coalitions is provided

on finite potential games a linear system called the potential equation pe is presented it is proved that a finite game is potential if and only if its potential equation has solution some properties of the potential equation are obtained based on these properties a closed form solution of the pe is obtained moreover a formula based on the solution of the pe is obtained to calculate the potential function finally it is proved that a networked evolutionary game is potential if and only if its fundamental network game is potential some interesting examples are presented to illustrate the theoretical results

a new look at the role of players weights in the weighted shapley value abstract everal new families of semivalues for weighted n person transferable utility games are axiomatically constructed and discussed under increasing collections of axioms where the weighted shapley value arises as the resulting one member family a more general approach to such weighted games defined in the form of two components a weight vector and a classical tu game v is provided the proposed axiomatizations are done both in terms of and v several new axioms related to the weight vector are discussed including the so called amalgamating payoffs axiom which characterizes the value of a weighted game in terms of another game with a smaller number of players they allow for a new look at the role of players weights in the context of the weighted shapley value for the model of weighted games giving new properties of it besides another simple formula for the weighted shapley value is found and examples illustrating some surprising behavior of it in the context of players weights are given the paper contains a wide discussion of the results obtained

egalitarian solutions of large games i a continuum of players this is the first of two papers devoted to the study of egalitarian solutions for nontransferable utility ntu games with a large number of players this paper is concerned with the construction of egalitarian solutions for the limit situation with a continuum of players we build on the concept of the potential introduced in hart and mas colell hart s a mas colell 1989 potential value and consistency econometrica57 589 614 and exploit partial differential equations techniques in particular we associate to the egalitarian solutions a variational problem which may be viewed as a generalization to the nontransferable utility context of the diagonal principle of aumann and shapley aumann r j l s shapley 1974 values of non atomic games princeton university press princeton new jersey in the transferable utility setting

egalitarian solutions of large games ii the asymptotic approach this is the second of two papers devoted to the study of egalitarian solutions for nontransferable utility ntu games with a large number of players this paper is concerned with the egalitarian solutions of finite games as the number of players increases we show that these converge to the egalitarian solution of the limit game with a continuum of players as defined in our previous paper the same convergence holds for the underlying potential functions these asymptotic results are particularly significant since they provide the definitive justification for our definitions in the limit continuum case

cooperation indices and weighted shapley values the weighted shapley values are extended to situations defined by a cooperative game and a cooperation index two main axiomatic characterizations for the modified values are provided we also develop further axiomatizations of the classical values and discuss two examples

potential consistency and cost allocation prices in a typical cost allocation problem a decision maker must allocate the joint cost of producing a specified vector of goods or services using prices in earlier work billera heath and raanan applied the theory of values of nonatomic games of aumann and shapley to develop a pricing mechanism called aumann shapley pricing the aumann shapley value for nonatomic games has an axiomatic foundation that was adapted to the cost allocation context by billera and heath and mirman and tauman in this paper we develop the notions of reduced cost function consistency and potential for cost allocation problems and we provide a new axiomatic characterization of symmetric and weighted aumann shapley pricing in terms of consistency

designing network protocols for good equilibria designing and deploying a network protocol determines the rules by which end users interact with each other and with the network we consider the problem of designing a protocol to optimize the equilibrium behavior of a network with selfish users we consider network cost sharing games where the set of nash equilibria depends fundamentally on the choice of an edge cost sharing protocol previous research focused on the shapley protocol in which the cost of each edge is shared equally among its users we systematically study the design of optimal cost sharing protocols for undirected and directed graphs single sink and multicommodity networks and different measures of the inefficiency of equilibria our primary technical tool is a precise characterization of the cost sharing protocols that induce only network games with pure strategy nash equilibria we use this characterization to prove among other results that the shapley protocol is optimal in directed graphs and that simple priority protocols are essentially optimal in undirected graphs

the shapley value for arbitrary families of coalitions abstract we address the problem of finding a suitable definition of a value similar to that of shapley s when the games are defined on a subfamily of coalitions with no structure we present two frameworks one based on the familiar efficiency linearity and null player axioms and the other on linearity and the behavior on unanimity games we give several properties and examples in each case and give necessary and sufficient conditions on the family of coalitions for the approaches to coincide

potential value and consistency let p be a real valued function defined on the space of cooperative games with transferable utility satisfying the following condition in every game the marginal contributions of all players are efficient it is proved that there exists just one such function p called the potential and moreover that the resulting payoff vector coincides with the shapley value

demand compatible equitable cost sharing prices we propose here a new approach for equitable cost sharing pricing based upon the shapley value for nonatomic games however it is shown that the proposed price mechanism can be justified on economic terms since it is uniquely determined by a set of axioms involving only cost functions and quantities consumed and not any notion of game theory moreover taking into account the utilities of the consumers one can prove the existence of an equilibrium under this price mechanism for a general class of cost functions this approach has the advantage of not involving any interpersonal comparisons of utilities

new mathematical properties of the banzhaf value abstract a new axiomatic characterization of the banzhaf value for a cooperative n person game with transferable utilities is given by using a new potential function in the space of all games with a fixed set of players a potential basis has been found which allows an explicit representation of all games with an apriori given banzhaf value

the pairwise egalitarian solution abstract the main aim of this paper is to introduce an ad hoc solution concept for transportation games this solution is related to the structure of the underlying transportation problem in the game in particular to the optimal solutions for it this is significantly called the pairwise egalitarian solution we compare the new solution with the core and the shapley value of the game finally we study the properties satisfied by the pairwise egalitarian solution and provide two axiomatic characterizations of it

derivation of equivalent pipe network analogues for three dimensional discrete fracture networks by the boundary element method discrete fracture network dfn models generally require solution of flow and transport equations in three dimensional networks of either disc polygonal or pipe elements pipe network elements have significant advantages in computation for both flow and transport however there is a need to develop an efficient procedure for derivation of the properties of these pipes to ensure that they are hydraulically equivalent to the dfn network of polygonal elements in this study a boundary element procedure for derivation of pipe properties is developed and demonstrated the results show that the hydraulic behavior of pipe networks can be equivalent to that of polygonal element dfn models

a new shapley value for games with fuzzy coalitions abstract this paper deals with cooperative games over fuzzy coalitions in these situations there is a continuous set of fuzzy coalitions instead of a finite set of them as in the classical case the unit square in an n dimensional space there exist in the literature two different extensions of the known shapley value for crisp games to games with fuzzy coalitions the crisp shapley value and the diagonal value the first value only uses a finite information in the set of fuzzy coalitions the vertices of the square while the second one uses a neighbourhood of the diagonal of the square we propose a new extension of the shapley value improving the crisp shapley value for games with fuzzy coalitions this new version uses the faces of the square namely an infinity quantity of information we analyze several properties of the new value we endow it with an axiomatization and we study the behavior when it is applied to known fuzziness of crisp games

on the connectivity of three dimensional fault networks natural fault networks involve a very broad range of fault lengths modeled in general by a power law length distribution n l al such a scaling law does not allow to define any a priori pertinent scale of observation for hydraulic field experiments in fractured media to investigate the relative effects of faults depending on their length we undertake in the spirit of percolation theory a theoretical and numerical study of the connectivity of three dimensional fault networks following power law length distributions we first establish the correct analytical expression of a percolation parameter p which describes the connectivity of the system the parameter p is found to be dependent on the third moment of the length distribution for fault planes it allows us to identify different regimes of connectivity depending on a the exponent of the fault length distribution the geometrical properties of the infinite cluster which partly control transport properties are also established at the percolation threshold for natural fault networks our theoretical analysis suggests that faults larger than a critical length scale may form a well connected network while smaller faults may be not connected on average this result which implies an increase of the connectivity with scale is consistent with scaling effects observed on permeability measurements

yetter drinfeld modules under cocycle twists abstract we give an explicit formula for the correspondence between simple yetter drinfeld modules for certain finite dimensional pointed hopf algebras h and those for cocycle twists h of h this implies an equivalence between modules for their drinfeld doubles to illustrate our results we consider the restricted two parameter quantum groups u r s sl n under conditions on the parameters guaranteeing that u r s sl n is a drinfeld double of its borel subalgebra we determine explicit correspondences between u r s sl n modules for different values of r and s and provide examples where no such correspondence can exist our examples were obtained via the computer algebra system singular plural

a quiver quantum group we construct quantum groups at a root of unity and we describe their monoidal module category using techniques from the representation theory of finite dimensional associative algebras

indecomposable decomposition of tensor products of modules over the restricted quantum universal enveloping algebra associated to sl2 we study the tensor structure of the category of finite dimensional modules of the restricted quantum enveloping algebra associated to sl2 tensor product decomposition rules for all indecomposable modules are explicitly given as a by product it is also shown that the category of finite dimensional modules of the restricted quantum enveloping algebra associated to sl2 is not a braided tensor category

potentials and weighted values of nonatomic games the potential approach to value theory for finite games was introduced by hart and mas colell hart s a mas colell 1989 potential value and consistency econometrica57 589 614 here this approach is extended to non atomic games on appropriate spaces of differentiable games there is a unique potential operator that generates the aumann and shapley aumann r j l s shapley 1974 values of nonatomic games princeton university press princeton new jersey value as a corollary we obtain the uniqueness of the aumann shapley value on certain subspaces of games next the potential approach is applied to the weighted case leading to weighted non atomic values it is further shown that the asymptotic weighted value is well defined and that it coincides with the weighted value generated by the potential

refinement derivatives and values of games a definition of setwise differentiability for set functions is given through refining the partitions of sets such a construction is closely related to the one proposed by rosenmuller rosenmuller j 1977 extreme games and their solutions springer verlag berlin epstein epstein l 1999 a definition of uncertainty aversion rev econom stud 66 579 608 and epstein and marinacci epstein l m marinacci 2001 the core of large differentiable tu games j econom theory100 235 273 we present several classes of transferable utility tu games that are differentiable and study differentiation rules the last part of this paper applies refinement derivatives to the computation of value of games following hart and mas colell hart s a mas colell 1989 potential value and consistency econometrica57 589 614 we define an operator through the refinement derivative of the potential of the game we show that this operator is a value when restricted to the spaces pm and pot2 the latter space is closely related to myerson s balanced contributions axiom

potential games are necessary to ensure pure nash equilibria in cost sharing games we consider the problem of designing distribution rules to share welfare cost or revenue among individually strategic agents there are many known distribution rules that guarantee the existence of a pure nash equilibrium in this setting e g the shapley value and its weighted variants however a characterization of the space of distribution rules that guarantees the existence of a nash equilibrium is unknown our work provides an exact characterization of this space for a specific class of scalable and separable games that includes a variety of applications such as facility location routing network formation and coverage games given arbitrary local welfare functions x1d568 we prove that a distribution rule guarantees equilibrium existence for all games i e all possible sets of resources agent action sets etc if and only if it is equivalent to a generalized weighted shapley value on some ground welfare functions x1d568 which can be distinct from x1d568 however if budget balance is required in

modules over mathfrak u _q mathfrak s mathfrak l _2 the restricted quantum universal enveloping algebra mathfrak u q mathfrak s mathfrak l 2 decomposes in a canonical way into a direct sum of indecomposable left or right ideals they are useful for determining the direct summands which occur in the tensor product of two simple mathfrak u q mathfrak s mathfrak l 2 the indecomposable finite dimensional mathfrak u q mathfrak s mathfrak l 2 are classified and located in the auslander reiten quiver

a survey of consistency properties in cooperative game theory the main purpose of this survey paper is to review the axiomatic characterizations of the shapley value the prekernel the prenucleolus and the core by means of a consistency property in terms of the reduced games whenever possible new results and new proofs are added

a new approach to simulating flow in discrete fracture networks with an optimized mesh natural fractured media are highly unpredictable because of existing complex structures at the fracture and at the network levels fractures are by themselves heterogeneous objects of broadly distributed sizes shapes and orientations that are interconnected in large correlated networks with little field data and evidence numerical modeling can provide important information on the underground hydraulic phenomena however it must overcome several barriers first the complex network structure produces a structure difficult to mesh second the absence of a priori homogenization scale along with the double fracture and network heterogeneity levels requires the calculation of large but finely resolved fracture networks resulting in very large simulation domains to tackle these two related issues we reduce the highly complex geometry of the fractures by applying a local transformation that suppresses the cumbersome meshing configurations while keeping the networks fundamental geological and geometrical characteristics we show that the flow properties are marginally affected while the problem complexity i e memory capacity and resolution time can be divided by orders of magnitude the goal of this article is to propose a method of resolution which takes into account the geometrical complexity met in the networks and which makes it possible to treat a few thousand fractures the principal aim of this article is to present a tool to slowly modify the structures of the fracture networks to have a good quality mesh with a marginal loss in precision

distributed welfare games game theoretic tools are becoming a popular design choice for distributed resource allocation algorithms a central component of this design choice is the assignment of utility functions to the individual agents the goal is to assign each agent an admissible utility function such that the resulting game possesses a host of desirable properties including scalability tractability and existence and efficiency of pure nash equilibria in this paper we formally study this question of utility design on a class of games termed distributed welfare games we identify several utility design methodologies that guarantee desirable game properties irrespective of the specific application domain lastly we illustrate the results in this paper on two commonly studied classes of resource allocation problems coverage problems and coloring problems

power and potential maps induced by any semivalue some algebraic properties and computation by multilinear extensions the notions of total power and potential both defined for any semivalue give rise to two endomorphisms of the vector space of cooperative games on any given player set where the semivalue is defined several properties of these linear mappings are stated and the role of unanimity games as eigenvectors is described we also relate in both cases the multilinear extension of the image game to the multilinear extension of the original game as a consequence we derive a method to compute for any semivalue by means of multilinear extensions in the original game and also in all its subgames a the total power b the potential and c the allocation to each player given by the semivalue

consistency for the additive efficient normalization of semivalues abstract this paper contributes to consistency for the additive efficient normalization of semivalues motivated from the additive efficient normalization of a semivalue being a b revision of the shapley value we introduce the b reduced game which is an extension of sobolev s reduced game then the additive efficient normalization of a semivalue is axiomatized as the unique value satisfying covariance symmetry and b consistency furthermore by means of the path independently linear consistency together with the standardness for two person games the additive efficient normalization of semivalues is also characterized accessorily the additive efficient normalization of semivalues is directly verified as the linear consistent least square values see ruiz et al 1998

max consistency complement consistency and the core of fuzzy games recently hwang introduced two extensions of the max reduced game to fuzzy games by reducing the number of the players based on these reduced games he offered analogous axiomatizations of the core related to serrano and volij in the context of fuzzy games here we continue and develop hwang s work on similar topics however we turn to a different definition of the reduced game by simultaneously reducing both the number of the players and the participation levels we propose such extensions of the complement reduced game and of the max reduced game to fuzzy games and define the related properties of consistency and converse consistency based on these properties we offer several analogous characterizations of the core related to peleg serrano and volij and tadenuma respectively

twisting of quantum differentials and the planck scale hopf algebra we show that the crossed modules and bicovariant differential calculi on two hopf algebras related by a cocycle twist are in 1 1 correspondence in particular for quantum groups which are cocycle deformation quantisations of classical groups the calculi are obtained as deformation quantisations of the classical ones as an application we classify all bicovariant differential calculi on the planck scale hopf algebra this is a quantum group which has an limit as the functions on a classical but non abelian group and a limit as flat space quantum mechanics we further study the noncommutative differential geometry and fourier theory for this hopf algebra as a toy model for planck scale physics the fourier theory implements a t duality like self duality the noncommutative geometry turns out to be singular when and is therefore not visible in flat space quantum mechanics alone

modules over uq sl2 the restricted quantum universal enveloping algebra u q sl 2 decomposes in a canonical way into a direct sum of indecomposable lett or right ideals they are useful for determining the direct summands which occur in the tensor product of two simple u q sl 2 modules the indecomposable finite dimensional u q sl 2 modules are classified and located in the auslander reiten quiver

allocation of shared costs a set of axioms yielding a unique procedure often when several goods or services are produced by a common process or organization some estimate of the per unit costs of these goods is required in this note we consider cost allocation procedures and show that there is exactly one such procedure which possesses four desirable properties both the methods and the result were inspired by the recent work of aumann and shapley on nonatomic games

the within groups and the between groups myerson values abstract in this paper we revisit the additive decomposition that gomez et al 2003 introduced for the myerson value of a symmetric game when viewed as a centrality measure first we generalize this decomposition extending it to general games this approach permits us to look at the myerson value of a player as a certain modulus of a two component vector one of them the within groups myerson value determines which part corresponds to the profit from the coalitions that a given player is in whereas the other the between groups myerson value evaluates the opportunities that player has as intermediary in the communication among others these two values are then characterized using additivity and other properties related with previous interpretation a the competitive advantages or disadvantages of a null player in a game with restrictions given by a graph measured in terms of his myerson value are due to his ability to intermediate among the others b in the same context those players essential to coalitions that generate worth cannot obtain profit by intermediating when restricted to certain symmetric games the corresponding values can be considered as centrality measures as they satisfy natural properties that reinforce this interpretation

green rings of pointed rank one hopf algebras of nilpotent type let h be a finite dimensional pointed rank one hopf algebra of nilpotent type we first determine all finite dimensional indecomposable h modules up to isomorphism and then establish the clebsch gordan formulas for the decompositions of the tensor products of indecomposable h modules by virtue of almost split sequences the green ring r h of h will be presented in terms of generators and relations it turns out that the green ring r h is commutative and is generated by one variable over the grothendieck ring g0 h of h modulo one relation moreover r h is frobenius and symmetric with dual bases associated to almost split sequences and its jacobson radical is a principal ideal finally we show that the stable green ring the green ring of the stable module category is isomorphic to the quotient ring of r h modulo all projective modules it turns out that the complexified stable green algebra is a group like algebra and hence a bi frobenius algebra

the equal allocation of nonseparable costs an extension under fuzzy behavior by considering the players and the activity levels simultaneously we propose a consistent solution which is a generalization of the equal allocation of nonseparable costs eansc on fuzzy games we also adopt two pre existing concepts from traditional game theory and reinterpret them in the framework of fuzzy games first based on the consistency which related to an extended reduced game we offer two axiomatizations of the extended eansc second by applying the excess function we propose a dynamic process to illustrate that the extended eansc can be reached by players who start from an arbitrary efficient solution and make consecutive amendments

the equalizer and the lexicographical solutions for cooperative fuzzy games characterization and properties in this paper we analyze the lexicographical solution for fuzzy tu games we study its properties and obtain a characterization the lexicographical solution was introduced by sakawa and nishizaki fuzzy sets and systems 61 1994 265 275 as a solution for crisp tu games and then extended as a value for fuzzy tu games we approach the problem by means of the close relationship that exists between the lexicographical solution for crisp tu games and the least square nucleolus a crisp value defined by ruiz et al internat j game theory 25 1996 113 134 previously and also based on this relationship we axiomatically characterize the equalizer solution for fuzzy tu games both values the equalizer and the lexicographical solutions are based on the consideration of a measure of dissatisfaction of players rather than coalitions

multicomponent fluid flow by discontinuous galerkin and mixed methods in unfractured and fractured media 1 a discrete fracture model for the flow of compressible multicomponent fluids in homogeneous heterogeneous and fractured media is presented in single phase in the numerical model we combine the mixed finite element mfe and the discontinuous galerkin dg methods we use the cross flow equilibrium concept to approximate the fractured matrix mass transfer the discrete fracture model is numerically superior to the single porosity model and overcomes limitations of the dual porosity models including the use of a shape factor the mfe method provides a direct and accurate approximation for the velocity field which is crucial for the convective terms in the flow equations the dg method associated with a slope limiter is used to approximate the species balance equations this method can capture the sharp moving fronts the calculation of the fracture fracture flux across three and higher intersecting fracture branches is a challenge in this work we provide an accurate approximation of these fluxes by using the mfe formulation numerical examples in unfractured and fractured media illustrate the efficiency and robustness of the proposed numerical model

quantifying inefficiency in cost sharing mechanisms in a cost sharing problem several participants with unknown preferences vie to receive some good or service and each possible outcome has a known cost a cost sharing mechanism is a protocol that decides which participants are allocated a good and at what prices three desirable properties of a cost sharing mechanism are incentive compatibility meaning that participants are motivated to bid their true private value for receiving the good budget balance meaning that the mechanism recovers its incurred cost with the prices charged and economic efficiency meaning that the cost incurred and the value to the participants are traded off in an optimal way these three goals have been known to be mutually incompatible for thirty years nearly all the work on cost sharing mechanism design by the economics and computer science communities has focused on achieving two of these goals while completely ignoring the third we introduce novel measures for quantifying efficiency loss in cost sharing mechanisms and prove simultaneous approximate budget balance and approximate efficiency guarantees for mechanisms for a wide range of cost sharing problems including all submodular and steiner tree problems our key technical tool is an exact characterization of worst case efficiency loss in moulin mechanisms the dominant paradigm in cost sharing mechanism design

the representation ring of the quantum double of a finite group abstract we present some results about the representation ring of the quantum double of a finite group over fields of arbitrary characteristic we give a direct sum decomposition of this representation ring into ideals involving green rings of subgroups given characters of such green rings we construct characters of the representation ring of the quantum double and show that all characters arise in this fashion we prove that the characters thereby obtained from brauer characters separate modules of the quantum double up to composition factors

on simulations of discrete fracture network flows with an optimization based extended finite element method following the approach introduced in siam j sci comput 35 2013 pp b487 b510 we consider the formulation of the problem of fluid flow in a system of fractures as a pde constrained optimization problem with discretization performed using suitable extended finite elements the method allows independent meshes on each fracture thus completely circumventing meshing problems usually related to the discrete fracture network dfn approach the application of the method to dfns of medium complexity is fully analyzed here accounting for several issues related to viable and reliable implementations of the method in complex problems

tensor categories with fusion rules of self duality for finite abelian groups abstract semisimple tensor categories with fusion rules of self duality for finite abelian groups are classified as an application we prove that the tannaka duals of the dihedral and the quaternion groups of order 8 and the eight dimensional hopf algebra of kac and paljutkin are not isomorphic as abstract tensor categories whereas they have the same fusion rule

twisting algebras using non commutative torsors explicit computations non commutative torsors equivalently two cocycles for a hopf algebra can be used to twist comodule algebras we prove a theorem that affords a presentation by generators and relations for the algebras obtained by such twisting we give a number of examples including new constructions of the quantum affine spaces and the quantum tori

fuzzy games a characterization of the core in this paper we extend to the cooperative fuzzy games case the reduced game introduced by davis and maschler the kernel of a cooperative game naval res logist quart 12 1965 223 259 we shall introduce two types of such a reduced game to cooperative fuzzy games and define the related properties of consistency and converse consistency we further offer two axiomatizations of the core on the domain of all cooperative fuzzy games by means of consistency and its converse