modeling interaction phenomena using fuzzy measures on the notions of interaction and independence interaction phenomena among elements of a finite set can be modeled by a discrete fuzzy measure the notion of marginal interaction between two elements is at the root of the definition of interaction we first extend this notion by defining that of marginal interaction among pairwise disjoint subsets and we study some of its properties then we generalize the notion of interaction index to pairwise disjoint subsets finally we formalize the intuitive notion of independence and we propose the concept of measure of marginal amount of interaction in order to fill the gap between the notions of interaction and independence

on topological dynamics of turing machines abstract we associate to a turing machine two dynamical systems which we call turing machine with moving tape tmt and turing machine with moving head tmh tmt are equivalent to generalized shifts of moore 1990 and they include two sided full shifts tmh are shift commuting maps of two sided sofic systems in both classes we characterize systems with the shadowing property show that a bijective expansive tmt is conjugate to a subshift of finite type and that topological entropy of every tmh is zero we conjecture that every tmt has a periodic point

a 3d brick element based on hu washizu variational principle for mesh distortion in order to improve the accuracy of the mixed element for irregular meshes a penalty equilibrating 3d mixed element based on the hu washizu variational principle has been proposed in this paper the key idea in this work is to introduce a penalty term into the hu washizu three field functional which can enforce the stress components to satisfy the equilibrium equations in a weak form compared with the classical hybrid and mixed elements this technique can efficiently reduce the sensitivity of the element to mesh distortion the reason for the better results of this penalty technique has been investigated by considering a simple 2d problem from this investigation it has been found that the penalty parameter here plays the role of a scaling factor to reduce the influence of the parasitic strain or stress which is similar to the devised selective scaling factor proposed by sze furthermore compared with the hybrid stress element the proposed element based on the three field variational principle is more suitable for material non linear analysis numerical examples have demonstrated the improved performance of the present element especially in stress computation when fem meshes are irregular copyright 2002 john wiley sons ltd

an axiomatic approach to the measurement of the amount of interaction among criteria or players in the framework of multicriteria decision making based on fuzzy measures or cooperative game theory an axiomatization of the concept of amount of interaction index is given it is based on four axioms a natural property called absence of interaction a boundary condition for which the index reduces to the shapley or banzhaf interaction index a pseudo additivity axiom and a recursivity property the resulting index which can be interpreted as a measure of the average degree of independence among criteria or players takes a particularly simple and natural form for supermodular or submodular measures the approach to the notion of interaction adopted in this paper can be seen as complementary to that recently adopted by grabisch and roubens

minimum cost spanning tree games we consider the problem of cost allocation among users of a minimum cost spanning tree network it is formulated as a cooperative game in characteristic function form referred to as a minimum cost spanning tree m c s t game we show that the core of a m c s t game is never empty in fact a point in the core can be read directly from any minimum cost spanning tree graph associated with the problem for m c s t games with efficient coalition structures we define and construct m c s t games on the components of the structure we show that the core and the nucleolus of the original game are the cartesian products of the cores and the nucleoli respectively of the induced games on the components of the efficient coalition structure

multivariate integration of functions depending explicitly on the minimum and the maximum of the variables abstract by using some basic calculus of multiple integration we provide an alternative expression of the integral a b n f x min x i max x i d x in which the minimum and the maximum are replaced with two single variables we demonstrate the usefulness of that expression in the computation of orness and andness average values of certain aggregation functions by generalizing our result to riemann stieltjes integrals we also provide a method for the calculation of certain expected values and distribution functions

time space trade offs for reversible computation a reversible turing machine is one whose transition function is 1 1 so that no instantaneous description id has more than one predecessor using a pebbling argument this paper shows that for any varepsilon 0 ordinary multitape turing machines using time t and space s can be simulated by reversible ones using time o t 1 varepsilon and space o s log t or in linear time and space o st varepsilon the former result implies in particular that reversible machines can simulate ordinary ones in quadratic space these results refer to reversible machines that save their input thereby insuring a global 1 1 relation between initial and final ids even when the function being computed is many to one reversible machines that instead erase their input can of course compute only 1 1 partial recursive functions and indeed provide a godel numbering of such functions the time space cost of computing a 1 1 function on such a machine is equal within a small polynomial to the cost of co

estimation of the weights of interacting criteria from the set of profiles by means of information theoretic functionals abstract following the recent work of marichal and roubens eur j operat res 124 2000 641 on fuzzy measure identification in multicriteria decision problems we propose an alternative unsupervised identification method based on the estimation of the fuzzy measure coefficients by means of information theoretic functionals

an axiomatic approach to the definition of the entropy of a discrete choquet capacity to extend the classical shannon entropy to nonadditive measures marichal recently introduced the concept of generalized entropy for discrete choquet capacities we provide a first axiomatization of this new concept on the basis of three axioms the symmetry property a boundary condition for which the entropy reduces to the shannon entropy and a generalized version of the well known recursivity property we also show that this generalized entropy fulfills several properties considered as requisites for defining an entropy like measure lastly we provide an interpretation of it in the framework of aggregation by the discrete choquet integral

weighted banzhaf power and interaction indexes through weighted approximations of games the banzhaf power index was introduced in cooperative game theory to measure the real power of players in a game the banzhaf interaction index was then proposed to measure the interaction degree inside coalitions of players it was shown that the power and interaction indexes can be obtained as solutions of a standard least squares approximation problem for pseudo boolean functions considering certain weighted versions of this approximation problem we define a class of weighted interaction indexes that generalize the banzhaf interaction index we show that these indexes define a subclass of the family of probabilistic interaction indexes and study their most important properties finally we give an interpretation of the banzhaf and shapley interaction indexes as centers of mass of this subclass of interaction indexes

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

universality of a reversible two counter machine abstract a k counter machine cm k is an automaton having k counters as an auxiliary memory it has been shown by minsky that a cm 2 can simulate any turing machine and thus it is universal in this paper we investigate the computing ability of reversible i e backward deterministic cms we first show that any irreversible cm k can be simulated by a reversible cm k 2 in this simulation however the reversible cm k 2 leaves a large number as a garbage in some counter when it halts we then show that if k more counters are added this garbage information is erased reversibly finally we prove that any reversible cm k k 1 2 3 can be simulated by a reversible cm 2 from these results computation universality of a reversible cm 2 is established

assumed strain stabilization procedure for the 9 node lagrange shell element an assumed strain strain interpolation method is used to construct a stabilization matrix for the 9 node shell element the stabilization procedure can be justified based on the hellinger reissner variational method it involves a projection vector which is orthogonal to both linear and quadratic fields in the local co ordinate system of each quadrature point all terms in the development involve 2 2 quadrature in the 9 node element example problems show good accuracy and an almost optimal rate of convergence

canonical representation of set functions the representation of a cooperative transferable utility game as a linear combination of unanimity games may be viewed as an isomorphism between no necessarily additive set functions on the players space and additive ones on the coalitions space or alternatively between nonadditive probability measures on a state space and additive ones on the space of events we extend the unanimity basis representation to general infinite spaces of players study spaces of games which satisfy certain properties and provide some conditions for additivity of the resulting additive set function on the space at coalitions these results also allow us to extend some representations of the choquet integral from finite to infinite spaces

optimistic weighted shapley rules in minimum cost spanning tree problems abstract we introduce optimistic weighted shapley rules in minimum cost spanning tree problems we define them as the weighted shapley values of the optimistic game v introduced in bergantinos and vidal puga bergantinos g vidal puga j j forthcoming the optimistic tu game in minimum cost spanning tree problems international journal of game theory available from we prove that they are obligation rules tijs s branzei r moretti s norde h 2006 obligation rules for minimum cost spanning tree situations and their monotonicity properties european journal of operational research 175 121 134

a homology theory for etale groupoids etale groupoids arise naturally as models for leaf spaces of foliations for orbifolds and for orbit spaces of discrete group actions in this paper we introduce a sheaf homology theory for etale groupoids we prove its invariance under morita equivalence as well as verdier duality between haeiger cohomology and this homology we also discuss the relation to the cyclic and hochschild homologies of connes convolution algebra of the groupoid and derive some spectral sequences which serve as a tool for the computation of these homologies

a new one point quadrature enhanced assumed strain eas solid shell element with multiple integration points along thickness part i geometrically linear applications a new one point quadrature eas

a new efficient approach to the formulation of mixed finite element models for structural analysis abstract a new finite element formulation is developed based on the hellinger reissner principle with independent strain by dividing the assumed strain into the lower order part and the higher order part the new formulation can be made much more efficient than the standard mixed formulation in addition the present new approach provides a rational way of introducing stabilization matrix to suppress undesirable kinematic modes author

higher dimensional generalizations of the thompson groups abstract motivated by the goal of generalizing the cuntz krieger algebras and making heavy use of the pioneering work of robertson and steger kumjian and pask generalized the notion of a directed graph to what they termed a higher rank graph the c algebras constructed from such higher rank graphs have proved to be highly interesting higher rank graphs are in fact a class of cancellative categories and so the one vertex higher rank graphs are therefore a class of cancellative monoids in this paper we call them k monoids finite direct products of free monoids belong to this family but there are many examples not of this form it is well known that the classical thompson groups arise from the free monoids and it is easy to show that brin s higher dimensional thompson groups arise from finite direct products of free monoids in this paper we generalize these constructions and show how to construct a family of new groups with simple commutator subgroups from arbitrary aperiodic k monoids thereby subsuming all the above examples although we give simple direct constructions of our groups a key feature of our paper is that we also show that they arise as topological full groups of the usual etale groupoids associated with k monoids in this way our groups are naturally associated with c algebras the question of the mutual isomorphisms amongst this family of groups appears to be a delicate one and is not handled here

some undecidability results for asynchronous transducers and the brin thompson group 2v using a result of kari and ollinger we prove that the torsion problem for elements of the brin thompson group 2v is undecidable as a result we show that there does not exist an algorithm to determine whether an element of the rational group r of grigorchuk nekrashevich and sushchanskii has finite order a modification of the construction gives other undecidability results about the dynamics of the action of elements of 2v on cantor space arzhantseva lafont and minasyanin prove in 2012 that there exists a finitely presented group with solvable word problem and unsolvable torsion problem to our knowledge 2v furnishes the first concrete example of such a group and gives an example of a direct undecidability result in the extended family of r thompson type groups

constructing finitely presented simple groups that contain grigorchuk groups abstract we construct infinite finitely presented simple groups that have subgroups isomorphic to grigorchuk groups we also prove that up to one possible exception all previously known finitely presented simple groups are torsion locally finite

control of zero energy modes in 9 node plane element for plane stress plane strain analysis the 9 node quadrilateral element performs better than the corresponding 8 node element especially for non rectangular shapes for improved element flexibility and lower computer cost 2 2 quadrature is generally preferable to 3 3 quadrature unfortunately the 9 node element contains spurious zero energy modes when under integrated a method is proposed to restrain these modes without significant loss of accuracy or added cost

equivalent representations of set functions this paper introduces four alternative representations of a set function the ma bius transformation the co ma bius transformation and the interactions between elements of any subset of a given set as extensions of shapley and banzhaf values the links between the five equivalent representations of a set function are emphasized in this presentation

presentations of higher dimensional thompson groups in a previous paper we defined a higher dimensional analog of thompson s group v and proved that it is simple infinite finitely generated and not isomorphic to any of the known thompson groups there are other thompson groups that are infinite simple and finitely presented here we show that the new group is also finitely presented by calculating an explicit finite presentation

extreme points of the harsanyi set and the weber set abstract in this paper we present firstly a matrix approach by moebius transformation to axiomatize the harsanyi payoff vectors in the traditional worth system instead of the dividend system then by this approach the weber set is also characterized as the set of specialized harsanyi payoff vectors the study of marginal contribution vectors the extreme points of the weber set is pivotal to characterize the weber set recall that an extreme point of a linear system can be recognized by its carriers a linear system associated to the weber set is constructed and a second approach to investigate their extreme points is accessed by the concept of carrier we apply the same technique to study the extreme points of the harsanyi set together with the core type structure of the harsanyi set we present a recursive algorithm for computing the extreme points of the harsanyi set for any game

interaction transform for bi set functions over a finite set set functions appear as a useful tool in many areas of decision making and operations research and several linear invertible transformations have been introduced for set functions such as the mobius transform and the interaction transform the present paper establish similar transforms and their relationships for bi set functions i e functions of two disjoint subsets bi set functions have been recently introduced in decision making bi capacities and game theory bi cooperative games and appear to open new areas in these fields

etale groupoids arising from products of shifts of finite type abstract two conjectures about homology groups k groups and topological full groups of minimal etale groupoids on cantor sets are formulated we verify these conjectures for many examples of etale groupoids including products of etale groupoids arising from one sided shifts of finite type furthermore we completely determine when these product groupoids are mutually isomorphic also the abelianization of their topological full groups is computed they are viewed as generalizations of the higher dimensional thompson groups

spaces of tilings finite telescopic approximations and gap labeling the continuous hull of a repetitive tiling t in d with the finite pattern condition fpc inherits a minimal d lamination structure with flat leaves and a transversal open image in new window which is a cantor set this class of tiling includes the penrose the amman benkker ones in 2d as well as the icosahedral tilings in 3d we show that the continuous hull with its canonical d action can be seen as the projective limit of a suitable sequence of branched oriented and flat compact d manifolds as a consequence the longitudinal cohomology and the k theory of the corresponding c algebra open image in new window are obtained as direct limits of cohomology and k theory of ordinary manifolds moreover the space of invariant finite positive measures can be identified with a cone in the d th homology group canonically associated with the orientation of d at last the gap labeling theorem holds given an invariant ergodic probability measure on the hull the corresponding integrated density of states ids of any selfadjoint operators affiliated to open image in new window takes on values on spectral gaps in the module generated by the occurrence probabilities of finite patches in the tiling

a reduced integration solid shell finite element based on the eas and the ans concept geometrically linear problems in this paper a new reduced integration eight node solid shell finite element is presented the enhanced assumed strain eas concept based on the hu washizu variational principle requires only one eas degree of freedom to cure volumetric and poisson thickness locking one key point of the derivation is the taylor expansion of the inverse jacobian with respect to the element center which closely approximates the element shape and allows us to implement the assumed natural strain ans concept to eliminate the curvature thickness and the transverse shear locking the second crucial point is a combined taylor expansion of the compatible strain with respect to the center of the element and the normal through the element center leading to an efficient and locking free hourglass stabilization without rank deficiency hence the element requires only a single integration point in the shell plane and at least two integration points in thickness direction the formulation fulfills both the membrane and the bending patch test exactly which has to the authors knowledge not yet been achieved for reduced integration eight node solid shell elements in the literature owing to the three dimensional modeling of the structure fully three dimensional matenal models can be implemented without additional assumptions

a note on the sobol indices and interactive criteria the choquet integral and the owen extension or multilinear extension are the most popular tools in multicriteria decision making to take into account the interaction between criteria it is known that the interaction transform and the banzhaf interaction transform arise as the average total variation of the choquet integral and multilinear extension respectively we consider in this note another approach to define interaction by using the sobol indices which are related to the analysis of variance of a multivariate model we prove that the sobol indices of the multilinear extension give the square of the fourier transform a well known concept in computer sciences we also relate the latter to the banzhaf interaction transform and compute the sobol indices for the 2 additive choquet integral

homology and topological full groups of etale groupoids on totally disconnected spaces for almost finite groupoids we study how their homology groups reflect dynamical properties of their topological full groups it is shown that two clopen subsets of the unit space has the same class in h0 if and only if there exists an element in the topological full group which maps one to the other it is also shown that a natural homomorphism called the index map from the topological full group to h1 is surjective and any element of the kernel can be written as a product of four elements of finite order in particular the index map induces a homomorphism from h1 to k1 of the groupoid c algebra explicit computations of homology groups of af groupoids and etale groupoids arising from subshifts of finite type are also given

tolerant or intolerant character of interacting criteria in aggregation by the choquet integral abstract in many multi criteria decision making problems the decision criteria present some interaction whose nature may vary from one situation to another for example some criteria may be statistically correlated thus making them somewhat redundant or opposed some others may be somewhat substitutive or complementary depending on the behavior of the decision maker some others may be decisive in the sense that the global score of any alternative obtained by aggregation is bounded by the partial score along one of them in this paper we analyze this latter form of interaction when a criterion bounds the global score from above it is called a blocker or a veto due to its rather intolerant character when it bounds the global score from below it is then called a pusher or a favor we thus investigate the tolerance of criteria or equivalently the tolerance of the weighted aggregation operator here the choquet integral that is used to aggregate criteria more specifically we propose axiomatically indices to appraise the extent to which each criterion behaves like a veto or a favor in the aggregation by the choquet integral previous to this we also propose global tolerance degrees measuring the extent to which the choquet integral is conjunctive or disjunctive

the expressibility of functions on the boolean domain with applications to counting csps an important tool in the study of the complexity of constraint satisfaction problems csps is the notion of a relational clone which is the set of all relations expressible using primitive positive formulas over a particular set of base relations post s lattice gives a complete classification of all boolean relational clones and this has been used to classify the computational difficulty of csps motivated by a desire to understand the computational complexity of weighted counting csps we develop an analogous notion of functional clones and study the landscape of these clones one of these clones is the collection of log supermodular lsm functions which turns out to play a significant role in classifying counting csps in the conservative case where all nonnegative unary functions are available we show that there are no functional clones lying strictly between the clone of lsm functions and the total clone containing all functions thus any counting csp that contains a single nontrivial non lsm function is computationally as hard to approximate as any problem in p furthermore we show that any nontrivial functional clone in a sense that will be made precise contains the binary function implies as a consequence in the conservative case all nontrivial counting csps are as hard to approximate as bis the problem of counting independent sets in a bipartite graph given the complexity theoretic results it is natural to ask whether the implies clone is equivalent to the clone of lsm functions we use the mobius transform and the fourier transform to show that these clones coincide precisely up to arity 3 it is an intriguing open question whether the lsm clone is finitely generated finally we investigate functional clones in which only restricted classes of unary functions are available

measuring the interactions among variables of functions over the unit hypercube abstract by considering a least squares approximation of a given square integrable function f 0 1 n r by a multilinear polynomial of a specified degree we define an index which measures the overall interaction among variables of f this definition extends the concept of banzhaf interaction index introduced in cooperative game theory our approach is partly inspired from multilinear regression analysis where interactions among the independent variables are taken into consideration we show that this interaction index has appealing properties which naturally generalize several properties of the banzhaf interaction index in particular we interpret this index as an expected value of the difference quotients of f or under certain natural conditions on f as an expected value of the derivatives of f finally we discuss a few applications of the interaction index in aggregation function theory

the reliability importance of components and prime implicants in coherent and non coherent systems including total order interactions abstract in the management of complex systems knowledge of how components contribute to system performance is essential to the correct allocation of resources recent works have renewed interest in the properties of the joint j and differential d reliability importance measures however a common background for these importance measures has not been developed yet in this work we build a unified framework for the utilization of j and d in both coherent and non coherent systems we show that the reliability function of any system is multilinear and its taylor expansion is exact at an order t we then introduce a total order importance measure d t that coincides with the exact portion of the change in system reliability associated with any finite or infinitesimal change in component reliabilities we show that d t synthesizes the birnbaum joint and differential importance of all orders in one unique indicator we propose an algorithm that enables the numerical estimation of d t by varying one probability at a time making it suitable in the analysis of complex systems findings demonstrate that the simultaneous utilization of d t and j provides reliability analysts with a complete dissection of system performance

the measure of interaction among players in games with fuzzy coalitions in this paper the derivative among participation levels of players in games with fuzzy coalitions which measures the simultaneous interaction among players with certain participation levels is defined some properties of the derivative of fuzzy game with k monotonicity are studied furthermore the interaction index among participation levels is established based on the assumption that fuzzy characteristic functions are continuous the integral index of absolute interaction among levels is proposed and the integral index of absolute interaction among players is defined as well at last the shapley total integral index of interaction among players is constructed and a series of properties relative to the index are proved

investigation on irreducible cost vectors in minimum cost arborescence problems abstract we study cost allocation rules in minimum cost arborescence problems where agents need to build a network to a source in order to obtain some resource provided a vector of costs of edges agent source pairs the agents cooperate to construct a minimum cost arborescence rooted at the source in order to reduce the total building cost minimum cost arborescence problems are extensions of well studied minimum cost spanning tree problems to deal with asymmetric edge costs regarding cost allocation rules in minimum cost arborescence problems dutta and mishra 2012 extended the folk rule which is one of the most important rules in minimum cost spanning tree problems based on the problem with the vector of the most reduced costs called irreducible form in minimum cost spanning tree problems several axiomatic characterizations of the folk rule have been proposed however it is difficult to extend them in minimum cost arborescence problems one of the reasons is that strong and reasonable axioms in minimum cost spanning tree problems which imply irreducible form dependence of cost allocation rules are not satisfied by the folk rule in minimum cost arborescence problems hence we search for other axioms which imply irreducible form dependence for this purpose we investigate irreducible cost vectors in minimum cost arborescence problems and characterize the irreducible form

entropy of discrete choquet capacities we introduce a measure of entropy for any discrete choquet capacity and we interpret it in the setting of aggregation by the choquet integral

numerical integration with taylor truncations for the quadrilateral and hexahedral finite elements for general quadrilateral or hexahedral meshes the finite element methods require evaluation of integrals of rational functions instead of traditional polynomials it remains as a challenge in mathematics to show the traditional gauss quadratures would ensure the correct order of approximation for the numerical integration in general however in the case of nested refinement the refined quadrilaterals and hexahedra converge to parallelograms and parallelepipeds respectively based on this observation the rational functions of inverse jacobians can be approximated by the taylor expansion with truncation then the gauss quadrature of exact order can be adopted for the resulting integrals of polynomials retaining the optimal order approximation of the finite element methods a theoretic justification and some numerical verification are provided in the paper

isoperimetric functions of groups and computational complexity of the word problem we prove that the word problem of a finitely generated group g is in np solvable in polynomial time by a nondeterministic turing machine if and only if this group is a subgroup of a finitely presented group h with polynomial isoperimetric function the embedding can be chosen in such a way that g has bounded distortion in h this completes the work started in 6 and 25

interaction indices for games on combinatorial structures with forbidden coalitions abstract the notion of interaction among a set of players has been defined on the boolean lattice and cartesian products of lattices the aim of this paper is to extend this concept to combinatorial structures with forbidden coalitions the set of feasible coalitions is supposed to fulfil some general conditions this general representation encompasses convex geometries antimatroids augmenting systems and distributive lattices two axiomatic characterizations are obtained they both assume that the shapley value is already defined on the combinatorial structures the first one is restricted to pairs of players and is based on a generalization of a recursivity axiom that uniquely specifies the interaction index from the shapley value when all coalitions are permitted this unique correspondence cannot be maintained when some coalitions are forbidden from this a weak recursivity axiom is defined we show that this axiom together with linearity and dummy player are sufficient to specify the interaction index the second axiomatic characterization is obtained from the linearity dummy player and partnership axioms an interpretation of the interaction index in the context of surplus sharing is also proposed finally our interaction index is instantiated to the case of games under precedence constraints

enrichment of linear hexahedral finite elements using rotations of a virtual space fiber summary the present paper deals with the enrichment of 3d low order finite elements the used concept is based on the idea that a 3d virtual fiber after a spatial rotation introduces an enhancement of the strain field tensor approximation a consistent stiffness matrix is obtained allowing a better approximation of the actual solution compared with that resulting from low order finite elements implemented for two eight node hexahedral elements the performance of the space fiber rotation concept is assessed by running some classical beam plate and shell benchmarks and the obtained results are compared especially with those given by linear eight node and quadratic 20 node hexahedral elements in particular it is shown that the developed elements accuracy is significantly superior to that of the classical eight node hexahedral element and close to that of the classical 20 node hexahedral element copyright 2013 john wiley sons ltd

a multiple quadrature eight node hexahedral finite element for large deformation elastoplastic analysis abstract a multiple quadrature underintegrated hexahedral finite element which is free of volumetric and shear locking and has no spurious singular modes is described and implemented for nonlinear analysis finite element formulations are derived in the corotational coordinate system the use of consistent tangent operators for large deformation elastoplasticity with nonlinear isotropic kinematic hardening rules preserves the quadratic rate of convergence of the newton s iteration method in static analysis test problems studied demonstrate the efficiency and effectiveness of this element in solving a wide variety of problems including sheet metal forming processes

deciding stability and mortality of piecewise affine dynamical systems in this paper we study problems such as given a discrete time dynamical system of the form x t 1 f x t where f r n r n is a piecewise affine function decide whether all trajectories converge to 0 we show in our main theorem that this attractivity problem is undecidable as soon as n greater than or equal to2 the same is true of two related problems stability is the dynamical system globally asymptotically stable and mortality do all trajectories go through 0 we then show that am activity and stability become decidable in dimension 1 for continuous functions c 2001 elsevier science b v all rights reserved

on the limits of finite element perfectability it has been shown2 that a four noded membrane element of trapezoidal shape must either lock or fail constant strain patch tests that result is generalized here to establish similar limitations for all finite elements a modal analysis is used to show that essential coupling exists between low modes whose displacement states can be exactly represented by an element s basis functions and higher modes whose displacement states cannot be so represented such coupling can be avoided only when an element has particular shapes in all other cases the element designer is faced with the choice of patch test failure in a low mode or locking in a higher mode several examples are described

submodularity supermodularity and higher order monotonicities of pseudo boolean functions classes of set functions defined by the positivity or negativity of the higher order derivatives of their pseudo boolean polynomial representations generalize those of monotone supermodular and submodular functions in this paper these classes are characterized by functional inequalities and are shown to be closed both under algebraic closure conditions and a local closure criterion it is shown that for everym 1 in addition to the class of all set functions there are only three other classes satisfying these algebraic and local closure conditions those having positive respectively negative mth order derivatives and those having a polynomial representation of degree less thanm

interaction transform of set functions over a finite set the paper introduces a new transform of set functions over a finite set which is linear and invertible as the well known mobius transform in combinatorics this transform leads to the interaction index a central concept in multicriteria decision making the interaction index of a singleton happens to be the shapley value of the set function or in terms of cooperative game theory of the value function of the game properties of this new transform are studied in detail and some illustrative examples are given

on the core and nucleolus of minimum cost spanning tree games we develop two efficient procedures for generating cost allocation vectors in the core of a minimum cost spanning tree m c s t game the first procedure requires o n 2 elementary operations to obtain each additional point in the core wheren is the number of users the efficiency of the second procedure which is a natural strengthening of the first procedure stems from the special structure of minimum excess coalitions in the core of an m c s t game this special structure is later used i to ease the computational difficulty in computing the nucleolus of an m c s t game and ii to provide a geometric characterization for the nucleolus of an m c s t game this geometric characterization implies that in an m c s t game the nucleolus is the unique point in the intersection of the core and the kernel we further develop an efficient procedure for generating fair cost allocations which in some instances coincide with the nucleolus finally we show that by employing sterns transfer scheme we can generate a sequence of cost vectors which converges to the nucleolus

hourglass control in linear and nonlinear problems abstract mesh stabilization techniques for controlling the hourglass modes in under integrated hexahedral and quadrilateral elements are described it is shown that the orthogonal hourglass techniques previously developed can be obtained from simple requirements that insure the consistency of the finite element equations in the sense that the gradients of linear fields are evaluated correctly it is also shown that this leads to an hourglass control that satisfies the patch test the nature of the parameters which relate the generalized stresses and strains for controlling hourglass modes is examined by means of a mixed variational principle and some guidelines for their selection are discussed finally effective means of implementing these hourglass procedure in computer codes are described applications to both the laplace equation and the equations of solid mechanics in 2 and 3 dimensions are considered

k order additive discrete fuzzy measures and their representation abstract in order to face with the complexity of discrete fuzzy measures we propose the concept of k orderadditive fuzzy measure including usual additive measures and fuzzy measures every discrete fuzzy measure is a k order additive fuzzy measure for a unique k a related topic of the paper is to introduce an alternative representation of fuzzy measures called the interaction representation which sets and extends in a common framework the shapley value and the interaction index proposed by murofushi and soneda

minimum cost spanning tree games and population monotonic allocation schemes in this paper we present the subtraction algorithm that computes for every classical minimum cost spanning tree game a population monotonic allocation scheme as a basis for this algorithm serves a decomposition theorem that shows that every minimum cost spanning tree game can be written as nonnegative combination of minimum cost spanning tree games corresponding to 0 1 cost functions it turns out that the subtraction algorithm is closely related to the famous algorithm of kruskal for the determination of minimum cost spanning trees for variants of the classical minimum cost spanning tree games we show that population monotonic allocation schemes do not necessarily exist

freeness of automaton groups vs boundary dynamics abstract we prove that the boundary dynamics of the semi group generated by the enriched dual transducer characterizes the algebraic property of being free for an automaton group we specialize this result to the class of bireversible transducers and we show that the property of being not free is equivalent to the existence of a finite schreier graph in the boundary of the enriched dual pointed at some essentially non trivial point from these results we derive some consequences from the algebraic algorithmic and dynamical points of view

an axiomatic approach of the discrete choquet integral as a tool to aggregate interacting criteria the most often used operator to aggregate criteria in decision making problems is the classical weighted arithmetic mean however in many problems the criteria considered interact and a substitute to the weighted arithmetic mean has to be adopted we show that under rather natural conditions the discrete choquet integral is an adequate aggregation operator that extends the weighted arithmetic mean by taking into consideration of the interaction among criteria the axiomatic that supports the choquet integral is presented and an intuitive approach is proposed as well

decomposition and representation of coalitional games a coalitional game is a real valued set function defined on an algebra f of subsets of a space x such that o 0 we prove the existence of a one to one correspondence between coalitional games bounded with respect to the composition norm and countably additive measures defined on an appropriate space

isoperimetric and isodiametric functions of groups this is the first of two papers devoted to connections between asymptotic functions of groups and computational complexity in particular we show how to construct a finitely presented group with np complete word problem one of the main results of this paper states that if a real number cx 4 is computable in time 0 then na is equivalent big o to the dehn function of a finitely presented group the smallest isodiametric function of this group is n3 8 4 on the other hand if na is equivalent to the dehn function of a finitely presented group then oe is computable in time 4 are equivalent to dehn functions of some finitely presented groups and that n1r and na for all rational numbers oe 3 are equivalent to the smallest isodiametric functions of finitely presented groups moreover we describe all dehn functions of finitely presented groups f n4 as time functions of turing machines modulo two conjectures

cantor systems piecewise translations and simple amenable groups we provide the rst examples of nitely generated simple groups that are amenable and innite to this end we prove that topological full groups of minimal systems are amenable this follows from a general existence result on invariant states for piecewise translations of the integers the states are obtained by constructing a suitable family of densities on the classical bernoulli space

the word problem of the brin thompson group is conp complete abstract we prove that the word problem of the brin thompson group nv over a finite generating set is conp complete for every n 2 it is known that n v n 1 is an infinite family of infinite finitely presented simple groups we also prove that the word problem of the thompson group v over a certain infinite set of generators related to boolean circuits is conp complete

on importance indices in multicriteria decision making we address in this paper the problem of how to define an importance index in multicriteria decision problems when a numerical representation of preference is given we make no restrictive assumption on the model which could have discrete or continuous attributes and in particular it is not assumed that the model is monotonically increasing or decreasing with respect to w r t the attributes our analysis first considers discrete models which are seen to be equivalent to multichoice games we propose essentially two importance indices namely the signed importance index and the absolute importance index both based on the average variation of the value of the model induced by a given attribute we provide several axiomatizations for these importance indices extend them to the continuous case and finally illustrate them with examples classical simple models and a example of discomfort evaluation based on real data

interaction indices for multichoice games abstract models in multicriteria decision analysis mcda can be analyzed by means of an importance index and an interaction index for every group of criteria we consider first discrete models in mcda without further restriction which amounts to considering multichoice games that is cooperative games with several levels of participation we propose and axiomatize two interaction indices for multichoice games the signed interaction index and the absolute interaction index in a second part we consider the continuous case supposing that the continuous model is obtained from a discrete one by means of the choquet integral we show that as in the case of classical games the interaction index defined for continuous aggregation functions coincides with the signed interaction index up to a normalizing coefficient

aggregation functions means this two part state of the art overview on aggregation theory summarizes the essential information concerning aggregation issues an overview of aggregation properties is given including the basic classification on aggregation functions in this first part the stress is put on means i e averaging aggregation functions both with fixed arity n ary means and with multiple arities extended means

three dimensional 8 node and 20 node refined hybrid isoparametric elements in this paper a new hybrid variational principle with independent variables of strain stress and displacement and with a weaker constraint condition of interelement continuity is proposed based on this functional a general formulation of a refined hybrid isoparametric element method has been established by the orthogonal approach the present formulation is a rational approach to be adopted for deriving high performance three dimensional hybrid isoparametric elements even up to the higher order 20 node element several numerical examples are presented to show that the present elements rgh8 8 node and rgh20 20 node have high accuracy excellent computational efficiency and less sensitivity to mesh distortion

a weight based approach to the measurement of the interaction among criteria in the framework of aggregation by the bipolar choquet integral in the context of aggregation the choquet integral arises as a natural generalization of the weighted arithmetic mean in their seminal work on bi capacities grabisch and labreuche have recently proposed an extension of the choquet integral adapted to the situation where the values to be aggregated lie on a bipolar scale in such a framework they have derived generalizations of the shapley value and of the shapley interaction index that can be used to apprehend the main behavioral characteristics of the aggregation founding our approach on the intuitive notion of weight of a criterion we propose alternative definitions of importance and interaction indices that may be more easily interpretable and we study their properties

a consistent control of spurious singular modes in the 9 node lagrange element for the laplace and mindlin plate equations abstract when 2 2 quadrature is used with the 9 node lagrange element which is essential in c 0 plate elements to avoid locking spurious singular modes appear on the element level which can lead to singularity or near singularity of the global equations here these modes are controlled by a procedure that introduces additional generalized stresses and strains so that the spurious modes are eliminated and the consistency of the resulting finite difference equations is not impaired hence the procedure passes the patch test applications to the diffusion and mindlin plate equations are presented results show that h 3 convergence in the l 2 norm is almost retained

control of spurious modes in the nine node quadrilateral element the nine node quadrilateral is much more accurate than its eight node relative if elements are non rectangular however the nine node element may display spurious low energy modes under 2 2 gauss quadrature these modes can be controlled by using the 3 3 quadrature rule but at added cost this paper investigates two inexpensive control devices that can be used with 2 2 gauss quadrature

on the closure of families of fuzzy measures under eventwise aggregations the paper contains some results on eventwise aggregation of fuzzy measures from the various families of lower probabilities this investigation includes coherent lower probabilities k monotone measures belief measures etc we study sufficient and necessary conditions on aggregation operators satisfying the closure property it is necessary to guarantee that the aggregation belongs to the same family as generating measures we also propose an efficient way for constructing aggregation operators using the found unique properties of multilinear extension this representation method for fuzzy measures generalizes to the n dimensional case the well known one giving distorted probabilities

an automaton group with undecidable order and engel problems abstract for every turing machine we construct an automaton group that simulates it precisely starting from an initial configuration of the turing machine we explicitly construct an element of the group such that the turing machine stops if and only if this element is of finite order if the turing machine is universal the corresponding automaton group has an undecidable order problem this solves a problem raised by grigorchuk the above group also has an undecidable engel problem there is no algorithm that given g h in the group decides whether there exists an integer n such that the n iterated commutator g h h h is the identity or not this solves a problem raised by bartholdi

a generalization of obligation rules for minimum cost spanning tree problems tijs et al 23 introduce the family of obligation rules for minimum cost spanning tree problems we give a generalization of such family we prove that our family coincides with the set of rules satisfying an additivity property and a cost monotonicity property we also provide two new characterizations for the family of obligation rules using the previous properties in the first one we add a property of separability and in the second one we add core selection

hexahedral volume coordinate method hvcm and improvements on 3d wilson hexahedral element abstract a new volume coordinate method for developing 3d hexahedral elements called hexahedral volume coordinate method hvcm is systematically established in this paper i several characteristic parameters of a hexahedron are defined and the degeneration conditions under which a hexahedron degenerates into other special polyhedrons are given ii the volume coordinates l 1 l 2 l 3 l 4 l 5 l 6 of any point within a convex hexahedron are defined iii transformation relations between the volume coordinates and the cartesian or isoparametric coordinates are presented iv the differential formulas for volume coordinates in hexahedral elements are given this new coordinate system can keep not only the advantages of local natural coordinate system but also a linear relation with the cartesian coordinate system then for checking the validity of the new hvcm it is used to formulate three new incompatible eight node hexahedral elements hvcc8 hvcc8 es and hvcc8 em by a similar procedure of famous wilson s incompatible mode numerical results show that the present elements exhibit much better performance than that of conventional isoparametric elements in most distorted mesh cases especially for macneal s thin beam problem it demonstrates that the new hvcm is a powerful tool for constructing high performance hexahedral finite element models

an empirical study of statistical properties of the choquet and sugeno integrals this paper investigates the statistical properties of the choquet and sugeno integrals used as multiattribute models the investigation is done on an empirical basis and focuses on two topics the distribution of the output of these integrals when the input is corrupted with noise and the robustness of these models when they are identified using some set of learning data through some learning procedure

high accuracy low order three dimensional brick elements this paper presents a family of low order high accuracy three dimensional brick elements the elements are formulated via a three field variational principle the assumed independent strain field is constructed from two disjointed distributions the first contains the lower order distribution and its dimension is the minimum required to satisfy stability requirements an energy constraint which is enforced weakly at the element level is used to relate the second distribution to the first the stress field is chosen to a priori satisfy a similar energy constraint as a result internal constraints e g incompressibility are automatically satisfied by these fields and locking behaviour is avoided a j2 plasticity model illustrates the proposed elements performance in nonlinear solids the excellent performance of the proposed elements is demonstrated with numerous challenging examples including many that are usually modelled by shell elements

hybrid hexahedral element for solids plates shells and beams by selective scaling a robust two field hexahedral element capable of handling plate shell beam and nearly incompressible material analyses without locking are presented starting with the assumed stress element of pian and tong 7 parasitic strain components leading to locking in plate shell and beam analyses are first identified locking can be alleviated by scaling down selectively the parasitic strain components in the leverage matrix unfortunately the element then fails the patch test however patch test correction and reduction in computation can be achieved by the recently proposed admissible matrix formulation the resulting element is lock free and very efficient all matrices involved in constructing the stiffness matrix can be derived explicitly the accuracy of the element is tested by popular bench mark problems

topological full groups of one sided shifts of finite type we explore the topological full group g of an essentially principal etale groupoid g on a cantor set when g is minimal we show that g and its certain normal subgroup is a complete invariant for the isomorphism class of the etale groupoid g furthermore when g is either almost finite or purely infinite the commutator subgroup d g is shown to be simple the etale groupoid g arising from a onesided irreducible shift of finite type is a typical example of a purely infinite minimal groupoid for such g g is thought of as a generalization of the higman thompson group we prove that g is of type f and so in particular it is finitely presented this gives us a new infinite family of finitely presented infinite simple groups also the abelianization of g is calculated and described in terms of the homology groups of g