on non corotational rates of oldroyd s type and relevant issues in rate constitutive formulations the lower and upper oldroyd rates are two wellknown objective noncorotational rates a remarkable property of these rates is that they establish direct relationships between finite strain measures

sharing the cost of multicast transmissions in wireless networks a crucial issue in non cooperative wireless networks is that of sharing the cost of multicast transmissions to different users residing at the stations of the network each station acts as a selfish agent that may misreport its utility i e the maximum cost it is willing to incur to receive the service in terms of power consumption in order to maximize its individual welfare defined as the difference between its true utility and its charged cost a provider can discourage such deceptions by using a strategyproof cost sharing mechanism that is a particular public algorithm that by forcing the agents to truthfully reveal their utility starting from the reported utilities decides who gets the service the receivers and at what price a mechanism is said budget balanced bb if the receivers pay exactly the possibly minimum cost of the transmission and approximate budget balanced bb if the total cost charged to the receivers covers the overall cost and is at most times the optimal one while it is efficient if it maximizes the sum of the receivers utilities minus the total cost over all receivers sets in this paper we first investigate cost sharing strategyproof mechanisms for symmetric wireless networks in which the powers necessary for exchanging messages between stations may be arbitrary and we provide mechanisms that are either efficient or bb when the power assignments are induced by a fixed universal spanning tree or 3 ln k 1 bb k is the number of receivers otherwise then we consider the case in which the stations lay in a d dimensional euclidean space and the powers fall as 1 d and provide strategyproof mechanisms that are either 1 bb or efficient for 1 or d 1 finally we show the existence of 2 3d 1 bb strategyproof mechanisms in any d dimensional space for every d for the special case of d 2 such a result can be improved to achieve 12 bb mechanisms

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

cooperative interval games mountain situations with interval data in this paper we extend mountain situations by using interval calculus we define the interval bird allocation and show that this allocation is a special core element of the interval cost game corresponding to an interval mountain situation we deal with the interval cost sharing problem by introducing the cooperative interval cost game further we consider a subset of the interval core of the related interval cost game each element of this set is extendable to a population monotonic interval allocation scheme or shortly pmias finally we show that each interval core element of an interval connection game is extendable to bi monotonic interval allocation scheme or shortly bi mias

ordinary and strong ellipticity in the equilibrium theory of incompressible hyperelastic solids in this paper explicit necessary and sufficient conditions are established for the ordinary and strong ellipticity of the three dimensional field equations in the nonlinear equilibrium theory of incompressible homogeneous and isotropic hyperelastic solids the resulting system of inequalities involves the local principal stretches directly and in addition restricts the first and second partial derivatives of the strain energy density with respect to the deformation invariants or the principal stretches the conditions of ordinary and strong ellipticity are found to coalesce for materials that obey the baker ericksen inequalities and possess a positive shear modulus at infinitesimal deformations various implications of these ellipticity conditions for special classes of materials and deformations are explored

on the concavity of delivery games abstract delivery games introduced by hamers borm van de leensel and tijs in 1994 are combinatorial optimization games that arise from delivery problems closely related to the chinese postman problem cpp they showed that delivery games are not necessarily balanced for delivery problems corresponding to the class of bridge connected euler graphs they showed that the related games are balanced this paper focuses on the concavity property for delivery games a delivery game arising from a delivery model corresponding to a bridge connected euler graph need not be concave the main result will be that for delivery problems corresponding to the class of bridge connected cyclic graphs which is a subclass of the class of bridge connected euler graphs the related delivery games are concave further we discuss some extreme points of the core and the value for this class of concave delivery games

ellipticity and deformations with discontinuous gradients in finite elastostatics loss of ellipticity of the equilibrium equations of finite elastostatics is closely related to the possible emergence of elastostatic shocks i e deformations with discontinuous gradients in certain situations where constitutive response functions are essentially one dimentional such as anti plane shear or bar theories strong ellipticity is closely related to convexity of the elastic potential and invertibility of certain constitutive response functions the present work addresses the analogous issues within the context of three dimensional elastostatics of compressible but not necessarily isotropic hyperelastic materials a certain direction dependent resolution of the deformation gradient is introduced and its existence and uniqueness for a given direction are established the elastic potential is expressed as a function of kinematic variables arising from this resolution strong ellipticity is shown to be equivalent to the positive definiteness of the hessian matrix of this function thus sufficing for its strict convexity the underlying variables are interpretable physically as simple shears and extensions their work conjugates define a traction response mapping it is shown that discontinuous deformation gradients are sustainable if and only if this mapping fails to be invertible this result is explicit in the sense that it characterizes the set of all possible piecewise homogeneous deformations given the elastic potential function

classical injective solutions in the large in incompressible nonlinear elasticity we consider a general class of parametrized displacement boundary value problems in incompressible nonlinear elasticity we prove the existence of an unbounded solution branch of classical injective solutions emanating from the unforced stress free reference configuration a sharp global implicit function theorem the ramifications of this are that there exists at least one solution for any given applied loading and or there exists solutions of arbitrarily large there norm for some finite loading we refer to this as solutions in the large the nonlinear constraint equation enforcing incompressibility obviates the direct use of either the leray schauder degree or an oriented degree previously developed for compressible problems instead we employ the nonlinear fredholm degree for proper maps constructed in fitzpatrick et al j reine angew math 427 1 33 1992 pejsachowicz and rabier j anal math 76 265 288 1998 we establish the requisite admissibility properties in the presence of the constraint equation before proving the main results

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

noetherian rings of finite global dimension a commutative noetherian local ring of finite global dimension is a regular local ring and the structure of such a ring is well described 1n many texts see 1 9 it is perhaps surprising that very little seems to be known about the corresponding non commutat1ve rings and it is our aim 1n this thesis to examine some of the ways in which the commutative theory can and cannot be extended to a right noetherian local ring of finite right global dimension chapter 1 contains basic definitions and in chapter 2 results are obtained on the projective and injective dimensions of modules over right noetherian local rings commutative regular local rings are domains and we begin chapter 3 by considering the question of when a right noetherian local ring r of finite right global dimension is a prime ring an example of stafford s shows that r is not necessarily prime however by examining the nilpotent radical of r we are able to extend results of ramras 57 and walker 75 and show that r is indeed prime when certain prime ideals are localisable in chapter 4 we consider the lattice of prime ideals of r when r is an ar r1ng and provide theorems which generalise some of the basic results from the theory of commutative regular local rings section 4 3 contains examples which not only illustrate points arising in chapters 3 and 4 but also show that some of the techniques which are mainstays of the commutative theory fall dramatically in a non commutat1ve setting in chapter 5 we generalise the concepts of regular sequences and cohen macaulay rings enabling us to prove in 5 2 and chapter 6 that a right noetherian local ring of finite right global dimension which 1s integral over its centre is a prime ring and exhibits many properties similar to those enjoyed by commutative regular local rings examples are provided which show that some alternative approaches are not applicable to the rings considered in these chapters regular local rings are gorensteln rings and as such are the subject of an elegant structure theorem due to bass 5 in chapter 7 we generalise his theorem to the situation of rings integral over their centres each chapter begins with a summary of the results contained in that chapter

multi criteria minimum cost spanning tree games abstract the minimum cost spanning tree game mcst game is a well known model within operations research games that has been widely studied in the literature in this paper we introduce the multi criteria version of the mcst game as a set valued tu game we prove that the extension of bird s cost allocation rule provides dominance core elements in this game we also give a family of core solutions that are different from the previous one these solutions are based on proportional allocations obtained using scalar solutions of the multi criteria spanning tree problem besides we prove necessary and sufficient conditions ensuring that the preference core of this game is not empty

cost allocation for a tree network with heterogeneous customers we analyze a cost allocation problem which could naturally arise from a situation wherein a tree networkt n 0 e serving heterogeneous customers has to be constructed the customers located atn require some service from a central supplier located at vertex 0 the customers have heterogeneous preferences for the level or quality of service received from the central supplier we formulate the above cost allocation problem as a cooperative game referred to as anextended tree game the extended tree game is a proper extension of megiddo s 1978 tree game wherein all the customers have identical preferences regarding the level of service received we prove that an extended tree game is convex and we show that its shapley value can be computed in p n time wherep is the number of distinct preference levels we further provide a complete facial description of the core polytope of an extended tree game and demonstrate that even when there are only two classes of customers the number of nonredundant core constraints could be exponential in n nevertheless we are able to construct an p n algorithm to check the core membership of an arbitrary cost allocation which can be used to construct an p n 3 combinatorial algorithm to compute the nucleolus of an extended tree game finally we show that the complements of the facet defining coalitions for the core are all connected in an auxiliary tree graph with node setn

computing the nucleolus of some combinatorially structured games in this paper we introduce the prenucleolus for a transferable utility game n v where 2 n the prenucleolus is a straightforward generalization of the ordinary prenucleolus where only the coalitions in determine the outcome we impose a combinatorial structure on the collection which enables us to compute the prenucleolus in n 3 time the algorithm can be used for computing the nucleolus of several classes of games among which is the class of minimum cost spanning tree games

congestion network problems and related games this paper analyzes network problems with congestion effects from a cooperative game theoretic perspective it is shown that for network problems with convex congestion costs the corresponding games have a non empty core if congestion costs are concave then the corresponding game has not necessarily core elements but it is derived that contrary to the convex congestion situation there always exist optimal tree networks extensions of these results to a class of relaxed network problems and associated games are derived

the computation of the exponential and logarithmic mappings and their first and second linearizations we describe two simple methods for the evaluation of the exponential and logarithmic mappings and their first and second linearizations based on the taylor expansion and the spectral representation we also provide guidelines for switching between those representations on the basis of the size of the argument the first and second linearizations of the exponential and logarithmic mappings provided here are based directly on the exponential formula for the solutions of systems of linear ordinary differential equations this representation does not require the use of perturbation formulae for eigenvalues and eigenvectors our approach leads to workable and straightforward expressions for the first and second linearizations of the exponential and logarithmic mappings regardless of degeneracies in the spectral decomposition of the argument

new techniques for cost sharing in combinatorial optimization games combinatorial optimization games form an important subclass of cooperative games in recent years increased attention has been given to the issue of finding good cost shares for such games in this paper we define a very general class of games called integer minimization games which includes the combinatorial optimization games in the literature as special cases we then present new techniques based on row and column generation for computing good cost shares for these games to illustrate the power of these techniques we apply them to traveling salesman and vehicle routing games our results generalize and unify several results in the literature the main underlying idea is that suitable valid inequalities for the associated combinatorial optimization problems can be used to derive improved cost shares

finite strain generalization of smallstrain constitutive relations for any finite strain tensor and additive volumetric deviatoric split abstract the paper deals with finite strain generalization of small strain constitutive equations for isotropic materials for which the strain is split into a volumetric part and a deviatoric part the latter characterizing the isochoric strain i e a strain at constant volume the volumetric deviatoric split has so far been handled by a multiplicative decomposition of the transformation tensor but the existing sophisticated complex constitutive models for small strains of cohesive pressure sensitive dilatant materials such as concrete and geomaterials involve an additive decomposition and would be difficult to convert a multiplicative decomposition it is shown that an additive decomposition of any finite strain tensor and of the green lagrange strain tensor in particular is possible provided that the higher order terms of the deviatoric strain tensor are allowed to depend on the volumetric strain this dependence is negligible for concrete and geomaterials because the volumetric strains are normally small whether or not the deviatoric strains are large furthermore the related question of the choice of the finite strain measure to be used for the finite strain generalization is analysed a transformation of the green lagrange finite strain tensor whose parameters approximately reflect the degrees of freedom equivalent to replacing the small strain tensor by any other possible finite strain measure is proposed finally a method by which the stress tensor that is workconjugate to any finite strain tensor can be converted to the green lagrange strain tensor is presented

a novel non linearly explicit second order accurate l stable methodology for finite deformation hypoelastic hypoelasto plastic structural dynamics problems a novel non linearly explicit second order accurate l stable computational methodology for integrating the non linear equations of motion without non linear iterations during each time step and the underlying implementation procedure is described emphasis is placed on illustrative non linear structural dynamics problems employing both total updated lagrangian formulations to handle finite deformation hypoelasticity hypoelasto plasticity models in conjunction with a new explicit exact integration procedure for a particular rate form constitutive equation illustrative numerical examples are shown to demonstrate the robustness of the overall developments for non linear structural dynamics applications

on the development of explicit robust schemes for implementation of a class of hyperelastic models in large strain analysis of rubbers the issue of developing effective and robust schemes to implement a class of the ogden type hypereiastic constitutive models for large strain analysis of rubber like materials is addressed to this end explicit forms for the corresponding material tangent stiffness tensors are developed and these are valid for the entire deformation range i e with both distinct as well as repeated principal stretch values throughout the analysis the various implications of the underlying property of separability of the strain energy functions are exploited thus leading to compact final forms of the tensor expressions in particular this facilitated the treatment of the complex cases of uncoupled volumetric deviatoric formulations for incompressible materials which are becoming increasingly popular in recent years the forms derived are also amenable for use with symbolic manipulation packages for systematic code generation

on objective corotational rates and their defining spin tensors abstract in this paper we prove a general result on objective corotational rates and their defining spin tensors let be a spin tensor that is associated with the rotation and deformation of a deforming material body in an arbitrary manner indicated by y b d w where b and d and w are the left cauchy green tensor and the stretching tensor and the vorticity tensor respectively then the corotational rate of defined by the spin i e the tensor field is objective for every time differentiable objective eulerian symmetric tensor field a if and only if the spin tensor assumes the form w y b d where y b d is an antisymmetric tensor valued isotropic function furthermore by virtue of certain necessary or reasonable requirements it is found that a single antisymmetric function of two positive real variables can be introduced to characterize a general class of spin tensors defining objective corotational rates accordingly a general explicit basis free expression for the latter is established in terms of the left cauchy green tensor b the vorticity tensor w and the stretching tensor d as well as the introduced antisymmetric function by choosing several particular forms of the latter it is shown that all commonly used spin tensors are incorporated into this general expression in a natural way

the stress conjugate to logarithmic strain abstract a stress s is said to be conjugate to a strain measure e if the inner product s e is the power per unit volume the logarithmic strain in u with u the right stretch tensor has been considered an interesting strain measure because of the relationship of its material time derivative ln u with the stretching tensor d in a previous article int j solids structures 22 1019 1032 1986 a formula for ln u was obtained in direct notation for the cases where the principal stretches are repeated as well as for the case where they are all distinct here the formula for ln u and the definition of conjugate stress are used to derive an explicit properly invariant expression for the stress conjugate to the logarithmic strain

on generalized dedekind prime rings abstract let r be a maximal order and a b be r ideals of r clearly a b b a is satisfied and if r is a dedekind prime ring the equality holds i e a b b a however the equality is not true in general in this paper we answer the question if r is a maximal order when is a b b a for all non zero r ideals of r we call prime noetherian maximal orders satisfying this property generalized dedekind prime rings we give several characterizations of g dedekind prime rings and show that being a g dedekind prime ring is a morita invariant moreover we prove that if r is a pi g dedekind prime ring then the polynomial ring r x and the rees ring r x t associated to an invertible ideal x are also pi g dedekind prime rings

void nucleation and growth for a class of incompressible nonlinearly elastic materials abstract in this paper a bifurcation problem for a solid sphere subjected to uniform tensile dead loading p 0 at its boundary is examined within the framework of finite elastostatics the sphere is composed of a particular class of homogeneous isotropic incompressible nonlinearly elastic materials namely those of power law type one solution to the problem for all values of p 0 corresponds to a homogeneous state in which the sphere remains undeformed while stressed however for sufficiently large values of p 0 there is in addition a second possible configuration involving an internal traction free spherical cavity the dependence on constitutive parameters of the critical load at which bifurcation occurs is examined as well as the subsequent void growth the stress distribution after cavitation occurs is also described the results are obtained in closed analytic form

cost allocation in the chinese postman problem this paper considers a cost allocation problem that arises from a delivery problem associated with the chinese postman problem cpp a delivery problem is described by a connected undirected graph in which each edge belongs to a different player a cost function on the edges of this graph and a fixed vertex which is referred to as the post office assume that the post office is providing some service to the players the nature of this service which can be thought of as mail delivery requires that a server will travel along the edges of the graph and returns to the post office the cost allocation problem is concerned with the cost of providing the service to all players a specific cost allocation rule is introduced and characterized further the class of delivery problems gives rise to a new class of cooperative combinatorial optimization games called delivery games it is shown that the outcome of the allocation rule with respect to a bridge connected euler graph is a core element of the corresponding delivery game

limitations to the large strain theory in the formulation of a large strain problem the euler cauchy stokes decomposition and the eulerian objective stress and strain rates used for the formulation of the problem are actually applicable only for some special cases and are not suitable for general large strain and rotation rates in this paper the limitations and applicabilities of the conventional large strain formulation under various deformation cases will be studied

the material time derivative of logarithmic strain abstract in this article we derive explicit formulas for the time rate of change of the logarithmic strains ln u and ln v where u and v are the right and left stretch tensors respectively results are obtained in both two and three dimensions for the cases where the principal stretches are repeated as well as for the case where they are distinct the formulas are displayed in terms of v the stretching tensor d the rotation r and the principal stretches finally we consider the corotational and jaumann derivatives of ln v and establish conditions under which these logarithmic strain rates are equal to the stretching tensor

highway games on weakly cyclic graphs a highway problem is determined by a connected graph which provides all potential entry and exit vertices and all possible edges that can be constructed between vertices a cost function on the edges of the graph and a set of players each in need of constructing a connection between a specific entry and exit vertex mosquera 2007 introduce highway problems and the corresponding cooperative cost games called highway games to address the problem of fair allocation of the construction costs in case the underlying graph is a tree in this paper we study the concavity and the balancedness of highway games on weakly cyclic graphs a graph g is called highway game concave if for each highway problem in which g is the underlying graph the corresponding highway game is concave we show that a graph is highway game concave if and only if it is weakly triangular moreover we prove that highway games on weakly cyclic graphs are balanced

on the core and nucleolus of directed acyclic graph games we introduce directed acyclic graph dag games a generalization of standard tree games to study cost sharing on networks this structure has not been previously analyzed from a cooperative game theoretic perspective every monotonic and subadditive cost game including monotonic minimum cost spanning tree games can be modeled as a dag game we provide an efficiently verifiable condition satisfied by a large class of directed acyclic graphs that is sufficient for the balancedness of the associated dag game we introduce a network canonization process and prove various structural results for the core of canonized dag games in particular we characterize classes of coalitions that have a constant payoff in the core in addition we identify a subset of the coalitions that is sufficient to determine the core this result also guarantees that the nucleolus can be found in polynomial time for a large class of dag games

complexity of the minimum base game on matroids this paper studies the complexity of computing solution concepts for a cooperative game called the minimum base game mbg e c where its characteristic function c 2e is defined as c s the weight w b of a minimum weighted base b s for a given matroid m e and a weight function w e the minimum base game contains as a special case the minimum spanning tree game mstg in an edge weighted graph in which players are located on the edges by interpreting solution concepts of games such as core value and shapley value in terms of matroid theory we obtain the core of mbg is nonempty if and only if the matroid m has no circuit consisting only of edges with negative weights checking the concavity and subadditivity of an mbg can be done in oracle polynomial time the value of an mbg exists if and only if the core is not empty the value of mstg can be computed in polynomial time while there is no oracle polynomial algorithm for a general mbg computing the shapley value

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

rotations stress rates and strain measures in homogeneous deformation processes abstract the article draws the distinction between homogeneous and pure homogeneous deformation in the latter mode an orthogonal triad can be identified the principal axes which remain orthogonal throughout the deformation an appropriate strain measure in such processes is that of logarithmic strain furthermore its material derivative equals the rate of deformation tensor in homogeneous processes the deformation gradient tensor is unsymmetric and there is no triad which remains orthogonal throughout this often leads to a description of the actual deformation by means of the polar decomposition theorem the material derivative of the tensor logorithm is no longer simply related to the rate of deformation tensor and this is exemplified herein as a result of material rotation the stress components will vary and constitutive equations which involve stress rate must be formulated to compensate for the rotation a number of objective stress rates are examined herein and employed in a constitutive equation describing a hypoelastic solid the effect of stress rate on the evolution of stresses in the deforming solid is demonstrated for the case when the body undergoes simple rectilinear shear

on the core of network synthesis games we use polynomial formulations to show that several rational and discrete network synthesis games including the minimum cost spanning tree game satisfy the assumptions of owen s linear production game model we also discuss computational issues related to finding and recognizing core points for these classes of games

sharing the cost of a capacity network we consider a communication network where each pair of users requests a connection guaranteeing a certain capacity the cost of building capacity is identical across pairs efficiency is achieved by any maximal cost spanning tree we construct cost sharing methods ensuring standalone core stability monotonicity of one s cost share in one s capacity requests and continuity in everyone s requests we define a solution for simple problems where each pairwise request is zero or one and extend it piecewise linearly to all problems the uniform solution obtains if we require one s cost share to be weakly increasing in everyone s capacity request in the solution we propose on the contrary one s cost share is weakly decreasing in other agents requests the computational complexity of both solutions is polynomial in the number of users the uniform solution admits a closed form expression and is the analog of a popular solution for the minimal cost spanning tree problem

a generalized linear production model a unifying model we introduce a generalized linear production model whose attractive feature being that the resources held by any subset of producerss is not restricted to be the vector sum of the resources held by the members ofs we provide sufficient conditions for the non emptiness of the core of the associated generalized linear production game and show that if the core of the game is not empty then a solution in it can be produced from a dual optimal solution to the associated linear programming problem our generalized linear production model is a proper generalization of the linear production model introduced by owen and it can be used to analyze cooperative games which cannot be studied in the ordinary linear production model framework we use the generalized model to show that the cooperative game induced by a network optimization problem in which players are the nodes of the network has a non empty core we further employ our model to prove the non emptiness of the core of two other classes of cooperative games which were not previously studied in the literature and we also use our generalized model to provide an alternative proof for the non emptiness of the core of the class of minimum cost spanning tree games thus it appears that the generalized linear production model is a unifying model which can be used to explain the non emptiness of the core of cooperative games generated by various seemingly different optimization models

on the conditions of potentiality in finite elasticity and hypo elasticity abstract thermodynamic approaches to finite elasticity are almost generally accepted nevertheless there is still a lack of proof for the necessity of potential strain stress relations in generally defined elasticity and hypo elasticity this situation has resulted in ambiguous applications of the general concept of elasticity to the description of irreversible phenomena in viscoelastic solids and liquids this paper makes a brief review of the general concepts of elasticity and hypo elasticity with most of the attention paid to the eulerian description employed in viscoelastic theories then it is demonstrated that all hypothetical materials with non potential finite elastic or hypo elastic constitutive relations can create an energy from nothing i e work as perpetual motion machines this gives a physical proof of necessity of potential conditions in general finite elasticity and hypo elasticity and their extensions to finite viscoelasticity

floating stress point integration meshfree method for large deformation analysis of elastic and elastoplastic materials summary a new meshfree formulation of stress point integration called the floating stress point integration meshfree method is proposed for the large deformation analysis of elastic and elastoplastic materials this method is a galerkin meshfree method with an updated lagrangian procedure and a quasi implicit time advancing scheme without any background cell for domain integration its new formulation is based on incremental equilibrium equations derived from the incremental virtual work equation which is not generally used in meshfree formulations hence this technique allows the temporal continuity of the mechanical equilibrium to be naturally achieved the details of the new formulation and several examples of the large deformation analysis of elastic and elastoplastic materials are presented to show the validity and accuracy of the proposed method in comparison with those of the finite element method copyright 2012 john wiley sons ltd

a cooperative location game based on the 1 center location problem abstract in this paper we introduce and analyze new classes of cooperative games related to facility location models defined on general metric spaces the players are the customers demand points in the location problem and the characteristic value of a coalition is the cost of serving its members specifically the cost in our games is the service radius of the coalition we call these games the minimum radius location games mrlg we study the existence of core allocations and the existence of polynomial representations of the cores of these games focusing on network spaces i e finite metric spaces induced by undirected graphs and positive edge lengths and on the lp metric spaces defined over r d

on the relationship between the logarithmic strain rate and the stretching tensor abstract in this paper we investigate the relationship between the stretching tensor d and the logarithmic hencky strain in v with v the left stretch tensor we establish the simple formula 1 which holds for arbitrary three dimensional motions here f is the deformation gradient is the time derivative of in v measured in a coordinate system which rotates with the left principal strain axes and is the spin of the right principal strain axes we use this formula to show that or equrvatently the jaumann derivative of ln v if and only if the characteristic spaces of the right stretch tensor u are constant on any time interval in which the number of distinct principal stretches is constant finally we show that the asymptotic approximation 3 holds whenever the displacement gradient h satisfies

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

on some network flow games we analyze three subclasses of cooperative games arising from network optimization problems in which the resources such as arcs or nodes in the network are controlled by individuals who have conflicting objectives the first subclass of cooperative games is induced by network optimization problems over directed augmented trees we show that for this subclass of games the kernel coincides with the nucleolus and that the nucleolus can be characterized as the unique revenue allocation vector in which every pair of arc owners who are adjacent in the tree are located symmetrically with respect to their bargaining range we further give a linear characterization of the core of this subclass of games which is then used to provide a more explicit representation of the nucleolus and to construct a strongly polynomial algorithm for generating it the second subclass of cooperative games is induced by maximum flow problems in simple undirected networks we provide a useful parametric representation of the core of this subclass of games which is used to characterize the nucleolus and the intersection of the core and the kernel explicitly we show that the intersection of the core and the kernel consists of all revenue allocations in the core which assign equal payoffs to any pair of unseparated arc owners we further demonstrate that among the core vectors the nucleolus is the unique revenue allocation vector in which the smallest allocations are maximized in a lexicographical sense the third cooperative game that we study is the assignment game introduced by shapley and shubik 1972 this game is induced by the assignment problem which can be cast as a network optimization problem we investigate the relationship between the kernel and the core of the assignment game and provide a necessary and sufficient condition for the core to be contained in the kernel we further show that in general the intersection of the kernel and the core is not a convex set we also exhibit that under certain conditions the nucleolus has a simple characterization as the unique vector in the core in which the smallest revenue allocations are maximized in a lexicographical sense finally we consider the horse market example of bohm bawerk 1923 for which it is shown that the core is contained in the kernel and that the nucleolus is the midpoint of the core

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

on copositive matrices and strong ellipticity for isotropic elastic materials on etablit les conditions necessaires et suffisantes pour une forte ellipticite des equations d un materiau elastique non lineaire isotrope compressible a l equilibre on utilise un theoreme de representation de matrices copositives du a cottle habetler et lemke 1970

unified explicit basis free expressions for time rate and conjugate stress of an arbitrary hill s strain abstract this paper provides simple and unified explicit basis free expressions for time rate and conjugate stress of an arbitrary hill s strain for the first time which are valid for all cases of the eigenvalues of the right stretch tensors

shortest path games abstract we study cooperative games that arise from the problem of finding shortest paths from a specified source to all other nodes in a network such networks model among other things efficient development of a commuter rail system for a growing metropolitan area we motivate and define these games and provide reasonable conditions for the corresponding rail application we show that the core of a shortest path game is nonempty and satisfies the given conditions but that the shapley value for these games may lie outside the core however we show that the shortest path game is convex for the special case of tree networks and we provide a simple polynomial time formula for the shapley value in this case in addition we extend our tree results to the case where users of the network travel to nodes other than the source finally we provide a necessary and sufficient condition for shortest paths to remain optimal in dynamic shortest path games where nodes are added to the network sequentially over time

constitutive inequalities for an isotropic elastic strain energy function based on hencky s logarithmic strain tensor hencky s strain energy function for finite isotropic elasticity is obtained by the replacement of the infinitesimal strain measure occurring in the classical strain energy function of infinitesimal

a new rule for source connection problems abstract in this paper we study situations where a group of agents require a service that can only be provided from a source the so called source connection problems these problems contain the standard fixed tree the classical minimum spanning tree and some other related problems such as the k hop the degree constrained and the generalized minimum spanning tree problems among others our goal is to divide the cost of a network among the agents to this end we introduce a rule which will be referred to as a painting rule because it can be interpreted by means of a story about painting some meaningful properties in this context and a characterization of the rule are provided

traveling salesman games in this paper we discuss the problem of how to divide the total cost of a round trip along several institutes among the institutes visited we introduce two types of cooperative games fixed route traveling salesman games and traveling salesman games as a tool to attack this problem under very mild conditions we prove that fixed route traveling salesman games have non empty cores if the fixed route is a solution of the classical traveling salesman problem core elements provide us with fair cost allocations a traveling salesman game may have an empty core even if the cost matrix satisfies the triangle inequality in this paper we introduce a class of matrices defining ts games with non empty cores

dynamic linear programming games with risk averse players motivated by situations in which independent agents wish to cooperate in some uncertain endeavor over time we study dynamic linear programming games which generalize classical linear production games to multi period settings under uncertainty we specifically consider that players may have risk averse attitudes towards uncertainty and model this risk aversion using coherent conditional risk measures for this setting we study the strong sequential core a natural extension of the core to dynamic settings we characterize the strong sequential core as the set of allocations that satisfy a particular finite set of inequalities that depend on an auxiliary optimization model and then leverage this characterization to establish sufficient conditions for emptiness and non emptiness qualitatively whereas the strong sequential core is always non empty when players are risk neutral our results indicate that cooperation in the presence of risk aversion is much more difficult we illustrate this with an application to cooperative newsvendor games where we find that cooperation is possible when it least benefits players and may be impossible when it offers more benefit

on the invariant representation of spin tensors with applications abstract the invariant representation of the spin tensor defined as the rotation rate or a principal triad for a symmetric and non degenerate tensor is derived on the basis of the general solution of a linear tensorial equation the result can be naturally specified to study the spin of the stretch tensors and to investigate the relations between various rotation rate tensors encountered frequently in modern continuum mechanics a remarkable formula which relates the generalized stress conjugate to the generalized strain in hill s sense to cauchy stress is obtained in invariant form through the work conjugate principle particularly a detailed discussion on the time rate of logarithmic strain and its conjugate stress is made as the principal axes ofstrain are not fixed during deformation

sharing supermodular costs we study cooperative games with supermodular costs we show that supermodular costs arise in a variety of situations in particular we show that the problem of minimizing a linear function over a supermodular polyhedron a problem that often arises in combinatorial optimization has supermodular optimal costs in addition we examine the computational complexity of the least core and least core value of supermodular cost cooperative games we show that the problem of computing the least core value of these games is strongly np hard and in fact is inapproximable within a factor strictly less than 17 16 unless p np for a particular class of supermodular cost cooperative games that arises from a scheduling problem we show that the shapley value which in this case is computable in polynomial time is in the least core while computing the least core value is np hard

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

basis free representations for the stress rate of isotopic materials in terms of the principal components of stress tensor and a scalar response function two kinds of basis free representation for the stress rate are obtained which only include the time rate of the strain tensor functions and invariants of the strain tensor the expressions for the stress rate valid in the cases that the eigenvalues of the strain are distinct doubly coalescent and triply coalescent respectively