computational complexity of a cost allocation approach to a fixed cost spanning forest problem we present a computational analysis of a game theoretic approach to a cost allocation problem arising from a graph optimization problem referred to as the fixed cost spanning forest fcsf problem the customers in the fcsf problem represented by nodes in a graph g are in need of service that can be produced at some facilities yet to be constructed the cost allocation problem is concerned with the fair distribution of the cost of providing the service among customers we formulate this cost allocation problem as a cooperative game referred to as the fcsf game in general the core of a fcsf game may be empty however for the case when g is a tree it is shown that the core is not empty moreover we prove that in this case core points can be generated in strongly polynomial time we further provide a nonredundant characterization of the core of the fcsf game defined over a tree in the special case when all nodes are communities this is shown to lead in some instances to a strongly polynomial algorithm for computing the nucleolus

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

non linear vibrations of viscoelastic moving belts part i free vibration analysis abstract the non linear free vibration of viscoelastic moving belts is studied based on the linear viscoelastic differential constitutive law the generalized equation of motion is derived for a moving belt with geometric non linearities the method of multiple scales is applied directly to the governing equation which is in the form of continuous autonomous gyroscopic systems with weak non linearity this direct treatment does not involve a prior assumption regarding the spatial solutions the non linear natural frequencies and free response amplitude for autonomous systems are predicted by the perturbation method the results obtained with the quasi static assumption and those without this assumption are compared the effects of elastic and viscoelastic parameters axial moving speed and the geometric non linearity on natural frequencies and amplitudes of the free response are investigated from numerical examples

supercritical speed stability of the trivial equilibrium of an axially moving string on an elastic foundation the stability of an axially moving string supported by a discrete or distributed elastic foundation is examined analytically particular attention is directed at the distribution of the critical speeds and identifying the divergence instability of the trivial equilibrium the elastically supported string shows unique stability behavior that is considerably different from unsupported axially moving string in particular any elastic foundation discrete or distributed leads to multiple critical speeds and a single region of divergence instability above the first critical speed whereas the unsupported string has one critical speed and is stable at all supercritical speeds additionally the elastically supported string critical speeds are bounded above and the maximum critical speed is the upper bound of the divergent speed region the analysis draws on the self adjoint eigenvalue problem for the critical speeds and a perturbation analysis about the critical speeds neither numerical solution nor spatial discretization which can produce substantially incorrect results are required the system falls in the class of dispersive gyroscopic continua and its behavior provides a useful comparison for general gyroscopic systems the analytical findings also serve as a benchmark for approximate methods applied to gyroscopic continua

matching games the least core and the nucleolus a matching game is a cooperative game defined by a graph g n e the player set is n and the value of a coalition s n is defined as the size of a maximum matching in the subgraph induced by s we show that the nucleolus of such games can be computed efficiently the result is based on an alternative characterization of the least core which may be of independent interest the general case of weighted matching games remains unsolved

singularly perturbed critical choquard equations abstract in this paper we study the semiclassical limit for the singularly perturbed choquard equation e 2 u v x u e 3 r 3 q y g u y x y d y q x g u in r 3 where 0 3 e is a positive parameter v q are two continuous real function on r 3 and g is the primitive of g which is of critical growth due to the hardy littlewood sobolev inequality under suitable assumptions on g we first establish the existence of ground states for the critical choquard equation with constant coefficients next we establish existence and multiplicity of semi classical solutions and characterize the concentration behavior by variational methods

fem analysis of transverse vibrations of an axially moving membrane immersed in ideal fluid transverse vibrations of an axially moving travelling in its own plane membrane submerged in ideal fluid are analysed using the fem the discrete equations differ from the equations of the common coupled problem in that there appear two additional inertia terms due to the convective acceleration the effect of the density of the element mesh the effect of the truncation distance and the effect of various lumping techniques on the accuracy of the results are studied the fem results are compared with available analytical and experimental results the agreement seems to be rather good

the volume algorithm revisited relation with bundle methods we revise the volume algorithm va for linear programming and relate it to bundle methods when first introduced va was presented as a subgradient like method for solving the original problem in its dual form in a way similar to the serious null steps philosophy of bundle methods va produces green yellow or red steps in order to give convergence results we introduce in va a precise measure for the improvement needed to declare a green or serious step this addition yields a revised formulation rva that is halfway between va and a specific bundle method that we call bva we analyze the convergence properties of both rva and bva finally we compare the performance of the modified algorithms versus va on a set of rectilinear steiner problems of various sizes and increasing complexity derived from real world vlsi design instances

a strongly polynomial algorithm to solve combinatorial linear programs khachiyan and recently karmarkar gave polynomial algorithms to solve the linear programming problem these algorithms have a small theoretical drawback namely the number of arithmetic steps depends on the size of the input numbers we present a polynomial linear programming algorithm whose number of arithmetic steps depends only on the size of the numbers in the constraint matrix but is independent of the size of the numbers in the right hand side and objective vectors in particular it gives a polynomial algorithm for the minimum cost flow and multicommodity flow problems in which the number of arithmetic steps is independent of the size of the costs and capacities the algorithm makes use of an existing polynomial linear programming algorithm the problem of whether any algorithm has a running time that is independent even of the size of the numbers in the constraint matrix remains open

nodal solutions for the choquard equation abstract we consider the general choquard equations u u i u p u p 2 u where i is a riesz potential we construct minimal action odd solutions for p n n n n 2 and minimal action nodal solutions for p 2 n n 2 we introduce a new minimax principle for least action nodal solutions and we develop new concentration compactness lemmas for sign changing palais smale sequences the nonlinear schrodinger equation which is the nonlocal counterpart of the choquard equation does not have such solutions

generalized network problems yielding totally balanced games a class of multiperson mathematical optimization problems is considered and is shown to generate cooperative games with nonempty cores the class includes but is not restricted to numerous versions of network flow problems it was shown by owen that for games generated by linear programming optimization problems optimal dual solutions correspond to points in the core we identify a special class of network flow problems for which the converse is true i e every point in the core corresponds to an optimal dual solution

the existence of least energy nodal solutions for some class of kirchhoff equations and choquard equations in r n abstract in this paper we study the existence of least energy nodal solutions for a class of kirchhoff type problems in r n since the kirchhoff equation is a nonlocal one the variational setting to look for sign changing solutions is different from the local cases by using constrained minimization on the sign changing nehari manifold we prove the kirchhoff problem has a least energy nodal solution with its energy exceeding twice the least energy as a co product of our approaches we obtain the existence of least energy sign changing solution for choquard equations in r n and show that the sign changing solution has an energy strictly larger than the least energy and less than twice the least energy

a factoring approach for the steiner tree problem in undirected networks in communication networks many applications such as video on demand and video conferencing must establish a communications tree that spans a subset k in a vertex set the source node can then send identical data to all nodes in set k along this tree this kind of communication is known as multicast communication a network optimization problem called the steiner tree problem stp is presented to find a least cost multicasting tree in this paper an o e algorithm is presented to find a minimum steiner tree for series parallel graphs where e is the number of edges based on this algorithm we proposed an o 2 2 c e algorithm to solve the steiner tree problem for general graphs where c is the number of applied factoring procedures the c value is strongly related to the topology of a given graph this is quite different from other algorithms with exponential time complexities in k

fuzzy cooperative games arising from linear production programming problems with fuzzy parameters abstract in the present study we consider a production model in which multiple decision makers pool resources to produce finished goods such a production model which is assumed to be linear can be formulated as mathematical programming problems with fuzzy parameters from the viewpoint of experts imprecise or fuzzy understanding of the nature of parameters in a problem formulation process it is shown that a cooperative game with values of coalitions represented by fuzzy numbers arises from the linear production programming problem with fuzzy parameters and such a game is referred to as a fuzzy linear production programming game the values of coalitions of the game can be obtained by employing a parametric approach to solving the linear production programming problem with fuzzy parameters it is proven that the core of the game is not empty and an interval in the core is computed by using the ideas of sensitivity analysis and the duality theory of linear programming problems

solutions based on fuzzy goals in fuzzy linear programming games abstract in this paper we deal with linear programming problems with fuzzy parameters from the viewpoint of experts imprecise or fuzzy understanding of the nature of parameters in a problem formulation process and consider fuzzy linear programming games arising from the linear programming problems constructing fuzzy goals of coalitions with respect to payoff in order to suitably reflect fuzzy environments in which the linear programming games are formulated we define solutions maximizing minimal fuzzy goal and solutions maximizing the sum of fuzzy goals and develop computational methods for obtaining the solutions finally we give a numerical example to illustrate construction of a fuzzy linear programming game and derivation of the solutions

on computational methods for solutions of multiobjective linear production programming games abstract in this paper we consider a production model in which multiple decision makers pool resources to produce finished goods such a production model which is assumed to be linear can be formulated as a multiobjective linear programming problem it is shown that a multi commodity game arises from the multiobjective linear production programming problem with multiple decision makers and such a game is referred to as a multiobjective linear production programming game the characteristic sets in the game can be obtained by finding the set of all the pareto extreme points of the multiobjective programming problem it is proven that the core of the game is not empty and points in the core are computed by using the duality theory of multiobjective linear programming problems moreover the least core and the nucleolus of the game are examined finally we consider a situation that decision makers first optimize their multiobjective linear production programming problem and then they examine allocation of profits and or costs computational methods are developed and illustrative numerical examples are given

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

linear production games with fuzzy control the aim of this paper is to analyse linear production with committee control situations arising when controllers face the possibility of graduating their options in order to model these situations we consider several kinds of fuzzy controls which can be modelled as different simple fuzzy games an lp game which is an extension of lp games with committee control introduced in curiel et al on balanced games and games with committee control or spectrum 11 1989 83 88 is obtained and its core is studied

on nonlocal choquard equations with hardy littlewood sobolev critical exponents abstract we consider the following nonlinear choquard equation with dirichlet boundary condition u u 2 x y d y u 2 2 u f u in where is a smooth bounded domain of r n 0 n 3 0 n and 2 is the critical exponent in the sense of the hardy littlewood sobolev inequality under suitable assumptions on different types of nonlinearities f u we are able to prove some existence and multiplicity results for the equation by variational methods

classification of positive solitary solutions of the nonlinear choquard equation in this paper we settle the longstanding open problem concerning the classification of all positive solutions to the nonlinear stationary choquard equation delta u u 2u left frac 1 x u 2 right 0 quad u in h 1 mathbb r 3 which can be considered as a certain approximation of the hartree fock theory for a one component plasma as explained in lieb and lieb simon s papers starting from 1970s we first prove that all the positive solutions of this equation must be radially symmetric and monotone decreasing about some fixed point interestingly to use the new method of moving planes introduced by chen li ou we deduce the problem into an elliptic system as a key step we transform this differential system into a system of integral equations with the help of riesz and bessel potentials and then use the method of a moving plane in an integral form next using radial symmetry we deduce the uniqueness result from lieb s work our argument can be adapted well to study the radial symmetry of positive solutions of the equation in the generalized form u k 1 f left u k 2 u right

positive and sign changing solutions to a nonlinear choquard equation abstract we consider the problem u w x u 1 x u p u p 2 u u h 0 1 where is an exterior domain in r n n 3 0 n p 2 2 n n 2 w c 0 r n inf r n w 0 and w x v 0 as x under symmetry assumptions on and w which allow finite symmetries and some assumptions on the decay of w at infinity we establish the existence of a positive solution and multiple sign changing solutions to this problem having small energy

network strength games the core and the nucleolus the maximum number of edge disjoint spanning trees in a network has been used as a measure of the strength of a network it gives the number of disjoint ways that the network can be fully connected this suggests a game theoretic analysis that shows the relative importance of the different links to form a strong network we introduce the network strength game as a cooperative game defined on a graph g v e the player set is the edge set e and the value of a coalition s subseteq e is the maximum number of disjoint spanning trees included in s we study the core of this game and we give a polynomial combinatorial algorithm to compute the nucleolus when the core is non empty

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

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

travelling load response of an axially moving string abstract the classical moving load problem in which a mass traverses an elastic structure is extended to systems in which the guideway also has prescribed axial motion a monocable ropeway such as a tramway or ski lift is an example of such a traveling structure traveling load system and it is modeled herein as an axially moving string that transports an attached discrete mass between two supports the green s function methods for the two constituent systems the particle and the uniform traveling string are combined to derive a volterra integral equation with delay that governs the interaction force in the coupled system the calculated response of the traveling string particle system to arbitrary initial conditions and external excitation is compared to that predicted by the derived asymptotic solution for vanishing discrete mass repeated scattering by the particle of transverse waves in the string dominates the motion transient vibration as the particle is transported between the supports is maximized at a transport speed that can be substantially lower than the critical speed of divergence instability for the uniform traveling string agreement between responses measured in the laboratory and those predicted by the traveling structure traveling load theory supports the analysis

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

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

totally balanced games arising from controlled programming problems a cooperative game in characteristic function form is obtained by allowing a number of individuals to esercise partial control over the constraints of a generally nonlinear mathematical programming problem either directly or through committee voting conditions are imposed on the functions defining the programming problem and the control system which suffice to make the game totally balanced this assures a nonempty core and hence a stable allocation of the full value of the programming problem among the controlling palyers in the linear case the core is closely related to the solutions of the dual problem applications are made to a variety of economic models including the transferable utility trading economies of shapley and shubik and a multishipper one commodity transshipment model with convex cost functions and concave revenue functions dropping the assumption of transferable utility leads to a class of controlled multiobjective or pareto programming problems which again yield totally balanced games

lower and upper bounds for linear production games abstract we study the problem of allocating the total profit of a production enterprise among the resource owners using the game theoretic framework introduced by owen owen g 1975 on the core of linear production games mathematical programming 9 358 370 we provide lower upper bounds on the values of the game by aggregating over columns rows of the lp problem by choosing aggregation weights corresponding to optimal solutions of the primal dual lp problem we can create new games whose core form a superset subset of the original core an estimate of the resulting error in terms of an core is obtained by solving a mixed integer programming problem and we also suggest an iterative procedure for improving the bounds using a set of numerical examples we investigate how the performance of the aggregation approach depends on the structure of the problem data

infinitely many bound states for choquard equations with local nonlinearities abstract in this paper we consider the following choquard equation ch u u i u p u p 2 u v x u q 2 u in r n u h 1 r n where n 3 n 4 n p 2 n n 2 q 2 2 n n 2 1 p 1 n 2 n 2 1 2 n n n 2 p 1 n 2 and i is the riesz potential under some suitable decay assumptions but without any symmetry property on v x we prove that the problem has infinitely many solutions whose energy can be arbitrarily large

algorithmic aspects of the core of combinatorial optimization games we discuss an integer programming formulation for a class of cooperative games we focus on algorithmic aspects of the core one of the most important solution concepts in cooperative game theory central to our study is a simple but very useful observation that the core for this class is nonempty if and only if an associated linear program has an integer optimal solution based on this we study the computational complexity and algorithms to answer important questions about the cores of various games on graphs such as maximum flow connectivity maximum matching minimum vertex cover minimum edge cover maximum independent set and minimum coloring

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

the nehari manifold for a semilinear elliptic equation with a sign changing weight function abstract the nehari manifold for the equation u x a x u x b x u x 1u x for x together with dirichlet boundary conditions is investigated exploiting the relationship between the nehari manifold and fibrering maps i e maps of the form t j tu where j is the euler functional associated with the equation we discuss how the nehari manifold changes as changes and show how existence and non existence results for positive solutions of the equation are linked to properties of the manifold

groundstates of nonlinear choquard equations existence qualitative properties and decay asymptotics we consider a semilinear elliptic problem delta u u i alpha ast abs u p abs u p 2 u quad text in r n where i alpha is a riesz potential and p 1 this family of equations includes the choquard or nonlinear schr odinger newton equation for an optimal range of parameters we prove the existence of a positive groundstate solution of the equation we also establish regularity and positivity of the groundstates and prove that all positive groundstates are radially symmetric and monotone decaying about some point finally we derive the decay asymptotics at infinity of the groundstates

free in plane vibration of an axially moving membrane the free in plane vibration of an axially moving membrane is studied considering the effects of both the translating speed and aspect ratio of the membrane two sets of boundary conditions which are free and fixed constraints in the lateral direction at boundaries with mass transport are discussed in this study from the extended hamilton principle the coupled equations of the longitudinal and lateral motions are derived these equations are then discretized by using the galerkin method from the discretized equations the natural frequencies and mode shapes are obtained for the variations of the translating speed and aspect ratio the results show that the translating speed aspect ratio and boundary conditions have significant effects on the in plane vibrations of the moving membrane

sign changing solutions of a class of nonlocal quasilinear elliptic boundary value problems abstract this paper is concerned with nonlocal kirchhoff s equation a b u 2 u f x u in u 0 on via variational methods and invariant sets of descent flow we obtain existence of signed and sign changing solutions with asymptotically 3 linear bounded nonlinearity

sign changing and multiple solutions of kirchhoff type problems without the p s condition abstract the existence of nontrivial solutions of kirchhoff type equations is an important nonlocal quasilinear problem in this paper we use minimax methods and invariant sets of descent flow to prove two interesting existence theorems for the following 4 superlinear kirchhoff type problems without the p s condition one concerning the existence of a nontrivial solution and the other one concerning the existence of sign changing solutions and multiple solutions a b u 2 u f x u in u 0 on

existence of semiclassical ground state solutions for a generalized choquard equation abstract in this paper we study a generalized quasilinear choquard equation e p p u v x u p 2 u e n r n q y f u y x y q x f u in r n where p is the p laplacian operator 1 p n v and q are two continuous real functions on r n 0 n f s is the primate function of f s and e is a positive parameter under suitable assumptions on p and f we establish a new concentration behavior of solutions for the quasilinear choquard equation by variational methods the results are also new for the semilinear case p 2

existence of groundstates for a class of nonlinear choquard equations we prove the existence of a nontrivial solution h n to the nonlinear choquard equation i in n where i is a riesz potential under almost necessary conditions on the nonlinearity in the spirit of berestycki and lions this solution is a groundstate if moreover is even and monotone on 0 then is of constant sign and radially symmetric

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

accelerating benders decomposition algorithmic enhancement and model selection criteria this paper proposes methodology for improving the performance of benders decomposition when applied to mixed integer programs it introduces a new technique for accelerating the convergence of the algorithm and theory for distinguishing good model formulations of a problem that has distinct but equivalent mixed integer programming representations the acceleration technique is based upon selecting judiciously from the alternate optima of the benders subproblem to generate strong or pareto optimal cuts this methodology also applies to a much broader class of optimization algorithms that includes dantzig wolfe decomposition for linear and nonlinear programs and related cutting plane type algorithms that arise in resource directive and price decomposition when specialized to network location problems this cut generation technique leads to very efficient algorithms that exploit the underlying structure of these models in discussing the proper formulation of mixed integer programs we suggest criteri

dynamic responses of the in plane and out of plane vibrations for an axially moving membrane the dynamic responses of both the in plane and out of plane vibrations are investigated for an axially moving membrane using the extended hamilton principle equations of motion are derived for the moving membrane with no slip boundary conditions at rollers the equations of motion are discretized by using the galerkin method and then the generalized a time integration method is applied to compute the dynamic responses of the membrane based on the computed results the responses are compared between the in plane and out of plane vibrations in addition the effects of translating velocity acceleration critical speeds and velocity profiles on the dynamic behaviours for displacements and stresses are investigated and discussed r 2006 elsevier ltd all rights reserved

stability analysis of an axially accelerating string the dynamic response of an axially accelerating string is investigated the time dependent velocity is assumed to vary harmonically about a constant mean velocity approximate analytical solutions are sought using two different approaches in the first approach the equations are discretized first and then the method of multiple scales is applied to the resulting equations in the second approach the method of multiple scales is applied directly to the partial differential system principal parametric resonances and combination resonances are investigated in detail stability boundaries are determined analytically it is found that instabilities occur when the frequency of velocity fluctuations is close to two times the natural frequency of the constant velocity system or when the frequency is close to the sum of any two natural frequencies when the velocity variation frequency is close to zero or to the difference of two natural frequencies however no instabilities are detected up to the first order of perturbation numerical results are presented for a band saw and a threadline problem

ground state sign changing solutions for a class of subcritical choquard equations with a critical pure power nonlinearity in rn abstract in this paper we investigate the existence of ground state sign changing solutions for a class of choquard equations u 1 f x u i k u p k x u p 2 u u 2 2 u x r n where k and f are nonnegative functions n 3 2 2 n n 2 p 2 n n 2 1 0 and 1 is the first eigenvalue of the equation u u f x u in h 1 r n using the sign changing nehari manifold we prove that the choquard equation has at least one ground state sign changing solution this paper can be regarded as the complementary work of ghimenti and van schaftingen 2016 van schaftingen and xia 2017

a dual ascent approach for steiner tree problems on a directed graph the steiner tree problem on a directed graph stdg is to find a directed subtree that connects a root node to every node in a designated node setv we give a dual ascent procedure for obtaining lower bounds to the optimal solution value the ascent information is also used in a heuristic procedure for obtaining feasible solutions to the stdg computational results indicate that the two procedures are very effective in solving a class of stdg s containing up to 60 nodes and 240 directed 120 undirected arcs