an axiomatization of the serial cost sharing method we offer an axiomatization of the serial cost sharing method of friedman and moulin 1999 the key property in our axiom system is group demand monotonicity asking that when a group of agents raise their demands not all of them should pay less

modified r matrix and separation of variables for the modified korteweg de vries mkdv hierarchy abstract in this article it is first given that a lax representation in terms of 2 2 matrices for the completeey integrable finite dimensional hamiltonian system cifhs h produced through the nonlinearization procedure for the mkdv hierarchy and then an associated non dynamical modified r matrix is constructed by making use of this r matrix and matrix trace equality a set of finite dimensional involutive functions fm m 0 1 f0 h which guarantees the integrability of hamiltonian systems h and the lax representations in terms of 2 2 matrices for the whole hamiltonian hierarchies fm m 0 1 are obtained moreover the involutive solutions of the mkdv hierarchy are given finally it is found that the hamiltonian jacobi equation for the hamiltonian system h can be separable under a group of new coordinates introduced by the 2 2 lax matrix

mean field theory for usp 4 sime so 5 the simple lie algebra usp 4 so 5 is a ten dimensional algebra that contains the angular momentum algebra su 2 in nuclear structure physics the algebra so 5 describes beta rigid collective modes in the bohr mottelson and interacting boson models the so 5 dual space consists of density matrices which are defined by the expectations of so 5 generators a coadjoint orbit is a common level surface in the dual space of the two so 5 casimirs this paper develops mean field theory on any coadjoint orbit of so 5 densities when the densities of a set of quantum states lie on one orbit the system is said to have a weak dynamical symmetry a lax pair determines the dynamics of so 5 densities on each coadjoint orbit analytic solutions are reported for rotating so 5 densities in equilibrium for a particular energy function

on the symmetric representations of su 5 matrix elements of the generators in the so 3 basis by making use of the results of a previous paper j math phys 29 1958 1988 in which the matrix elements of the su 5 generators were found in closed form for symmetric representations and in an so 4 labeled state basis it is shown how the matrix elements of the generators can also be derived in the physical so 3 state basis the main step consists in studying the action of the su 5 generators upon a particular subset of so called intrinsic su 2 su 2 states out of which the physical so 3 states are projected by means of the hill wheeler technique

sl 2 modules by sl 2 coherent states irreducible sp 4 module with highest weight labeled by the azimuthal and magnetic quantum numbers l and m is split into the direct sums of the irreducible su 2 and su 1 1 submodules in four different ways finite integer unitary irreducible subspaces corresponding to the orbital angular momentum algebra su 2 infinite positive discrete series of su 1 1 with an arbitrary half integer bargmann index and the positive and negative discrete series of su 1 1 with both the bargmann indices 1 4 and 3 4 even and odd coherent states for the positive su 1 1 submodules with the bargmann indices 1 4 and 3 4 are constructed and it is shown that they enjoy the property of completeness by two appropriate positive definite measures we show that the even and odd coherent states themselves form the positive discrete series of su 1 1 with the bargmann indices 1 4 and 3 4 respectively for these even and odd coherent states we consider the uncertainty relations for the x and y components of the angular m

an application of the aumann shapley prices for cost allocation in transportation problems the aumann shapley a s prices are axiomatically determined on certain classes of piecewise continuously differentiable cost functions one of these classes consists of all cost functions derived from the transportation problems and some of their generalizations these prices are used here to allocate costs among destinations in a way that each destination will pay its real part in the total transportation costs an economic transportation model is presented in which the a s prices are compatible with consumer demands finally an algorithm is provided to calculate both the optimal solution and the associated a s prices for transportation problems

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

resolution of missing label problems a new perspective on k matrix theory k matrix theory is an effective algebraic way of determining inner products and constructing orthonormal bases vectors for the carrier spaces of induced representations of lie groups and lie algebras the theory is applied in this paper to give canonical resolutions of missing label problems

a new integrable symplectic map associated with lattice soliton equations a method is developed that extends the nonlinearization technique to the hierarchy of lattice soliton equations associated with a discrete 3 3 matrix spectral problem a new integrable symplectic map and its involutive system of conserved integrals are obtained by the nonlinearization of spatial parts and the time parts of lax pairs and their adjoint lax pairs of the hierarchy moreover the solutions of the typical system of lattice equations in the hierarchy are reduced to the solutions of a system of ordinary differential equations and a simple iterative process of the symplectic map

quadrupole collective variables in the natural cartan weyl basis the matrix elements of the quadrupole collective variables emerging from collective nuclear models are calculated in the natural cartan weyl basis of o 5 which is a subgroup of a covering su 1 1 o 5 structure making use of an intermediate set method explicit expressions of the matrix elements are obtained in a pure algebraic way fixing the rotational structure of collective quadrupole models

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

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

the space of polynomials in measures is internal we show that the algebra generated by nonatomic measures is an internal space we then provide a natural alternative proof for the existence of a unique value on pna

representation of the five and six dimensional harmonic oscillators in a u 5 so 5 so 3 basis the duality that exists between the two subgroups su 1 1 and o 5 of sp 5 r to construct basis states for the five dimensional harmonic oscillator which simultaneously reduce the sp 5 r u 5 o 5 so 3 and sp 5 r su 1 1 u 1 subgroup chains is used it is shown that the vector coherent state wave functions of the fundamental five dimensional so 5 irrep 1 0 realize the traceless bosons introduced by lohe and hurst to classify the irreps of the orthogonal groups and employed in chacon moshinsky and sharp s construction of a basis for the five dimensional harmonic oscillator moreover it is shown that vcs theory provides a simple mechanism for constructing matrix elements of the traceless boson operators these matrix elements are used to extend the vcs representations of so 5 in an so 3 basis given in a previous paper to irreps of u 5 in an so 5 so 3 basis the extension to u 6 u 5 so 5 so 3 is also given

finite dimensional integrable systems related to the n wave interaction equations under a constraint between the potentials and the eigenfunctions lax pairs and adjoint lax pairs of a soliton hierarchy associated with the n n generalized zakharov shabat eigenvalue problem are transformed into a spatial finite dimensional hamiltonian system and a hierarchy of temporal finite dimensional hamiltonian systems the lax representations r matrix structure and integrals of motion are explicitly presented these integrals of motion are functionally independent and in involution in pairs which shows that these systems especially the whole hierarchy of temporal finite dimensional hamiltonian systems are liouville integrable

nonlinearization of the lax pairs for discrete ablowitz ladik hierarchy abstract the discrete ablowitz ladik hierarchy with four potentials and the hamiltonian structures are derived under a constraint between the potentials and eigenfunctions the nonlinearization of the lax pairs associated with the discrete ablowitz ladik hierarchy leads to a new symplectic map and a class of finite dimensional hamiltonian systems the generating function of the integrals of motion is presented by which the symplectic map and these finite dimensional hamiltonian systems are further proved to be completely integrable in the liouville sense each member in the discrete ablowitz ladik hierarchy is decomposed into a hamiltonian system of ordinary differential equations plus the discrete flow generated by the symplectic map

vector coherent state representation theory a vector coherent state theory is formulated as a natural extension of standard coherent state theory it is shown that the godement representations and the coherent state representations of the sp n r groups of rowe and of deenen and quesne are special cases of this more general theory

a completely integrable system and parametric representation of solutions of the wadati konno ichikawa hierarchy a finite dimensional involutive system is presented and the wadati konno ichikawa wki hierarchy of nonlinear evolution equations and their commutator representations are discussed in this article by this finite dimensional involutive system it is proven that under the so called bargmann constraint between the potentials and the eigenfunctions the eigenvalue problem called the wki eigenvalue problem studied by wadati konno and ichikawa j phys soc jpn 47 1698 1979 is nonlinearized as a completely integrable hamiltonian system in the liouville sense moreover the parametric representation of the solution of each equation in the wki hierarchy is obtained by making use of the solution of two compatible systems

vector coherent state theory as a theory of induced representations a general definition is given of vector coherent state vcs representation theory it is shown that the theory is more general than suggested by previous applications and that it incorporates the standard theories of induced representations as special cases the associated k matrix theory is also given a fuller treatment than hitherto and shown to provide a rather general algorithm both for projecting vcs representations from larger representations in which they are embedded and for determining the hermitian form with respect to which an isometric equivalent representation is in fact isometric

a reducible weil representation of sp 4 realized by differential operators in the space of smooth functions on h2 s1 this work presents a novel way to obtain the associated romanovski functions rn m x with n m in the three separate regions in terms of n and m we obtain the raising and lowering relations with respect to the both indices simultaneously in the three regions then a reducible weil representation of the real lie algebra sp 4 is realized in the space of complex valued smooth functions on h2 s1 by differential forms for the cartan weyl basis its invariant subspace is the second rare instance of the highest weight irreducible representation of sp 4 all whose weight spaces are one dimensional

a generalization of the aumann shapley value for risk capital allocation problems abstract the paper proposes a new method to allocate risk capital to divisions or lines of business within a firm existing literature advocates an allocation rule that in game theoretic terms is equivalent to using the aumann shapley value as allocation mechanism the aumann shapley value however is only well defined if a specific differentiability condition is satisfied the rule that we propose is characterized as the limit of an average of path based allocation rules with grid size converging to zero the corresponding allocation rule is equal to the aumann shapley value if it exists if the aumann shapley value does not exist the allocation rule is equal to the weighted average of the aumann shapley values of nearby capital allocation problems

a similar extension of the wki hierarchy its hamiltonian structure and the associated finite dimensional hamiltonian system abstract an isospectral problem and a similar extension of the wadati konno ichikawa hierarchy are proposed by using the trace identity it is shown that the hierarchy of equations possesses a bi hamiltonian structure the eigenvalue problem is nonlinearized to a finite dimensional hamiltonian system under a constraint between the potentials and the eigenfunctions

design of price mechanisms for network resource allocation via price of anarchy we study the design of price mechanisms for communication network problems in which a user s utility depends on the amount of flow she sends through the network and the congestion on each link depends on the total traffic flows over it the price mechanisms are characterized by a set of axioms that have been adopted in the cost sharing games and we search for the price mechanisms that provide the minimum price of anarchy we show that given the non decreasing and concave utilities of users and the convex quadratic congestion costs in each link if the price mechanism cannot depend on utility functions the best achievable price of anarchy is 4 3 2 sqrt 2 approx 31 4 thus the popular marginal cost pricing with price of anarchy less than 1 3 33 3 is nearly optimal we also investigate the scenario in which the price mechanisms can be made contingent on the users preference profile while such information is available

noncommutative pfaffians and classification of states of five dimensional quasi spin noncommutative pfaffians associated with an orthogonal algebra on are some special elements of the universal enveloping algebra u on using pfaffians we construct the fourth quantum number which together with the naturally defined three quantum numbers allows to classify the states of a five dimensional quasi spin the pfaffians are treated as creation operators for the new quantum number

some new integrable systems constructed from the bi hamiltonian systems with pure differential hamiltonian operators abstract when both hamiltonian operators of a bi hamiltonian system are pure differential operators we show that the generalized kupershmidt deformation gkd developed from the kupershmidt deformation in 10 offers an useful way to construct new integrable system starting from the bi hamiltonian system we construct some new integrable systems by means of the generalized kupershmidt deformation in the cases of harry dym hierarchy classical boussinesq hierarchy and coupled kdv hierarchy we show that the gkd of harry dym equation gkd of classical boussinesq equation and gkd of coupled kdv equation are equivalent to the new integrable rosochatius deformations of these soliton equations with self consistent sources we present the lax pair for these new systems therefore the generalized kupershmidt deformation provides a new way to construct new integrable systems from bi hamiltonian systems and also offers a new approach to obtain the rosochatius deformation of soliton equation with self consistent sources

the trace identity a powerful tool for constructing the hamiltonian structure of integrable systems a new approach to hamiltonian structures of integrable systems is proposed by making use of a trace identity for a variety of isospectral problems that can be unified to one model x u it is shown that both the related hierarchy of evolution equations and the hamiltonian structure can be obtained from the same solution of the equation vx u v

vector coherent state representations of so 5 in an so 3 basis vector coherent state theory is used to give an algorithm for constructing the so 5 irreps of type n 0 and n n in the physical so 3 basis the construction is remarkably simple and permits the matrices of the so 5 operators for irreps of low dimension and or small multiplicities to be computed by hand the construction is applied to the 2 0 and 2 2 irreps to illustrate the process

racah s method for general subalgebra chains coupling coefficients of so 5 in canonical and physical bases it is shown that the method of infinitesimal generators racah s method can be broadly and systematically formulated as a method applicable to the calculation of reduced coupling coefficients for a generic subalgebra chain g h provided the reduced matrix elements of the generators of g and the recoupling coefficients of h are known the calculation of so 5 so 4 reduced coupling coefficients is considered as an example and a procedure for transformation of reduced coupling coefficients between canonical and physical subalegebra chains is presented the problem of calculating coupling coefficients for generic irreps of so 5 reduced with respect to any of its subalgebra chains is completely resolved by this approach

algebro geometric solution of the 2 1 dimensional burgers equation with a discrete variable the quasiperiodic solution of the 2 1 dimensional burgers equation with a discrete variable is obtained through three steps a decomposition into a symplectic map plus two finite dimensional hamiltonian systems b straightening out of both the discrete and the continuous flows in the jacobian variety c inversion into the original variables inner relation with the modified kadomtsev petviashvili equation is presented the explicit theta function solutions for these two 2 1 integrable models are given

discrete coupled derivative nonlinear schrodinger equations and their quasi periodic solutions a hierarchy of nonlinear differential difference equations associated with a discrete isospectral problem is proposed in which a typical differential difference equation is a discrete coupled derivative nonlinear schrodinger equation with the help of the nonlinearization of the lax pairs the hierarchy of nonlinear differential difference equations is decomposed into a new integrable symplectic map and a class of finite dimensional integrable hamiltonian systems based on the theory of algebraic curve the abel jacobi coordinates are introduced to straighten out the corresponding flows from which quasi periodic solutions for these differential difference equations are obtained resorting to the riemann theta functions moreover a 2 1 dimensional discrete coupled derivative nonlinear schrodinger equation is proposed and its quasi periodic solutions are derived

a hierarchy of coupled korteweg de vries equations and the normalisation conditions of the hilbert riemann problem the authors discuss the normalisation conditions of the hilbert riemann problem which is of importance for the construction of the ladder of soliton solutions for a given spectral problem they provide the prescription for constructing the appropriate normalisation condition all this is applied to a new hierarchy of coupled korteweg de vries equations to find the soliton solution which displays some peculiar phenomena

finite dimensional discrete systems and integrable systems through nonlinearization of the discrete eigenvalue problem a method is developed that extends the nonlinearization procedure of eigenvalue problems to the discrete case from which the finite dimensional discrete systems and finite dimensional completely integrable systems associated with the toda hierarchy are obtained a new model for solving discrete soliton equations is proposed which enables one to get the solutions of the toda lattice equations by solving the compatible systems of discrete equations and nonlinear ordinary differential equations

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

new finite dimensional integrable systems and explicit solutions of hirota satsuma coupled kortweg de vries equation the nonlinearization approach is extended to the hirota satsuma coupled kortweg de vries kdv equation associated with a 4 4 matrix spectral problem from which two new finite dimensional integrable hamiltonian systems are obtained in the liouville sense it is shown that the solutions of this coupled kdv equation are reduced to solving a compatible system of ordinary differential equations the reductions of the two hamiltonian systems and their separability are discussed an interesting connection between the two reduced hamiltonian systems in the case of one parameter and known two dimensional integrable systems is revealed as application some explicit solutions of the hirota satsuma coupled kdv equation are derived

diagonality of cost allocation prices the problem of allocating the production cost of a finite bundle of divisible consumption goods or services by means of per unit costs or prices is a basic problem in economics recently an axiomatic approach has been proposed billera and heath billera l j d c heath 1981 allocation of shared costs a set of axioms yielding a unique procedure math oper res 7 32 39 and mirman and tauman mirman l j y tauman 1981 demand compatible equitable cost sharing prices math oper res 7 40 56 in which one considers a class of cost problems and studies the mappings from that class of cost problems to prices by means of the properties these prices satisfy we look for a list of properties on the class of cost problems and the price mechanism that imply the diagonality of the price mechanism

some algebro geometric solutions for the coupled modified kadomtsev petviashvili equations arising from the neumann type systems a treatment is described for getting some algebro geometric solutions of the coupled modified kadomtsev petviashvili cmkp equations and a hierarchy of 1 1 dimensional integrable nonlinear evolution equations inlees by using the neumann type systems through three steps i according to the nonlinearization of lax pair the cmkp equations and the 1 1 dimensional inlees are reduced to a family of compatible neumann type systems on a symplectic submanifold whose involutive solutions give rise to the finite parametric solutions of the inlees in both 2 1 and 1 1 dimensions ii from the holomorphic differentials and the abel map on a hyperelliptic curve of riemman surface the abel jacobi variables are introduced to straighten out the neumann type flows the 1 1 and 2 1 dimensional flows giving the abel jacobi solutions iii based on the riemann theorem and the trace formulas the jacobi inversion is applied to the straightened flows for getting some new algebro geometric solutions of the cmkp equations and the 1 1 dimensional integrable hierarchy

nonlinearization of the 3 3 matrix eigenvalue problem related to coupled nonlinear schrodinger equations abstract the nonlinearization method is extended to the investigation of coupled nonlinear schrodinger equations associated with a 3 3 matrix eigenvalue problem from which a new finite dimensional hamiltonian system is obtained by nonlinearization of the eigenvalue problem and its adjoint one a scheme for generating involutive systems of conserved integrals is proposed by which the finite dimensional hamiltonian system is further proved to be completely integrable in the liouville sense

c neumann and bargmann systems associated with the coupled kdv soliton hierarchy under two different constraints between the potentials and the eigenfunctions the eigenvalue problem associated with the coupled kdv hierarchy is nonlinearised to be a completely integrable c neumann system on the tangent bundle of sphere tsn 1 with the hamiltonian h 1 2 lambda q p 1 2 q q p p 1 2 q p 2 1 2 q p lambda p p and a completely integrable bargmann system r2n dpdq h with the hamiltonian h 1 2 lambda q p 1 2 p p q p 1 2 q q respectively the involutive solutions of the coupled kdv equation associated with the two systems are given

the full positive flows of manakov hierarchy hamiltonian structures and conservation laws based on four sets of lenard recursion sequences and zero curvature equation we derive the full positive flows of the manakov hierarchy associated with a 3x3 matrix spectral problem from which some new nonlinear evolution equations are proposed with the help of the darboux transformation soliton solutions of two new nonlinear evolution equations in the manakov hierarchy are constructed as two special reductions the full positive flows of the coupled modified korteweg de vries hierarchy and the sasa satsuma hierarchy are deduced in which some new nonlinear evolution equations are included and then we construct the hamiltonian structures of the manakov hierarchy and infinite conservation laws of several nonlinear evolution equations

vector coherent state theory and its application to the orthogonal groups vector coherent state theory is developed and presented in a form that explicitly exhibits its general applicability to the ladder representations of all semisimple lie groups and their lie algebras it is shown that in a suitable basis the vector coherent state inner product can be inferred algebraically by k matrix theory and changed to a simpler bargmann inner product thereby facilitating the explicit calculation of the matrix representaions of lie algebras applications are made to the even and odd orthogonal lie algebras

a finite dimensional integrable system and the r matrix method the nonlinearization method is used on the soliton hierarchy associated with the 4 4 akns eigenvalue problem from which a new finite dimensional hamiltonian system is obtained by nonlinearization of the eigenvalue problem and its ajoint one a lax representation is deduced for the system the lax operator admits the representation of an r matrix the 4n functionally independent and involutive integrals of motion are obtained via the r matrix which shows that the system is completely integrable in the liouville sense

quasi periodic solutions of the modified kadomtsev petviashvili equation the 2 1 dimensional modified kadomtsev petviashvili equation is decomposed into systems of integrable ordinary differential equations resorting to the nonlinearization of lax pairs abel jacobi coordinates are introduced to straighten the flows from which quasi periodic solutions of the modified kadomtsev petviashvili equation are obtained in terms of riemann theta functions

induced shift tensors in vector coherent state theory it is shown that the so called shift tensors of biedenharn and louck have a natural expression within the framework of vector coherent state vcs theory vcs theory was developed to give a systematic construction of the representations of lie groups and to derive the corresponding matrices representing the elements of their lie algebras in this paper there are explicit realizations of shift tensors within the framework of vcs theory for semisimple lie groups in terms of shift tensors for suitably defined subgroups