injective hulls of simple modules over finite dimensional nilpotent complex lie superalgebras abstract we show that the finite dimensional nilpotent complex lie superalgebras g whose injective hulls of simple u g modules are locally artinian are precisely those whose even part g 0 is isomorphic to a nilpotent lie algebra with an abelian ideal of codimension 1 or to a direct product of an abelian lie algebra and a certain 5 dimensional or a certain 6 dimensional nilpotent lie algebra

the weil petersson metric and volumes of 3 dimensional hyperbolic convex cores we present a coarse interpretation of the weil petersson distance dwp x y between two finite area hyperbolic riemann surfaces x and y using a graph of pants decompositions introduced by hatcher and thurston the combinatorics of the pants graph reveal a connection between riemann surfaces and hyperbolic 3 manifolds conjectured by thurston the volume of the convex core of the quasi fuchsian manifold q x y with x and y in its conformal boundary is comparable to the weil petersson distance dwp x y in applications we relate the weil petersson distance to the hausdorff dimen sion of the limit set and the lowest eigenvalue of the laplacian for q x y and give a new finiteness criterion for geometric limits mathematics department university of chicago 5734 s university ave chicago il 60637 e mail address brock math uchicago edu

a fixed point theorem of discrete group actions on riemannian manifolds we prove a xed point theorem for a class of discrete group acting on man ifolds of nonpositive curvature by isometry these discrete groups include cocompact lattices in simply connected semisimple p adic groups of rank at least two and large p hence it gives a geometric generalization of margulis superrigidity theorem for the archimedean representation of these groups introduction let n be a complete simply connected riemannian manifold of non positive sectional curvature n has a natural compacti cation n n n by the sphere at in nity which is de ned as the equivalent classes of geodesic rays any group action on n by isometry extends to an action on n de nition a group is said to have property f if any isometric action of on any complete simply connected manifold of nonpositive sectional curvature n has a xed point in n in term of representations of property f has the following inter pretation let h be a simple noncompact lie group with trivial center if has property f then any homomorphism h with zariski dense image is precompact inh this is because the symmetric space as sociated with h has nonpositive curvature and the image being zariski received october and in revised form july

nash type equilibrium theorems and competitive nash type equilibrium theorems abstract in this paper we consider two types of equilibrium problems we study the constrained nash type equilibrium problems with multivalued payoff functions we also study the competitive nash type equilibrium problems with multivalued payoff functions in these two equilibrium problems we want to find a strategy combination such that each player wishes to find a minimal loss from his multivalued payoff function we use a fixed point theorem of park to prove the existence results of these two types of equilibrium problems

cohomology of heisenberg lie superalgebras suppose the ground field to be algebraically closed and of characteristic different from 2 and 3 all heisenberg lie superalgebras consist of two super versions of the heisenberg lie algebras x1d525 2m n and x1d51f x1d51e n with m a non negative integer and n a positive integer the space of a classical heisenberg lie superalgebra x1d525 2m n is the direct sum of a superspace with a non degenerate anti supersymmetric even bilinear form and a one dimensional space of values of this form constituting the even center the other super analog of the heisenberg lie algebra x1d51f x1d51e n is constructed by means of a non degenerate anti supersymmetric odd bilinear form with values in the one dimensional odd center in this paper we study the cohomology of x1d525 2m n and x1d51f x1d51e n with coefficients in the trivial module by using the hochschild serre spectral sequences relative to a suitable ideal in the characteristic zero case for any heisenberg lie superalgebra we determine completely the betti numbers and associative superalgebra structures for t

on systems of quasivariational inclusion problems in this paper new systems of quasivariational inclusion problems are presented and by using the cone continuity of vector mappings and the park s fixed point theorem the existence theorems of solutions and the closedness of the solution sets are obtained as applications existence theorems for symmetric strong vector quasiequilibrium problem and generalized ideal vector saddle point are derived main results of some recent research works are extended and improved

behavior of geodesic length functions on teichmuller space let t be the teichmuller space of marked genus g n punctured riemann surfaces with its bordification t the augmented teichmuller space of marked riemann surfaces with nodes abi77 ber74 pro vided with the wp metric t is a complete cat 0 metric space dw03 wol03 yam04 an invariant of a marked hyperbolic struc ture is the lengthof the geodesic in a free homotopy class a basic feature of teichmuller theory is the interplay of two dimensional hyperbolic geometry weil petersson wp geometry and the behavior of geodesic length functions our goal is to develop the understanding of the intrinsic local wp geometry through a study of the gradient and hessian of geodesic length functions considerations include ex pansions for the wp pairing of gradients expansions for the hessian and covariant derivative comparability models for the wp metric as well as the behavior of wp geodesics including a description of the alexandrov tangent cone at the augmentation approximations and applications for geodesics close to the augmentation are developed an application for fixed points of group actions is described bound ing configurations and functions on the hyperbolic plane is basic to our approach considerations include analyzing the orbit of a dis crete group of isometries and bounding sums of the inverse square exponential distance

vector quasivariational inequalities for fuzzy mappings ii abstract this paper is devoted to study the vector variational inequalities for fuzzy mappings by using the fan browder fixed point theorem the selection theorem of yannelis prabhakar 13 and the scalarization method of luc 9 10 some existence theorems for our inequalities are proved

heisenberg lie superalgebras and their invariant superorthogonal and supersymplectic forms abstract finite dimensional complex lie superalgebras of heisenberg type obtained from a given z 2 homogeneous supersymplectic form defined on a vector superspace are classified up to isomorphism those arising from even supersymplectic forms have an ordinary heisenberg lie algebra as its underlying even subspace whereas those arising from odd supersymplectic forms get based on abelian lie algebras the question of whether this sort of heisenberg lie superalgebras do or do not support a given invariant supergeometric structure is addressed and it is found that none of them do it is proved however that 1 dimensional extensions by appropriate z 2 homogeneous derivations do such appropriate derivations are characterized and the invariant supergeometric structures carried by the extensions they define are fully described furthermore necessary and sufficient conditions are obtained in order that any two 1 dimensional extensions by z 2 homogeneous derivations be isomorphic also necessary and sufficient conditions are obtained in order that any two extensions carrying invariant supergeometric structures be isometric

higher order rogue wave like solutions for a nonautonomous nonlinear schrodinger equation with external potentials abstract under investigation in this paper is the higher order rogue wave like solutions for a nonautonomous nonlinear schrodinger equation with external potentials which can be applied in the nonlinear optics hydrodynamics plasma physics and bose einstein condensation based on the kadomtsev petviashvili hierarchy reduction we construct the n th order rogue wave like solutions in terms of the gramian under the integrable constraint with the help of the analytic and graphic analysis we exhibit the first second and third order rogue wave like solutions through the different dispersion nonlinearity and linear potential coefficients we find that only if the dispersion and nonlinearity coefficients are proportional to each other heights of the background of those rogue waves maintain unchanged with time increasing due to the existence of complex parameters such nonautonomous rogue waves in the higher order cases have more complex features than those in the lower

rational solutions for a 2 1 dimensional nonlinear model in water waves generated by the jaulent miodek hierarchy abstract this paper deals with a 2 1 dimensional nonlinear evolution equation nlee generated by the jaulent miodek hierarchy for nonlinear water waves via the hirota s bilinear method and pfaffian first we construct rational solutions for general bilinear equations and then convert the target bilinear equations to the general ones to obtain their rational solutions the pfaffian plays a role to simplifying the computations compared with the determinant way in the existing literatures once the first and second order rational solutions have been obtained the higher order solutions can be derived by the same token figures for the first and second order rational solutions are plotted and analyzed as an application the rational solutions for the modified kadomtsev petviashvili equation have also been constructed the method might be used for some other nlees to construct their rational solutions

some minimax theorems of set valued maps and their applications abstract in the paper we consider two types of scalarization functions of sets and investigate their properties moreover based on two set relations we propose two kinds of minimax and maximin values of set valued maps respectively and show some minimax theorems of set valued maps with respect to those minimax and maximin values by using several properties of the above two functions as an application of these results we give common saddle point theorems of vector valued functions

generalized saddle points theorems for set valued mappings in locally generalized convex spaces abstract in the paper the notions of generalized loose weak saddle points for set valued mappings are introduced by applying the fixed point theorem and the scalarization method some new existence theorems for generalized loose weak saddle points are established in locally g convex space as applications some vector minimax theorems are given also

solvable lie algebras with heisenberg ideals all finite dimensional indecomposable solvable lie algebras l n f having the heisenberg algebra h n as the nilradical are constructed the number of non nilpotent elements f that can be added to h n satisfies f or n 1 the casimir and generalized casimir operators of the algebras l n f are obtained

on the constrained equilibrium problems with finite families of players in this paper we consider the equilibrium problem with finite number of families of players such that each family may not have the same number of players and finite number of families of constrained correspondences on the strategy sets we also consider the case with two finite families of constrained correspondences on the strategies sets we demonstrate an example of our equilibrium problem we derive a fixed point theorem for a family of multimaps and a coincidence theorem for two families of multimaps by using these results we establish the existence of a solution of our equilibrium problems the results of this paper generalize some known results in the literature