the topology on the primitive ideal space of transformation group c algebras and c c r transformation group c algebras if g 8 is a second countable transformation group and the stability groups are amenable then c g 8 is c c r if and only if the orbits are closed and the stability groups are c c r in addition partial results relating closed orbits to c c r algebras are obtained in the nonseparable case in several cases the topology of the primitive ideal space is calculated explicitly in particular if the stability groups are all contained in a fixed abelian subgroup h then the topology is computed in terms of h and the orbit structure provided c g 8 and c h 8 are eh regular these conditions are automatically met if g is abelian and g 8 is second countable

stable and finite morse index solutions on ⁿ or on bounded domains with small diffusion in this paper we study bounded solutions of u f u on r n where n 2 and sometimes n 3 and show that for most f s the weakly stable and finite morse index solutions are quite simple we then use this to obtain a very good understanding of the stable and bounded morse index solutions of e 2 u f u on with dirichlet or neumann boundary conditions for small e

the mackey glimm dichotomy for foliations and other polish groupoids abstract for polish groups acting on polish spaces e effros gave a condition under which 14 properties of the orbits or the orbit space of an anti ergodic character are equivalent he also raised the question of extending these results to polish groupoids and this paper gives an affirmative answer to that question the paper also includes results about totally disconnected quotient spaces and an application to indecomposable continua

solutions of systems of elliptic differential equations on circular domains abstract we study global bifurcation of weak solutions of systems of elliptic differential equations considered on so 2 invariant domains we formulate sufficient conditions for the existence of unbounded continua of nontrivial solutions branching from the trivial ones as the main tool we use the degree for so 2 equivariant gradient maps defined by the second author in rybicki nonlinear anal tma 23 1 1994 83

a correction for a paper by j smoller and a wasserman abstract in j differential equations 39 1981 269 290 j smoller and a wasserman presented some rich ideas and results on the bifurcation of steady state solutions of a reaction diffusion equation in one space variable however the proof of their theorem 2 1 is incorrect the case a 0 and to correct it we find one additional hypothesis is necessary

global branches of non radially symmetric solutions to a semilinear neumann problem in a disk let d r 2 be a disk and let f c 3 we assume that there is a r such that f a 0a ndf a 0 in this article we are concerned with the neumann problem u f u 0i nd u 0o n d we show the following there are unbounded continuums consisting of non radially symmetric solutions emanating from the second and third eigenvalues if f u u u u p 1 a 1 or if f is of bistable type then the unbounded branches emanating from non principal eigenvalues are unbounded in the positive direction of the branch emanating from the second eigenvalue is unique near the bifurcation point up to rotation the main tool of this article is the zero level set the nodal curve of u and ux

exact multiplicity of positive solutions for a class of semilinear problem ii we consider the positive solutions to the semilinear problem u f u 0 in b n u 0 on b n where bn is the unit ball in rn n 1 and is a positive parameter it is well known that if is a smooth function then any positive solution to the equation is radially symmetric and all solutions can be parameterized by their maximum values we develop a unified approach to obtain the exact multiplicity of the positive solutions for a wide class of nonlinear functions u and the precise shape of the global bifurcation diagrams are rigorously proved our technique combines the bifurcation analysis stability analysis and topological methods we show that the shape of the bifurcation curve depends on the shape of the graph of function u u as well as the growth rale of

nodal sets for groundstates of schrodinger operators with zero magnetic field in non simply connected domains we investigate nodal sets of magnetic schrodinger operators with zero magnetic field acting on a non simply connected domain in 2 for the case of circulation 1 2 of the magnetic vector potential around each hole in the region we obtain a characterisation of the nodal set and use this to obtain bounds on the multiplicity of the groundstate for the case of one hole and a fixed electric potential we show that the first eigenvalue takes its highest value for circulation 1 2

vertex operators in solvable lattice models the basic properties of q vertex operators are formulated in the context of the andrews baxter forrester abf series as an example of face interaction models the q difference equations satisfied by their correlation functions are derived and their connection with representation theory established the q difference equations of the kashiwara miwa km series are discussed as an example of edge interaction models next the ising model the simplest special case of both abf and km series is studied in more detail using the jordan wigner fermions in particular all matrix elements of vertex operators are calculated

the orbit spaces of groupoids whose c algebras are ccr abstract let g be a second countable locally compact hausdorff groupoid with a continuous haar system we show that if the groupoid c algebra of g is ccr then the orbits of g are closed and the stabilizers of g are ccr in particular we remove the assumption of amenability in a theorem of clark

global bifurcation of steady state solutions in this paper we study the bifurcation of steady state solutions of a reaction diffusion equation in one space variable the steady state solutions satisfy the equation a f u 0 on the interval l 0 or 0 for some nonzero function c c a for the neumann problem we use entirely different techniques to prove that s is never critical for any cubic polynomial j this implies at once that the neumann problem can have at most one nonconstant solution having a given number of maxima or minima this solution is necessarily strongly nondegenerate in the sense that zero is not contained in the spectrum of the linearized operator see 2 for the dirichlet problem the situation is far more complicated and the bifurcation diagrams undergo qualitative changes depending on the positions of the roots off for example fig 1 shows the bifurcation diagram for the positive solutions for two different cubic functions of the form f u a u u b u c it is interesting to note however that in every case we study there are at most three solutions to the dirichlet problem for each

dual field formulation of quantum integrable models equal time correlators are studied in completely integrable models the main example is the quantum non linear schrodinger equation introduction of an auxiliary fock space permits us to represent the generating functional of correlators in the form of a determinant of the integral operator

exact multiplicity of positive solutions for a class of semilinear problems we establish an exact multiplicity result of positive solutions of u f u 0inbn u 0on bn wherebnis the unit ball fsatisfiesf changes sign only once and asymptotically sublinear or linear the nonlinearities which we are concerned with here includef u u u b c u for 0 2b candf u up uqfor 1 p q precise global bifurcation diagrams are obtained

non existence of a secondary bifurcation point for a semilinear elliptic problem in the presence of symmetry abstract we give two sufficient conditions for a branch consisting of non trivial solutions of an abstract equation in a banach space not to have a secondary bifurcation point when the equation has a certain symmetry when the nonlinearity f is of allen cahn type for instance f u u u 3 we apply these results to an unbounded branch consisting of non radially symmetric solutions of the neumann problem on a disk d r 2 u f u 0 in d u 0 on d and emanating from the second eigenvalue we show that the maximal continuum containing this branch is homeomorphic to r s 1 and that its closure is homeomorphic to r 2

determinant representation for correlation functions of spin 1 2 xxx and xxz heisenberg magnets we consider zero temperature correlation functions of the spin 1 2 xxz heisenberg chain in the critical regime 1 1 in a magnetic field starting from the algebraic bethe ansatz we derive representations for various correlation functions in term of determinats of fredholm integral operators

the dynamics of rotating waves in scalar reaction diffusion equations on etudie l attracteur compact maximal pour l equation u t u xx f u u x avec des conditions aux limites periodiques on montre qu un ensemble limite contient une onde de rotation

the zero set of a solution of a parabolic equation on etudie l ensemble nul d une solution u t x de l equation u t a x t u xx b x t u x c x t u sous des hypotheses tres generales sur les coefficients a b et c

large time and distance asymptotics of field correlation function of impenetrable bosons at finite temperature abstract asymptotics of the temperature time dependent correlation function of two fields one dimensional bosons with infinite point like repulsion is calculated

on the neumann problem for some semilinear elliptic equations and systems of activator inhibitor type on deduit des estimations a priori pour des solutions positives du probleme de neumann pour des systemes elliptiques semilineaires ainsi que pour des equations isolees semilineaires reliees a ces systemes