a multiplicity result for the jumping nonlinearity problem abstract we consider a class of nonlinear problems of the form au g x u f where a is an unbounded self adjoint operator on a hilbert space h of l 2 functions r n an arbitrary domain and g r r is a jumping nonlinearity in the sense that the limits lim s g x s s a lim s g x s s b exist and jump over the principal eigenvalue of the operator a under rather general conditions on the operator l and for suitable a b we prove some multiplicity results applications are given to the wave equation and elliptic equations in the whole space r n

a class of interaction round a face models and its equivalence with an ice type model a new model called the temperley lieb interactions model is introduced in two dimensional lattice statistics on a square lattice the temperley lieb equivalence of this model to the six vertex self dual potts critical hard hexagons and critical nonintersecting string models is established a graphical equivalence of this model to the six vertex model generalizes this equivalence to noncritical cases of the above models the order parameters of a specialization of this model are studied

tensor space representations of temperley lieb algebra via orthogonal projections of rank r 1 unitary representations of the temperley lieb algebra tln q on the tensor space n n are considered two criteria are given for determining when an orthogonal projection matrix p of a rank r gives rise to such a representation the first of them is the equality of traces of certain matrices and the second is the unitary condition for a certain partitioned matrix some estimates are obtained on the lower bound of q for a given dimension n and rank r it is also shown that if 4r n2 then q can take only a discrete set of values determined by the value of n2 r in particular the only allowed value of q for n r 2 is q 2 finally properties of the clebsch gordan coefficients of the quantum hopf algebra uq su2 are used in order to find all r 1 and r 2 unitary tensor space representations of tln q such that q depends continuously on q and p is the projection in the tensor square of a simple uq su2 module on the subspace spanned by one or two joint eigenvectors of the casimir operator c and the

on the multiplicity of the solution set of some nonlinear boundary value problems ii on considere le probleme non lineaire lu f u s 1 h dans u 0 sur soit h l 2 f est de classe c et que f 1 et n f n 1 n 1 alors il existe s 0 tel que pour tout s s 0 l equation a au moins 2 solutions si n est impair et 3 solutions si n est pair

multiple nontrivial solutions for a floating beam equation via critical point theory abstract we study periodic flexings of a floating beam via critical point theory the beam is described by the nonlinear equation with free end boundary conditions described in the introduction we give a theorem of existence of two nontrivial solutions and a theorem of existence of four nontrivial solutions depending on the position of a suitable parameter with respect to the eigenvalues of the linear part

boundary conditions for integrable quantum systems a new class of boundary conditions is described for quantum systems integrable by means of the quantum inverse scattering r matrix method the method proposed allows the author to treat open quantum chains with appropriate boundary terms in the hamiltonian the general considerations are applied to the xxz and xyz models the nonlinear schrodinger equation and toda chain

multiple solutions for an asymptotically linear problem in rn abstract we consider a semilinear problem of the type lu f b u in l 2 r n where f b u bu as u 0 and f b u b u as u b b we assume that the essential spectrum of l is bounded below by a number greater than b and that there exist a finite number of eigenvalues between b and b we prove existence and multiplicity results for nontrivial solutions under suitable assumptions on g we give an application to the schrodinger equation

the spectra of q state vertex models and related antiferromagnetic quantum spin chains some exactly solvable q state vertex models are investigated the author employs inversion relations to determine directly the spectra of the transfer matrices in the thermodynamic limit by avoiding the more cumbersome bethe ansatz the results are applied to related quantum spin chains of which two families are su q and so q invariant respectively various quantities are calculated e g energy momentum excitations and the correlation length for q 3 the su q invariant chain is the pure biquadratic spin 1 hamiltonian which turns out to be non critical the ground state energy the gap and the correlation length are given

a finite horizon optimal multiple switching problem 1we consider the problem of optimal multiple switching in a finite horizon when the state of the system including the switching costs is a general adapted stochastic process the problem is formulated as an extended impulse control problem and solved using probabilistic tools such as the snell envelope of processes and reflected backward stochastic differential equations finally when the state of the system is a markov process we show that the associated vector of value functions provides a viscosity solution to a system of variational inequalities with interconnected obstacles

a note on graded yang baxter solutions as braid monoid invariants we construct two osp n mod 2m solutions of the graded yang baxter equation by using the algebraic braid monoid approach the factorizable s matrix interpretation of these solutions is also discussed

a remark on the existence of multiple solutions to a multiparameter nonlinear elliptic system abstract in this work motivated by t f wu the nehari manifold for a semilinear elliptic system involving sign changing weight function nonlinear anal 68 2008 1733 1745 and using recent ideas from brown and wu k j brown t f wu a semilinear elliptic system involving nonlinear boundary condition and sign changing weight function j math anal appl 337 2008 1326 1336 we prove the existence of nontrivial nonnegative solutions to the nonlinear elliptic system p u m x u p 2 u u 2 u c x u 2 u v x p v m x v p 2 v v 2 v c x u v 2 v x u 0 v x here p denotes the p laplacian operator defined by p z div z p 2 z p 2 r n is a bounded domain with smooth boundary 1 1 2 p p p p n n p if n p p if n p n is the outer normal derivative r 2 0 0 the weight m x is a bounded function with m 0 and c x is a continuous function which changes sign in

optimal switching in an economic activity under uncertainty this paper considers the problem of finding the optimal sequence of opening starting and closing stopping times of a multi activity production process given the costs of opening running and closing the activities and assuming that the state of the economic system is a stochastic process the problem is formulated as an extended impulse control problem and solved using stochastic calculus as an application the optimal starting and stopping strategy are explicitly found for a resource extraction when the price of the resource is following a geometric brownian motion

on the ambrosetti prodi problem for non variational elliptic systems we study the ambrosetti prodi problem for nonlinear elliptic equations and systems with uniformly elliptic operators in non divergence form and non smooth coefficients and with non linearities with linear or power growth

theorie generale du controle impulsionnel markovien this paper is concerned with the optimal control of a markov process which is submitted to a sequence of changes of state and law at times t 1 t 2 cdots t n cdots the cost is made with an impulse cost which is positive and a continuous cost the modelization is deeply inspired by the theory of renewal for markov processes by p a meyer the main result is the markovian form of the value function of this problem then under smooth additional conditions we prove the existence of an optimal control

finitely correlated states on quantum spin chains we study a construction that yields a class of translation invariant states on quantum spin chains characterized by the property that the correlations across any bond can be modeled on a finite dimensional vector space these states can be considered as generalized valence bond states and they are dense in the set of all translation invariant states we develop a complete theory of the ergodic decomposition of such states including the decomposition into periodic neel ordered states the ergodic components have exponential decay of correlations all states considered can be obtained as local functions of states of a special kind so called purely generated states which are shown to be ground states for suitably chosen finite range vbs interactions we show that all these generalized vbs models have a spectral gap our theory does not require symmetry of the state with respect to a local gauge group in particular we illustrate our results with a one parameter family of examples which are not isotropic except for one special case this isotropic model coincides with the one dimensional antiferromagnet recently studied by affleck kennedy lieb and tasaki

geometric aspects of quantum spin states a number of interesting features of the ground states of quantum spin chains are analyzed with the help of a functional integral representation of the system s equilibrium states methods of general applicability are introduced in the context of the su 2s 1 invariant quantum spin s chains with the interaction p o wherep o is the projection onto the singlet state of a pair of nearest neighbor spins the phenomena discussed here include the absence of neel order the possibility of dimerization conditions for the existence of a spectral gap and a dichotomy analogous to one found by affleck and lieb stating that the systems exhibit either slow decay of correlations or translation symmetry breaking our representation elucidates the relation evidence for which was found earlier of the p o spin s systems with the potts and the fortuin kasteleyn random cluster models in one more dimension the method reveals the geometric aspects of the listed phenomena and gives a precise sense to a picture of the ground state in which the spins are grouped into random clusters of zero total spin e g within such structure the dichotomy is implied by a topological argument and the alternatives correspond to whether or not the clusters are of finite mean length

spin swapping operator as an entanglement witness for quantum heisenberg spin s systems using the su n representation of the group theory we derive the general form of the spin swapping operator for the quantum heisenberg spin s systems we further prove that such a spin swapping operator is equal to the spin singlet pairing operator under the partial transposition for su 2 invariant states it is shown that the expectation value of the spin swapping operator and its generalizations the permutations can be used as an entanglement witness especially for the formulation of observable conditions of entanglement

solution examples of an impulse control problem we study an impulse control problem with switching technology in infinite horizon we solve the impulse control problem in case of deterministic impulse times on specific transition kernel examples our objective is to exhibit an optimal strategy which maximizes the value function in these cases

on the starting and stopping problem application in reversible investments in this work we solve completely the starting and stopping problem when the dynamics of the system are a general adapted stochastic process we use backward stochastic differential equations bsdes and snell envelopes finally we give some numerical results

exactly soluble isotropic spin ladder models the undeformed limit of the dilute two colour braid monoid algebra gives a natural basis for the description of spin ladder models and allows different baxterization ansatze based on this observation we find the complete classification of exactly soluble generalized isotropic spin ladder models

q state potts models in hamiltonian field theory for q 4 in 1 1 dimensions finite lattice sequence extrapolation methods are applied to the q state potts models in 1 1 d hamiltonian field theory thermal exponents nu 0 71 or 0 02 alpha 0 53 or 0 02 are obtained for the four state model methods are discussed for treating the first order transitions for q 4 and a sequence extrapolation is used to estimate the latent heat exact analytic formulae are derived for the ground state energy the mass gap and the latent heat at the transition point these are compared with the numerical results

the relaxed stochastic maximum principle in singular optimal control of diffusions this paper studies optimal control of systems driven by stochastic differential equations where the control variable has two components the first being absolutely continuous and the second singular our main result is a stochastic maximum principle for relaxed controls where the first part of the control is a measure valued process to achieve this result we establish first order optimality necessary conditions for strict controls by using strong perturbation on the absolutely continuous component of the control and a convex perturbation on the singular one the proof of the main result is based on the strict maximum principle ekeland s variational principle and some stability properties of the trajectories and adjoint processes with respect to the control variable

graded representations of the temperley lieb algebra quantum supergroups and the jones polynomial it is shown that from each self dual representation of a quantum supergroup with nonvanishing q superdimension a graded representation of the temperley lieb algebra can be constructed which in turn gives rise to a solution of the graded yang baxter equation as examples the vector irrep of uq osp m 2n and all the finite dimensional irreps of uq osp 1 2 are studied and the corresponding graded matrices are obtained explicitly a general method is also given to obtain link polynomials from graded matrices applied to the ones associated with graded representations of the temperley lieb algebra the method yields the jones polynomial

on the superlinear ambrosetti prodi problem l et be a smooth bounded domain in r n we consider the semilinear elliptic boundary value problem

a pde approach to regularity of solutions to finite horizon optimal switching problems we study optimal 2 switching and n switching problems and the corresponding system of variational inequalities we obtain results on the existence of viscosity solutions for the 2 switching problem

state space structure and entanglement of rotationally invariant spin systems we investigate the structure of so 3 invariant quantum systems which are composed of two particles with spins j1 and j2 the states of the composite spin system are represented by means of two complete sets of rotationally invariant operators namely by the projections pj onto the eigenspaces of the total angular momentum j and by certain invariant operators qk which are built out of spherical tensor operators of rank k it is shown that these representations are connected by an orthogonal matrix whose elements are expressible in terms of wigner s 6 j symbols the operation of the partial time reversal of the combined spin system is demonstrated to be diagonal in the qk representation these results are employed to obtain a complete characterization of spin systems with j1 1 and arbitrary j2 1 we prove that the peres horodecki criterion of positive partial transposition ppt is necessary and sufficient for separability if j2 is an integer while for half integer spins j2 there always exist entangled ppt states bound entanglement we construct an optimal entanglement witness for the case of half integer spins and design a protocol for the detection of entangled ppt states through measurements of the total angular momentum

the nehari manifold for a class of concave convex elliptic systems involving the p laplacian and nonlinear boundary condition abstract the existence and multiplicity of weak solutions is established for a class of concave convex elliptic systems of the form p u m x u p 2 u a x u 2 u x p v m x v p 2 v b x v 2 v x u p 2 u n u 2 u v v p 2 v n u v 2 v x here p denotes the p laplacian operator defined by p z div z p 2 z p 2 r n is a bounded domain with smooth boundary 1 1 2 p p p p n n p if n p p if n p n is the outer normal derivative r 2 0 0 the weight m x is a positive bounded function and a x b x c are functions which change sign in our technical approach is based on the nehari manifold which is similar to the fibering method of drabek and pohozaev 1997 29 together with the recent idea from brown and wu 2008 10

spin s quantum chains and temperley lieb algebras the authors construct a family of isotropic spin s quantum chains consisting of sums of operators satisfying a temperley lieb algebra exact values for the infinite lattice limit of the ground state energy per site and for the non zero gap to the lowest energy excited state follow from the temperley lieb equivalence with a bethe ansatz soluble xxz model the family of spin chains includes the biquadratic spin 1 model

deterministic impulse control problems we prove that the optimal cost function of a deterministic impulse control problem is the unique viscosity solution of a first order hamilton jacobi quasi variational inequality in mathbb r n