current algebra of classical non linear sigma models the current algebra of classical non linear sigma models on arbitrary riemannian manifolds is analyzed it is found that introducing in addition to the noether currentj associated with the global symmetry of the theory a composite scalar fieldj the algebra closes under poisson brackets

higher local conservation laws for nonlinear sigma models on symmetric spaces we show that for the classical two dimensional nonlinear model on a riemannian symmetric space of dimensionm and rankp there existp independent series of higher local conservation laws and we reduce the field equations of the model to a system of nonlinear partial differential equations possessing an associated lax pair and involvingm p independent variables

quadratic pseudopotentials for gl n c principal sigma models abstract matrix pseudopotentials for the gl n c principal sigma model in two dimensional minkowski space are derived through the method of closed differential ideals the structure of the pseudopotential equations is chosen to contain only quadratic nonlinearities of the matrix riccati type a set of further constraints is deduced which leads to inner backlund transformations depending on two complex parameters through a geometrical interpretation of such matrix riccati equations and the associated constraints a linearization procedure is derived and the equations are reduced to those of zakharov mikhailov and shabat 7 10 an inductive procedure is applied to explicitly solve an iterated sequence of such backlund transformations through a purely algebraic transformation of solutions to the first step the resulting nonlinear superposition formula is used to demonstrate a permutability theorem and to analyse the appearance of singularities fr nous deduisons les pseudo potentiels matriciels pour le modele sigma principal a valeurs dans gl n c defini sur l espace de minkowski bi dimensionnel en utilisant la methode des ideaux differentiels fermes on restreint la structure des equations des pseudopotentiels de facon a ce que n apparaissent que des non linearites quadratiques du type riccati matriciel nous deduisons un ensemble de contraintes supplementaires menant a des transformations de backlund internes dependantes de deux parametres complexes gr ce a l interpretation geometrique de ces equations de riccati matricielles et des contraintes associees nous deduisons un procede de linearisation et les equations se reduisent a celles de zakharov mikhailov et shabat 7 10 un procede inductif est utilise pour resoudre explicitement une succession de transformations de backlund par une transformation purement algebrique des solutions de la premiere etape la formule de superposition non lineaire qui en resulte permet de demontrer un theoreme de permutabilite et d analyser l apparition de singularites

linear integral transformations and hierarchies of integrable nonlinear evolution equations abstract integrable hierarchies of nonlinear evolution equations are investigated on the basis of linear integral equations these are riemann hilbert type of integral transformations which leave invariant an infinite sequence of ordinary differential matrix equations of increasing order in an indefinite parameter k the potential matrices in these equations obey a set of nonlinear recursion relations leading to a heirarchy of nonlinear partial differential equations in decreasing order the same equations give rise to a reciprocal hierarchy associated with heisenberg ferromagnet type of equations central in the treatment is an embedding of the hierarchy into an infinite matrix structure which is constructed on the basis of the integral equations in terms of this infinite matrix structure the equations governing the hierarchies become quite simple furthermore it leads in a straightforward way to various generalizations such as to other types of linear spectral problems multicomponent system and lattice equations generalizations to equations associated with noncommuting flows follow as a direct consequence of the treatment finally some results on conserved densities and the hamiltonian structure are briefly discussed

the algebraic curve of classical superstrings on ads5 s5 we investigate the monodromy of the lax connection for classical iib superstrings on ads5 s5 for any solution of the equations of motion we derive a spectral curve of degree 4 4 the curve consists purely of conserved quantities all gauge degrees of freedom have been eliminated in this form the most relevant quantities of the solution such as its energy can be expressed through certain holomorphic integrals on the curve this allows for a classification of finite gap solutions analogous to the general solution of strings in flat space the role of fermions in the context of the algebraic curve is clarified finally we derive a set of integral equations which reformulates the algebraic curve as a riemann hilbert problem they agree with the planar one loop open image in new window supersymmetric gauge theory proving the complete agreement of spectra in this approximation

finiteness and quasi simplicity for symmetric k3 surfaces we compare the smooth and deformation equivalence of actions of finite groups on k3 surfaces by holomorphic and anti holomorphic transformations we prove that the number of deformation classes is finite and in a number of cases establish the expected coincidence of the two equivalence relations more precisely in these cases we show that an action is determined by the induced action in the homology on the other hand we construct two examples to show that first in general the homological type of an action does not even determine its topological type and second that k3 surfaces x and x with the same klein action do not need to be equivariantly deformation equivalent even if the induced action on h 2 0 x is real i e reduces to multiplication by 1 1 1 questions in this paper we study equivariant deformations of complexk3 surfaces with symmetry groups where by a symmetry we mean an either holomor phic or anti holomorphic transformation of the surface although the automor phism group of a particular k3 surface may be infinite we confine ourselves to finite group actions and address the following two questions see 1 4 1 6 for precise definitions finiteness whether the number of actions counted up to equivariant deforma

some characterizations of optimal trajectories in control theory several characterizations of optimal trajectories for the classical mayer problem in optimal control are provided for this purpose the regularity of directional derivatives of the value function is studied for instance it is shown that for smooth control systems the value function v is continuously differentiable along an optimal trajectory x t 0 1 to bf r n provided v is differentiable at the initial point t 0 x t 0 then the upper semicontinuity of the optimal feedback map is deduced the problem of optimal design is addressed obtaining sufficient conditions for optimality finally it is shown that the optimal control problem may be reduced to a viability one

derivative nonlinear schrodinger equations and hermitian symmetric spaces it is shown that to each hermitian symmetric space there corresponds an integrable system of generalised derivative nonlinear schrodinger equations nls the nonlinear terms are related to the curvature tensor of the associated symmetric space the hamiltonian form of the equations is presented the results are an extension of those presented in an earlier paper 1983 on generalised nls equations associated with symmetric and reductive homogeneous spaces

integrable extension of nonlinear sigma model we propose an integrable extension of nonlinear sigma model on the target space of hermitian symmetric space hss starting from a discussion of soliton solutions of o 3 model and an integrally extended version of it we construct general theory defined on arbitrary hss by using the coadjoint orbit method it is based on the exploitation of a covariantized canonical structure on hss this term results in an additional first order derivative term in the equation of motion which accommodates the zero curvature representation infinite conservation laws of nonlocal charges in this model are derived

estimates of the domain of dependence for scalar conservation laws abstract we consider the cauchy problem for a multidimensional scalar conservation law and construct an outer estimate for the domain of dependence of its kru kov solution the estimate can be represented as the controllability set of a specific differential inclusion in addition reachable sets of this inclusion provide outer estimates for the support of the wave profiles both results follow from a modified version of the classical kru kov uniqueness theorem which we also present in the paper finally the results are applied to a control problem consisting in steering a distributed quantity to a given set

epi lipschitzian reachable sets of differential inclusions abstract the reachable sets of a differential inclusion have nonsmooth topological boundaries in general the main result of this paper is that under the well known assumptions of filippov s existence theorem about solutions of differential inclusions every epi lipschitzian initial compact set k r n preserves this regularity for a short time i e f t k is also epi lipschitzian for all small t 0 the proof is based on rockafellar s geometric characterization of epi lipschitzian sets and uses a new result about the inner semicontinuity of clarke tangent cone t y t f t k c y r n with respect to both arguments

orientability for gauge theories on calabi yau manifolds abstract we study orientability issues of moduli spaces from gauge theories on calabi yau manifolds our results generalize and strengthen those for donaldson thomas theory on calabi yau manifolds of dimensions 3 and 4 we also prove a corresponding result in the relative situation which is relevant to the gluing formula in dt theory

darboux transformation and exact multisolitons of cpn nonlinear sigma model abstract exact multisolitons of c p n sigma model are obtained by using darboux transformation in terms of quasideterminant darboux matrix the multisoliton solutions are shown to be expressed in terms of quasideterminants of gelfand and retakh 1991 10 the method of quasideterminant darboux matrix has been shown to be related with the dressing method that has already been used to compute iteratively exact multisolitons of the c p n sigma model by means of nonlinear superposition principle of backlund transformations explicit expressions of one two and three soliton solutions of c p 1 model have been computed by using properties of quasideterminants

boundary regularity of reachable sets of control systems abstract the reachable set of a differential inclusion has nonsmooth boundary in general now we give sufficient conditions on the compact initial set and the differential inclusion x t f t x t u t a e so that this topological boundary has positive erosion i e it satisfies a uniform interior sphere condition the proof is based on the close relation between the semiconcave value function of a suitable mayer problem and its epigraph with positive erosion

the relationship between the maximum principle and dynamic programming let v t x be the infimum cost of an optimal control problem viewed as a function of the initial time and state t x dynamic programming is concerned with the properties of v cdot cdot and in particular with its characterization as a solution to the hamilton jacobi bellman equation heuristic arguments have long been advanced relating the maximum principle to dynamic programming according to p t v x left t x 0 t right here x 0 cdot is the minimizing state function under consideration and p cdot is the costate function of the maximum principle in this paper we examine the validity of such claims and find that this relationship interpreted as a differential inclusion involving the generalized gradient is indeed true almost everywhere and at the endpoints for a very large class of nonsmooth optimal control problems

on deformation types of real elliptic surfaces we study real elliptic surfaces and trigonal curves over a base of an arbitrary genus and their equivariant deformations we calculate the real tate shafarevich group and reduce the deformation classification to the combinatorics of a real version of grothendieck s it dessins d enfants as a consequence we obtain an explicit description of the deformation classes of m and m 1 i e maximal and submaximal in the sense of the smith inequality curves and surfaces

magnetic monopoles on three manifolds on etudie des monopoles magnetiques sur une 3 variete de riemann complete orientee m on associe a m une collection d espaces de modules de solutions des equations des monopoles pourvu que m soit non compacte et que la metrique de riemann sur m soit bonne pres de l infini

new topological field theories in two dimensions it is shown that two 1 1 dimensional 2d free abelian and self interacting non abelian gauge theories without any interaction with matter fields belong to a new class of topological field theories tfts these new theories capture together some of the key features of witten and schwarz types of tft because they are endowed with symmetries that are reminiscent of the schwarz type theories but their lagrangian density has the appearance of the witten type theories the topological invariants for these theories are computed on a 2d compact manifold and their recursion relations are obtained these new theories are shown to provide a class of tractable field theoretical models for the hodge theory in two dimensions of flat minkowski spacetime where there are no propagating degrees of freedom associated with the 2d gauge boson

homogeneous kahler manifolds paving the way towards new supersymmetric sigma models homogeneous kahler manifolds give rise to a broad class of supersymmetric sigma models containing as a rather special subclass the more familiar supersymmetric sigma models based on hermitian symmetric spaces in this article all homogeneous kahler manifolds with semisimple symmetry groupg are constructed and are classified in terms of dynkin diagrams explicit expressions for the complex structure and the kahler structure are given in terms of the lie algebra g ofg it is shown that for compactg one can always find an einstein kahler structure which is unique up to a constant multiple and for which the kahler potential takes a simple form

some series of infinitely many symmetry generators in symmetric space chiral models this paper shows that starting from any conserved current generated by some given infinitesimal symmetry generator one may use finite dual transformations to induce infinitely many infinitesimal symmetry generators thus besides starting from ordinary isotopic and space time translation this paper also discovers the infinitesimal generators for backlund transformation for dual symmetry itself and other general cases and then uses them to generate infinitely many local or nonlocal currents respectively

local differentiability of distance functions recently clarke stern and wolenski characterized in a hilbert space the closed subsets c for which the distance function dc is continuously differentiable everywhere on an open tube of uniform thickness around c here a corresponding local theory is developed for the property of dc being continuously differentiable outside of c on some neighborhood of a point x c this is shown to be equivalent to the prox regularity of c at x which is a condition on normal vectors that is commonly fulfilled in variational analysis and has the advantage of being verifiable by calculation additional characterizations are provided in terms of dc being locally of class c 1 or such that dc 2 is convex around x for some 0 prox regularity of c at x corresponds further to the normal cone mapping nc having a hypomonotone truncation around x and leads to a formula for pc by way of nc the local theory also yields new insights on the global level of the clarke stern wolenski results and on a property of sets introduced by shapiro as well as on the concept of sets with positive reach considered by federer in the finite dimensional setting

second order sensitivity relations and regularity of the value function for mayer s problem in optimal control this paper investigates the value function v of a mayer optimal control problem with the state equation given by a differential inclusion first we obtain an invariance property for the proximal and frechet subdifferentials of v along optimal trajectories then we extend the analysis to the sub and superjets of v obtaining new sensitivity relations of second order by applying sensitivity analysis to exclude the presence of conjugate points we deduce that the value function is twice differentiable along any optimal trajectory starting at a point at which v is proximally subdifferentiable we also provide sufficient conditions for the local c 2 regularity of v on neighborhoods of optimal trajectories

real rational surfaces are quasi simple we show that real rational over c surfaces are quasi simple i e that such a surface is determined up to deformation in the class of real surfaces by the topological type of its real structure

unknottedness of real lagrangian tori in s 2 times s 2 we prove the hamiltonian unknottedness of real lagrangian tori in the monotone s 2 times s 2 namely any real lagrangian torus in s 2 times s 2 is hamiltonian isotopic to the clifford torus the proof is based on a neck stretching argument gromov s foliation theorem and the cieliebak schwingenheuer criterion

an application of gauge theory to four dimensional topology soit x une u variete compacte reguliere simplement connexe orientee avec la propriete que la forme associee q est definie positive alors cette forme est equivalente sur les entiers a la forme diagonale standard soit dans une base q u 1 u 2 u 2 u 2 1 u 2 2 u 2 2