games and full abstraction for fpc a new category of games is developed which improves over existing such categories in that it interprets sums as well as products function spaces and recursive types a model of fpc a sequential functional language with just this type structure is described and shown to be fully abstract

on the validity of the maximum principle and of the euler lagrange equation for a minimum problem depending on the gradient we consider the limiting case alpha infty of the problem of minimizing int omega nabla u x alpha g u dx hbox on u in u 0 w 1 alpha 0 omega where g is differentiable and strictly monotone if this infimum is finite it is evidently attained we show that any minimizing function u satisfies the appropriate form of the euler lagrange equation i e for some function p div p x g u x quad rm for quad p x in partial j b nabla u x where jb is the indicator function of the closed unit ball in the euclidean norm of bbb r n and partial is the subdifferential of the convex function jb

full abstraction for pcf an intensional model for the programming language pcf is described in which the types of pcf are interpreted by games and the terms by certain history free strategies this model is shown to capture definability in pcf more precisely every compact strategy in the model is definable in a certain simple extension of pcf we then introduce an intrinsic preorder on strategies and show that it satisfies some striking properties such that the intrinsic preorder on function types coincides with the pointwise preorder we then obtain an order extensional fully abstract model of pcf by quotienting the intensional model by the intrinsic preorder this is the first syntax independent description of the fully abstract model for pcf hyland and ong have obtained very similar results by a somewhat different route independently and at the same time we then consider the effective version of our model and prove a universality theorem every element of the effective extensional model is definable in pcf equivalently every recursive strategy is definable up to observational equivalence

musings around the geometry of interaction and coherence we introduce the danos regnier category dr m of a linear inverse monoid m as a categorical description of geometries of interaction goi inspired from the weight algebra the natural setting for goi is that of a so called weakly cantorian linear inverse monoid in which case dr m is a kind of symmetrized version of the classical abramsky haghverdi scott construction of a weak linear category from a goi situation it is well known that goi is perfectly suited to describe the multiplicative fragment of linear logic and indeed dr m will be a autonomous category in this case it is also well known that the categorical interpretation of the other linear connectives conflicts with goi interpretations we make this precise and show that dr m has no terminal object no cartesian product of any two objects and no exponential whatever m is unless m is trivial however a form of coherence completion of dr m a la hu joyal which for additives resembles a layered approach a la hughes van glabbeek provides a model of full classical linear logic as soon as m is weakly cantorian one finally notes that girard s notion of coherence is pervasive and instrumental in every aspect of this work

game semantics for a polymorphic programming language this article presents a game semantics for higher rank polymorphism leading to a new model of the calculus system f and a programming language which extends it with mutable variables in contrast to previous game models of polymorphism it is quite concrete extending existing categories of games by a simple development of the notion of question answer labelling and the associated bracketing condition to represent copycat links between positive and negative occurrences of type variables some well known system f encodings of type constructors correspond in our model to simple constructions on games such as the lifted sum we characterize the generic types of our model those for which instantiation reflects denotational equivalence and show how to construct an interpretation in which all types are generic we show how mutable variables a la scheme may be interpreted in our model allowing the definition of polymorphic objects with local state by proving definability of finitary elements in this model using a decomposition argument we establish a full abstraction result

a class of hamiltonian systems with increasing periods on considere un systeme hamiltonien de la forme x g y y f x ou h f et h g satisfont certaines hypotheses on montre qu il y a un intervalle maximal 0 a a 0 tel que chaque solution x t y t avec x 0 a 0 a y 0 0 est periodique avec son orbite enfermant 0 0 soit p a la plus petite periode de cette solution alors p 0 a r est differentiable avec p a 0

weighted models for higher order computation abstract we study a class of quantitative models for higher order computation lafont categories with infinite biproducts each of these has a complete internal semiring and can be enriched over its modules we describe a semantics of nondeterministic pcf weighted over this semiring in which fixed points are obtained from the bifree algebra over its exponential structure by characterizing them concretely as infinite sums of approximants indexed over nested finite multisets we prove computational adequacy we can construct examples of our semantics by weighting existing models such as categories of games over a complete semiring this transition from qualitative to quantitative semantics is characterized as a change of base of enriched categories arising from a monoidal functor from coherence spaces to modules over a complete semiring for example the game semantics of idealized algol is coherence space enriched and thus gives rise to to a weighted model which is fully abstract

a generic property of families of lagrangian systems we prove that a generic lagrangian has finitely many minimizing measures for every cohomology class

finitary pcf is not decidable the question of the decidability of the observational ordering of finitary pcf was raised jung and stoughton in m bezem j f groote eds typed lambda calculi and applications lecture notes in computer science vol 664 springer berlin 1993 pp 230 244 to give mathematical content to the full abstraction problem for pcf milner theoret comput sci 4 1977 1 22 we show that the ordering is in fact undecidable this result places limits on how explicit a representation of the fully abstract model can be it also gives a slight strengthening of the author s earlier result on typed ability loader in a anderson m zeleny eds church memorial volume kluwer academic press dordrecht to appear copyright 2001 elsevier science b v

closing geodesics in c 1 topology given a closed riemannian manifold we show how to close an orbit of the geodesic ow by a small perturbation of the metric in the c1 topology

the genericity theorem and parametricity in the polymorphic l calculus abstract this paper focuses on how terms of the polymorphic calculus which may take types as inputs depend on types these terms are generally understood in all models to have an essentially constant meaning on input types we show the proof theory of polymorphic calculus suggests a clear syntactic description of this phenomenon namely under a reasonable condition we show that if two polymorphic functions agree on a single type then they agree on all types equivalently types are generic inputs

holder regularity of the normal distance with an application to a pde model for growing sandpiles given a bounded domain omega in mathbb r 2 with smooth boundary the cut locus overline sigma is the closure of the set of nondifferentiability points of the distance d from the boundary of omega the normal distance to the cut locus tau x is the map which measures the length of the line segment joining x to the cut locus along the normal direction dd x whenever x notin overline sigma recent results show that this map restricted to boundary points is lipschitz continuous as long as the boundary of omega is of class c 2 1 our main result is the global holder regularity of tau in the case of a domain omega with analytic boundary we will also show that the regularity obtained is optimal as soon as the set of the so called regular conjugate points is nonempty in all the other cases lipschitz continuity can be extended to the whole domain omega the above regularity result for tau is also applied to derive the holder continuity of the solution of a system of partial differential equations that arises in granular matter theory and optimal mass transfer

syntax vs semantics a polarized approach we present a notion of sliced proof nets for the polarized fragment of linear logic and a corresponding game model we show that the connection between them is very strong through an equivalence of categories this contains soundness full completeness and faithful completeness

relative definability of boolean functions via hypergraphs the aim of this work is to show how hypergraphs can be used as a systematic tool in the classification of continuous boolean functions according to their degree of parallelism intuitively f is less parallel than g if it can be defined by a sequential program using g as its only free variable it turns out that the poset induced by this preorder is as for the degrees of recursion a sup semilattice although hypergraphs have already been used in bucciarelli theoret comput sci to appear as a tool for studying degrees of parallelism no general result relating the former to the latter has been proved in that work we show that the sup semilattice of degrees has a categorical counterpart we define a category of hypergraphs such that every object represents a monotone boolean function finite coproducts in this category correspond to lubs of degrees unlike degrees of recursion where every set has a recursive upper bound monotone boolean functions may have no sequential upper bound however the ones which do have a sequential upper bound can be nicely characterised in terms of hypergraphs these subsequential functions play a major role in the proof of our main result namely that f is less parallel than g if there exists a morphism between their associated hypergraphs

dulac time of a resonant saddle in the loud family abstract we study the critical periods of the loud family of quadratic centers we give the first terms of the asymptotic expansion of the period function and we conclude that no bifurcation occurs for certain values of the parameters this result contributes to complete the bifurcation diagram of critical periods in the loud family

existence of c 1 critical subsolutions of the hamilton jacobi equation let m be a c second countable manifold without boundary we denote by tm the tangent bundle and by tm m the canonical projection a point in tm will be denoted by x v with x m and v tx m 1 x in the same way a point of the cotangent space t m will be denoted by x p with x m and p t x m a linear form on the vector space tx m we will suppose that g is a complete riemannian metric on m for v tx m the norm v is g v v 1 2 we will denote by the dual norm on t x m we will also use the notations v x for v tx m and p x for v t x m we will assume in the whole paper that h t m r is a function of class at least c2 which satisfies the following three conditions 1 uniform superlinearity for every k 0 there exists c k r such that

a stable programming language it is well known that stable models as di domains qualitative domains and coherence spaces are not fully abstract for the language pcf this fact is related to the existence of stable parallel functions and of stable functions that are not monotone with respect to the extensional order which cannot be defined by programs of pcf in this paper a paradigmatic programming language named st pcf is proposed which extends the language pcf with two additional operators the operational description of the extended language is presented in an effective way although the evaluation of one of the new operators cannot be formalized in a pcf like rewrite system since st pcf can define all finite cliques of coherence spaces the above gap with stable models is filled consequently stable models are fully abstract for the extended language

the free boundary of variational inequalities with gradient constraints abstract in this paper we prove that the free boundary of the minimizer of i v u 1 2 d v 2 v d x subject to the pointwise gradient constraint d v p 1 is as regular as the tangent bundle of the boundary of the domain to this end we study a generalized notion of ridge of a domain in the plane which is the set of singularity of the distance function in the p norm to the boundary of the domain

on the hausdorff dimension of the mather quotient under appropriate assumptions on the dimension of the ambient manifold and the regularity of the hamiltonian we show that the mather quotient is small in term of hausdorff dimension then we present applications in dynamics

asymptotic expansion of the period function abstract let p be a not necessarily bounded polycycle of an analytic vector field on an open set of the plane suppose that the singularities which appear after desingularization of the vertices of p are formally linearizable consider the function t defined by the return time near p it is shown that the function t and its derivative t have asymptotic expansions in x r and x log x r it is also shown that under some other conditions imposed on the polycycle vertices the asymptotic expansions of t and t converge absolutely and uniformly to these functions respectively these results are applied to the polycycles of the analytic vector fields which have a darboux first integral in particular it is obtained that if p is a polycycle of a hamiltonian vector field with an analytic polynomial if p is unbounded hamiltonian function t is a nonoscillating function another application concerns the nilpotent centers or focus since the singularities which appear after desingularization of such a singularity have analytic first integrals

from algol to polymorphic linear lambda calculus in a linearly typed functional language one can define functions that consume their arguments in the process of computing their results this is reminiscent of state transformations in imperative languages where execition of an assignment statement alters the contents of the store we explore this connection by translating two variations on algol 60 into a purely functional language with polymorphic linear types on the one hand the translations lead to a semantic analysis of algol like programs in terms of a model of the linear language on the other hand they demonstrate that a linearly typed functional language can be at least as expressive as algol

game semantics for dependent types abstract we present a model of dependent type theory dtt with 1 and intensional id types which is based on a slight variation of the call by name category of ajm games and history free winning well bracketed strategies the model satisfies streicher s criteria of intensionality and refutes function extensionality the principle of uniqueness of identity proofs is satisfied we show it contains a submodel as a full subcategory which gives a faithful interpretation of dtt with 1 and intensional id types and additionally finite inductive type families this smaller model is fully and faithfully complete with respect to the syntax at the type hierarchy built without id types as well as at the more general class of types where we allow for one strictly positive occurrence of an id type definability for the full type hierarchy with id types remains to be investigated

hardyʼs inequality and curvature a hardy inequality of the form f x pdx p 1p p 1 a x f x p x pdx for all f c0 r is considered for p 1 p 1 where is a domain in rnrn n 2n 2 r r is the ridge of and x x is the distance from x x to the boundary the main emphasis is on determining the dependence of a a on the geometric properties of a hardy inequality is also established for any doubly connected domain in r2r2 in terms of a uniformization of that is any conformal univalent map of onto an annulus

decidability and syntactic control of interference we investigate the decidability of observational equivalence and approximation in reynolds syntactic control of interference sci a prototypical functional imperative language in which covert interference between functions and their arguments is prevented by the use of an affine typing discipline by associating denotations of terms in a fully abstract relational model of finitary basic sci due to reddy with multitape finite state automata we show that observational approximation is not decidable even at first order but that observational equivalence is decidable for all terms we then consider the same problems for basic sci extended with non local control in the form of backwards jumps we show that both observational approximation and observational equivalence are decidable in this observably sequential version of the language by describing a fully abstract games model in which strategies are regular languages

a full continuous model of polymorphism we introduce a model of the second order lambda calculus such a model is a scott domain whose elements are themselves scott domains and in it polymorphic maps are interpreted by generic continous maps

a fully abstract denotational semantics for the calculus of higher order communicating systems abstract in this paper we study the calculus of higher order communicating systems chocs thomsen proc of popl 89 acm 1989 pp 143 154 inform comput 116 1 1995 38 57 in a denotational setting we present a construction of a denotational semantics for chocs which resides in a domain constructed using the standard constructions of separated sum cartesian product the plotkin power domain constructor and recursively defined domains we show under mild restrictions that the denotational semantics and the operational semantics of chocs are fully abstract we have previously proved using bisimulation arguments that processes as first class objects are powerful enough to simulate recursion however the proof is very long and tedious to demonstrate the power of the denotational approach we use it to obtain a very simple proof of the simulation of recursion result

hardy inequalities for p laplacians with robin boundary conditions in this paper we study the best constant in a hardy inequality for the p laplace operator on convex domains with robin boundary conditions we show in particular that the best constant equals p

operational domain theory and topology of sequential programming languages a number of authors have exported domain theoretic techniques from denotational semantics to the operational study of contextual equivalence and order we further develop this and moreover we additionally export topological techniques in particular we work with an operational notion of compact set and show that total programs with values on certain types are uniformly continuous on compact sets of total elements we apply this and other conclusions to prove the correctness of non trivial programs that manipulate infinite data what is interesting is that the development applies to sequential programming languages in addition to languages with parallel features

sequential algorithms and strongly stable functions intuitionistic proofs and pcf programs may be interpreted as functions between domains or as strategies on games the two kinds of interpretation are inherently different static vs dynamic extensional vs intentional it is thus extremely instructive to compare and to connect them in this article we investigate the extensional content of the sequential algorithm hierarchy sds introduced by berry and curien we equip every sequential game t sds of the hierarchy with a realizability relation between plays and extensions in this way the sequential game t sds becomes a directed acyclic graph instead of a tree this enables to define a hypergraph t hc on the extensions or terminal leaves of the game t sds we establish that the resulting hierarchy hc coincides with the strongly stable hierarchy introduced by bucciarelli and ehrhard we deduce from this a gametheoretic proof of ehrhard s collapse theorem which states that the strongly stable hierarchy coincides with the extensional collapse of the sequential algorithm hierarchy

on the return time function around monodromic polycycles abstract in this paper we study the period function of centers of planar polynomial differential systems with a convenient compactification of the phase portrait the boundary of the period annulus of the center has two connected components the center itself and a polycycle we are interested in the behaviour of the period function near the polycycle the desingularization of its critical points gives rise to a new polycycle monodromic as well with hyperbolic saddles or saddle nodes at the vertices in this paper we compute the first terms in the asymptotic development of the time function around any orbitally linearizable saddle that may come from this desingularization process in addition we use these developments to study the bifurcation diagram of the period function of the dehomogenized loud s centers more generally the tools developed here can be used to study the return time function around a monodromic polycycle this work is a continuation of the results in p mardesic d marin j villadelprat on the time function of the dulac map for families of meromorphic vector fields nonlinearity 16 2003 855 881 p mardesic d marin j villadelprat the period function of reversible quadratic centers j differential equations 224 2006 120 171

a variational approach to the macroscopic electrodynamics of anisotropic hard superconductors we consider bean s critical state model for anisotropic superconductors a variational problem solved by the quasi static evolution of the internal magnetic field is obtained as the limit of functionals arising from maxwell s equations combined with a power law for the dissipation moreover the quasi static approximation of the internal electric field is recovered using a first order necessary condition if the sample is a long cylinder subjected to an axial uniform external field the macroscopic electrodynamics is explicitly determined

hardy inequalities for robin laplacians abstract in this paper we establish a hardy inequality for laplace operators with robin boundary conditions for convex domains in particular we show explicitly how the corresponding hardy weight depends on the coefficient of the robin boundary conditions we also study several extensions to non convex and unbounded domains

the regular language semantics of second order idealized algol we explain how recent developments in game semantics can be applied to reasoning about equivalence of terms in a non trivial fragment of idealized algol ia by expressing sets of complete plays as regular languages being derived directly from the fully abstract game semantics for ia our model inherits its good theoretical properties in fact for second order ia taken as a stand alone language the regular language model is fully abstract the method is algorithmic and formal which makes it suitable for automation we show how reasoning is carried out using a meta language of extended regular expressions a language for which equivalence is decidable

the system f of variable types fifteen years later the semantic study of system f stumbles on the problem of variable types for which there was no convincing interpretation we develop here a semantics based on the category theoretic idea of direct limit so that the behaviour of a variable type on any domain is determined by its behaviour on finite ones thus getting rid of the circularity of variable types to do so one has first to simplify somehow the extant semantic ideas replacing scott domains by the simpler and more finitary qualitative domains the interpretation obtained is extremely compact as shown on simple examples the paper also contains the definitions of a very small universal model of lambda calculus and investigates the concept totality

darboux linearization and isochronous centers with a rational first integral abstract in this paper we study isochronous centers of polynomial systems it is known that a center is isochronous if and only if it is linearizable we introduce the notion of darboux linearizability of a center and give an effective criterion for verifying darboux linearizability if a center is darboux linearizable the method produces a linearizing change of coordinates most of the known polynomial isochronous centers are darboux linearizable moreover using this criterion we find a new two parameter family of cubic isochronous centers and give the linearizing changes of coordinates for centers belonging to that family we also determine all hamiltonian cubic systems which are darboux linearizable in the second part of this work we restrict to the study of isochronous centers having a rational first integral we prove that under certain conditions the cycle vanishing at the isochronous center is either zero homologous in the closure of a generic fiber or the function obtained from the first integral by eliminating the indeterminacy points has several critical points in the singular fiber passing through the isochronous center

the period function of the generalized lotka volterra centers abstract the present paper deals with the period function of the quadratic centers in the literature different terminologies are used to classify these centers but essentially there are four families hamiltonian reversible q 3 r codimension four q 4 and generalized lotka volterra systems q 3 lv chicone c chicone review in mathscinet ref 94h 58072 conjectured that the reversible centers have at most two critical periods and that the centers of the three other families have a monotonic period function with regard to the second part of this conjecture only the monotonicity of the hamiltonian and q 4 families w a coppel l gavrilov the period function of a hamiltonian quadratic system differential integral equations 6 1993 1357 1365 y zhao the monotonicity of period function for codimension four quadratic system q 4 j differential equations 185 2002 370 387 has been proved concerning the q 3 lv family no substantial progress has been made since the middle 80s when several authors showed independently the monotonicity of the classical lotka volterra centers f rothe the periods of the volterra lokta system j reine angew math 355 1985 129 138 r schaaf global behaviour of solution branches for some neumann problems depending on one or several parameters j reine angew math 346 1984 1 31 j waldvogel the period in the lotka volterra system is monotonic j math anal appl 114 1986 178 184 by means of the first period constant one can easily conclude that the period function of the centers in the q 3 lv family is monotone increasing near the inner boundary of its period annulus i e the center itself thus according to chicone s conjecture it should be also monotone increasing near the outer boundary which in the poincare disc is a polycycle in this paper we show that this is true in addition we prove that except for a zero measure subset of the parameter plane there is no bifurcation of critical periods from the outer boundary finally we show that the period function is globally i e in the whole period annulus monotone increasing in two other cases different from the classical one

adapting innocent game models for the bohm tree λ theory we present a game model of the untyped calculus with equational theory equal to the bohm tree theory b which is universal i e every element of the model is definable by some term this answers a question of di gianantonio franco and honsell we build on our earlier work which uses the methods of innocent game semantics to develop a universal model inducing the maximal consistent sensible theory h to our knowledge these are the first syntax independent universal models of the untyped calculus

constructing differential categories and deconstructing categories of games differential categories were introduced by blute cockett and seely to axiomatize categorically ehrhard and regnier s syntactic differential operator we present an abstract construction that takes a symmetric monoidal category and yields a differential category and show how this construction may be applied to categories of games in one instance we recover the category previously used to give a fully abstract model of a nondeterministic imperative language the construction exposes the differential structure already present in this model and shows how the differential combinator may be encoded in the imperative language the second instance corresponds to a new cartesian differential category of games we give a model of a simply typed resource calculus resource pcf in this category and show that it possesses the finite definability property comparison with a semantics based on bucciarelli ehrhard and manzonetto s relational model reveals that the latter also possesses this property and is fully abstract

multigames and strategies coalgebraically coalgebraic games have been recently introduced as a generalization of conway games and other notions of games arising in different contexts using coalgebraic methods games can be viewed as elements of a final coalgebra for a suitable functor and operations on games can be analyzed in terms of generalized coiteration schemata coalgebraic games are sequential in nature i e at each step either the left l or the right r player moves global polarization moreover only a single move can be performed at each step recently in the context of game semantics concurrent games have been introduced where global polarization is abandoned and multiple moves are allowed in this paper we introduce coalgebraic multigames which are situated half way between traditional sequential games and concurrent games global polarization is still present however multiple moves are possible at each step i e a team of l r players moves in parallel coalgebraic operations such as sum and negation can be naturally defined on multigames interestingly sum on coalgebraic multigames turns out to be related to conway s selective sum on games rather than the usual sequential disjoint sum selective sum has a parallel nature in that at each step the current player performs a move in at least one component of the sum game while on disjoint sum the current player performs a move in exactly one component at each step a presentation of strategies on coalgebraic games is given via a final coalgebra of a pair of mutually recursive functors and a suitable notion of simulation a monoidal closed category of coalgebraic multigames in the vein of a joyal category of conway games is then built the relationship between coalgebraic multigames and games is then formalized via an equivalence of the multigame category and a monoidal closed category of coalgebraic games where tensor is selective sum

the link between the shape of the irrational aubry mather sets and their lyapunov exponents we consider the irrational aubry mather sets of an exact symplectic monotone c 1 twist map of the two dimensional annulus introduce for them a notion of c 1 regularity related to the notion of bouligand paratingent cone and prove that a mather measure has zero lyapunov exponents if and only if its support is c 1 regular almost everywhere a mather measure has nonzero lyapunov exponents if and only if its support is c 1 irregular almost everywhere an aubry mather set is uniformly hyperbolic if and only if it is irregular everywhere the aubry mather sets which are close to the kam invariant curves even if they may be c 1 irregular are not too irregular i e have small paratingent cones the main tools that we use in the proofs are the so called green bundles

the category theoretic solution of recursive domain equations recursive specifications of domains plays a crucial role in denotational semantics as developed by scott and strachey and their followers the purpose of the present paper is to set up a categorical framework in which the known techniques for solving these equations find a natural place the idea is to follow the well known analogy between partial orders and categories generalizing from least fixed points of continuous functions over cpos to initial ones of continuous functors over omega categories to apply these general ideas we introduce wand s bf o categories where the morphism sets have a partial order structure and which include almost all the categories occurring in semantics the idea is to find solutions in a derived category of embeddings and we give order theoretic conditions which are easy to verify and which imply the needed categorical ones the main tool is a very general form of the limit colimit coincidence remarked by scott in the concluding section we outline how compatibilit

bifurcation of critical periods for plane vector fields on etudie un probleme de bifurcation dans des familles de champs de vecteurs analytiques plans qui ont un centre non degenere a l origine pour toutes les valeurs d un parametre r n on definit la fonction periode p on determine les points critiques de cette fonction pres du centre avec comme parametre de bifurcation

the geodesic x ray transform with matrix weights author s paternain gp salo m uhlmann g zhou h abstract 2019 by johns hopkins university press consider a compact riemannian manifold of dimension 3 with strictly convex boundary such that the manifold admits a strictly convex function we show that the attenuated ray transform in the presence of an arbitrary connection and higgs field is injective modulo the natural obstruction for functions and one forms we also show that the connection and the higgs field are uniquely determined by the scattering relation modulo gauge transformations the proofs involve a reduction to a local result showing that the geodesic x ray transform with a matrix weight can be inverted locally near a point of strict convexity at the boundary and a detailed analysis of layer stripping arguments based on strictly convex exhaustion functions as a somewhat striking corollary we show that these integral geometry problems can be solved on strictly convex manifolds of dimension 3 having nonnegative sectional curvature similar results were known earlier in negative sectional curvature we also apply our methods to solve some inverse problems in quantum state tomography and polarization tomography

finiteness for critical periods of planar analytic vector fields limburgs univ centrum dept math b 3610 diepenbeek belgium chicone c univ missouri dept math columbia mo 65211

regularity of optimal transport in curved geometry the nonfocal case we explore some geometric and analytic consequences of a curvature condition introduced by ma trudinger and wang in relation to the smoothness of optimal transport in curved geometry we discuss a conjecture according to which a strict version of the ma trudinger wang condition is sufficient to prove regularity of optimal transport on a riemannian manifold we prove this conjecture under a somewhat restrictive additional assumption of nonfocality at the same time we establish the striking geometric property that the tangent cut locus is the boundary of a convex set partial extensions are presented to the case when there is no pure focalization on the tangent cut locus

extending regular expressions with iterated shuffle it is shown that every finite expression which uses the operations union product kleene star and iterated shuffle in any order starting with finite sets defines a language which can be recognized non deterministically by some multicounter machine in quasirealtime it is known that this family is in general not closed with respect to iterated shuffle as a consequence of the characterization each such language is in nspace log n and thus in p however if p np then also neither p nor nspace log n are closed under iterated shuffle the proof uses the new concept of so called shuffle schemes and a number of results on algebraic language theory

algebraic particular integrals integrability and the problem of the center in this work we clarify the global geometrical phenomena corresponding to the notion of center for plane quadratic vector fields we first show the key role played by the algebraic particular integrals of degrees less than or equal to three in the theory of the center these curves control the changes in the systems as parameters vary the bifurcation diagram used to prove this result is realized in the natural topological space for the situation considered namely the real four dimensional projective space next we consider the known four algebraic conditions for the center for quadratic vector fields one of them says that the system is hamiltonian a condition which has a clear geometric meaning we determine the geometric meaning of the remaining other three algebraic conditions i ii iii

parallel and serial hypercoherences abstract it is known that the strongly stable functions which arise in the semantics of pcf can be realized by sequential algorithms which can be considered as deterministic strategies in games associated to pcf types studying the connection between strongly stable functions and sequential algorithms two dual classes of hypercoherences naturally arise the parallel and serial hypercoherences the objects belonging to the intersection of these two classes are in bijective correspondence with the so called serial parallel graphs that can essentially be considered as games we show how to associate to any hypercoherence a parallel hypercoherence together with a projection onto the given hypercoherence and present some properties of this construction intuitively it makes explicit the computational time of a hypercoherence

closing aubry sets ii given a tonelli hamiltonian h t m of class ck with k 2 we prove the following results 1 assume there exist a recurrent point of the projected aubry set and a critical viscosity subsolution u such that u is a c1 critical solution in an open neighborhood of the positive orbit of suppose further that u is c2 at then there exists a ck potential v m small in c2 topology for which the aubry set of the new hamiltonian h v is either an equilibrium point or a periodic orbit 2 if m is two dimensional 1 holds replacing c1 critical solution c2 at by cm3 critical subsolution these results can be considered as a first step through the attempt of proving the mane s conjecture in c2 topology in a second paper 27 we will generalize 2 to arbitrary dimension moreover such an extension will need the introduction of some new techniques which will allow us to prove in 27 the mane s density conjecture in c1 topology our proofs are based on a combination of techniques coming from finite dimensional control theory and hamilton jacobi theory together with some of the ideas that were used to prove c1 closing lemmas for dynamical systems 2014 wiley periodicals inc

generalizations and properties of the principal eigenvalue of elliptic operators in unbounded domains using three different notions of the generalized principal eigenvalue of linear second order elliptic operators in unbounded domains we derive necessary and sufficient conditions for the validity of the maximum principle as well as for the existence of positive eigenfunctions for the dirichlet problem relations between these principal eigenvalues their simplicity and several other properties are further discussed 2015 wiley periodicals inc

generic hyperbolicity of aubry sets on surfaces given a tonelli hamiltonian of class c 2 on the cotangent bundle of a compact surface we show that there is an open dense set of potentials in the c 2 topology for which the aubry set is hyperbolic in its energy level

the lipschitz continuity of the distance function to the cut locus let n be a closed submanifold of a complete smooth riemannian manifold m and uv the total space of the unit normal bundle of n for each v c uv let p v denote the distance from n to the cut point of n on the geodesic y with the velocity vector tyv 0 v the continuity of the function p on uv is well known in this paper we prove that p is locally lipschitz on which p is bounded in particular if m and n are compact then p is globally lipschitz on uy therefore the canonical interior metric 6 may be introduced on each connected component of the cut locus of n and this metric space becomes a locally compact and complete length space let n be an immersed submanifold of a complete cc riemannian manifold m and 7 uv n the unit normal bundle of n for each positive integer k and vector v c uv let a number k v denote the parameter value of fy where 7yv denotes the geodesic for which the velocity vector is v at t 0 such that yv ak v is the k th focal point conjugate point for the case in which n is a point of n along y counted with focal or conjugate multiplicities a unit speed geodesic segment 0 a m emanating from n is called an n segment if t d n y t on 0 a by the first variation formula an n segment is orthogonal to n a point 7y to on an n segment 7y v e uv is called a cut point of n if there is no n segment properly containing y o to for each v c uv let p v denote the distance from n to the cut point on y of n whitehead 27 investigated the structure of the conjugate locus and the cut locus of a point on a real analytic finsler manifold he determined the structure of the conjugate locus around a conjugate point for which the conjugate multiplicity is locally constant on its neighborhood cf also 25 and proved the continuity of the function p in compact symmetric spaces t sakai 19 and m takeuchi 23 determined the detailed structure of the cut locus of a point the detailed structure of the cut locus of a point in a 2 dimensional riemannian manifold has been investigated by poincare myers and others 7 11 13 hartman first tried to show the absolute continuity of the function p when m is 2 dimensional he proved in 8 that if p is of bounded variation then p is absolutely continuous recently hebda 11 and the first named author 13 independently proved ambrose s problem by showing that p is absolutely continuous on a closed arc on which p is bounded when n is a point in a 2 dimensional riemannian manifold therefore the cut locus of a point in a compact 2 dimensional received by the editors october 14 1998 and in revised form april 13 1999 2000 mathematics subject classification primary 53c22 secondary 28a78 supported in part by a grant in aid for scientific research from the ministry of education science sports and culture japan 2000 american mathematical society

an exact correspondence between a typed pi calculus and polarised proof nets this paper presents an exact correspondence in typing and dynamics between polarised linear logic and a typed p calculus based on io typing the respective incremental constraints one on geometric structures of proof nets and one based on types precisely correspond to each other leading to the exact correspondence of the respective formalisms as they appear in olivier laurent 2003 27 for proof nets and kohei honda et al 2004 24 for the p calculus

a type assignment system for game semantics we present a type assignment system that provides a finitary interpretation of lambda terms in a game semantics model traditionally type assignment systems describe the semantic interpretation of terms in domain theoretic models quite surprisingly the type assignment system presented in this paper is very similar to the traditional ones the main difference being the omission of the subtyping rules

a structural approach to reversible computation reversibility is a key issue in the interface between computation and physics and of growing importance as miniaturization progresses towards its physical limits most foundational work on reversible computing to date has focussed on simulations of low level machine models by contrast we develop a more structural approach we show how high level functional programs can be mapped compositionally i e in a syntax directed fashion into a simple kind of automata which are immediately seen to be reversible the size of the automaton is linear in the size of the functional term in mathematical terms we are building a concrete model of functional computation this construction stems directly from ideas arising in geometry of interaction and linear logic but can be understood without any knowledge of these topics in fact it serves as an excellent introduction to them at the same time an interesting logical delineation between reversible and irreversible forms of computation emerges from our analysis

on the number of mather measures of lagrangian systems in 1996 ricardo ricardo mane discovered that mather measures are in fact the minimizers of a universal infinite dimensional linear programming problem this fundamental result has many applications of which one of the most important is to the estimates of the generic number of mather measures mane obtained the first estimation of that sort by using finite dimensional approximations recently we were able with gonzalo contreras to use this method of finite dimensional approximation in order to solve a conjecture of john mather concerning the generic number of mather measures for families of lagrangian systems in the present paper we obtain finer results in that direction by applying directly some classical tools of convex analysis to the infinite dimensional problem we use a notion of countably rectifiable sets of finite codimension in banach and frechet spaces which may deserve independent interest

types and full abstraction for polyadic π calculus a type system for terms of the monadic p calculus is introduced and used to obtain a full abstraction result for the translation of the polyadic p calculus into the monadic calculus well sorted terms of the polyadic calculus are barbed congruent iff their translations are typed barbed congruent

glueing and orthogonality for models of linear logic we present the general theory of the method of glueing and associated technique of orthogonality for constructing categorical models of all the structure of linear logic in particular we treat the exponentials in detail we indicate simple applications of the methods and show that they cover familiar examples

building continuous webbed models for system f we present here a large family of concrete models for girard and reynolds polymorphism system f in a noncategorical setting the family generalizes the construction of the model of barbanera and berardi tech report university of turin 1997 hence it contains complete models for f a complete model for system f preprint june 1998 and we conjecture that it contains models which are complete for f it also contains simpler models the simplest of them e2 being a second order variant of the engeler plotkin model e all the models here belong to the continuous semantics and have underlying prime algebraic domains all have the maximum number of polymorphic maps the class contains models which can be viewed as two intertwined compatible webbed models of untyped calculus in the sense of berline from computations to foundations the calculus and its webbed models revised version theoret comput sci 86 pp to appear but it is much larger than this finally many of its models might he read as two intertwined strict intersection type systems

strong normalisation in the π calculus we introduce a typed calculus where strong normalisation is ensured by typability strong normalisation is a useful property in many computational contexts including distributed systems in spite of its simplicity our type discipline captures a wide class of converging name passing interactive behaviour the proof of strong normalisability combines methods from typed calculi and linear logic with process theoretic reasoning it is adaptable to systems involving state non determinism polymorphism control and other extensions strong normalisation is shown to have significant consequences including finite axiomatisation of weak bisimilarity a fully abstract embedding of the simply typed calculus with products and sums and basic liveness in interaction strong normalisability has been extensively studied as a fundamental property in functional calculi term rewriting and logical systems this work is one of the first steps to extend theories and proof methods for strong normalisability to the context of name passing processes

kripke logical relations and pcf abstract sieber has described a model of pcf consisting of continuous functions that are invariant under certain finitary logical relations and shown that it is fully abstract for closed terms of up to third order types we show that one may achieve full abstraction at all types using a form of kripke logical relations introduced by jung and tiuryn to characterize definability

stability analysis for semilinear parabolic problems in general unbounded domains abstract we introduce several notions of generalised principal eigenvalue for a linear elliptic operator on a general unbounded domain under boundary condition of the oblique derivative type we employ these notions in the stability analysis of semilinear problems some of the properties we derive are new even in the dirichlet or in the whole space cases as an application we show the validity of the hair trigger effect for the fisher kpp equation on general uniformly smooth domains

call by name call by value call by need and the linear lambda calculus abstract girard described two translations of intuitionistic logic into linear logic one where a b maps to a b and another where it maps to a b we detail the action of these translations on terms and show that the first corresponds to a call by name calculus while the second corresponds to call by value we further show that if the target of the translation is taken to be an affine calculus where controls contraction but weakening is allowed everywhere then the second translation corresponds to a call by need calculus as recently defined by ariola felleisen maraist odersky and wadler thus the different calling mechanisms can be explained in terms of logical translations bringing them into the scope of the curry howard isomorphism our results extend neatly to translations of extensions for recursion in the call by name and call by value calculi and in general to extensions for products and for the corresponding untyped systems