countable nondeterminism and random assignment four semantics for a small programming language involving unbounded but countable nondeterminism are provided these comprise an operational semantics two state transformation semantics based on the egli milner and smyth orders respectively and a weakest precondition semantics their equivalence is proved a hoare like proof system for total correctness is also introduced and its soundness and completeness in an appropriate sense are shown finally the recursion theoretic complexity of the notions introduced is studied admission of countable nondeterminism results in a lack of continuity of various semantic functions and this is shown to be necessary for any semantics satisfying appropriate conditions in proofs of total correctness one resorts to the use of countable ordinals and it is shown that all recursive ordinals are needed

strichartz estimates for the wave and schrodinger equations with the inverse square potential abstract we prove spacetime weighted l 2 estimates for the schrodinger and wave equation with an inverse square potential we then deduce strichartz estimates for these equations

transition system specifications with negative premises abstract in this article the general approach to plotkin style operational semantics of groote and vaandrager 1989 is extended to transition system specifications tsss with rules that may contain negative premises two problems arise firstly the rules may be inconsistent and secondly it is not obvious how a tss determines a transition relation we present a general method based on the stratification technique in logic programming to prove consistency of a set of rules and we show how a specific transition relation can be associated with a tss in a natural way then a special format for the rules the ntyft ntyxt format is defined it is shown that for this format three important theorems hold the first theorem says that bisimulation is a congruence if all operators are defined using this format the second theorem states that under certain restrictions a tss in ntyft format can be added conservatively to a tss in pure ntyft ntyxt format finally it is shown that the trace congruence for image finite processes induced by the pure ntyft ntyxt format is precisely bisimulation equivalence

ordered sos process languages for branching and eager bisimulation we present a general and uniform method for defining structural operational semantics sos of process operators by traditional plotkin style transition rules equipped with orderings this new feature allows one to control the order of application of rules when deriving transitions of process terms our method is powerful enough to deal with rules with negative premises and copying we show that rules with orderings called ordered sos rules have the same expressive power as gsos rules we identify several classes of process languages with operators defined by rules with and without orderings in the setting with silent actions and divergence we prove that branching bisimulation and eager bisimulation relations are preserved by all operators in process languages in the relevant classes

strichartz estimates for the schrodinger equation with time periodic ln 2 potentials abstract we prove strichartz estimates for the schrodinger operator h v t x with time periodic complex potentials v belonging to the scaling critical space l x n 2 l t in dimensions n 3 this is done directly from estimates on the resolvent rather than using dispersive bounds as the latter generally require a stronger regularity condition than what is stated above in typical fashion we project onto the continuous spectrum of the operator and must assume an absence of resonances eigenvalues are permissible at any location in the spectrum including at threshold energies provided that the associated eigenfunction decays sufficiently rapidly

the uncertainty principle on considere l existence et la regularite des solutions d equations aux derivees partielles la construction de solutions fondamentales explicites et les valeurs propres d operateurs de schrodinger

structural operational semantics for weak bisimulations in this study we present rule formats for four main notions of bisimulation with silent moves weak bisimulation is a congruence for any process algebra defined by wb cool rules we have similar results for rooted weak bisimulation milner s observational equivalence branching bisimulation and rooted branching bisimulation the theorems stating that say observational equivalence is an appropriate notion of equality for ccs are corollaries of the results of this paper we also give sufficient conditions under which equational axiom systems can be generated from operational rules indeed many equational axiom systems appearing in the literature are instances of this general theory

on guarded recursion abstract we introduce a logical notion of well guardedness for recursive terms on arbitrary signatures defined in plotkin s framework of structural operational specifications restricted by se simone s realizability requirements we then suggest a simpler form for the logical rule that gives the behaviour of a recursively defined expression in terms of the behaviour of its unfoldings for well guarded terms the simplified rule is logically equivalent to the general rule but it does not have the drawback of asking for premises more complex than consequences

non trapping magnetic fields and morrey campanato estimates for schrodinger operators abstract we prove some uniform in a priori estimates for solutions of the equation i a 2 u v x u i u f 0 0 the estimates are obtained in terms of morrey campanato norms and can be used to prove absence of zero resonances in a suitable sense for electromagnetic hamiltonians quantitative conditions on the size of the trapping component of the magnetic field and the non repulsive component of the electric field are given

bisimulation can t be traced in the concurrent language ccs two programs are considered the same if they are bisimilar several years and many researchers have demonstrated that the theory of bisimulation is mathematically appealing and useful in practice however bisimulation makes too many distinctions between programs we consider the problem of adding operations to ccs to make bisimulation fully abstract we define the class of gsos operations generalizing the style and technical advantages of ccs operations we characterize gsos congruence in as a bisimulation like relation called ready simulation bisimulation is strictly finer than ready simulation and hence not a congruence for any gsos language

tile formats for located and mobile systems abstract standard sos formats are limited in their ability to define the operational semantics of process calculi with concurrency causality and mobility and with bound names and name generation mechanisms in this paper we describe a general approach based on the tile model to the definition of the operational semantics of process calculi by providing tile systems for located ccs and asynchronous calculus we demonstrate that the proposed approach is more suited than sos to provide a uniform treatment of concurrency and mobility within a compositional framework

the forward problem for the electromagnetic helmholtz equation with critical singularities abstract we study the forward problem of the magnetic schrodinger operator with potentials that have a strong singularity at the origin we obtain new resolvent estimates and give some applications on the spectral measure and on the solutions of the associated evolution problem

remarks on endpoint strichartz estimates for schrodinger equations with the critical inverse square potential abstract the purpose of this paper is to study the validity of global in time strichartz estimates for the schrodinger equation on r n n 3 with the negative inverse square potential x 2 in the critical case n 2 2 4 it turns out that the situation is different from the subcritical case n 2 2 4 in which the full range of strichartz estimates is known to be hold more precisely splitting the solution into the radial and non radial parts we show that i the radial part satisfies a weak type endpoint estimate which can be regarded as an extension to higher dimensions of the endpoint strichartz estimate with radial data for the two dimensional free schrodinger equation ii other endpoint estimates in lorentz spaces for the radial part fail in general iii the non radial part satisfies the full range of strichartz estimates

scattering theory for nonlinear schrodinger equations with inverse square potential abstract we study the long time behavior of solutions to nonlinear schrodinger equations with some critical rough potential of a x 2 type the new ingredients are the interaction morawetz type inequalities and sobolev norm property associated with p a a x 2 we use such properties to obtain the scattering theory for the defocusing energy subcritical nonlinear schrodinger equation with inverse square potential in energy space h 1 r n

gsos and finite labelled transition systems recently there has been considerable interest in studying formats of plotkin style inference rules which ensure that the induced labelled transition system semantics have certain properties in this note i shall give a contribution to this line of research by giving a restricted version of bloom istrail and meyer s gsos format bloom et al 1988 bloom 1989 which induces finite labelled transition systems

endpoint strichartz estimates we prove an abstract strichartz estimate which implies previously unknown endpoint strichartz estimates for the wave equation in dimension n 4 and the schrodinger equation in dimension n 3 three other applications are discussed local existence for a nonlinear wave equation and strichartz type estimates for more general dispersive equations and for the kinetic transport equation

testing equivalences for processes abstract given a set of processes and a set of tests on these processes we show how to define in a natural way three different equivalences on processes these equivalences are applied to a particular language ccs we give associated complete proof systems and fully abstract models these models have a simple representation in terms of trees

weighted calderon zygmund and rellich inequalities in l p we find necessary and sufficient conditions for the validity of weighted rellich and calderon zygmund inequalities with respect to l p norm 1 le p le infty for functions in the whole space and in the half space with dirichlet boundary conditions general operators like l vardelta c frac x x 2 cdot nabla frac b x 2 are considered we compute best constants in some situations

strichartz estimates for long range perturbations we study local in time strichartz estimates for the schroedinger equation associated to long range perturbations of the flat laplacian on the euclidean space we prove that in such a geometric situation outside of a large ball centered at the origin the solutions of the schroedinger equation enjoy the same strichartz estimates as in the non perturbed situation the proof is based on the isozaki kitada parametrix construction if in addition the metric is non trapping we prove that the strichartz estimates hold in the whole space

zero energy asymptotics of the resolvent for a class of slowly decaying potentials we prove a limiting absorption principle at zero energy for two body schrodinger operators with long range potentials having a positive virial at infinity more precisely we establish a complete asymptotic expansion of the resolvent in weighted spaces when the spectral parameter tends to zero in cones which are adjacent to the positive real axis the principal tools are absence of eigenvalue at zero singular mourre theory and microlocal estimates

endpoint strichartz estimates for the magnetic schrodinger equation abstract we prove strichartz estimates for the schrodinger equation with an electromagnetic potential in dimension n 3 the decay and regularity assumptions on the potentials are almost critical i e close to the coulomb case in addition we require repulsivity and a nontrapping condition which are expressed as smallness of suitable components of the potentials while the potentials themselves can be large the proof is based on smoothing estimates and new sobolev embeddings for spaces associated to magnetic potentials

a theory of communicating processes with value passing a semantic theory of process algebras which allows processes to communicate values is described a behavioural theory of testing is given for such processes and is modelled by an extension of acceptance trees a proof system is also given for this model and is shown to be both sound and complete finally the model is shown to be fully abstract with respect to the behavioural theory

cpo models for compact gsos languages in this paper we present a general way of giving denotational semantics to a class of languages equipped with an operational semantics that fits the gsos format of bloom istrail and meyer the canonical model used for this purpose will be abramsky s domain of synchronization trees and the denotational semantics automatically generated by our methods will be guaranteed to be fully abstract with respect to the finitely observable part of the bisimulation preorder in the process of establishing the full abstraction result we also obtain several general results on the bisimulation preorder including a complete axiomatization for it and give a novel operational interpretation of gsos languages

strichartz estimates and local smoothing estimates for asymptotically flat schrodinger equations abstract in this article we study global in time strichartz estimates for the schrodinger evolution corresponding to long range perturbations of the euclidean laplacian this is a natural continuation of a recent article d tataru parametrices and dispersive estimates for schrodinger operators with variable coefficients amer j math 130 2008 571 634 of the third author where it is proved that local smoothing estimates imply strichartz estimates by d tataru parametrices and dispersive estimates for schrodinger operators with variable coefficients amer j math 130 2008 571 634 the local smoothing estimates are known to hold for small perturbations of the laplacian here we consider the case of large perturbations in three increasingly favorable scenarios i without non trapping assumptions we prove estimates outside a compact set modulo a lower order spatially localized error term ii with non trapping assumptions we prove global estimates modulo a lower order spatially localized error term and iii for time independent operators with no resonance or eigenvalue at the bottom of the spectrum we prove global estimates for the projection onto the continuous spectrum

modal logics for communicating systems abstract simple modal logics for milner s sccs and ccs are presented we offer sound and complete axiomatizations of validity relative to these calculi as models also we present compositional proof systems for when a program satisfies a formula these involve proof rules which are like gentzen introduction rules except that there are also introduction rules for the program combinators of sccs and ccs the compositional rules for restriction or hiding and parallel combinators arise out of a simple semantic strategy

strichartz estimates via the schrodinger maximal operator we consider the schrodinger operator e it delta acting on initial data f in dot h s we show that an affirmative answer to a question of carleson concerning the sharp range of s for which lim t to 0 e it delta f x f x a e x in mathbb r n would imply an affirmative answer to a question of planchon concerning the sharp range of q and r for which e it delta is bounded in l x q mathbb r n l r t mathbb r when n 2 we unconditionally improve the range for which the mixed norm estimates hold

maximal functions associated to filtrations abstract let t be a bounded linear or sublinear operator from lp y to lq x a maximal operator t f x supj t f yj x is associated to any sequence of subsets yj of y under the hypotheses that q p and the sets yj are nested we prove that t is also bounded classical theorems of menshov and zygmund are obtained as corollaries multilinear generalizations of this theorem are also established these results are motivated by applications to the spectral analysis of schrodinger operators

bisimulation and divergence abstract behavioural preorders based on the idea of bisimulation but refining the notion of bisimulation equivalence and providing explicit treatments of the phenomenon of divergence in communicating systems are investigated particular study is made of these preorders in the context of milner s calculus of communicating systems the precongruence relations generated by the preorders are characterized and axiomatized on the classes of finite closed terms and sequential terms a verification technique based on the theory of the preorders is introduced and illustrated

morrey campanato estimates for helmholtz equations abstract we derive uniform weighted l 2 and morrey campanato type estimates for helmholtz equations in a medium with a variable index which is not necessarily constant at infinity our technique is based on a multiplier method with appropriate weights which generalize those of morawetz for the wave equation we also extend our method to the wave equation

effective limiting absorption principles and applications the limiting absorption principle asserts that if h is a suitable schrodinger operator and f lives in a suitable weighted l2 space namely h 0 1 2 sigma for some sigma 0 then the functions r lambda i varepsilon f h lambda i varepsilon 1 f converge in another weighted l2 space h 0 1 2 sigma to the unique solution u of the helmholtz equation h lambda u f which obeys the sommerfeld outgoing radiation condition in this paper we investigate more quantitative or effective versions of this principle for the schrodinger operator on asymptotically conic manifolds with short range potentials and in particular consider estimates of the form r lambda i varepsilon f h 0 1 2 sigma leq c lambda h f h 0 1 2 sigma we are particularly interested in the exact nature of the dependence of the constants c lambda h on both lambda and h it turns out that the answer to this question is quite subtle with distinctions being made between low energies lambda ll 1 medium energies lambda sim 1 and large energies lambda gg 1 and there is also a non trivial distinction between qualitative estimates on a single operator h possibly obeying some spectral condition such as non resonance or a geometric condition such as non trapping and quantitative estimates which hold uniformly for all operators h in a certain class using elementary methods integration by parts and ode techniques we give some sharp answers to these questions as applications of these estimates we present a global in time local smoothing estimate and pointwise decay estimates for the associated time dependent schrodinger equation as well as an integrated local energy decay estimate and pointwise decay estimates for solutions of the corresponding wave equation under some additional assumptions on the operator h

algebraic laws for nondeterminism and concurrency since a nondeterministic and concurrent program may in general communicate repeatedly with its environment its meaning cannot be presented naturally as an input output function as is often done in the denotational approach to semantics in this paper an alternative is put forth first a definition is given of what it is for two programs or program parts to be equivalent for all observers then two program parts are said to be observation congruent if they are in all program contexts equivalent the behavior of a program part that is its meaning is defined to be its observation congruence class the paper demonstrates for a sequence of simple languages expressing finite terminating behaviors that in each case observation congruence can be axiomatized algebraically moreover with the addition of recursion and another simple extension the algebraic language described here becomes a calculus for writing and specifying concurrent programs and for proving their properties

analytic and asymptotic analysis of bayesian cramer rao bound for dynamical phase offset estimation in this paper we present a closed form expression of a bayesian cramer rao lower bound for the estimation of a dynamical phase offset in a non data aided bpsk transmitting context this kind of bound is derived considering two different scenarios a first expression is obtained in an offline context and then a second expression in an online context logically follows the snr asymptotic expressions of this bound drive us to introduce a new asymptotic bound namely the asymptotic bayesian cramer rao bound this bound is close to the classical bayesian bound but is easier to evaluate

low energy asymptotics for schrodinger operators with slowly decreasing potentials low energy behavior of schrodinger operators with potentials which decay slowly at infinity is studied it is shown that if the potential is positive then the zero energy is very regular and the resolvent is smooth near 0 this implies rapid local decay for the solutions of the schrodinger equation on the other hand if the potential is negative then the resolvent has discontinuity at zero energy thus one cannot expect local decay faster than ordert 1 ast

calculi for synchrony and asynchrony abstract a calculus for distributed computation is studied based upon four combinators a central idea is an abelian group of actions which models the interfaces between components of a distributed computing agent using a notion of bisimulation congruence relations are defined over computing agents and thence an algebraic theory is derived the calculus models both synchronous and asynchronous computation in particular it is shown that the author s calculus of communicating systems 1980 which is an asynchronous model is derivable from the calculus presented here

turning sos rules into equations abstract many process algebras are defined by structural operational semantics sos indeed most such definitions are nicely structured and fit the gsos format of bloom et al j assoc comput mach to appear we give a procedure for converting any gsos language definition to a finite complete equational axiom system possibly with one infinitary induction principle which precisely characterizes strong bisimulation of processes

a format for semantic equivalence comparison this paper presents a new format for process algebras the extended tyft tyxt format which generalises the tyft tyxt format of groote and vaandrager the format differs from most previous formats in that the labels on transitions are treated as many sorted terms bisimulation is a congruence for all operators defined by extended transition system specifications in this format when one extended transition system specification is summed with another the resulting bisimulation can either identify more terms an abstracting extension up to bisimulation or fewer terms a refining extension up to bisimulation than the original bisimulation on the individual system the notions of abstracting extension and refining extension are defined and two theorems are presented giving conditions required for achieving each type of extension these results provide a way to compare different semantic equivalences defined for different process algebras finally an application of this theory to semantic equivalence comparison is given for a new result relating castellani s pomset equivalence and krishan s multiprocessor equivalence

time decay for solutions of schrodinger equations with rough and time dependent potentials in this paper we establish dispersive estimates for solutions to the linear schrodinger equation in three dimensions frac 1 i partial t psi triangle psi v psi 0 qquad psi s f 0 1 where v t x is a time dependent potential that satisfies the conditions sup t v t cdot l frac 3 2 mathbb r 3 sup x in mathbb r 3 int mathbb r 3 int infty infty frac v hat tau x x y d tau dy c 0 here c0 is some small constant and v hat tau x denotes the fourier transform with respect to the first variable we show that under these conditions 0 1 admits solutions l t l2x 3 l2t l6x 3 for any f l2 3 satisfying the dispersive inequality psi t infty le c t s frac32 f 1 text for all times t s 0 2 for the case of time independent potentials v x 0 2 remains true if int mathbb r 6 frac v x v y x y 2 dxdy 4 pi 2 text and v mathcal k sup x in mathbb r 3 int mathbb r 3 frac v y x y dy 4 pi we also establish the dispersive estimate with an e loss for large energies provided v mathcal k v 2 infty

termination deadlock and divergence in this paper a process algebra that incorporates explicit representations of successful termination deadlock and divergence is introduced and its semantic theory is analyzed both an operational and a denotational semantics for the language is given and it is shown that they agree the operational theory is based upon a suitable adaptation of the notion of bisimulation preorder the denotational semantics for the language is given in terms of the initial continuous algebra that satisfies a set of equations e ci e it is shown that ci e is fully abstract with respect to our choice of behavioral preorder several results of independent interest are obtained namely the finite approximability of the behavioral preorder and a partial completeness result for the set of equations e with respect to the preorder