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

algebras polynomial and programs abstract this paper presents an introduction to some of the more algebraic applications of elementary category theory in computer science topics include a category based look at universal algebra the definition of polynomials over arbitrary algebras and their application to the study of substitution a development of lawvere algebraic theories based on polynomials and the application of such theories to algebra and to the study of iteration and recursion in programming languages

mixed quasi variational inequalities in this paper we use the resolvent operator and auxiliary principle techniques to suggest and analyze several iterative algorithms for solving mixed quasi variational inequalities and related problems we study the convergence criteria of these algorithms under mild conditions we also study the global stability and existence of a unique solution of these quasi variational inequalities by using the dynamical systems approach our results represent refinement and improvement of the previously known results for variational inequalities

dissipative boundary conditions for 2 2 hyperbolic systems of conservation laws for entropy solutions in bv in this article we investigate the bv stability of 2 2 hyperbolic systems of conservation laws with strictly positive velocities under dissipative boundary conditions more precisely we derive sufficient conditions guaranteeing the exponential stability of the system under consideration for entropy solutions in bv our proof is based on a front tracking algorithm used to construct approximate piecewise constants solutions whose bv norms are controlled through a lyapunov functional this lyapunov functional is inspired by the one proposed in j glimm s seminal work j glimm comm pure appl math 18 697 715 1965 modified with some suitable weights in the spirit of the previous works j m coron g bastin and b d andrea novel siam j control optim 47 3 1460 1498 2008 and j m coron b d andrea novel and g bastin ieee trans automat control 52 1 2 11 2007

on the controllability of the non isentropic 1 d euler equation in this paper we examine the question of the boundary controllability of the one dimensional non isentropic euler equation for compressible polytropic gas in the context of weak entropy solutions we consider the system in eulerian coordinates and the one in lagrangian coordinates we obtain for both systems a result of controllability toward constant states with the limitation gamma frac 5 3 on the adiabatic constant for the lagrangian system the solutions that we obtain remain of small total variation in space if the initial condition is itself of sufficiently small total variation

optimal control of cell mass and maturity in a model of follicular ovulation in this paper we study optimal control problems associated with a scalar hyperbolic conservation law modeling the development of ovarian follicles changes in the age and maturity of follicular cells are described by a two dimensional conservation law where the control terms act on the velocities the control problem consists in optimizing the follicular cell resources so that the follicular maturity reaches a maximal value in fixed time formulating the optimal control problem within a hybrid framework we prove necessary optimality conditions in the form of the hybrid maximum principle then we derive the optimal strategy and show that there exists at least one optimal bang bang control with one single switching time

generalized mixed quasi variational like inequalities in this paper we use the auxiliary principle technique to suggest and analyze some iterative methods for solving generalized mixed quasi variational like inequalities we show that the convergence of the proposed method requires either pseudomonotonicity or partially relaxed strongly monotonicity under some mild condition as special cases one can obtain a number of new and known algorithms for solving variational inequalities and complementarity problems our results represent significant and important refinements of the previously known results

on the boundary controllability of first order hyperbolic systems abstract we discuss some results concerning the boundary controllability and stabilizability of a hyperbolic system of conservation laws u t f u x 0 t 0 x 0 1 where we regard the boundary data or a partial number of their components as boundary input controls in particular we consider the problem of the global exact boundary controllability of a first order linear hyperbolic system with constant coefficients relative to the linear boundary conditions under generic orthogonality assumptions on the boundary and control matrices and assuming a non resonance condition of the characteristic speeds we show that one can steer in finite time the solution from any initial condition l 1 to any terminal state l 1 even in the case where only a partial control of the boundary values is available

readies and failures in the algebra of communicating processes readiness and failure semantics are studied in the setting of algebra of communicating processes acp a model of process graphs modulo readiness equivalence respectively failure equivalence is constructed and an equational axiom system is presented which is complete for this graph model an explicit representation of the graph model is given the failure model whose elements are failure sets furthermore a characterisation of failure equivalence is obtained as the maximal congruence which is consistent with trace semantics by suitably restricting the communication format in acp this result is shown to carry over to subsets of hoare s communicating sequential processes csp and milner s calculus of communicating systems ccs also the characterisation implies a full abstraction result for the failure model in the above we restrict ourselves to finite processes without tau steps at the end of the paper a comment is made on the situation for infinite processes with tau steps notably w

the complexity of computing the number of strings of given length in context free languages abstract computing the number of strings of given length contained in a language is related to classical problems of combinatorics formal languages and computational complexity here we study the complexity of this problem in the case of context free languages it is shown that for unambiguous context free languages such a computation is easy and can be carried out by efficient parallel algorithms on the contrary for some context free languages of ambiguity degree two the problem becomes intractable these results are related to other classical subjects concerning counting problems exponential time recognizable languages and sparse sets

continuous dependence for 2 2 conservation laws with boundary on the domain 0 t x r t 0 and x 9 t for some boundary profile 9 r r as usual 1 1 is assumed to be strictly hyperbolic and with each characteristic field either linearly degenerate or genuinely non linear an initial data u 0 x u x having sufficiently small total variation is given we consider two different kinds of boundary conditions along x 9 t and in both cases we construct a lipschitzean flow whose trajectories are solutions of an initial boundary value problem for 1 1 thus we prove the continuous dependence of the solution upon the initial data upon the boundary condition and upon the boundary profile the existence theory for global bv solutions to the cauchy problem for 1 1 goes back to the fundamental paper 15 by glimm more recently in 6 a new approach has been introduced it relies on the construction of a lipschitzean semigroup the standard riemann semigroup srs whose trajectories extend the local standard lax 17 solutions of riemann problems at present such a srs has been constructed in the 2 2 case in 8 9 while for the general n n case see 7 10 and 3 in article no de973274

co coercivity and its role in the convergence of iterative schemes for solving variational inequalities this paper stresses the role of co coercivity and related notions in the convergence of iterative schemes for solving monotone but not necessarily strongly or even strictly monotone variational inequalities the analysis will be conducted within the conceptual framework of the auxiliary problem principle

hemiequilibrium like problems abstract in this paper we introduce and consider a new class of equilibrium problems known as hemiequilibrium like problems this new class includes hemiequilibrium equilibrium like problems and several classes of variational inequalities as special cases a number of iterative methods for solving hemiequilibrium like problems are suggested and analyzed by using the auxiliary principle technique we also study the convergence analysis of these iterative methods under some mild conditions the results obtained in this paper can be considered as a novel application of the auxiliary principle technique

implicit dynamical systems and quasi variational inequalities in this paper we propose and analyze some implicit projected dynamical systems associated with quasi variational inequalities by using the techniques of the projection and the wiener hopf equations we prove that the globally asymptotic stability of these dynamical systems requires only the pseudomonotonicity of the operator which is a weaker condition than monotonicity we also discuss some special cases which can be obtained from our main results the results obtained in this paper represent a significant improvement of the previously known results

hemivariational like inequalities in this paper we introduce and consider a new class of variational inequalities known as the hemivariational like inequalities it is shown that the hemivariational like inequalities include hemivariational inequalities variational like inequalities and the classical variational inequalities as special cases the auxiliary principle is used to suggest and analyze some iterative methods for solving hemivariational like inequalities under mild conditions the results obtained in this paper can be considered as a novel application of the auxiliary principle technique

exact boundary observability for a kind of second order quasilinear hyperbolic system abstract in this paper by means of a constructive method based on the existence and uniqueness of the semi global classical solution we establish the local exact boundary observability for a kind of second order quasilinear hyperbolic system in which the number of positive eigenvalues and the number of negative ones are not equal as an application we obtain the one sided local exact boundary observability and two sided local exact boundary observability with fewer observed values for first order quasilinear hyperbolic systems of diagonal form with boundary conditions in which the diagonal variables corresponding to the positive eigenvalues and those corresponding to the negative ones are decoupled

backstepping boundary control for first order hyperbolic pdes and application to systems with actuator and sensor delays abstract we consider a problem of boundary feedback stabilization of first order hyperbolic partial differential equations pdes these equations serve as a model for physical phenomena such as traffic flows chemical reactors and heat exchangers we design controllers using a backstepping method which has been recently developed for parabolic pdes with the integral transformation and boundary feedback the unstable pde is converted into a delay line system which converges to zero in finite time we then apply this procedure to finite dimensional systems with actuator and sensor delays to recover a well known infinite dimensional controller analog of the smith predictor for unstable plants we also show that the proposed method can be used for the boundary control of a korteweg de vries like third order pde the designs are illustrated with simulations

implicit resolvent dynamical systems for quasi variational inclusions in this paper we suggest and analyze a class of implicit resolvent dynamical systems for quasi variational inclusions by using the resolvent operator technique we show that the trajectory of the solution of the implicit dynamical system converges globally exponentially to the unique solution of the quasi variational inclusions our results can be considered as a significant extension of the previously known results

a complex analytic approach to the problem of uniform controllability of a transport equation in the vanishing viscosity limit abstract we revisit a result by coron and guerrero stating that the one dimensional transport diffusion equation u t m u x e u x x 0 in 0 t 0 l controlled by the left dirichlet boundary value is zero controllable at a bounded cost as e 0 when t 4 3 l m if m 0 and when t 57 2 l m if m 0 by a completely different method relying on complex analysis we prove that this still holds when t 4 2 l m if m 0 and when t 6 1 l m if m 0

on the attainable set for temple class systems with boundary controls consider the initial boundary value problem for a strictly hyperbolic genuinely nonlinear temple class system of conservation laws begin equation label eq 1 u t f u x 0 qquad u 0 x ov u x qquad left begin array ll u t a widetilde u a t 2pt u t b widetilde u b t end array right end equation on the domain omega t x in r 2 t geq 0 a le x leq b we study the mixed problem ref eq 1 from the point of view of control theory taking the initial data overline u fixed and regarding the boundary data widetilde u a widetilde u b as control functions that vary in prescribed sets u a u b of li boundary controls in particular we consider the family of configurations a t doteq u t cdot u mbox is a sol to ref eq 1 widetilde u a in u a widetilde u b in u b that can be attained by the system at a given time t 0 and we give a description of the attainable set a t in terms of suitable oleinik type conditions we also establish closure and compactness of the set a t in the lu topology

full abstraction and recursion the question of extending semantic models for a programming language without recursion to a larger language supporting recursion is of fundamental importance if one wants to develop a modular approach to building models in our previous work 14 we showed how to extend models for a language without recursion to models for a language in which unnested recursion was supported via simultaneous systems of recursive equations in that setting we proved that modest assumptions about the models enabled us to lift adequacy and full abstraction for the models of the base language to analogous results for the models of the extended language in this paper we tackle similar problems for languages with explicit recursion operators starting with a base language l we define what it means for an ordered denotational model for l to be order adequate and strongly order fully abstract with respect to an ordered operational model for l by freely adding identifiers x x and recursion operators x for each x x we obtain an extended language l x in which we single out the sublanguage l c of closed terms we then give general conditions which ensure that an ordered operational model o l o and a related order adequate and strongly order fully abstract denotational model d l d can be extended to an ordered operational model o c l c o and a related ordered denotational model d c l c d which also is order adequate and strongly order fully abstract

penalty techniques for state constrained optimal control problems with the wave equation we consider a system that is governed by a pde of hyperbolic type namely the wave equation and is controlled by a dirichlet boundary control for the penalization of terminal constraints we compare the convergence of three penalization techniques a differentiable penalty method an exact penalization and a smoothed exact penalization the error of the solution of the differentiably penalized problem is at most of the order 1 sqrt gamma where gamma is the penalty parameter the exact penalization yields the exact solution if gamma is sufficiently large if gamma is sufficiently large for the smoothed exact penalization we obtain an error bound of the order 1 sqrt beta where beta is the additional smoothing parameter this method yields differentiable objective functions that remain uniformly strongly convex since gamma need not tend to infinity to obtain convergence we also consider the penalization of distributed inequality state constraints that prescribe an upper bound for the l infty norm of the state we prove the convergence with respect to the l 2 norm for a penalization of the constraint violation measured in the l 1 norm we use this penalization technique to prove the existence of optimal controls for the inequality state constrained problem

exact controllability of scalar conservation laws with an additional control in the context of entropy solutions in this paper we study the exact controllability problem for nonlinear scalar conservation laws on a compact interval with a regular convex flux and in the framework of entropy solutions with the boundary data and a source term depending only on the time as controls we provide sufficient conditions for a state to be reachable in arbitrary small time to do so we introduce a slightly modified wave front tracking algorithm

non well founded sets modeled as ideal fixed points abstract motivated by ideas from the study of abstract data types we show how to interpret non well founded sets as fixed points of continuous transformations of an initial continuous algebra we conisder a preordered structure closely related to the set hf of well founded hereditarily finite sets by taking its ideal completion we obtain an initial continuous algebra in which we are able to solve all of the usual systems of equations that characterize hereditarily finite non well founded sets in this way we are able to obtain a structure which is isomorphic to hf 1 the non well founded analog of hf

some new projection methods for variational inequalities in this paper we propose some new double projection methods for solving variational inequalities by using the wiener hopf equations technique it is shown that these methods converge linearly under mild conditions and include some existing projection methods as special cases some examples are given to illustrate the efficiency of the proposed methods

exact boundary controllability for quasi linear hyperbolic systems using a result on the existence and uniqueness of the semiglobal c1 solution to the mixed initial boundary value problem for first order quasi linear hyperbolic systems with general nonlinear boundary conditions we establish the exact boundary controllability for quasi linear hyperbolic systems if the c1 norm of initial and final states is small enough

some aspects of variational inequalities abstract in this paper we provide an account of some of the fundamental aspects of variational inequalities with major emphasis on the theory of existence uniqueness computational properties various generalizations sensitivity analysis and their applications we also propose some open problems with sufficient information and references so that someone may attempt solution s in his her area of special interest we also include some new results which we have recently obtained

on a class of variational inequalities in this paper we introduce and study a new unified and general class of variational inequalities we derive the general error estimates for the finite element solutions of variational inequalities it has been shown that a class of contact problems with friction terms arising in elastostatics can be studied in the framework of variational inequalities several special cases which can be obtained from the general results are also discussed

time varying riemann solvers for conservation laws on networks abstract we consider a conservation law on a network and generic riemann solvers at nodes depending on parameters which can be seen as control functions assuming that the parameters have bounded variation as functions of time we prove existence of solutions to cauchy problems on the whole network

new extragradient type methods for general variational inequalities in this paper we consider and analyze a new class of extragradient type methods for solving general variational inequalities the modified methods converge for pseudomonotone operators which is weaker condition than monotonicity our proof of convergence is very simple as compared with other methods the proposed methods include several new and known methods as special cases our results present a significant improvement of previously known methods for solving variational inequalities and related optimization problems

on the boundary control of systems of conservation laws this paper is concerned with the boundary controllability of entropy weak solutions to hyperbolic systems of conservation laws we prove a general result on the asymptotic stabilization of a system near a constant state on the other hand we give an example showing that exact controllability in finite time cannot be achieved in general

a class of projection methods for general variational inequalities abstract in this paper we consider and analyze a new class of projection methods for solving pseudomonotone general variational inequalities using the wiener hopf equations technique the modified methods converge for pseudomonotone operators our proof of convergence is very simple as compared with other methods the proposed methods include several known methods as special cases

on the attainable set for scalar nonlinear conservation laws with boundary control we consider the initial value problem with boundary control for a scalar nonlinear conservation law begin equation u t f u x 0 qquad qquad u 0 x 0 qquad u cdot 0 tilde u in cal u tag ast end equation on the domain omega t x in real 2 t geq 0 x geq 0 here u u t x is the state variable cal u is a set of bounded boundary data regarded as controls and f is assumed to be strictly convex we give a characterization of the set of attainable profiles at a fixed time t 0 and at a fixed point bar x 0 begin equation begin aligned rag u t cdot u hbox is a solution of ast ragx u cdot bar x u hbox is a solution of ast end aligned qquad quad cal u ellein bbb r end equation moreover we prove that rag and ragx are compact subsets of elleuno and elleuno loc respectively whenever cal u is a set of controls which pointwise satisfy closed convex constraints together with some additional integral inequalities

regularity and lyapunov stabilization of weak entropy solutions to scalar conservation laws we consider the problem of lyapunov boundary stabilization of the weak entropy solution to a scalar conservation law with strictly convex flux in one dimension of space around a uniform equilibrium we show that for a specific class of boundary conditions the solution to the initial boundary value problem for an initial condition with bounded variations can be approximated arbitrarily closely in the l 1 norm by a piecewise smooth solution with finitely many discontinuities the constructive method we present designs explicit boundary conditions in this class which guarantee lyapunov stability of the weak entropy solution to the initial boundary value problem we show how the greedy control obtained by maximizing the decrease of the natural lyapunov function may fail to asymptotically stabilize and a brute force control generates unbounded variation of traces we then design a stabilizing control which avoid oscillations and propose a nonlocal technique depending on time and the whole initial datum which optimizes the convergence time controllers performance is illustrated on numerical benchmarks using the godunov scheme