nonlinear elliptic equations with singular boundary conditions and stochastic control with state constraints hamiltoniens sousquadratiques conditions aux limites infinies et donnees d explosion hamiltoniens superquadratiques formulation viscosite des conditions aux limites le probleme ergodique commande stochastique optimale avec contraintes d etat

on the large time behavior of solutions of hamilton jacobi equations associated with nonlinear boundary conditions in this article we study the large time behavior of solutions of first order hamilton jacobi equations set in a bounded domain with nonlinear neumann boundary conditions including the case of dynamical boundary conditions we establish general convergence results for viscosity solutions of these cauchy neumann problems by using two fairly different methods the first one relies only on partial differential equations methods which provides results even when the hamiltonians are not convex and the second one is an optimal control dynamical system approach named the weak kam approach which requires the convexity of hamiltonians and gives formulas for asymptotic solutions based on aubry mather sets

perron s method for hamilton jacobi equations on considere l existence des solutions d equations aux derivees partielles non lineaires scalaires d ordre 1 f x u du 0 dans ou est un sous ensemble ouvert de r n f r r n r est continue u r est l inconnue

performance analysis of music type high resolution estimators for direction finding in correlated and coherent scenes an asymptotic analysis is presented of a class of high resolution estimators for resolving correlated and coherent plane waves in noise these estimators are in turn constructed from certain eigenvectors associated with spatially smoothed or unsmoothed covariance matrices generated from a uniform array the analysis is first carried out for the smoothed case and from this the conventional i e unsmoothed multiple signal classification music scheme follows as a special case independent of the total number of sources present in the scene the variance of the conventional music estimator along the true arrival angles is shown to be zero within a first order approximation the bias expressions in the smoothed case are used to obtain a resolution threshold for two coherent equipowered plane waves in white noise and the result is compared to the one derived by kaveh et al 1986 for two uncorrelated equipowered plane waves

continuum theory of epitaxial crystal growth i we present various continuum limits to describe epitaxial thin film growth we consider a hierarchy of models which can take into account the diffusion of terrace adatoms attachment and detachment of edge adatoms vapor phase diffusion and the effect of multiple species the starting point is the burton cabrera frank type step flow model we have obtained partial differential equations in the form of a coupled system of diffusion equation for the adatom density and a hamilton jacobi equation for the film height function this is supplemented with appropriate boundary conditions at the continuum level to describe the growth at the peaks and valleys on the film the results here can be used in a macroscopic description of thin film growth

forward backward spatial smoothing techniques for coherent signal identification a spatial smoothing scheme is further investigated in the context of coherent signal classification it is shown that by making use of a set of forward and complex conjugated backward subarrays simultaneously it is always possible to estimate any k directions of arrival using at most 3k 2 sensor elements this is achieved by creating a smoothed array output covariance matrix that is structurally identical to a covariance matrix in some noncoherent situation by incorporating eigenstructure based techniques on this smoothed covariance matrix it then becomes possible to correctly identify all directions of arrival irrespective of their correlation

large time asymptotics for one dimensional dirichlet problems for hamilton jacobi equations with noncoercive hamiltonians we study large time asymptotics for a class of noncoercive hamilton jacobi equations with dirichlet boundary condition in one space dimension we prove that the average growth rate of a solution is constant only in a subset of the whole domain and give the asymptotic profile in the subset we show that the large time behavior for noncoercive problems may depend on the space variable in general which is different from the usual results under the coercivity condition this work is an extension with more rigorous analysis of a recent paper by e yokoyama y giga and p rybka in which a growing crystal model is established and the asymptotic behavior described above is first discovered

source enumeration via mdl criterion based on linear shrinkage estimation of noise subspace covariance matrix numerous methodologies have been investigated for source enumeration in sample starving environments for those having their root in the framework of random matrix theory the involved distribution of the sample eigenvalues is required instead of relying on the eigenvalue distribution this work devises a linear shrinkage based minimum description length ls mdl criterion by utilizing the identity covariance matrix structure of noise subspace components with linear shrinkage and gaussian assumption of the observations an accurate estimator for the covariance matrix of the noise subspace components is derived the eigenvalues obtained from the estimator turn out to be a linear function of the corresponding sample eigenvalues enabling the ls mdl criterion to accurately detect the source number without incurring significantly additional computational load furthermore the strong consistency of the ls mdl criterion for m n and m n c 0 is proved where m and n are the antenna number and snapshot number respectively simulation results are included for illustrating the effectiveness of the proposed criterion

global renaming operators in concrete process algebra renaming operators are introduced in concrete process algebra concrete means that abstraction and silent moves are not considered examples of renaming operators are given encapsulation pre abstraction and localization we show that renamings enhance the defining power of concrete process algebra by using the example of a queue we give a definition of the trace set of a process see when equality of trace sets implies equality of processes and use trace sets to define the restriction of a process finally we describe processes with actions that have a side effect on a state space and show how to use this for a translation of computer programs into process algebra

on cell problems for hamilton jacobi equations with non coercive hamiltonians and their application to homogenization problems abstract we study a cell problem arising in homogenization for a hamilton jacobi equation whose hamiltonian is not coercive we introduce a generalized notion of effective hamiltonians by approximating the equation and characterize the solvability of the cell problem in terms of the generalized effective hamiltonian under some sufficient conditions the result is applied to the associated homogenization problem we also show that homogenization for non coercive equations fails in general

performance analysis of esprit and tam in determining the direction of arrival of plane waves in noise the authors evaluate two subspace based methods esprit and the toplitz approximation method tam for estimating the direction of arrival doa of plane waves in white noise in the case of linear equispaced sensor array it is shown that the least squares versions of esprit and tam result in the same estimate and are statistically equivalent it is also shown that asymptotically the estimates obtained using least squares esprit and total least squares esprit have the same mean squared error expressions for the asymptotic mean squared error in the estimates of the doa are derived for both methods simple closed form expressions are derived for the one and two source cases to get further insight computer simulation results are provided to substantiate the analysis

stochastic homogenization of interfaces moving with changing sign velocity abstract we are interested in the averaging behavior of interfaces moving in stationary ergodic environments with oscillatory normal velocity which changes sign the problem can be reformulated as the homogenization of a hamilton jacobi equation with a positively homogeneous of degree one non coercive hamiltonian the periodic setting was studied earlier by cardaliaguet lions and souganidis 2009 16 here we concentrate in the random media and show that the solutions of the oscillatory hamilton jacobi equation converge in l weak to a linear combination of the initial datum and the solutions of several initial value problems with deterministic effective hamiltonian s determined by the properties of the random media

hamilton jacobi equations with state constraints in the present paper we consider hamilton jacobi equations of the form h x u vu 0 x e q where q is a bounded open subset of rn h is a given continuous real valued function of x s p e q x r x rn and vu is the gradient of the unknown function u we are interested in particular solutions of the above equation which are required to be supersolutions in a suitable weak sense of the same equation up to the boundary of q this requirement plays the role of a boundary condition the main motivation for this kind of solution comes from deterministic optimal control and differential games problems with constraints on the state of the system as well from related questions in constrained geodesics

large time behavior of solutions of hamilton jacobi equations with periodic boundary data abstract we study the large time behavior of viscosity solutions of hamilton jacobi equations with periodic boundary data on bounded domains we establish a result on convergence of viscosity solutions to state constraint asymptotic solutions or periodic asymptotic solutions depending on the sign of critical value as time goes to infinity

neumann type boundary conditions for hamilton jacobi equations abstract in this paper we present a notion of viscosity solutions of hamilton jacobi equations for neumann type boundary conditions or more generally oblique derivative in particular we prove the existence uniqueness stability of such solutions and we show that the vanishing viscosity method yields such solutions next we check that value functions of control problems or differential games problems for reflected dynamical processes are solutions in that sense of the associated bellman or isaacs equations finally we consider the ergodic problems

process algebra with language matching abstract an axiom system acp lm is presented as a variant of the process algebra acp the acronym acp lm stands for acp with abstraction extended with operators and axioms for language matching language matching is a technique based on trace information for labelling and cutting off process terms that do not match some given language or set of traces it is shown that in combination with the axioms for action alphabets interesting results are derivable the most important of which is the redundancy theorem 3 3 6 which roughly states that if no trace labels occur in the expression h pl q where pl is a labelled version of some process p then it holds that h pl q h p q it is shown that under certain natural conditions a similar result holds when abstraction is applied to pl and p in order to illustrate the use of language matching the concurrent alternating bit protocol cabp is verified the cabp is a simple communication protocol which can be recursively specified over the signature of acp and it may be regarded as a slightly more sophisticated variant of the well known alternating bit protocol earlier studies of this protocol have already demonstrated that redundancies in a context make this protocol hard to verify our verification is carried out by means of acp with language matching extended with the abstraction rule cfar itb and the conditional alphabet axioms the verification is split into two parts so that it is modular and in the verification some basic knowledge about the expected behaviour of the system is used in order to allow the effective application of language matching

optimal control with state space constraint i optimal control of piecewise deterministic processes with state space constraint is studied under appropriate assumptions it is shown that the optimal value function is the only viscosity solution on the open domain which is also a supersolution on the closed domain finally the uniform continuity of the value function is obtained under a condition on the deterministic drift

r dimensional esprit type algorithms for strictly second order non circular sources and their performance analysis high resolution parameter estimation algorithms designed to exploit the prior knowledge about incident signals from strictly second order so noncircular nc sources allow for a lower estimation error and can resolve twice as many sources in this paper we derive the r mathchar 702dd nc standard esprit and the r mathchar 702dd nc unitary esprit algorithms that provide a significantly better performance compared to their original versions for arbitrary source signals they are applicable to shift invariant r mathchar 702dd antenna arrays and do not require a centro symmetric array structure moreover we present a first order asymptotic performance analysis of the proposed algorithms which is based on the error in the signal subspace estimate arising from the noise perturbation the derived expressions for the resulting parameter estimation error are explicit in the noise realizations and asymptotic in the effective signal to noise ratio snr i e the results become exact for either high snrs or a large sample size we also provide mean squared error mse expressions where only the assumptions of a zero mean and finite so moments of the noise are required but no assumptions about its statistics are necessary as a main result we analytically prove that the asymptotic performance of both r mathchar 702dd nc esprit type algorithms is identical in the high effective snr regime finally a case study shows that no improvement from strictly non circular sources can be achieved in the special case of a single source

modular specification of process algebras abstract this paper proposes a modular approach to the algebraic specification of process algebras this is done by means of the notion of a module the simplest modules are building blocks of operators and axioms each block describing a feature of concurrency in a certain semantical setting these modules can then be combined by means of a union operator an export operator allowing to forget some operators in a module an operator h changing semantics by taking homomorphic images and an operator s which takes subalgebras these operators enable us to combine modules in a subtle way when the direct combination would be inconsistent we give a presentation of equational logic infinitary conditional equational logic of which we also prove the completeness and first order logic and show how the notion of a formal proof of a formula from a theory can be generalized to that of a proof of a formula from a module this module logic is then applied in process algebra we show how auxiliary process algebra operators can be hidden when this is needed moreover we demonstrate how new process combinators can be defined in terms of more elementary ones in a clean way as an illutration of our approach we specify some fifo queues and verify several of their properties

branching time and abstraction in bisimulation semantics in comparative concurrency semantics one usually distinguishes between linear time and branching time semantic equivalences milner s notion of observatin equivalence is often mentioned as the standard example of a branching time equivalence in this paper we investigate whether observation equivalence really does respect the branching structure of processes and find that in the presence of the unobservable action of ccs this is not the case therefore the notion of branching bisimulation equivalence is introduced which strongly preserves the branching structure of processes in the sense that it preserves computations together with the potentials in all intermediate states that are passed through even if silent moves are involved on closed ccs terms branching bisimulation congruence can be completely axiomatized by the single axion scheme a y z y a y z where a ranges over all actions and the usual loaws for strong congruence we also establish that for sequential processes observation equivalence is not preserved under refinement of actions whereas branching bisimulation is for a large class of processes it turns out that branching bisimulation and observation equivalence are the same as far as we know all protocols that have been verified in the setting of observation equivalence happen to fit in this class and hence are also valid in the stronger setting of branching bisimulation equivalence

a microscopic time scale approximation to the behavior of the local slope on the faceted surface under a nonuniformity in supersaturation abstract the morphological stability of a growing faceted crystal is discussed we argue that the interplay between nonuniformity in supersaturation on a growing facet and anisotropy of surface kinetics derived from the lateral motion of steps leads to a faceted instability qualitatively speaking as long as the nonuniformity in supersaturation on the facet is not too large it can be compensated for by a variation of step density along the facet and the faceted crystal can grow in a stable manner the problem can be modeled as a hamilton jacobi equation for height of the crystal surface the notion of a maximal stable region of a growing facet is introduced for microscopic time scale approximation of the original hamilton jacobi equation it is shown that the maximal stable region keeps its shape determined by profile of the surface supersaturation with constant growth rate by studying large time behavior of solution of macroscopic time scale approximation a quantitative criterion for the facet stability is given

long time behavior of solutions of hamilton jacobi equations with convex and coercive hamiltonians we investigate the long time behavior of viscosity solutions of hamilton jacobi equations in mathbb r n with convex and coercive hamiltonians and give three general criteria for the convergence of solutions to asymptotic solutions as time goes to infinity we apply the criteria to obtain more specific sufficient conditions for the convergence to asymptotic solutions and then examine them with examples we take a dynamical approach based on tools from weak kam theory such as extremal curves aubry sets and representation formulas for solutions for these investigations

analytical performance assessment of multi dimensional matrix and tensor based esprit type algorithms in this paper we present a generic framework for the asymptotic performance analysis of subspace based parameter estimation schemes it is based on earlier results on an explicit first order expansion of the estimation error in the signal subspace obtained via an svd of the noisy observation matrix we extend these results in a number of aspects firstly we demonstrate that an explicit first order expansion of the higher order svd hosvd based subspace estimate can be derived secondly we show how to obtain explicit first order expansions of the estimation error of arbitrary esprit type algorithms and provide the expressions for r d standard esprit r d unitary esprit r d standard tensor esprit as well as r d unitary tensor esprit thirdly we derive closed form expressions for the mean square error mse and show that they only depend on the second order moments of the noise hence to apply this framework we only need the noise to be zero mean and possess finite second order moments additional assumptions such as gaussianity or circular symmetry are not needed