a refined exact algorithm for edge dominating set in this paper we present a new exact algorithm for the edge dominating set problem and analyze its running time by the measure and conquer method our algorithm runs in 1 3160 n n o 1 time for a graph with n vertices which is the currently fastest known time for the edge dominating set problem by designing new branching rules based upon conceptually simple local structures which we call clique producing vertices and cycles we obtain an algorithm that is simpler than the previously fastest known algorithm and has an improved time bound as well

non uniform specification and large deviations for weak gibbs measures we establish bounds for the measure of deviation sets associated to continuous observables with respect to not necessarily invariant weak gibbs measures under some mild assumptions we obtain upper and lower bounds for the measure of deviation sets of some non uniformly expanding maps including quadratic maps and robust multidimensional non uniformly expanding local diffeomorphisms for that purpose a measure theoretical weak form of specification is introduced and proved to hold for the robust classes of multidimensional non uniformly expanding local diffeomorphisms and viana maps

non lacunary gibbs measures for certain fractal repellers in this paper we study non uniformly expanding repellers constructed as the limit sets for a non uniformly expanding dynamical systems we prove that given a holder continuous potential satisfying a summability condition there exists non lacunary gibbs measure for with positive lyapunov exponents and infinitely many hyperbolic times almost everywhere moreover this non lacunary gibbs measure is an equilibrium measure for

ergodic theory for markov fibred systems and parabolic rational maps a paraboiic rational map of the riemann sphere admits a non atomic h conformal measure on its julia set where h the hausdorff dimension of the julia set and satisfies 1 2 h 2 with respect to this measure the rational map is conservative exact and there is an equivalent a finite invariant measure finiteness of the measure is characterised central limit theorems are proved in the case of a finite invariant measure and return sequences are identified in the case of an infinite one a theory of markov fibred systems is developed and parabolic rational maps are considered within this framework

maps of intervals with indifferent fixed points thermodynamic formalism and phase transitions we develop the thermodynamic formalism for a large class of maps of the interval with indifferent fixed points for such systems the formalism yields onedimensional systems with many body infinite range interactions for which the thermodynamics is well defined but gibbs states are not piecewise linear systems of this kind yield the soluble in a sense fisher models we prove that such systems exhibit phase transitions the order of which depends on the behavior at the indifferent fixed points we obtain the critical exponent describing the singularity of the pressure and analyze the decay of correlations of the equilibrium states at all temperatures our technique relies on establishing and exploiting a relation between the transfer operators of the original map and its suitable expanding induced version the technique allows one also to obtain a version of the bowen ruelle formula for the hausdorff dimension of repellers for maps with indifferent fixed points and to generalize fisher results to some nonsoluble models

on the dimension of deterministic and random cantor like sets symbolic dynamics and the eckmann ruelle conjecture in this paper we unify and extend many of the known results on the dimension of deterministic and random cantor like sets in n and apply these results to study some problems in dynamical systems in particular we verify the eckmann ruelle conjecture for equilibrium measures for holder continuous conformal expanding maps and conformal axiom a topologically hyperbolic homeomorphims we also construct a holder continuous axiom a homeomorphism of positive topological entropy for which the unique measure of maximal entropy is ergodic and has different upper and lower pointwise dimensions almost everywhere this example shows that the non conformal holder continuous version of the eckmann ruelle conjecture is false

weighted analytic regularity in polyhedra we explain a simple strategy to establish analytic regularity for solutions of second order linear elliptic boundary value problems the abstract framework presented here helps to understand the proof of analytic regularity in polyhedral domains given in the authors paper in m costabel m dauge s nicaise analytic regularity for linear elliptic systems in polygons and polyhedra math models methods appl sci 22 8 2012 we illustrate this strategy by considering problems set in smooth domains in corner domains and in polyhedra

large deviations for countable to one markov systems in this paper we study large deviation properties for countable to one markov systems associated to weak gibbs measures for non holder potentials furthermore we establish multifractal large deviation laws for countable to one piecewise conformal markov systems which are derived systems constructed over hyperbolic regions for certain nonhyperbolic systems exhibiting intermittency we apply our results to higher dimensional number theoretical transformations

weak expansion properties and large deviation principles for expanding thurston maps abstract in this paper we prove that an expanding thurston map f s 2 s 2 is asymptotically h expansive if and only if it has no periodic critical points and that no expanding thurston map is h expansive as a consequence for each expanding thurston map without periodic critical points and each real valued continuous potential on s 2 there exists at least one equilibrium state for such maps we also establish large deviation principles for iterated preimages and periodic points it follows that iterated preimages and periodic points are equidistributed with respect to the unique equilibrium state for an expanding thurston map without periodic critical points and a potential that is holder continuous with respect to a visual metric on s 2

the h p version of the coupling of finite element and boundary element methods for transmission problems in polyhedral domains this paper analyzes the rate of convergence of the h p version of the coupling of the finite element and boundary element method for transmission problems with a linear differential operator with variable coefficients in a bounded polyhedral domain omega 1 and with constant coefficients in the exterior domain omega 2 bbb r 3 backslash overline omega 1 this procedure uses the variational formulation of the differential equation in omega 1 and involves integral operators on the interface between omega 1 and omega 2 the finite elements are used to obtain approximate solutions of the differential equation in omega 1 and the boundary elements are used to obtain approximate solutions of the integral equations for given piecewise analytic data we show that the galerkin solution of this coupling procedure converges exponentially fast in the energy norm if the h p version is used both for finite elements and boundary elements

general edge asymptotics of solutions of second order elliptic boundary value problems i this is the first of two papers in which we study the singularities of solutions of second order linear elliptic boundary value problems at the edges of piecewise analytic domains in 3 when the opening angle at the edge is variable there appears the phenomenon of crossing of the exponents of singularities for this case we introduce the appropriate combinations of the simple tensor product singularities that allow us to give estimates in ordinary and weighted sobolev spaces for the regular part of the solution and for the coefficients of the singularities these combinations appear in a natural way as sections of an analytic bundle above the edge their behaviour is described with the help of divided differences of powers of the distance to the edge the class of operators considered includes second order elliptic operators with analytic complex valued coefficients with mixed dirichlet neumann or oblique derivative conditions with our description of the singularities we are able to remove some restrictive hypotheses that were previously made in other works in this first part we prove the basic facts in a simplified framework nevertheless the tools we use are essentially the same in the general situation

regularity of the solutions for elliptic problems on nonsmooth domains in r3 part 2 regularity in neighborhoods of edges this paper is the second in a series of three devoted to the analysis of the regularity of solutions of elliptic problems on nonsmooth domains in 3 the present paper concentrates on the regularity of solutions of the poisson equation in neighbourhoods of edges of a polyhedral domain in the framework of the weighted sobolev spaces and countably normed spaces these results can be generalised to elliptic problems arising from mechanics and engineering for instance the elasticity problem on polyhedral domains hence the results are not only important to understand comprehensively the qualitative and quantitative aspects of the behaviours of the solution and its derivatives of all orders in neighbourhoods of edges but also essential to design an effective computation and analyse the optimal convergence of the finite elements solutions for these problems

approximation properties of the h p version of the finite element method abstract the paper surveys the approximation and convergence properties of the h p version of the finite element method the basic theoretical results together with the main ideas of the proofs numerical examples are given

a multifractal formalism let x be a metric space and a borel probability measure on x for q t r and e x write formula then hq t and pq t are borel measures hq t is a multifractal generalization of the centered hausdorff measure and pq t is a multifractal generalization of the packing measure the measures hq t and pq t define for a fixed q in the usual way a generalized hausdorff dimension dimq e and a generalized packing dimension dimq e of subsets e of x we study the functions b q dimq supp b q dimq supp and their relation to the so called multifractal spectra functions of formula we prove among other things that f f is bounded from above by the legendre transform of b b and that equality holds for graph directed self similar measures and cookie cutter measures finally we discuss the connection with generalized renyi dimensions

a multifractal analysis of equilibrium measures for conformal expanding maps and moran like geometric constructions in this paper we establish the complete multifractal formalism for equilibrium measures for holder continuous conformal expanding maps andexpanding markov moran like geometric constructions examples include markov maps of an interval beta transformations of an interval rational maps with hyperbolic julia sets and conformal toral endomorphisms we also construct a holder continuous homeomorphism of a compact metric space with an ergodic invariant measure of positive entropy for which the dimension spectrum is not convex and hence the multifractal formalism fails

dimension spectra of hyperbolic flows for flows with a conformal hyperbolic set we establish a conditional variational principle for the dimension spectra of holder continuous functions we consider simultaneously birkhoff averages into the future and into the past we emphasize that the description of the spectra is not a consequence of the existing results for birkhoff averages into the future or into the past the main difficulty is that even though the local product structure is bi lipschitz the level sets of the birkhoff averages are never compact our proof is based on the use of markov systems and is inspired in earlier arguments in the case of discrete time

weak gibbs measures for intermittent systems and weakly gibbsian states in statistical mechanics in this paper we associate weak gibbs measures for intermittent maps with non gibbsian weakly gibbsian states in statistical mechanics in the sense of dobrushin 4 5 we show a higher dimensional intermittent map of which the sinai bowen ruelle measure is a weak gibbs equilibrium state and a weakly gibbsian state in the sense of dobrushin admitting essential discontinuities in its conditional probabilities

adaptive galerkin boundary element methods with panel clustering in this paper we will propose a boundary element method for solving classical boundary integral equations on complicated surfaces which possibly contain a large number of geometric details or even uncertainties in the given data the small size of such details is characterised by a small parameter varepsilon and the regularity of the solution is expected to be low in such zones on the surface which we call the wire basket zones we will propose the construction of an initial discretisation for such type of problems afterwards standard strategies for boundary element discretisations can be applied such as the h p and the adaptive hp version in a straightforward way for the classical boundary integral equations we will prove the optimal approximation results of our so called wire basket boundary element method and discuss the stability aspects then we construct the panel clustering and mathcal h matrix approximations to the corresponding galerkin bem stiffness matrix the method is shown to have an almost linear complexity with respect to the number of degrees of freedom located on the wire basket

phase transitions for uniformly expanding maps given a uniformly expanding map of two intervals we describe a large class of potentials admitting unique equilibrium measures this class includes all holder continuous potentials but goes far beyond them we also construct a family of continuous but not holder continuous potentials for which we observe phase transitions this provides a version of the example in 9 for uniformly expanding maps

domain decomposition method for the h p version finite element method domain decomposition method for the h p version of the finite element method in two and three dimensions are discussed using the framework of additive schwarz method various iterative methods are described with their condition numbers estimated further to reduce the cost for solving the sub problems on element interfaces different inexact interface solvers are proposed the effects on the overall condition number as well as their efficient implementation are analyzed

on rigorous mathematical definitions of correlation dimension and generalized spectrum for dimensions we consider different definitions of the correlation dimension and find some relationships between them and other characteristics of dimension type such as hausdorff dimension box dimension etc we also introduce different ways to define and study the generalized spectrum for dimensions a one parameter family of characteristics of dimension type

continuous phase transitions for dynamical systems we study the asymptotic expansion of the topological pressure of one parameter families of potentials at a point of non analyticity the singularity is related qualitatively and quantitatively to non gaussian limit laws and to slow decay of correlations with respect to the equilibrium measure

multifractal measures and a weak separation condition abstract we define a new separation property on the family of contractive similitudes that allows certain overlappings this property is weaker than the open set condition of hutchinson it includes the well known class of infinite bernoulli convolutions associated with the p v numbers and the solutions of the two scale dilation equations our main purpose in this paper is to prove the multifractal formalism under such condition

the hp adaptive fem based on continuous sobolev embeddings isotropic refinements the aim of this paper is to present a new class of smoothness testing strategies in the context of hp adaptive refinements based on continuous sobolev embeddings in addition to deriving a modified form of the 1d smoothness indicators introduced in 26 they will be extended and applied to a higher dimensional framework a few numerical experiments in the context of the hp adaptive fem for a linear elliptic pde will be performed

multifractal analysis of lyapunov exponent for continued fraction and manneville pomeau transformations and applications to diophantine approximation we extend some of the theory of multifractal analysis for conformal expanding systems to two new cases the non uniformly hyperbolic example of the manneville pomeau equation and the continued fraction transformation a common point in the analysis is the use of thermodynamic formalism for transformations with infinitely many branches

the dimension spectrum of some dynamical systems we analyze the dimension spectrum previously introduced and measured experimentally by jensen kadanoff and libchaber using large deviation theory we prove for some invariant measures of expanding markov maps that the hausdorff dimensionf of the set on which the measure has a singularity is a well defined concave and regular function in particular we show that this is the case for the accumulation of period doubling and critical mappings of the circle with golden rotation number we also show in these particular cases that the functionf is universal

regularity of the solutions for elliptic problems on nonsmooth domains in ℝ3 part i countably normed spaces on polyhedral domains this is the first of a series of three papers devoted to the regularity of solutions of elliptic problems on nonsmooth domains in 3 the present paper introduces various weighted spaces and countably weighted spaces in the neighbourhood of edges and vertices of polyhedral domains and it concentrates on exploring the structure of these spaces such as the embeddings of weighted sobolev spaces the relation between weighted sobolev spaces and weighted continuous function spaces and the relations between the weighted sobolev spaces and countably weighted sobolev spaces in cartesian coordinates and in the spherical and cylindrical coordinates these well defined spaces are the foundation for the comprehensive study of the regularity theory of elliptic problems with piecewise analytic data in 3 which are essential for the design of effective computation and the analysis of the h p version of the finite element method for solving elliptic problems in three dimensional nonsmooth domains arising from mechanics and engineering

new parameterized algorithms for the edge dominating set problem an edge dominating set of a graph g v e is a subset email protected e of edges in the graph such that each edge in e m is incident with at least one edge in m in an instance of the parameterized edge dominating set problem we are given a graph g v e and an integer k and we are asked to decide whether g has an edge dominating set of size at most k in this paper we show that the parameterized edge dominating set problem can be solved in o 2 3147 k time and polynomial space we also show that this problem can be reduced to a quadratic kernel with o k 3 edges

parameterized edge dominating set in graphs with degree bounded by 3 in this paper we present an o 2 1479 k time algorithm to decide whether a graph of maximum degree 3 has an edge dominating set of size at most k or not which is based on enumeration of vertex covers and improves all previous results on this problem we first enumerate partial vertex covers of size at most 2k and then construct an edge dominating set based on each vertex cover to find a required edge dominating set to effectively enumerate vertex covers we adopt a branch and reduce method and use some techniques such as pseudo cliques and amortized transfer of cliques to analyze the running time bound

multifractal decompositions of digraph recursive fractals we prove that the multifractal decomposition behaves as expected for a family of sets k known as digraph recursive fractals using measures of markov type for each value of a parameter between a minimum min and maximum max we define multifractal components k of k and show that they are fractals in the sense of taylor the dimension f of k is computed from the data of the problem the typical concave multifractal f dimension spectrum curve results

on the existence of conformal measures a general notion of conformal measure is introduced and some basic properties are studied sufficient conditions for the existence of these measures are obtained using a general construction principle the geometric properties of conformal measures relate equilibrium states and hausdorff measures this is shown for invariant subsets of s under expanding maps

an improved multifractal formalism and self similar measures abstract to characterize the geometry of a measure its generalized dimensions dq have been introduced recently the mathematically precise definition given by falconer fractal geometry 1990 turns out to be unsatisfactory for reasons of convergence as well as of undesired sensitivity to the particular choice of coordinates in the negative q range a new definition is introduced which is also based on box counting but which carries relevant information about for negative q also in particular the legendre connection between generalized dimensions and the multifractal spectrum is established using large deviations and rigorous proofs are provided for the implicit formula giving the generalized dimensions of selfsimilar measures which was until now known only for positive q

thermodynamic formalism for countable to one markov systems for countable to one transitive markov systems we establish thermodynamic formalism for non holder potentials in nonhyperbolic situations we present a new method for the construction of conformal measures that satisfy the weak gibbs property for potentials of weak bounded variation and show the existence of equilibrium states equivalent to the weak gibbs measures we see that certain periodic orbits cause a phase transition non gibbsianness and force the decay of correlations to be slow we apply our results to higher dimensional maps with indifferent periodic points

dimension spectrum of axiom a diffeomorphisms ii gibbs measures we compute the dimension spectrum f t of the singularity sets of a gibbs measure defined on a two dimensional compact manifold and invariant with respect to a c 2 axiom a diffeomorphism this case is the generalization of the case where the measure studied is the bowen margulis measure the one that realizes the topological entropy we obtain similar results for example the function f is the legendre fenchel transform of a free energy function which is real analytic linear in the degenerate case the function fis also real analytic on its definition domain defined in one point in the degenerate case and is related to the hausdorff dimensions of gibbs measures singular with respect to each other and whose supports are the singularity sets and we finally decompose these sets

multifractal analysis of weak gibbs measures for intermittent systems in this paper we establish a multifractal formalism of weak gibbs measures associated to potentials of weak bounded variation for certain nonhyperbolic systems we apply our results to manneville pomeau type maps and a piecewise conformal two dimensional countable markov map with indifferent periodic points which is related to a complex continued fraction

generalised spectra for the dimensions of strange sets the author gives a thermodynamical description of the spectrum of generalised dimensions for invariant sets recently proposed by tel 1986 the author s approach allows a definition of an uncountable set of generalised spectra depending on the equilibrium measure supported by the set and the author indicates that the dimensions are independent of the measurable partition of the set