structural induction and coinduction in a fibrational setting we present a categorical logic formulation of induction and coinduction principles for reasoning about inductively and coinductively defined types our main results provide sufficient criteria for the validity of such principles in the presence of comprehension the induction principle for initial algebras is admissible and dually in the presence of quotient types the coinduction principle for terminal coalgebras is admissible after giving an alternative formulation of induction in terms of binary relations we combine both principles and obtain a mixed induction coinduction principle which allows us to reason about minimal solutionsx x wherexmay occur both positively and negatively in the type constructor we further strengthen these logical principles to deal with contexts and prove that such strengthening is valid when the abstract logic we consider is contextually functionally complete all the main results follow from a basic result about adjunctions between categories of algebras inserters

invariant manifolds for impulsive equations and nonuniform polynomial dichotomies for impulsive differential equations in banach spaces we construct stable and unstable invariant manifolds for sufficiently small perturbations of a polynomial dichotomy we also consider the general case of nonuniform polynomial dichotomies moreover we introduce the notions of polynomial lyapunov exponent and of regularity coefficient for a linear impulsive differential equation and we show that when the lyapunov exponent never vanishes the linear equation admits a nonuniform polynomial dichotomy

exit problems associated with affine reflection groups we obtain a formula for the distribution of the first exit time of brownian motion from the alcove of an affine weyl group in most cases the formula is expressed compactly in terms of pfaffians expected exit times are derived in the type widetilde a case the results extend to other markov processes we also give formulas for the real eigenfunctions of the dirichlet and neumann laplacians on alcoves observing that the hot spots conjecture of j rauch is true for alcoves

schur subalgebras and an application to the symmetric group abstract let k be an infinite field of prime characteristic p and let d r be positive integers of the same parity satisfying a certain congruence condition we prove that the schur algebra s 2 d is isomorphic to a subalgebra of the form es 2 r e where e is a certain idempotent of s 2 r translating this result via ringel duality to the symmetric groups d and r we obtain lattice isomorphisms between specht modules between young modules and between permutation modules here modules labelled by the partitions r k k correspond to modules labelled by d k k this provides a representation theoretical interpretation for part of the fractal structures observed for the decomposition numbers of the symmetric groups corresponding to two part partitions

coalgebras in functional programming and type theory this is a survey article on the use of coalgebras in functional programming and type theory it presents the basic theory underlying the implementation of coinductive types families and predicates it gives an overview of the application of corecursive methods to the study of general recursion formal power series tabulations of functions on inductive data it also sketches some advanced topics in the study of the solutions to non guarded corecursive equations and the design of non standard type theory

a solution to an open problem for wave equations with generalized wentzell boundary conditions in this paper we solve an open problem put forward by a favini g r goldstein j a goldstein and s romanelli concerning the mixed problem for wave equations with generalized wentzell boundary conditions as a consequence we also develop the previous wellposedness result regarding the mixed problem for heat equations with generalized wentzell boundary conditions

generic formulas for the values at the singular points of some special monic classical hq ω orthogonal polynomials it is well known that the classical orthogonal polynomials of jacobi bessel laguerre and hermite are solutions of a sturm liouville problem of the type s x y n email protected x y n email protected ny n 0 where s and t are polynomials such that email protected 2 and email protected 1 and l n is a constant independent of x recently based on the hypergeometric character of the solutions of this differential equation w koepf and m masjed jamei a generic formula for the values at the boundary points of monic classical orthogonal polynomials j comput appl math 191 2006 98 105 found a generic formula only in terms of the coefficients of s and t for the values of the classical orthogonal polynomials at the singular points of the above differential hypergeometric equation in this paper we generalize the mentioned result giving the analogous formulas for both the classical q orthogonal polynomials of the q hahn tableau and the classical d w orthogonal polynomials both are special cases of the classical h q w orthogonal polynomials which are solutions of the hypergeometric type difference equation s x h q wh 1 q wy email protected x h q wy email protected ny n 0 where h q w is the difference operator introduced by hahn and s t and l n being as above our approach is algebraic and it does not require hypergeometric functions

an algorithm for the optimization of directionally stretched triangulations a procedure for the optimization of stretched triangular grids is described the method is based on the construction and minimization of a function that represents a generalized version for stretched grids of a non linear spring system the function is minimized using a gradient method based on the steepest descent examples are provided to show the applicability of the method to computational fluid dynamics problems

classes of representable disjoint np pairs for a propositional proof system p we introduce the complexity class dnpp p of all disjoint np pairs for which the disjointness of the pair is efficiently provable in the proof system p we exhibit structural properties of proof systems which make canonical np pairs associated with these proof systems hard or complete for dnpp p moreover we demonstrate that non equivalent proof systems can have equivalent canonical pairs and that depending on the properties of the proof systems different scenarios for dnpp p and the reductions between the canonical pairs exist

a nonterminating 8 φ 7 summation for the root system c r using multiple q integrals and a determinant evaluation we establish a nonterminating 8 7 summation for the root system cr we also give some important specializations explicitly

universal coalgebra a theory of systems in the semantics of programming finite data types such as finite lists have traditionally been modelled by initial algebras later final coalgebras were used in order to deal with infinite data types coalgebras which are the dual of algebras turned out to be suited moreover as models for certain types of automata and more generally for transition and dynamical systems an important property of initial algebras is that they satisfy the familiar principle of induction such a principle was missing for coalgebras until the work of aczel 1988 on a theory of non wellfounded sets in which he introduced a proof principle nowadays called coinduction it was formulated in terms of bisimulation a notion originally stemming from the world of concurrent programming languages milner 1980 park 1981 using the notion of coalgebra homomorphism the definition of bisimulation on coalgebras can be shown to be formally dual to that of congruence on algebras aczel and mendler 1989 thus the three basic notions of universal algebra algebra homomorphism of algebras and congruence turn out to correspond to coalgebra homomorphism of coalgebras and bisimulation respectively in this paper the latter are taken as the basic ingredients of a theory called universal coalgebra some standard results from universal algebra are reformulated using the afore mentioned correspondence and proved for a large class of coalgebras leading to a series of results on e g the lattices of subcoalgebras and bisimulations simple coalgebras and coinduction and a covariety theorem for coalgebras similar to birkhoff s variety theorem

groupes commutatifs d automorphismes d une variete kahlerienne compacte let v be a compact kahler manifold let gbe a commutative subgroup of aut v and u the set of elements of zero entropy of g then u is a group and gis isomorphic to the direct product g u g where g is a subgroup of gsuch that all elements of g id are of positive entropy moreover g is a free commutative group with rank g dim v 1 the estimate is sharp when rank g dim v 1 u is finite rank g satisfies other inequalities involving the dimensions of dolbeault cohomology groups of v

infinite horizon backward stochastic differential equations and elliptic equations in hilbert spaces solutions of semilinear elliptic differential equations in infinite dimensional spaces are obtained by means of forward and backward infinite dimensional stochastic evolution equations the backward equation is considered on an infinite time horizon and a suitable growth condition replaces the final condition elliptic equations are intended in a mild sense suitable also for applications to optimal control we finally notice that due to the lack of smoothing properties the elliptic partial differential equation considered here could not be treated by analytic methods

de bakker zucker processes revisited the sets of compact and of closed subsets of a metric space endowed with the hausdorff metric are studied both give rise to a functor on the category of 1 bounded metric spaces and nonexpansive functions it is shown that the former functor has a terminal coalgebra and that the latter does not

double centralizing theorems for the alternating groups let v n be the n fold tensor product of a vector space v following i schur we consider the action of the symmetric group sn on v n by permuting coordinates in the super z2 graded case v v0 v1 a sign is added these actions give rise to the corresponding schur algebras s sn v here s sn v is compared with s an v the schur algebra corresponding to the alternating subgroup an sn while in the classical signless case these two schur algebras are the same for n large enough it is proved that in the super case where dim v0 dim v1 s an v is isomorphic to the cross product algebra s an v s sn v z2

robust nonuniform dichotomies and parameter dependence abstract we establish the robustness of linear cocycles with an exponential dichotomy under sufficiently small lipschitz perturbations in the sense that the existence of an exponential dichotomy for a given cocycle persists under these perturbations we consider cocycles in banach spaces as well as the general case of nonuniform exponential dichotomies and also the general case of an exponential behavior e c n given by an arbitrary sequence n including the usual exponential behavior n n as a very special case moreover we show that the projections of the exponential dichotomies obtained from the perturbation vary continuously with the parameter and in fact that they are locally lipschitz on finite dimensional parameters

simulations in coalgebra a new approach to simulations is proposed within the theory of coalgebras by taking a notion of order on a functor as primitive such an order forms a basic building block for a lax relation lifting or relator as used by other authors simulations appear as coalgebras of this lifted functor and similarity as greatest simulation two way similarity is then similarity in both directions in general it is different from bisimilarity in the usual coalgebraic sense but a sufficient condition is formulated and illustrated to ensure that bisimilarity and two way similarity coincide also suitable conditions are identified which ensures that similarity on a final coalgebra forms an algebraic dcpo structure this involves a close investigation of the iterated applications fn 0 and fn 1 of a functor f with an order to the initial algebras and final objects

a categorical outlook on relational modalities and simulations we characterise bicategories of spans relations and partial maps universally in terms of factorisations involving maps we apply this characterisation to show that the standard modalities and arise canonically as extensions of a predicate logic from functions to abstract relations when relations and partial maps are representable we exhibit logical predicates for the power object and partial map classifier monads we also show that the modality gives the relevant pullbacks of subobjects in the internal logic of categories of partial maps organising modal formulae fibrationally we exhibit an intrinsic relationship between their satisfaction relative to transition systems and the notion of simulation in this setting we use the biclosed structure of the bicategory of relations to give a new proof of the standard fact that observational similarity implies similarity

coding the principal character formula for affine kac moody lie algebras in this paper an algorithm for computing the principal character for affine lie algebras is discussed and presented the principal characters discovered using this program are given and or proven results include level 2 and 3 character formulas in a2n 1 2 and the sole existence of the rogers ramanujan products in a1 1 a2 1 a2 2 c3 1 f4 1 g2 1 a7 2

zeros of jones polynomials for families of knots and links abstract we calculate jones polynomials v l t for several families of alternating knots and links by computing the tutte polynomials t g x y for the associated graphs g and then obtaining v l t as a special case of the tutte polynomial for each of these families we determine the zeros of the jones polynomial including the accumulation set in the limit of infinitely many crossings a discussion is also given of the calculation of jones polynomials for non alternating links

constant sign solutions of a system of volterra integral equations we consider the following system of volterra integral equations u i t 0 tg i t s f i s u 1 s u 2 s u n s h i s u 1 s u 2 s u n s ds t 0 t 1 i n and some of its particular cases that arise from physical problems criteria are offered for the existence of one and more constant sign solutions u u 1 u 2 u n of the system in c 0 t n we say u is of constant sign if for each 1 i n q iu i t 0 for all t 0 t where q i 1 1 is fixed examples are also included to illustrate the results obtained

modular invariant of quantum tori the quantum modular invariant j qt of 2r is defined as a discontin uous pgl2 z invariant multi valued map using the distance to the nearest integer function k k for 2 q it is shown that j qt 1 and for quadratic irrationalities pari gp experiments suggest that j qt is a finite set in the case of the golden mean we produce explicit formulas involving weighted versions of the rogers ramanujan functions for the experimental supremum and infimum we then define a universal modular invariant j a mod c as a continuous and single valued map of ultrasolenoids such that 1 the classical modular invariant is a quotient of the re striction of j to a subsolenoid mod cl a mod fibering over the classical moduli space of elliptic curves and 2 the quantum modular invariant is a quotient of the restric tion of j to a subsolenoid mod qt a mod fibering over the moduli space of elliptic curves equipped with a kronecker foliation

comprehension categories and the semantics of type dependency abstract a comprehension category is defined as a functor p e b satisfying a a cod p is a fibration and b f is cartesian in e implies that p f is a pullback in b this notion captures many structures which are used to describe type dependency like display map categories taylor 1986 hyland and pitts 1989 and lamarche 1988 categories with attributes cartmell 1978 and moggi 1991 d categories ehrhard 1988 and comprehensive fibrations pavlovic 1990 it also captures comprehension as occurring in topos theory and as described by lawvere s 1970 hyperdoctrines this paper is meant as an introduction to these comprehension categories a comprehension category will be called closed if it has appropriate dependent products and sums a few examples of closed comprehension categories will be described here more of them may be found in jacobs 1991 applications occur in jacobs 1991 and jacobs et al 1991

invariant measures and regularity properties of perturbed ornstein uhlenbeck semigroups abstract this paper deals with perturbations of the ornstein uhlenbeck operator on l 2 spaces with respect to a gaussian measure we perturb the generator of the ornstein uhlenbeck semigroup by a certain unbounded non linear drift and show various properties of the perturbed semigroup such as compactness and positivity strong feller property existence and uniqueness of an invariant measure are discussed as well

combining hook length formulas and bg ranks for partitions via the littlewood decomposition recently the first author has studied hook length formulas for partitions in a systematic manner in the present paper we show that most of those hook length formulas can be generalized and include more variables via the littlewood decomposition which maps each partition to its t core and t quotient in the case t 2 we ob tain new formulas by combining hook lengths and bg ranks introduced by berkovich and garvan as applications we list several multivari able generalizations of classical and new hook length formulas including the nekrasov okounkov the han carde loubert potechin sanborn the bessenrodt bacher manivel the okada panova and the stanley panova formulas summary

trace representation of some generalized cyclotomic sequences of length pq this paper contributes to trace representation of some generalized cyclotomic sequences of length pq p qprime which are defined by ding and helleseth from the relations between these sequences and the legendre sequence we firstly confirm the defining pairs of these sequences of arbitrary order then we obtain their trace representation from which we give their linear complexity using key s method it can be seen that bai et al s conclusion is a special case of our result when the order is two finally an example is given to illustrate the validity of our result

generic weakest precondition semantics from monads enriched with order we devise a generic framework where a weakest precondition semantics in the form of indexed posets is derived from a monad whose kleisli category is enriched by posets it is inspired by jacobs recent identification of a categorical structure that is common in various predicate transformers but adds generality in the following aspects 1 different notions of modality such as may vs must are captured by eilenberg moore algebras 2 nested alternating branching like in games and in probabilistic systems with nondeterministic environments is modularly modeled by a monad on the eilenberg moore category of another

lattices on simplicial partitions which are not simply connected in this paper d 1 pencil lattices on simplicial partitions in r d which are not simply connected are studied it is shown how the fact that a partition is not simply connected can be used to increase the flexibility of a lattice a local modification algorithm is developed also to deal with slight partition topology changes that may appear afterwards a lattice has already been constructed

adaptive remeshing for compressible flow computations an adaptive mesh procedure for improving the quality of steady state solutions of the euler equations in two dimensions is described the procedure is implemented in conjunction with a finite element solution algorithm using linear triangular elements and an explicit time stepping scheme the mesh adaptation is accomplished by regeneration using information provided by the computed solution on the current mesh the meshes produced are characterised by the appearance of stretched elements in the vicinity of one dimensional flow features and can exhibit a large variation in element size this allows solutions of enhanced quality to be produced in a computationally efficient manner

coalgebraic modal logic soundness completeness and decidability of local consequence this paper studies finitary modal logics interpreted over coalgebras for an endofunctor and establishes soundness completeness and decidability results the logics are studied within the abstract framework of coalgebraic modal logic which can be instantiated with arbitrary endofunctors on the category of sets this is achieved through the use of predicate liftings which generalise atomic propositions and modal operators from kripke models to arbitrary coalgebras predicate liftings also allow us to use induction along the terminal sequence of the underlying endofunctor as a proof principle this induction principle is systematically exploited to establish soundness completeness and decidability of the logics we believe that this induction principle also opens new ways for reasoning about modal logics our proof of completeness does not rely on a canonical model construction and the proof of the finite model property does not use filtrations

automorphism groups of positive entropy on projective threefolds we prove two results about the natural representation of a group g of automorphisms of a normal projective threefold x on its second cohomology we show that if x is minimal then g modulo a normal subgroup of null entropy is embedded as a zariski dense subset in a semi simple real linear algebraic group of real rank 2 next we show that x is a complex torus if the image of g is an almost abelian group of positive rank and the kernel is infinite unless x is equivariantly non trivially fibred

nuclearity of hankel operators for ultradifferentiable control systems nuclearity of the hankel operator is a known sufficient condition for convergence of lyapunov balanced truncations we show how a previous result on nuclearity of hankel operators of systems with an analytic semigroup can be extended to systems with a semigroup of class dp with p 1 the case p 1 being the analytic case for semigroups that are generated by a dunford schwartz spectral operator we prove that being of class dp is equivalent to being gevrey ultradifferentiable of order p we illustrate how for certain partial differential equations our results lead to an easy way of showing nuclearity of the hankel operator for a wide range of control and observation operators by considering several examples of damped beams

a characterization of compact complex tori via automorphism groups we show that a compact kahler manifold x is a complex torus if both the continuous part and discrete part of some automorphism group g of x are infinite groups unless x is bimeromorphic to a non trivial g equivariant fibration some applications to dynamics are given

generation of localization in a discrete chain with periodic boundary conditions numerical and analytical results we study the generation of localization in a discrete chain composed of n subsystems and periodic boundary conditions strongly localized motions are studied that is time periodic motions where nearly all of the energy is spatially confined to a single subsystem for varying n numerical results indicate that the strongly localized solutions are generated through a bifurcation from an in phase spatially extended solution however in the limit as n rightarrow infty the bifurcation point tends to infinity and a smooth transition from localization to nonlocalization occurs we then present an analytic technique to complement the numerical results it is based on the matching local asymptotic expansions of a solution branch using pade approximants this leads to global analytic representations of the considered solutions valid over the entire range of the control parameter

strictly nef divisors 0 introduction 565 1 basic definitions known results and main problems 567 2 results in case of non negative kodaira dimension 569 3 the albanese map 572 4 fano fibrations 575 5 birational maps 578 6 higher dimensions 583

compact kahler manifolds admitting large solvable groups of automorphisms abstract let g be a group of automorphisms of a compact kahler manifold x of dimension n and n g the subset of null entropy elements suppose g admits no non abelian free subgroup improving the known tits alternative we obtain that up to replace g by a finite index subgroup either g n g is a free abelian group of rank n 2 or g n g is a free abelian group of rank n 1 and x is a complex torus or g is a free abelian group of rank n 1 if the last case occurs x is g equivariant birational to the quotient of an abelian variety provided that x is a projective manifold of dimension n 3 and is not rationally connected we also prove and use a generalization of a theorem by fujiki and lieberman on the structure of aut x

the complexity of weighted boolean csp with mixed signs we give a complexity dichotomy for the problem of computing the partition function of a weighted boolean constraint satisfaction problem such a problem is parameterized by a set c of rational valued functions which generalize constraints each function assigns a weight to every assignment to a set of boolean variables our dichotomy extends previous work in which the weight functions were restricted to being non negative we represent a weight function as a product of the form 1 sg where the polynomial s determines the sign of the weight and the non negative function g determines its magnitude we show that the problem of computing the partition function the sum of the weights of all possible variable assignments is in polynomial time if either every function in c can be defined by a pure affine magnitude with a quadratic sign polynomial or every function can be defined by a magnitude of product type with a linear sign polynomial in all other cases computing the partition function is fp p complete

bialgebras for structural operational semantics bialgebras and distributive laws are an abstract categorical framework to study various flavors of structural operational semantics this paper aims to introduce the reader to the basics of bialgebras for operational semantics and to sketch the state of the art in this research area

recursively defined metric spaces without contraction in this paper we use the theory of accessible categories to find fixed points of endofunctors on the category of 1 bounded complete metric spaces and nonexpansive functions in contrast to previous approaches we do not assume that the endofunctors are locally contractive and our results do not depend on banach s fixed point theorem our approach is particularly suitable for constructing models of systems that feature quantitative data for instance using the kantorovich metric on probability measures we construct a quantitative model for probabilistic transition systems the metric in our model can reasonably be seen as measuring the behavioural distance between states of the system it depends exclusively on the transition probabilities and not on an arbitrary discount factor

new combinatorial interpretations of ramanujan s partition congruences mod 5 7 and 11 soit p n le nombre de partitions non restreintes de n on donne de nouvelles interpretations combinatoires des congruences p 5n 4 p 7n 5 et p 11n 6 0 mod 5 7 et 11 respectivement

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

a theorem of tits type for compact kahler manifolds we prove a theorem of tits type about automorphism groups for compact kahler manifolds which has been conjectured in the paper 9

linear codes interpolation from noisy patterns by means of a vector quantization process abstract an algorithm inferring a boolean linear code from noisy patterns received by a noisy channel under the assumption of uniform occurrence distribution over the codewords and an upper bound to the amount of data are presented a vector quantizer is designed from the noisy patterns choosing the obtained codebook as code approximation it is shown both theoretically and experimentally that when the data are affected by independent random errors this strategy requires a small number of patterns to obtain a good identification with high probability of the code from the noisy data

a de giorgi nash type theorem for time fractional diffusion equations we study the regularity of weak solutions to linear time fractional diffusion equations in divergence form of arbitrary time order alpha in 0 1 the coefficients are merely assumed to be bounded and measurable and they satisfy a uniform parabolicity condition our main result is a de giorgi nash type theorem which gives an interior holder estimate for bounded weak solutions in terms of the data and the l infty bound of the solution the proof relies on new a priori estimates for time fractional problems and uses de giorgi s technique and the method of non local growth lemmas which has been introduced recently in the context of nonlocal elliptic equations involving operators like the fractional laplacian

some inequalities for the q beta and the q gamma functions via some q integral inequalities some new inequalities for the q gamma the q beta and the q analogue of the psi functions are established via some q integral inequalities

fast algorithms for toeplitz and hankel matrices abstract the paper gives a self contained survey of fast algorithms for solving linear systems of equations with toeplitz or hankel coefficient matrices it is written in the style of a textbook algorithms of levinson type and schur type are discussed their connections with triangular factorizations pade recursions and lanczos methods are demonstrated in the case in which the matrices possess additional symmetry properties split algorithms are designed and their relations to butterfly factorizations are developed

stopping criteria for rational matrix functions of hermitian and symmetric matrices building upon earlier work by golub meurant strakos and tich we derive new a posteriori error bounds for krylov subspace approximations to f a b the action of a function f of a real symmetric or complex hermitian matrix a on a vector b to this purpose we assume that a rational function in partial fraction expansion form is used to approximate f and the krylov subspace approximations are obtained as linear combinations of galerkin approximations to the individual terms in the partial fraction expansion our error estimates come at very low computational cost in certain important special situations they can be shown to actually be lower bounds of the error our numerical results include experiments with the matrix exponential as used in exponential integrators and with the matrix sign function as used in lattice quantum chromodynamics simulations and demonstrate the accuracy of the estimates the use of our error estimates within acceleration procedures is also discussed

the asymptotic bounds of solutions of linear delay systems abstract our aim is to obtain conditions under which every solutionyof the vector functional differential equation formula can be estimated in terms of a solution of a scalar functional equation formula wherea x is a suitable real positive function andbis a suitable real negative constant moreover ifb x is diagonal matrix we derive more precise estimates ofyin terms of a solution of a vector functional equation formula where the elements ofa x are formed by the absolute values of the corresponding elements ofa x these asymptotic results enable us to obtain sharp estimates of solutions of certain linear delay systems

the derived categories of some blocks of symmetric groups and a conjecture of broue abstract a well known conjecture of broue in the representation theory of finite groups involves equivalences of derived categories of blocks the aim of this paper is to verify this conjecture for defect 2 blocks of symmetric groups actually we prove for these blocks a refinement of broue s conjecture due to rickard

kernel methods for learning languages this paper studies a novel paradigm for learning formal languages from positive and negative examples which consists of mapping strings to an appropriate high dimensional feature space and learning a separating hyperplane in that space such mappings can often be represented flexibly with string kernels with the additional benefit of computational efficiency the paradigm inspected can thus be viewed as that of using kernel methods for learning languages we initiate the study of the linear separability of automata and languages by examining the rich class of piecewise testable languages we introduce a subsequence feature mapping to a hilbert space and prove that piecewise testable languages are linearly separable in that space the proof makes use of word combinatorial results relating to subsequences we also show that the positive definite symmetric kernel associated to this embedding is a rational kernel and show that it can be computed in quadratic time using general purpose weighted automata algorithms our examination of the linear separability of piecewise testable languages leads us to study the general problem of separability with other finite regular covers we show that all languages linearly separable under a regular finite cover embedding a generalization of the subsequence embedding we use are regular we give a general analysis of the use of support vector machines in combination with kernels to determine a separating hyperplane for languages and study the corresponding learning guarantees our analysis includes several additional linear separability results in abstract settings and partial characterizations for the linear separability of the family of all regular languages

strong categorical datatypes ii a term logic for categorical programming abstract this paper lifts earlier category theoretic results on datatypes to the level of an abstract language suitable for categorical programming language implementation the earlier work built a strongly normalizing categorical combinator reduction system based entirely on functorial strength which allows the distribution of context to the interior of datatypes here we declare inductive initial and coinductive final datatypes in a hagino wraith style to provide an expressive computing environment an inductive resp coinductive datatype consists of a strong type forming functor accompanied by 1 a collection of constructors resp destructors and 2 a fold resp unfold which is parametrized by state transformations to realize the appropriate universal property the high complexity of programming exclusively in categorical notation combinators warrants the development of a friendlier language isomorphic to the distributive categorical setting in this paper such a term logic which is also the programming language of the charity programming system is described this logic is first order and is dictated directly by the underlying categorical semantics it embodies primitive inductive and coinductive principles which reflect the uniqueness properties of the fold and unfold combinators several basic progam equivalences are demonstrated to illustrate how these inductive and coinductive principles can be used

the x ray transform and its inversion for the series expansion basis functions in three dimensional tomography a formula for the three dimensional x ray transform and an expression for its inversion have been derived the spherical harmonics and the rotation matrices in terms of euler angles are used in the generalized fourier series expansion some properties of the transformed fourier components are discussed

numerical simulation of the gas flow in a circuit breaker a computational methodology for the solution of unsteady two dimensional axisymmetric euler equations within geometries with moving boundaries is presented the flow simulation is carried out by applying a finite volume method which makes use of a lagrangian eulerian version of roe s approximate riemann solver the domain discretization is handled via unstructured triangular grids grid adaptation is applied on the basis of geometric and physical requirements the importance of the implicit treatment of the space conservation laws based on geometric analysis is evoked the procedure for reconstructing roe s method for moving meshes is described and validated finally the ability of the method for the prediction of the transient flow in a circuit breaker during its opening phase is illustrated

quasidiagonality of direct sums of weighted shifts let h be a separable hilbert space a bounded linear operator a defined on h is said to be quasidiagonal if there exists a sequence p n of projections of finite rank such that p n i strongly and ap n p n a 0 as n we give a necessary and sufficient condition for a finite direct sum of weighted shifts to be quasidiagonal the condition is stated using a markedgraph a graph with a 0 or attached to its vertices that can be associated with the direct sum

adaptive mesh generation for viscous flows using delaunay triangulation abstract a method for generating an unstructured triangular mesh in two dimensions suitable for computing high reynolds number flows over arbitrary configurations is presented the method is based on a delaunay triangulation which is perfored in a locally stretched space in order to obtain very high aspect ratio tiangles in the boundary layer and wake regions it is shown how the method can be coupled with an unstructured navier stokes solver to produce a solution adaptive mesh generation procedure for viscous flows

wavelets of multiplicity r a multiresolution approximation km m z of l2 r is of multi plicity r 0 if there are r functions x r whose translates form a riesz basis for v in the general theory we derive necessary and sufficient conditions for the translates of x r y x y r to form a riesz basis for v the resulting reconstruction and decomposition sequences lead to the construction of dual bases for v0 and its orthogonal complement w0 in vx the general theory is applied in the construction of spline wavelets with mul tiple knots algorithms for the construction of these wavelets for some special cases are given

parametrized data types do not need highly constrained parameters data types may be considered as objects in any suitable category and need not necessarily be ordered structures or many sorted algebras arrays may be specified having as parameter any object from a category plane1d 4a6 with finite products and coproducts if products distribute over coproducts the lehmann smith least fixpoint approach to recursively defined data types is extended by introducing the dual notion of greatest fixpoint which allows the definition of infinite lists and trees without recourse to domains bearing a partial order structure finally the least fixpoint approach is shown allowing the definition of queues directly in terms of stacks rather than through a separate equational specification

an improved sectional anosov closing lemma we prove that all nonwandering points of a sectional anosov flow on a compact 3 manifold can be approximated by periodic points or by points for which the omega limit set is a singularity this improves the closing lemma in morales mich math j 56 1 29 53 2008 we also describe a sectional anosov flow for which the recurrent points are not dense in the nonwandering set

n point pade approximants to real valued stieltjes series with nonzero radii of convergence abstract by employing special continued fractions to two stieltjes series with nonzero radii of convergence we extend the inequalities for one point pade approximants reported by baker 1975 corollory 17 1 to the case of two point pade approximants we prove that some convergents of the continued fractions form a monotone sequences of upper and lower bounds converging uniformly to stieltjes function x1 x on compact subsets of r where r is a radius of convergence of an expansion of x f1 x at x 0 for an illustration of theoretical results we provide nontrivial numerical examples as an application to real physical problems second order pade approximants bounds on the effective conductivity of a square array of cylinders are evaluated

should annual maximum temperatures follow a generalized extreme value distribution summary motivated by the study of annual temperature extremes two new results on the limiting distribution of block maxima of random variables with varying upper bounds are obtained one gives a generalized extreme value distribution as the limit but with a different shape parameter from that obtained when the bound on the random variables does not vary the other gives a limiting distribution that is only a generalized extreme value in certain cases both results consider triangular arrays of random variables in order to mimic the property of an upper bound that changes slowly with the day of the year as seems to occur for temperature data at many locations an analysis of 140 years of daily temperatures in new york city shows mixed results in terms of the ability of the theory presented here to provide new insights into the behaviour of extreme temperatures at this location

partition identities involving gaps and weights we obtain interesting new identities connecting the famous partition functions of euler gauss lebesgue rogers ramanujan and others by attaching weights to the gaps between parts the weights are in general multiplicative some identities involve powers of 2 as weights and yield combinatorial information about some remarkable partition congruences modulo powers of 2

a modular approach to defining and characterising notions of simulation we propose a modular approach to defining notions of simulation and modal logics which characterise them we use coalgebras to model state based systems relators to define notions of simulation for such systems and inductive techniques to define the syntax and semantics of modal logics for coalgebras we show that the expressiveness of an inductively defined logic for coalgebras w r t a notion of simulation follows from an expressivity condition involving one step in the definition of the logic and the relator inducing that notion of simulation moreover we show that notions of simulation and associated characterising logics for increasingly complex system types can be derived by lifting the operations used to combine system types to a relational level as well as to a logical level we use these results to obtain baltag s logic for coalgebraic simulation as well as notions of simulation and associated logics for a large class of non deterministic and probabilistic systems

central limit theorem for products of random matrices using the semigroup product formula of p chernoff a central limit theorem is derived for products of random matrices applications are presented for representations of solutions to linear systems of stochastic differential equations and to the corresponding partial differential evolution equations included is a discussion of stochastic semigroups and a stochastic version of the lie trotter product formula

a co induction principle for recursively defined domains abstract this paper establishes a new property of predomains recursively defined using the cartesian product disjoint union partial function space and convex powerdomain constructors we prove that the partial order on such a recursive predomain d is the greatest fixed point of a certain monotone operator associated to d this provides a structurally defined family of proof principles for these recursive predomains to show that one element of d approximates another it suffices to find a binary relation containing the two elements that is a post fixed point for the associated monotone operator the statement of the proof principles is independent of any of the various methods available for explicit construction of recursive predomains following milner and tofte 1991 the method of proof is called co induction it closely resembles the way bisimulations are used in concurrent process calculi milner 1989 two specific instances of the co induction principle already occur in the work of abramsky 1990 1991 in the form of internal full abstraction theorems for denotational semantics of sccs and lazy lambda calculus in the first case post fixed binary relations are precisely abramsky s partial bisimulations whereas in the second case they are his applicative bisimulations the co induction principle also provides an apparently useful tool for reasoning about equality of elements of recursively defined datatypes in strict or lazy higher order functional programming languages

on the q analogues of some transformations of nearly poised hypergeometric series a number of transformation formulas for very well poised basic hypergeometric series have been obtained which in the limit q 1 approach the known transformation formulas for nearly poised ordinary hypergeometric series

on modular homology in the boolean algebra iii abstract let be a set ra ring of characteristicp 0 and denote bymkther module withk element subsets of as basis theset inclusion map mk mk 1is the homomorphism which associates to ak element subset the sum 1 2 kof all its k 1 element subsets i in this paper we study the chain formula arising from we introduce the notion ofp exactness for a sequence if is infinite we show that isp exact for all prime characteristicsp 0 this result can be extended to various submodules and quotient modules and we give general constructions arising from permutation groups with a finitary section two particular applications are the following the orbit module sequence of such a permutation group on isp exact for every primep and we give a formula for thep rank of the orbit inclusion matrix if the group has finitely many orbits onk element subsets

exponents of nonnegative matrix pairs the notions of primitivity and exponent of a square nonnegative matrix a are classical a is primitive provided there is a nonnegative integer k such that a k is entrywise positive and in the case a is primitive the exponent of a is the smallest such k fornasini and valcher have extended the notion of primitivity to pairs a b of square nonnegative matrices of the same order the pair a b is primitive provided there exist nonnegative integers h and k such that the sum of all products formed by words consisting of ha s and kb s is entrywise positive this paper defines the exponent of a nonnegative matrix pair to be the smallest value of h k over all such h and k it is then shown that the largest exponent of a primitive pair of n by n nonnegative matrices lies in the interval n 3 5n 2 2 3n 3 2n 2 2n 2 in addition the exponent of a pair of nonnegative matrices is related to properties of an associated twodimensional dynamical system 2001 elsevier science inc all rights reserved

on null controllability of linear systems in banach spaces abstract our aim here is to give characterizations for the null controllability of linear systems in general banach spaces the starting point of this paper is the work of pengnian chen and huashu qin systems control lett 45 2002 155 which solves the problem of exact controllability in fact the results of systems control lett 45 2002 155 say that in case of setting in general banach spaces there are the same characterizations of exact controllability as in the case of reflexive banach spaces an open problem raised in systems control lett 45 2002 155 is the validity of a similar result for null controllability we give here a positive answer to this problem however it seems to us that the technique of systems control lett 45 2002 155 does not work for null controllability and consequently our approach is completely different