energy decay rate of wave equations with indefinite damping abstract we consider the one dimensional wave equation with an indefinite sign damping and a zero order potential term using a shooting method we establish the asymptotic expansion of eigenvalues and eigenvectors of the damped wave equation for a large class of coefficients in addition if the damping coefficient is more positive than negative we prove that the energy of system decays uniformly exponentially to zero this sharp result generalizes a previous work of freitas and zuazua 1996

discovering multi label temporal patterns in sequence databases sequential pattern mining is one of the most important data mining techniques previous research on mining sequential patterns discovered patterns from point based event data interval based event data and hybrid event data in many real life applications however an event may involve many statuses it might not occur only at one certain point in time or over a period of time in this work we propose a generalized representation of temporal events we treat events as multi label events with many statuses and introduce an algorithm called mltpm to discover multi label temporal patterns from temporal databases the experimental results show that the efficiency and scalability of the mltpm algorithm are satisfactory we also discuss interesting multi label temporal patterns discovered when mltpm was applied to historical nasdaq data

exponential decay of energy of evolution equations with locally distributed damping consider an evolution equation with energy dissipation frac partial partial t y x t ay x t by x t on a bounded x domain omega where by signifies a dissipative perturbation to an otherwise energy conserving system this dissipation may be due to medium impurities viscous effects or artificially imposed dampers and stabilizers it is distributed over only part of the domain omega the question of when the dissipation is effective enough to cause uniform exponential decay of energy is examined because of the locally distributed nature of energy dissipation the problem lacks coercivity and is not directly solvable by energy identities thus to get conditions sufficient for uniform exponential decay a different approach needs to be taken provided here is a set of tight sufficient conditions in terms of the influence of the dissipative operatorbon the separated eigenmodes or clustered eigenmodes ofa the main theorems are general enough to treat the wave and bea

stability analysis of the zero solution for two class evolution equations abstract by constructing some suitable lyapunov type functionals and applying the theory of the definite quadratic form we obtain the stability of the zero solution of two classes of evolution equations with delays including reaction diffusion equations and damped wave equations our criteria depend on the derivatives of delays consequently when the delays are constants these criteria are independent of the magnitudes of the delays so the delays are harmless for the stability of the zero solution

canonical extensions of the johnson homomorphisms to the torelli groupoid abstract we prove that every trivalent marked bordered fatgraph comes equipped with a canonical generalized magnus expansion in the sense of kawazumi this magnus expansion is used to give canonical extensions of the higher johnson homomorphisms m for m 1 to the torelli groupoid and we provide a recursive combinatorial formula for tensor representatives of these extensions in particular we give an explicit 1 cocycle in the dual fatgraph complex which extends 2 and thus answer affirmatively a question of morita and penner to illustrate our techniques for calculating higher johnson homomorphisms in general we give explicit examples calculating m for m 3

knowledge gathering of fuzzy multi time interval sequential patterns mining sequential patterns to find ordered events or subsequence patterns is essential in many applications such as analysis of consumer shopping data web clickstreams and biological sequences traditional patterns reveal which items are frequently purchased together and in what order however information about the time intervals between purchases is missing therefore yang proposed using multi time interval sequential patterns to consider the time intervals between each pair of items in a pattern for example means that bread is bought before milk within an interval of ti 1 and jam is bought after bread and milk within intervals of ti 2 and ti 1 respectively where ti 1 and ti 2 are predefined time intervals although this new type of pattern considers the intervals between all pairs of items it contains a sharp boundary problem that is when the time interval between two purchases is near the boundary of two predetermined time ranges we either ignore or overemphasize it in this study we applied the concept of fuzzy sets to solve the sharp boundary problem the discovered patterns called fuzzy multi time interval sequential patterns describe time intervals in linguistic terms for better understanding two algorithms fuzzmi apriori and fuzzmi prefixspan were developed for mining fuzzy multi time interval patterns experiments using synthetic and real datasets showed the algorithms computational efficiency scalability and effectiveness

timoshenko systems with indefinite damping abstract we consider the timoshenko system in a bounded domain 0 l r 1 the system has an indefinite damping mechanism i e with a damping function a a x possibly changing sign present only in the equation for the rotation angle we shall prove that the system is still exponentially stable under the same conditions as in the positive constant damping case and provided a 0 l a x d x 0 and a a l 2 for small enough the decay rate will be described explicitly in the arguments we shall also give a new proof of exponential stability for the constant case a a moreover we give a precise description of the decay rate and demonstrate that the system has the spectrum determined growth sdg property i e the type of the induced semigroup coincides with the spectral bound for its generator

perturbative series and the moduli space of riemann surfaces on utilise des techniques de la theorie quantique des champs pour calculer des quantites reliees aux groupes de symetrie de paires f g ou f est une surface et g une epine de f

the second homology group of the mapping class group of an orientable surface in i 7 mumford shows that the picard group p ic is isomorphic to h2 f 2 and conjectures the latter is rank one g 3 we prove this below for g 5 another interpretation of this theorem may be obtained by identifying h2 f as bordism classes of fiber bundles f w4 t where t is a closed oriented surface sect 0 when f is closed every such bundle is bordant to f w t a bundle admitting a section s t w the theorem then says that

spectral properties of two parameter eigenvalue problems ii we study the self adjoint eigenvalue problem w x 0 in hilbert space for one equation in two parameters here is bounded below with compact resolvent for each 1 2 we give necessary and sufficient conditions for the existence of so that holds with w 0 and we investigate the geometry of the set z 0 of such we also discuss higher order solution sets z i where the ith eigenvalue of w vanishes deriving various asymptotic results in a unified fashion

the virtual cohomological dimension of the mapping class group of an orientable surface let f f r be the mapping class group of a surface f of genus g with s punctures and r boundary components the purpose of this paper is to establish cohomology properties of f parallel to those of the arithmetic groups if g is a linear algebraic group defined over q x is the symmetric space associated to g and a is an arithmetic subgroup of g then a is virtually torsion free and acts properly discontinuously on x the rational homology of a is the same as that of x a furthermore there is a bordification of x bs to a manifold with corners 3 and an extension of the action of a to a properly discontinuous action on jf so that the quotient x a is compact the boundary of jf is homotopy equivalent to a wedge of spheres say of dimension d and the virtual cohomological dimension of a is n d 1 where n is the dimension of x in the case of the mapping class group there is no analog for g ivanov unpublished has proven that f is not arithmetic nevertheless f acts properly discontinuously on teichmiiller space r which is homeomorphic to euclidean space of dimension 6 g 6 2 s 3 will play the role of the symmetric space the quotient of 9by f is the moduli space of curves whose rational homology is then identified with that of e harvey har has constructed a borel serre bordification j of 3 by analytic methods in the case where f has punctures we will build g by a different combinatorial method in addition we will explicitly describe inside y a cell complex y of dimension 4 g 4 s onto which j may be f equivariantly retracted thus establishing an analog of the constructions for sl n by serre soul6 sol and ash a this complex will be of the lowest possible dimension because we will use j to prove our main result

the decorated teichmuller space of punctured surfaces a principal 5 bundle over the usual teichmuller space of ans times punctured surface is introduced the bundle is mapping class group equivariant and admits an invariant foliation several coordinatizations of the total space of the bundle are developed there is furthermore a natural cell decomposition of the bundle finally we compute the coordinate action of the mapping class group on the total space the total space is found to have a rich equivariant geometric structure we sketch some connections with arithmetic groups diophantine approximations and certain problems in plane euclidean geometry furthermore these investigations lead to an explicit scheme of integration over the moduli spaces and to the construction of a universal teichmuller space which we hope will provide a formalism for understanding some connections between the teichmuller theory the kp hierarchy and the virasoro algebra these latter applications are pursued elsewhere

schrodinger operator with a strong varying interaction on a curve in r2 in this paper we study a two dimensional quantum system governed by the hamiltonian corresponding to the formal expression where 0 is a continuous compactly supported function and is a curve in r2 we derive the asymptotics of eigenvalues for and analyze consequences of introducing varying delta potential

eigencurves for two parameter self adjoint ordinary differential equations of even order abstract the eigenvalue problem ly x x r x y x is considered for a self adjoint 2nth order operator l which is bounded below with compact resolvent on l2 a b and for real functions f r with certain restrictions it is shown that the eigencurves are piecewise analytic with no line segments unless s f r is constant a e when the curves are lines and possesses left right hand asymptotes iff s attains its minimum maximum value a e on some interval the asymptote equations are given explicitly in terms of the eigenvalues of certain simpler boundary value problems the second order case is discussed in detail

instability results for the damped wave equation in unbounded domains abstract we extend some previous results for the damped wave equation in bounded domains in r d to the unbounded case in particular we show that if the damping term is of the form a with bounded a taking on negative values on a set of positive measure then there will always exist unbounded solutions for sufficiently large positive in order to prove these results we generalize some existing results on the asymptotic behaviour of eigencurves of one parameter families of schrodinger operators to the unbounded case which we believe to be of interest in their own right

fast discovery of sequential patterns in large databases using effective time indexing sequential pattern mining algorithms can often produce more accurate results if they work with specific constraints in addition to the support threshold many systems implement time independent constraints by selecting qualified patterns this selection cannot implement time dependent constraints because the support computation process must validate the time attributes of every data sequence during mining therefore we propose a memory time indexing approach called metisp to discover sequential patterns with time constraints including minimum gap maximum gap exact gap sliding window and duration constraints metisp scans the database into memory and constructs time index sets for effective processing metisp uses index sets and a pattern growth strategy to mine patterns without generating any candidates or sub databases the index sets narrow down the search space to the sets of designated in memory data sequences and speed up the counting of potential items within the indicated ranges our comprehensive experiments show that metisp has better efficiency even with low support and large databases than the well known gsp and delisp algorithms metisp scales up linearly with respect to database size

boundary problems of the second order with an indefinite weight function on considere des problemes aux limites de la forme au wu ou est un domaine borne de r n u w 1 2 soit a q soit a d p x d dx dx q x pour n 1 on suppose que w est une fonction de signe indefinie dans tandis que a a un spectre negatif

stability results for the wave equation with indefinite damping abstract the one dimensional wave equation with damping of indefinite sign in a bounded interval with dirichlet boundary conditions is considered it is proved that solutions decay uniformly exponentially to zero provided the damping potential is in thebv class has positive average is small enough and satisfies a finite number of further constraints guaranteeing that the derivative of the real part of the eigenvalues is negative when the damping vanishes this sharp result completes a previous one by the first author showing that an indefinite sign damping always produces unstable solutions if it is large enough and it answers by the afirmative to a conjecture concerning small damping terms the method of proof relies on the developments by s cox and the second author on the high frequency asymptotic expansion of the spectrum for damped wave equations and on the characterization of the decay rate in terms of the spectral abscissa