a study on the dimension of global sections of adjoint bundles for polarized manifolds abstract let x be a smooth complex projective variety of dimension n and let l be an ample line bundle on x in this paper in order to investigate the dimension of h 0 k x t l more systematically we introduce the invariant a i x l for every integer i with 0 i n furthermore we study this invariant for the case where l is ample and spanned by global sections as applications we get a lower bound resp an upper bound for the dimension of h 0 k x t l if l is ample and spanned by global sections resp very ample

the connection matrix theory for morse decompositions the connection matrix theory for morse decompositions is introduced the connection matrices are matrices of maps between the homology indices of the sets in the morse decomposition the connection matrices cover in a natural way the homology index braid of the morse decomposition and provide information about the structure of the morse decomposition the existence of connection matrices of morse decompositions is established and examples illustrating applications of the connection matrix are provided

the connection matrix theory for semiflows on not necessarily locally compact metric spaces abstract the index theory of rybakowski for isolated invariant sets and attractor repeller pairs in the setting of a semiflow on a not necessarily locally compact metric space is extended to include a connection matrix theory for morse decompositions partially ordered morse decompositions and attractor semifiltrations of invariant sets are defined and shown to be equivalent the definition and proof of existence of index filtrations for an ordered morse decomposition is provided via the index filtration the homology index braid and the connection matrices of the morse decomposition are defined

unfold fold transformation of stratified programs abstract this paper describes some extensions of tamaki sato s 1984 unfold fold transformation of definite programs we first propose unfold fold rules also preserving the finite failure set by sld resolution of a definite program which the original rules proposed by tamaki and sato do not then we show that our unfold fold rules can be extended to rules for stratified programs and prove that both the success set and the finite failure set by sldnf resolution of a stratified program are preserved preservation of equivalence of the perfect model semantics przymusinski 1988 is also discussed

vector bundles of rank 2 and linear systems on algebraic surfaces let s be a smooth complex algebraic surface and let l be a divisor on s it is well known that the linear system il ksi where ks is the canonical divisor plays an important role in understanding the geometry of s several authors see for example 8 11 studied various properties of this system our paper treats the same subject but the point of view is different from the works mentioned above the philosophy underlying our approach is almost classical points on s more generally effective 0 cycles in special position with respect to il ksi see definition below contain information about the geometry of s this point of view was recently revived in 5 also 10 in fact this paper contains the technique of going from the effective 0 cycle z in special position with respect to il ksi to the geometry of s for the sake of completeness we give a definition and state a theorem which can be found in 5 10

the morse index repeller attractor pairs and the connection index for semiflows on noncompact spaces abstract this paper extends the morse index theory of c c conley to semiflows on a noncompact meric space x is assumed to satisfy a hypothesis related to conditional contraction we collect background material define quasi index pairs and the morse index of a compact isolated invariant set k and prove that the morse index is a connected simple system we study repeller attractor pairs in k define index triples and prove their existence and several properties leading to the concepts of the connection index the connection map and the splitting class finally we consider paths continuous families of pairs k and study continuations of the morse and the connection indices along such paths the present paper is a sequel to the author s previous work on the homotopy index for infinite dimensional semiflows trans amer math soc 269 1982 351 382

the connection map for attractor repeller pairs on montre que l application de connexion est additive les proprietes de l application connexion conduisent a une caracterisation des ensembles invariants isoles avec des points critiques hyperboliques comme une paire attracteur repulseur

nested sequences of index filtrations and continuation of the connection matrix abstract in this paper we prove the existence of nested sequences of index filtrations for convergent sequences of admissible semiflows on a metric space this result is new even in the context of flows on a locally compact space the nested index filtration theorem implies the continuation of homology index braids which in turn implies the continuation of connection matrices in the infinite dimensional conley index theory

the connection matrix in morse smale flows ii given a connection matrix for a morse smale flow on a compact manifold if there are no periodic orbits of equal or adjacent indices related in the partial order we show that the periodic orbits can be replaced by doubly connected rest points in such a way that the given connection matrix induces the unique connection matrix for the resulting flow it follows that for this class of flows all nonuniqueness in the connection matrix is a consequence of the continuation theorem for connection matrices

on the adjunction mapping of very ample vector bundles of corank one let e be a very ample vector bundle of rank n 1 over a smooth complex projective variety x of dimension n 3 the structure of x e being known when k x det e 0 we investigate the structure of the adjunction mapping when 0 k x det e n

conley index and tubular neighborhoods ii abstract this paper is a sequel to our previous paper 11 we prove existence of nested index filtrations for tubular singular semiflow perturbations this generalizes a corresponding result from 7 and is applicable to cases in which the phase space of the perturbed semiflow is not necessarily homeomorphic to a product of metric spaces having as a factor the phase space of the limiting semiflow this result implies tubular homology index braid and connection matrix continuation principles

preservation of stronger equivalence in unfold fold logic program transformation abstract this paper shows that tamaki sato s unfold fold transformation of prolog programs preserves equivalence in a stronger sense that of the usual least herbrand model semantics which tamaki and sato originally showed conventionally the semantics of prolog program is defined by the least herbrand model however the least herbrand model does not always characterize what answer substitutions are returned this paper proves that any program obtained from an initial program by applying tamaki sato s transformation returns the same answer substitutions as the initial program for any given top level goal

homotopy invariants of repeller attractor pairs ii continuation of r a pairs on considere une famille continue a 1 parametre de flots dans le plan parametrise par 0 1 on etablit un cadre qui rend precise la notion de famille continue de paires de repulseur attracteurs on montre qu il y a des equivalences naturelles entre les suites d indices de 2 paires r a le long d un parcours de paires r a

on the homotopy index for infinite dimensional semiflows absrac r in this paper we consider semiflows whose solution operator is eventually a conditional a contraction such semiflows include solutions of retarded and neutral functional differential equations of parabolic and certain other classes of partial differential equations we prove existence of nonsmooth isolating blocks and index pairs for such semiflows via the construction of special lyapunov functionals we show that index pairs enjoy all the properties needed to define the notion of a homotopy index thus generalizing earlier results of conley 2 finally using a result of maii 9 we prove that under additional smoothness assumptions on the semiflow the homotopy index is essentially a finite dimensional concept this gives a formal justification of the applicability of waiewski s principle to infinite dimensional problems several examples illustrate the theory

transformations of clp modules we propose a transformation system for clp programs and modules the framework is inspired by the one of tamaki and sato for pure logic programs however the use of clp allows us to introduce some new operations such as splitting and constraint replacement we provide two sets of applicability conditions the first one guarantees that the original and the transformed programs have the same computational behaviour in terms of answer constraints the second set contains more restrictive conditions that ensure compositionality we prove that under these conditions the original and the transformed modules have the same answer constraints also when they are composed with other modules this result is proved by first introducing a new formulation in terms of trees of a resultants semantics for clp as corollaries we obtain the correctness of both the modular and the non modular system w r t the least model semantics

on the second sectional h arithmetic genus of polarized manifolds let x l be a polarized variety defined over the complex number field with dim x n in this paper we introduce the notion of the i th sectional h arithmetic genus hi x l for every integer i with 0 i n we expect that this invariant has a property similar to the euler poincare characteristic of the structure sheaf of i dimensional varieties in this paper we consider the case where x is smooth and i 2 and we study a polarized version of some results in the theory of surfaces

index filtrations and the homology index braid for partially ordered morse decompositions abstract on a morse decomposition of an invariant set in a flow there are partial orderings defined by the flow these are called admissable orderings of the morse decomposition the index filtrations for a total ordering of a morse decomposition are generalized in this paper with the definition and proof of existence of index filtrations for admissable partial orderings of a morse decomposition it is shown that associated to an index filtration there is a collection of chain complexes and chain maps called the chain complex braid of the index filtration the homology index braid of the corresponding admissable ordering of the morse decomposition is obtained by passing to homology in the chain complex braid keywords morse decomposition conley index index filtration

singular dynamics of strongly damped beam equation abstract the paper is devoted to the dynamics of the model for a beam with strong damping pe e 2 u t t e u t u x x x x u t x x x x g 0 l u 2 d e 0 l u t u d u x x 0 x t 0 l 0 where g r r is continuously differentiable r and l e 0 subject to boundary conditions corresponding to hinged or clamped ends we show that for e 0 the dynamics of the equation is close to the dynamics of equation p0 u t u g 0 l u 2 d a 1 2 u where a u u x x x x with the domain determined by one of the above boundary conditions specifically we show that isolated invariant sets of p0 continue to isolated invariant sets of pe e 0 small having the same conley index moreover isolated morse decompositions with respect to p0 continue to isolated morse decompositions of pe e 0 small having isomorphic homology index braids under some additional assumptions we establish existence and upper semicontinuity results for attractors of e 0 small extending previous results by sevcovic

the continuation theory for morse decompositions and connection matrices the continuation theory for ordered morse decompositions and the indices defined on them the honmology index braid and the connection matrices is established the equivalence between ordered morse decompositions and consistent attractor filtrations is displayed the spaces of ordered morse decompositions for a product parametrization of a local flow are introduced and the local continuation of ordered morse decompositions is obtained via the above described equivalence and the local continuation of attractors the homology index braid and the connection matrices of an admissible ordering of a morse decomposition are shown to be invariant on path components of the corresponding space of ordered morse decompositions this invariance is used to prove that the collection of connection matrices of a morse decomposition is upper semicontinuous over the space of morse decompositions and over the parameter space under local continuation introduction a theorem that describes the behavior of an index under continuous change in its domain is an important component of any index theory the conley index is defined for isolated invariant sets in a local flow and in 1 it is shown that for a product parameterization of a local flow isolated invariant sets continue locally and the conley index is invariant under the local continuation in 10 kurland establishes a corresponding continuation theory for the index defined on attractor repeller pairs it is the aim of this paper to extend these continuation results to a continuation theory for ordered morse decompositions and the indices the homology index braid and the connection matrices defined on them conley s and kurland s continuation theories actually contain more than the local continuation results described above these local results are a part of a broader global continuation scheme in particular in 1 conley defines the space of isolated invariant sets for a product parameterization of a local flow and shows that this space is locally homeomorphic to the parameter space this local homeomorphism then yields the notion of local continuation of isolated invariant sets next it is shown that the conley index is invariant on path components of the space of isolated invariant sets this yields the invariance of the index under local continuation in this paper we use the same approach we define the spaces of ordered morse decompositions for a product parameterization of a local flow the notion of local continuation of morse decompositions and of admissible orderings of morse received by the editors september 20 1987 1980 mathematics subject classification 1985 revision primary 58f35 secondary 58f12 34c35

on the spannedness of adjunction of vector bundles let x be a smooth projective variety of dimension n defined over the field of complex numbers and e be an ample vector bundle on x the linear system kx c e is called the adjoint bundle for vector bundle e the nefness and the ampleness of the adjoint bundle kx cl e have been investigated by several authors abw f p1 yz in this paper we shall investigate the base point freeness spannedness of the adjoint bundle kx c e i e we ask the following