parameterized algorithms and kernels for almost induced matching abstract the almost induced matching problem asks whether we can delete at most k vertices from the input graph such that each vertex in the remaining graph has a degree exactly one this paper studies parameterized algorithms for this problem by taking the size k of the deletion set as the parameter we give a 7k vertex kernel and an o 1 7485 k time and polynomial space algorithm both of which are the best known results the linear vertex kernel is obtained by using an extended crown decomposition and careful analysis and the parameterized algorithm is based on a branch and search paradigm

randomized divide and conquer improved path matching and packing algorithms we propose a randomized divide and conquer technique that leads to improved randomized and deterministic algorithms for np hard path matching and packing problems for the parameterized max path problem our randomized algorithm runs in time o 4 k k 2 7 m and polynomial space where m is the number of edges in the input graph improving the previous best randomized algorithm for the problem that runs in time o 5 44 k km and exponential space our randomized algorithms for the parameterized max r d matching and max r set packing problems run in time 4 r 1 k n o 1 and polynomial space improving the previous best algorithms for the problems that run in time 10 88 rk n o 1 and exponential space moreover our randomized algorithms can be derandomized to result in significantly improved deterministic algorithms for the problems and they can be extended to solve other matching and packing problems

approximation algorithms for np complete problems on planar graphs this paper describes a general technique that can be used to obtain approximation schemes for various np complete problems on planar graphs the strategy depends on decompos ing a planar graph into subgraphs of a form we call k outerplanar for fixed k the problems of interest are solvable optimally in linear time on k outerplanar graphs by dynamic programming for general planar graphs if the problem is a maximization problem such as maximum independent set this technique gives for each k a linear time algorithm that produces a solution whose size is at least k k 1 optimal if the problem is a minimization problem such as minimum vertex cover it gives for each k a linear time algorithm that produces a solution whose size is at most k 1 k optimal taking k c log log nl or k c log nl where n is the number of nodes and c is some constant we get polynomial time approximation algorithms whose solution sizes converge toward optimal as n increases the class of problems for which this approach provides approximation schemes includes maximum independent set maximum tile salvage partition into triangles maximum h matching minimum vertex cover minimum dominat ing set and minimum edge dominating set for these and certain other problems the proof of solvability on k outerplanar graphs also enlarges the class of planar gmphs for which the problems are known to be solvable in polynomial time

preservation under extensions on well behaved finite structures a class of relational structures is said to have the extension preservation property if every first order sentence that is preserved under extensions on the class is equivalent to an existential sentence the class of all finite structures does not have the extension preservation property we study the property on classes of finite structures that are better behaved we show that the property holds for classes of acyclic structures structures of bounded degree and more generally structures that are wide in a sense that we will make precise we also show that the preservation property holds for the class of structures of treewidth at most k for any k in contrast we show that the property fails for the class of planar graphs

on the cohen strongly p summing multilinear operators abstract in this paper we introduce and study a new concept of summability in the category of multilinear operators which is the cohen strongly p summing multilinear operators we prove a natural analog of the pietsch domination theorem and we compare the notion of p dominated multilinear operators with this class by generalizing a theorem of bu cohen

multiple rademacher means and their applications abstract we evaluate multiple rademacher means for various classes of multilinear operators under the assumption that the range has cotype q these results show that the class of multiple q 2 summing operators plays an important role further we get new extensions of bu s theorem in the multilinear case

structural modifications simulated by virtual distortions a numerical strategy for the simulation of structural modifications by virtual distortions is proposed two cases of structural modification are considered the first concerns modifications of material distribution and the second modifications of local constitutive relations e g unilateral constraints for stresses or deformations a formaulation of the fundamental equations of the simulation method is presented these equations are applicable to the general structural modification problem of a truss like structure then numerical algorithms which refer to particular applications such as progressive collapse analysis or the analysis of structures with gaps are discussed the versatility of the method is illustrated with a number of examples and the computational advantages of structural modification by the virtual distortion method are discussed

highly acyclic groups hypergraph covers and the guarded fragment we construct finite groups whose cayley graphs have large girth even with respect to a discounted distance measure that contracts arbitrarily long sequences of edges from the same color class subgroup and only counts transitions between color classes cosets these groups are shown to be useful in the construction of finite bisimilar hypergraph covers that avoid any small cyclic configurations we present two applications to the finite model theory of the guarded fragment a strengthening of the known finite model property for gf and the characterization of gf as the guarded bisimulation invariant fragment of first order logic in the sense of finite model theory

multiple summing operators on banach spaces abstract in this paper we improve some previous results about multiple p summing multilinear operators by showing that every multilinear form from l 1 spaces is multiple p summing for 1 p 2 the proof is based on the existence of a predual for the banach space of multiple p summing multilinear forms we also show the failure of the inclusion theorem in this class of operators and improve some results of y melendez and a tonge about dominated multilinear operators

strongly p summing multilinear operators abstract we define the concept of strongly p summing multilinear operators and prove that they have properly defined aron berner extensions some properties and examples are shown

on the complexity of connection games in this paper we study three connection games among the most widely played havannah twixt and slither we show that determining the outcome of an arbitrary input position is pspace complete in all three cases our reductions are based on the popular graph problem generalized geography and on hex itself we also consider the complexity of generalizations of hex parameterized by the length of the solution and establish that while short generalized hex is w1 hard short hex is fpt finally we prove that the ultra weak solution to the empty starting position in hex cannot be fully adapted to any of these three games the games of havannah twixt and slither are pspace complete the game of slither does not admit draws on finite planar grid boards short generalized hex is w1 hard and short hex is fixed parameter tractable

extensions of multilinear operators and banach space properties a new characterization of the dunford pettis property in terms of the extensions of multilinear operators to the biduals is obtained for the first time multilinear characterizations of the reciprocal dunford pettis property and pelczynski s property v are also found polynomial and holomorphic versions of these properties are given as well

parameterized approximation algorithms for packing problems parameterized approximation is a topic of considerable interest in the field of parameterized complexity in the past decade new color coding related techniques including the breakthrough representative sets technique have been proven extremely powerful in the design of fast parameterized algorithms furthermore packing problems which are often solved via color coding related techniques have enjoyed a race towards obtaining the fastest parameterized algorithms that solve them therefore it is natural to ask whether packing problems admit efficient parameterized approximation algorithms in this paper we answer this question affirmatively we present tradeoffs that improve the running times of algorithms for well known special cases of the 3 setk packing problem at the cost of their accuracy consider a packing problem for which there is no known algorithm with approximation ratio and a parameter k if the value of an optimal solution is at least k we seek a solution of value at least k otherwise we seek an arbitrary solution clearly if the best known parameterized algorithm that finds a solution of value t runs in time o f t for some function f we are interested in running times better than o f k our main contribution lies in the adaptation of notions fundamental to the representative sets technique to the design of approximation algorithms we introduce the definition of approximate lopsided universal sets combine partial executions of representative sets based algorithms with approximation algorithms and adapt the iterative expansion framework in the context of representative sets to the design of parameterized approximation algorithms our ideas are intuitive and may be relevant to the design of other parameterized approximation algorithms

some techniques on nonlinear analysis and applications in this paper we present two different results in the context of nonlinear analysis the first one is essentially a nonlinear technique that in view of its strong generality may be useful in different practical problems the second result more technical but also connected to the first one is an extension of the well known pietsch domination theorem the last decade witnessed the birth of different families of pietsch domination type results and some attempts of unification our result that we call full general pietsch domination theorem is potentially a definitive pietsch domination theorem which unifies the previous versions and delimits what can be proved in this line the connections to the recent notion of weighted summability are traced

dominating set is fixed parameter tractable in claw free graphs we show that the dominating set problem parameterized by solution size is fixed parameter tractable fpt in graphs that do not contain the claw k 1 3 the complete bipartite graph on four vertices where the two parts have one and three vertices respectively as an induced subgraph we present an algorithm that uses 2 o k 2 n o 1 time and polynomial space to decide whether a claw free graph on n vertices has a dominating set of size at most k note that this parameterization of dominating set is w 2 hard on the set of all graphs and thus is unlikely to have an fpt algorithm for graphs in general the most general class of graphs for which an fpt algorithm was previously known for this parameterization of dominating set is the class of k i j free graphs which exclude for some fixed i j n the complete bipartite graph k i j as a subgraph for i j 2 the class of claw free graphs and any class of k i j free graphs are not comparable with respect to set inclusion we thus extend the range of graphs over which this parameterization of dominating set is known to be fixed parameter tractable we also show that in some sense it is the presence of the claw that makes this parameterization of the dominating set problem hard more precisely we show that for any t 4 the dominating set problem parameterized by the solution size is w 2 hard in graphs that exclude the t claw k 1 t as an induced subgraph our arguments also imply that the related connected dominating set and dominating clique problems are w 2 hard in these graph classes finally we show that for any t n the clique problem parameterized by solution size which is w 1 hard on general graphs is fpt in t claw free graphs our results add to the small and growing collection of fpt results for graph classes defined by excluded subgraphs rather than by excluded minors

graph editing problems with extended regularity constraints graph editing problems offer an interesting perspective on sub and supergraph identification problems for a large variety of target properties they have also attracted significant attention in recent years particularly in the area of parameterized complexity as the problems have rich parameter ecologies in this paper we examine generalisations of the notion of editing a graph to obtain a regular subgraph in particular we extend the notion of regularity to include two variants of edge regularity along with the unifying constraint of strong regularity we present a number of results with the central observation that these problems retain the general complexity profile of their regularity based inspiration when the number of edits k and the maximum degree r are taken together as a combined parameter the problems are tractable i e in fpt but are otherwise intractable we also examine variants of the basic editing to obtain a regular subgraph problem from the perspective of parameterizing by the treewidth of the input graph in this case the treewidth of the input graph essentially becomes a limiting parameter on the natural k r parameterization

edge disjoint packing of stars and cycles abstract we study the parameterized complexity of two graph packing problems edge disjoint k packing of s stars and edge disjoint k packing of s cycles with respect to the choice of parameters we show that although the two problems are fpt with both k and s as parameters they are unlikely to be fixed parameter tractable when parameterized by only k or only s in terms of kernelization complexity we show that edge disjoint k packing of s stars has a kernel with size polynomial in both k and s but in contrast unless np conp poly edge disjoint k packing of s cycles does not have a kernel with size polynomial in both k and s and moreover does not have a kernel with size polynomial in s for any fixed k we also show that edge disjoint k packing of 4 cycles admits a 96 k 2 kernel in general graphs and a 96 k kernel in planar graphs

two lipschitz operator ideals abstract we introduce and investigate the concept of two lipschitz operator ideal between pointed metric spaces and banach spaces we show the basics of this new theory and we give a procedure to create a two lipschitz operator ideal from a linear operator ideal we apply our result to the ideals of strongly p summing and compact linear operator to obtain their corresponding two lipschitz operator ideal also we establish a natural relation between two lipschitz and bilinear maps and show that the two lipschitz factorable p dominated operators are those which are associated to the well known p semi integral bilinear operators

the elastic plastic analysis of frames by the theorems of structural variation the theorems of structural variation for rigidly jointed frames are extended to cover the nonlinear elastic plastic analysis of frames to collapse strain hardening and other material changes are included in the analysis it is shown that the entire load deflection history of a frame following the successive formation of plastic hinges up to and including collapse is obtained from a single initial elastic analysis the manner in which these theorems are used to insert real or plastic hinges to a frame is presented and details of the manual calculations involved in the elastic plastic analysis of a portal is given to demonstrate the simplicity of the method this is followed by a comparison of the results with those obtained experimentaly by baker and charlton the versatility of the method is then demonstrated by altering the shape of a frame before its elastic plastic analysis

fixed parameter tractability definability and model checking in this article we study parameterized complexity theory from the perspective of logic or more specifically descriptive complexity theory we propose to consider parameterized model checking problems for various fragments of first order logic as generic parameterized problems and show how this approach can be useful in studying both fixed parameter tractability and intractability for example we establish the equivalence between the model checking for existential first order logic the homomorphism problem for relational structures and the substructure isomorphism problem our main tractability result shows that model checking for first order formulas is fixed parameter tractable when restricted to a class of input structures with an excluded minor on the intractability side for every t ge 0 we prove an equivalence between model checking for first order formulas with t quantifier alternations and the parameterized halting problem for alternating turing machines with t alternations we discuss the close connection between this alternation hierarchy and downey and fellows w hierarchy on a more abstract level we consider two forms of definability called fagin definability and slicewise definability that are appropriate for describing parameterized problems we give a characterization of the class fpt of all fixed parameter tractable problems in terms of slicewise definability in finite variable least fixed point logic which is reminiscent of the immerman vardi theorem characterizing the class ptime in terms of definability in least fixed point logic

on preservation under homomorphisms and unions of conjunctive queries unions of conjunctive queries also known as select project join union queries are the most frequently asked queries in relational database systems these queries are definable by existential positive first order formulas and are preserved under homomorphisms a classical result of mathematical logic asserts that the existential positive formulas are the only first order formulas up to logical equivalence that are preserved under homomorphisms on all structures finite and infinite the question of whether the homomorphism preservation theorem holds for the class of all finite structures resisted solution for a long time it was eventually shown that unlike other classical preservation theorems the homomorphism preservation theorem does hold in the finite in this article we show that the homomorphism preservation theorem holds also for several restricted classes of finite structures of interest in graph theory and database theory specifically we show that this result holds for all classes of finite structures of bounded degree all classes of finite structures of bounded treewidth and more generally all classes of finite structures whose cores exclude at least one minor

factorization of absolutely continuous polynomials abstract in this paper we study the ideal of dominated p continuous polynomials that extend the nowadays well known ideal of p dominated polynomials to the more general setting of the interpolated ideals of polynomials we give the polynomial version of pietsch s factorization theorem for this new ideal although based on botelho et al in press 16 our factorization theorem requires new techniques inspired in the theory of banach lattices

an abstract result on cohen strongly summing operators abstract we present an abstract result that characterizes the coincidence of certain classes of linear operators with the class of cohen strongly summing linear operators our argument is extended to multilinear operators and as a consequence we establish some alternative characterizations for the class of cohen strongly summing multilinear operators

entire functions on c0 abstract it is shown that every holomorphic function on c 0 which is bounded on weakly compact sets is bounded on bounded sets

abstract extrapolation theorems for absolutely summing nonlinear operators in this paper we prove a general version of the extrapolation theorem for absolutely summing nonlinear operators it is explicitly shown that this result encompasses the previous old and recent linear and nonlinear extrapolation theorems as particular cases one of the steps of the proof provides another nonlinear extrapolation theorem of independent interest

large induced subgraphs via triangulations and cmso we obtain an algorithmic metatheorem for the following optimization problem let varphi be a counting monadic second order logic cmso formula and t geq 0 be an integer for a given graph g v e the task is to maximize x subject to the following there is a set f subseteq v such that x subseteq f the subgraph g f induced by f is of treewidth at most t and the structure g f x models varphi i e g f x models varphi we give an algorithm solving this optimization problem on any n vertex graph g in time cal o pi g cdot n t 4 cdot f t varphi where pi g is the set of all potential maximal cliques in g and f is a function of t and varphi only pipelined with the known bounds on the number of potential maximal cliques in different graph classes there are a plethora of algorithmic consequences extending and subsuming many known results on polynomial time algorithms for graph classes we also show that all potential maximal cliques of g can be enumerated in time cal o 1 7347 n this implies the existence of an exact exponential algorithm of running time cal o 1 7347 n for many np hard problems related to finding maximum induced subgraphs with different properties

weak strong continuity of multilinear mappings and the pelczynski pitt theorem abstract in generalizing a result of pelczynski the sequential weak to norm continuity ofn linear mappings between certain banach spaces including spaces of type and cotype will be studied in particular it is shown that everyn linear continuous mapping from lp1 lpninto lqis compact if and only if i 1n 1 pi

weakly continuous mappings on banach spaces abstract it is shown that every n homogeneous continuous polynomial on a banach space e which is weakly continuous on the unit ball of e is weakly uniformly continuous on the unit ball of e applications of the result to spaces of polynomials and holomorphic mappings on e are given

derivative and factorization of holomorphic functions for a holomorphic function f of bounded type on a complex banach space e we show that its derivative df e e takes bounded sets into certain families of sets if and only if f may be factored in the form f g s where s is in some associated operator ideal and g is a holomorphic function of bounded type we also prove that the multilinear and polynomial mappings factor in an analogous way if and only if they are k bounded

an eigen force method for finite element analysis and reanalysis this paper presents a force based finite element method that involves eigen space transformation of element stiffness matrices in the first analysis in each subsequent analysis reanalysis associated with structural variations the solution obtained previously is modified making use of intrinsic properties of eigen solutions and avoiding the time consuming task of solving a large system of equations the structural variations may involve changes in material properties birth or death of elements or change in boundary conditions numerical examples are presented to compare the accuracy and computational efficiency of the proposed method with the displacement based finite element method 1997 by john wiley sons ltd

a linear time algorithm for finding tree decompositions of small treewidth in this paper we give for constant k a linear time algorithm that given a graph g v e determines whether the treewidth of g is at most k and if so finds a tree decomposition of g with treewidth at most k a consequence is that every minor closed class of graphs that does not contain all planar graphs has a linear time recognition algorithm another consequence is that a similar result holds when we look instead for path decompositions with pathwidth at most some constant k

meta kernelization in a parameterized problem every instance i comes with a positive integer k the problem is said to admit a polynomial kernel if in polynomial time one can reduce the size of the instance i to a polynomial in k while preserving the answer in this work we give two meta theorems on kernelization the first theorem says that all problems expressible in counting monadic second order logic and satisfying a coverability property admit a polynomial kernel on graphs of bounded genus our second result is that all problems that have finite integer index and satisfy a weaker coverability property admit a linear kernel on graphs of bounded genus these theorems unify and extend all previously known kernelization results for planar graph problems

kernels for packing and covering problems abstract we show how the notion of combinatorial duality related to the well known notion of duality from linear programming may be used for translating kernel results obtained for packing problems into kernel results for covering problems we exemplify this approach by having a closer look at the problems of packing a graph with vertex disjoint trees or vertex disjoint stars with r edges the case r 2 has been studied in several other papers by establishing a general notion of a crown we show how linear size vertex kernels can be efficiently achieved for the mentioned problems

a constrained least squares approach to the rapid reanalysis of structures abstract a procedure to reanalyze a damaged structure using a finite element force method of analysis is presented perturbation analysis of constrained least squares problems is adapted to handle reanalysis by the force method and related theoretical and numerical results are presented

on summability of nonlinear mappings a new approach the main goal of this paper is to characterize arbitrary nonlinear non multilinear mappings f x 1 times cdots times x n rightarrow y between banach spaces that satisfy a quite natural pietsch domination type theorem around a given point a 1 ldots a n in x 1 times cdots times x n as a consequence of our approach a notion of weighted summability arises naturally which may be an interesting topic for further investigation

editing to a graph of given degrees we consider the editing to a graph of given degrees problem that asks for a graph g non negative integers d k and a function v g 1 d whether it is possible to obtain a graph g from g such that the degree of v is v for any vertex v by at most k vertex or edge deletions or edge additions we construct an fpt algorithm for editing to a graph of given degrees parameterized by d k we complement this result by showing that the problem has no polynomial kernel unless np conp poly

looking at the stars the problem of packing k vertex disjoint copies of a graph h into another graph g is np complete if h has more than two vertices in some connected component in the framework of parameterized complexity we analyze a particular family of instances of this problem namely the packing of stars we give a quadratic kernel for packing k copies of h k1 s when we consider the special case of s 2 i e h being a star with two leaves we give a linear kernel and an algorithm running in time o 25 301kk2 5 n3

finding large degree anonymous subgraphs is hard a graph is said to be k anonymous for an integer k if for every vertex in the graph there are at least k 1 other vertices with the same degree we examine the computational complexity of making a given undirected graph k anonymous either through at most s vertex deletions or through at most s edge deletions the corresponding problem variants are denoted by anonym v del and anonym e del we present a variety of hardness results most of them hold for both problems the two variants are intractable from the parameterized as well as from the approximation point of view in particular we show that both variants remain np hard on very restricted graph classes like trees even if k 2 we further prove that both variants are w1 hard with respect to the combined parameter solutions size s and anonymity level k with respect to approximability we obtain hardness results showing that neither variant can be approximated in polynomial time within a factor better than n 1 2 unless p np furthermore for the optimization variants where the solution size s is given and the task is to maximize the anonymity level k this inapproximability result even holds if we allow a running time of f s n o 1 for any computable function f on the positive side we classify both problem variants as fixed parameter tractable with respect to the combined parameter solution size s and maximum degree

the parameterized complexity of k edge induced subgraphs we prove that finding a k edge induced subgraph is fixed parameter tractable thereby answering an open problem of leizhen cai our algorithm is based on several combinatorial observations gauss famous eureka theorem and a generalization of the well known fpt algorithm for the model checking problem for first order logic on graphs with locally bounded tree width due to frick and grohe on the other hand we show that two natural counting versions of the problem are hard hence the k edge induced subgraph problem is one of the very few known examples in parameterized complexity that are easy for decision while hard for counting

rolle s theorem for polynomials of degree four in a hilbert space in an infinite dimensional real hilbert space we introduce a class of fourth degree polynomials which do not satisfy rolle s theorem in the unit ball extending what happens in the finite dimensional case we show that every fourth degree polynomial defined by a compact operator satisfies rolle s theorem

the approximation property for spaces of holomorphic functions on infinite dimensional spaces ii let h u denote the vector space of all complex valued holomorphic functions on an open subset u of a banach space e let and respectively denote the compact ported topology and the bornological topology on h u we show that if e is a banach space with a shrinking schauder basis and with the property that every continuous polynomial on e is weakly continuous on bounded sets then h u and h u have the approximation property for every open subset u of e the classical space c0 the original tsirelson space t and the tsirelson james space tj are examples of banach spaces which satisfy the hypotheses of our main result our results are actually valid for riemann domains

matching and weighted p2 packing algorithms and kernels parameterized algorithms and kernelization algorithms are presented for the weighted p 2 packing problem which is a generalization of the famous graph matching problem the parameterized algorithms are based on the following new techniques and observations 1 new study on structure relationship between graph matchings in general graphs and p 2 packings in bipartite graphs 2 an effective graph bi partitioning algorithm and 3 a polynomial time algorithm for a constrained weighted p 2 packing problem in bipartite graphs the kernelization algorithms are based on the following new techniques 1 the application of graph matching in kernelization 2 a crown reduction structure for weighted problems these techniques lead to randomized and deterministic parameterized algorithms that significantly improve the previous best upper bounds for the problem for both weighted and unweighted versions for the kernelization algorithm by using a weighted version of crown reduction a kernel of size o k 2 is presented where k is the given parameter of the problem

absolutely continuous multilinear operators abstract we introduce the new class of the p p 1 p m absolutely continuous multilinear operators that is defined using a summability property that provides the multilinear version of the p absolutely continuous operators we give an analogue of the pietsch domination theorem and a multilinear version of the associated factorization theorem that holds for p absolutely continuous operators obtaining in this way a rich factorization theory we present also a tensor norm which represents this multi ideal by trace duality as an application we show that p p 1 p m absolutely continuous multilinear operators are compact under some requirements applications to factorization of linear maps on banach function spaces through interpolation spaces are also given

on the treewidth of dynamic graphs dynamic graph theory is a novel growing area that deals with graphs that change over time and is of great utility in modeling modern wireless mobile and dynamic environments as a graph evolves possibly arbitrarily it is challenging to identify the graph properties that can be preserved over time and understand their respective computability in this paper we are concerned with the treewidth of dynamic graphs we focus on metatheorems which allow the generation of a series of results based on general properties of classes of structures in graph theory two major metatheorems on treewidth provide complexity classifications by employing structural graph measures and finite model theory courcelle s theorem gives a general tractability result for problems expressible in monadic second order logic on graphs of bounded treewidth and frick and grohe demonstrate a similar result for first order logic and graphs of bounded local treewidth we extend these theorems by showing that dynamic graphs of bounded local treewidth where the length of time over which the graph evolves and is observed is finite and bounded can be modeled in such a way that the local treewidth of the underlying graph is maintained we show the application of these results to problems in dynamic graph theory and dynamic extensions to static problems in addition we demonstrate that certain widely used dynamic graph classes have bounded local treewidth

deciding first order properties of locally tree decomposable structures we introduce the concept of a class of graphs or more generally relational structures being locally tree decomposable there are numerous examples of locally tree decomposable classes among them the class of planar graphs and all classes of bounded valence or of bounded tree width we also consider a slightly more general concept of a class of structures having bounded local tree width we show that for each property of structures that is definable in first order logic and for each locally tree decomposable class c of structures there is a linear time algorithm deciding whether a given structure a c has property for classes c of bounded local tree width we show that for every k 1 there is an algorithm solving the same problem in time o n1 1 k where n is the cardinality of the input structure

polynomial algebras and smooth functions in banach spaces abstract let a n x be the algebra of polynomials on a real banach space x which is generated by all continuous polynomials of degree not exceeding n let m be the minimal integer such that there is a non compact m homogeneous polynomial p p x m l 1 then n m implies that the uniform closure of a n x does not contain all polynomials of degree n 1 and hence the chain of closures a n x n m is strictly increasing in the rest of the note we give solutions to three problems concerning the behaviour of smooth functions on banach spaces posed in the literature in particular we construct an example of a uniformly differentiable real valued function f on the unit ball of a certain banach space x such that there exists no uniformly differentiable function g on b x for any 1 which coincides with f in some neighbourhood of the origin

extensions of smooth mappings into biduals and weak continuity abstract we study properties of uniformly differentiable mappings between real banach spaces among our main results are generalizations of a number of classical results for linear operators on l spaces into the setting of uniformly differentiable mappings denote by b x the closed unit ball of a banach space x let x be a l space 1 and let y be a banach space let t b x y be a continuous mapping which is uniformly differentiable in the open unit ball of x assuming that t is weakly compact then t can be extended preserving its best smoothness properties into the mapping from the 1 multiple of the unit ball of any superspace of the domain space x into the same range space y we also show that t maps weakly cauchy sequences from b x into norm convergent sequences in y this is a uniformly smooth version of the dunford pettis property for the l spaces we also show that a uniformly differentiable mapping t which is not necessarily weakly compact still maps weakly cauchy sequences from b x into norm convergent sequences in y provided y does not contain an isomorphic copy of c 0 we prove that for certain pairs of banach spaces the completion of the space of polynomials equipped with the topology of uniform convergence on the bounded sets of the functions and their derivatives up to order k coincides with the space of uniformly differentiable up to order k mappings our work is based on a number of tools that are of independent interest we prove for every pair of banach spaces x y that any continuous mapping t b x y which is uniformly differentiable of order up to k in the interior of b x can be extended preserving its best smoothness into a bidual mapping t b x y another main tool is a result of zippin s type we show that weakly cauchy sequences in x c k can be uniformly well approximated by weakly cauchy sequences from a certain c 0 is a countable ordinal subspace of x

polynomial properties of banach spaces abstract several properties defined by polynomials on a banach space are introduced and briefly studied we apply them to give necessary and sufficient conditions for the non containment of l 1 in a symmetric projective tensor product of banach spaces

multilinear variants of maurey and pietsch theorems and applications we prove composition results for multilinear operators and multilinear variants of maurey and pietsch theorems both for multiple p summing p dominated and p summing multilinear operators

asymptotic structure lp estimates of sequences and compactness of multilinear mappings abstract we relate the moduli of asymptotic uniform smoothness and convexity of a banach space with the existence of upper and lower l p estimates of sequences in the space to this end we introduce two properties which are related to the m p property defined by kalton and werner in this way we obtain a connection between the moduli of asymptotic uniform smoothness and convexity and compactness or weak sequential continuity of multilinear mappings finally we give some applications to the existence of analytic and asymptotically flat norms on a banach space

faster approximation schemes and parameterized algorithms on odd h minor free graphs we improve the running time of the general algorithmic technique known as baker s approach 1994 1 on h minor free graphs from o n f h to o f h n o 1 the numerous applications include e g a 2 approximation for coloring and ptases for various problems such as dominating set and max cut where we obtain similar improvements on classes of odd minor free graphs which have gained significant attention in recent time we obtain a similar acceleration for a variant of the structural decomposition theorem proved by demaine et al 2010 20 we use these algorithms to derive faster 2 approximations furthermore we present the first ptases and subexponential fpt algorithms for independent set and vertex cover on these graph classes using a novel dynamic programming technique we also introduce a technique to derive nearly subexponential parameterized algorithms on h minor free graphs our technique applies in particular to problems such as steiner tree directed subgraph with a property directed longest path and connected independent dominating set on some or all proper minor closed graph classes we obtain as a corollary that all problems with a minor monotone subexponential kernel and amenable to our technique can be solved in subexponential fpt time onh minor free graphs this results in a general methodology for subexponential parameterized algorithms outside the framework of bidimensionality

on cohen almost summing multilinear operators abstract we show that all cohen strongly p summing multilinear operators and polynomials on banach spaces are cohen almost summing if the range space is a hilbert space then all cohen strongly p summing multilinear operators and polynomials are strongly q summing 1 p q moreover if both domain and range spaces are hilbert spaces then all hilbert schmidt multilinear operators are cohen strongly 2 summing

factorization of injective ideals by interpolation we construct a factorization of certain multilinear mappings through linear operators belonging to closed injective operator ideals using interpolation technique an extension of the duality theorem for interpolation spaces is also obtained

weak sequential completeness of spaces of homogeneous polynomials abstract let p w e n f be the space of all continuous n homogeneous polynomials from a banach space e into another f that are weakly continuous on bounded sets we give sufficient conditions for the weak sequential completeness of p w e n f these sufficient conditions are also necessary if both e and f have the bounded compact approximation property we also show that the weak sequential completeness and the reflexivity of p w e n f are equivalent whenever both e and f are reflexive

duality in spaces of nuclear and integral polynomials abstract we study the spaces of nuclear and integral vector valued polynomials and their duals we prove that if e is asplund p n ne f p i ne f isometrically for any banach space f we describe p n ne f as a subspace of p ne f in terms of weak star continuous polynomials we show that p w ne f p c ne f when e has the approximation property

the parameterized complexity of editing graphs for bounded degeneracy we examine the parameterized complexity of the problem of editing a graph to obtain an r degenerate graph we show that for the editing operations vertex deletion and edge deletion both separately and combined the problem is w p complete and remains w p complete even if the input graph is already r 1 degenerate or has maximum degree 2r 1 for all r 2 we also demonstrate fixed parameter tractability for several clique based problems when the input graph has bounded degeneracy

on finding short resolution refutations and small unsatisfiable subsets we consider the parameterized problems of whether a given set of clauses can be refuted within k resolution steps and whether a given set of clauses contains an unsatisfiable subset of size at most k we show that both problems are complete for the class w 1 the first level of the w hierarchy of fixed parameter intractable problems our results remain true if restricted to 3 sat instances and or to various restricted versions of resolution including tree like resolution input resolution and read once resolution applying a metatheorem of frick and grohe we show that restricted to classes of sets of clauses of locally bounded treewidth the considered problems are fixed parameter tractable for example the problems are fixed parameter tractable for planar cnf formulas

deciding first order properties of nowhere dense graphs nowhere dense graph classes introduced by neset il and ossona de mendez 2010 2011 form a large variety of classes of sparse graphs including the class of planar graphs actually all classes with excluded minors and also bounded degree graphs and graph classes of bounded expansion we show that deciding properties of graphs definable in first order logic is fixed parameter tractable on nowhere dense graph classes parameterized by the length of the input formula at least for graph classes closed under taking subgraphs this result is optimal it was known before that for all classes c of graphs closed under taking subgraphs if deciding first order properties of graphs in c is fixed parameter tractable then c must be nowhere dense under a reasonable complexity theoretic assumption as a by product we give an algorithmic construction of sparse neighborhood covers for nowhere dense graphs this extends and improves previous constructions of neighborhood covers for graph classes with excluded minors at the same time our construction is considerably simpler than those our proofs are based on a new game theoretic characterization of nowhere dense graphs that allows for a recursive version of locality based algorithms on these classes on the logical side we prove a rank preserving version of gaifman s locality theorem

testing first order properties for subclasses of sparse graphs we present a linear time algorithm for deciding first order fo properties in classes of graphs with bounded expansion a notion recently introduced by neset il and ossona de mendez this generalizes several results from the literature because many natural classes of graphs have bounded expansion graphs of bounded tree width all proper minor closed classes of graphs graphs of bounded degree graphs with no subgraph isomorphic to a subdivision of a fixed graph and graphs that can be drawn in a fixed surface in such a way that each edge crosses at most a constant number of other edges we deduce that there is an almost linear time algorithm for deciding fo properties in classes of graphs with locally bounded expansion more generally we design a dynamic data structure for graphs belonging to a fixed class of graphs of bounded expansion after a linear time initialization the data structure allows us to test an fo property in constant time and the data structure can be updated in constant time after addition deletion of an edge provided the list of possible edges to be added is known in advance and their simultaneous addition results in a graph in the class all our results also hold for relational structures and are based on the seminal result of neset il and ossona de mendez on the existence of low tree depth colorings

rapid reanalysis by the force method abstract a procedure to reanalyze a damaged structure using a finite element force method of analysis is presented unlike similar methods that use the displacement method of analysis the procedure presented here yields a direct rather than an iterative method a computer program was written and illustrative examples were solved and are presented herein residual elastic strength is defined and calculated for damaged structures that were originally optimally designed for minimum weight