handlebody construction of stein surfaces the topology of stein surfaces and contact 3 manifolds is studied by means of handle decompositions a simple characterization of homeomorphism types of stein surfaces is obtained they correspond to open handlebodies with all handles of index 2 an uncountable collection of exotic l4 s is shown to admit stein structures new invariants of contact 3 manifolds are produced including a complete and computable set of invariants for determining the homotopy class of a 2 plane field on a 3 manifold these invariants are applicable to seiberg witten theory several families of oriented 3 manifolds are examined namely the seifert fibered spaces and all surgeries on various links in s3 and in each case it is seen that most members of the family are the

the functional central limit theorem under the strong mixing condition we prove a central limit theorem for strongly mixing sequences under a sharp sufficient condition which combines the rate of the strong mixing coefficient with the quantile function the result improves on all earlier central limit theorems for this type of dependence and answers a conjecture raised by bradley in 1997 moreover we derive the corresponding functional central limit theorem

likelihood based scoring rules for comparing density forecasts in tails abstract we propose new scoring rules based on conditional and censored likelihood for assessing the predictive accuracy of competing density forecasts over a specific region of interest such as the left tail in financial risk management these scoring rules can be interpreted in terms of kullback leibler divergence between weighted versions of the density forecast and the true density existing scoring rules based on weighted likelihood favor density forecasts with more probability mass in the given region rendering predictive accuracy tests biased toward such densities using our novel likelihood based scoring rules avoids this problem

a triangular norm based propositional fuzzy logic in 1997 wang introduced the formal system l for a type of fuzzy propositional calculus given by a particular t norm different from the three famous ones lukasiewicz godel product recently pei proved the completeness theorem for l with respect to w semantic by developing a theory of algebraic systems in this paper we aim to prove it by essentially metamathematical method furthermore we discussed originally the completeness for the schematic extension l n of l with respect to w n semantic

witten s complex and infinite dimensional morse theory we investigate the relation between the trajectories of a finite dimensional gradient flow connecting two critical points and the cohomology of the surrounding space the results are applied to an infinite dimensional problem involving the symplect c action function

undefinability of min conjunction in mtl firstly a sufficient and necessary condition is given to decide whether the lattice operations of a wnm chain can be definable from its other operations secondly we show that it is indeed necessary to introduce the min conjunction into mtl as a primitive connective by constructing a left continuous t norm such that in the propositional calculus defined by this t norm the min conjunction and max disjunction are not definable from the strong conjunction implication and truth constant email protected

a characterization theorem on the rotation construction for triangular norms the rotation construction for t norms is introduced in j appl non classical logics 10 2000 83 92 in the present paper we characterize the widest class of operators with which the rotation construction results in left continuous t norms with involutive associated negations

on a class of left continuous t norms in this paper we study the subclass of left continuous t norms n which are definable by an arbitrary continuous t norm and a weak i e non necessarily involutive negation n by putting x n y 0 if x n y x n y x y otherwise thus generalizing the construction of the so called nilpotent minimum t norms we provide the characterization of weak negations compatible with a given continuous t norm and conversely which are the continuous t norms compatible with a given weak negation function

central limit theorems for mixing sequences of random variables under minimal conditions soit xj j 1 une suite strictement stationnaire de variables aleatoires de moyenne nulle de variance finie et satisfaisant une condition de melange forte soit s n la nieme somme partielle et supposons var s n variant regulierement et d ordre 1 on demontre que si s n var s n 1 2 ne converge pas vers 0 en l 1 alors xj j 1 est dans le domaine d attraction partielle d une loi gaussienne

group actions corks and exotic smoothings of mathbb r 4 r 4 we provide the first information on diffeotopy groups of exotic smoothings of mathbb r 4 for each of uncountably many smoothings there are uncountably many isotopy classes of self diffeomorphisms we realize these by various explicit group actions there are also actions at infinity by nonfinitely generated groups for which no nontrivial element extends over the whole manifold in contrast every diffeomorphism of the end of the universal mathbb r 4 extends our techniques apply to many other open 4 manifolds and are related to cork theory we show that under broad hypotheses cork twisting is equivalent up to blowups to twisting on an exotic mathbb r 4 and give applications

the functional law of the iterated logarithm for stationary strongly mixing sequences let x i i z be a strictly stationary and strongly mixing sequence of real valued mean zero random variables let a n n 0 be the sequence of strong mixing coefficients we define the strong mixing function by t t and we denote by q the quantile function of x 0 assume that 0 1 1 t q 2 t dt where f 1 denotes the inverse of the monotonic function f the main result of this paper is that the functional law of the iterated logarithm lil holds whenever x i i z satisfies moreover it follows from doukhan massart and rio that for any positive there exists a stationary sequence x i i z with strong mixing coefficients n of the order of n such that the bounded lil does not hold if condition is violated the proof of the functional lil is mainly based on new maximal exponential inequalities for strongly mixing processes which are of independent interest

a fuzzy logic for an ordinal sum t norm among the class of residuated fuzzy logics a few of them have been shown to have standard completeness both for propositional and predicate calculus like godel nm and monoidal t norm based logic systems in this paper a new residuated logic nmg which aims at capturing the tautologies of a class of ordinal sum t norms and their residua is introduced and its standard completeness both for propositional calculus and for predicate calculus are proved

a decomposition theorem for h cobordant smooth simply connected compact 4 manifolds theorem let m and n be smooth h cobordant compact 1 connected 4 manifolds there exist decompositions m m0 m1 and n n0 n1 where m0 and n0 are smooth compact contractible 4 manifolds with boundary so that m1 and n1 are dieomorphic if m and n are closed then we may further arrange that m1 and n1 are 1 connected in fact if w is an h cobordism connecting m and n then w can be written w w0 i w1 where w0 m0 n0 is an often nontrivial h cobordism and w1 m1 n1 is smoothly the product h cobordism m1 i m1 f0 g m1 f1 g this theorem lies in the mainstream of combinatorial 4 manifold theory circa 1975 but oddly the result was overlooked it now ts into a rich context donaldson theory and raises new questions when compared with the known examples in 1988 akbulut a showed that a manifold x homotopy equivalent to a k3 surface could after blowing up a point be transformed into a rational surface q by cutting out and regluing a certain contractible mazur manifold by an involution of its boundary at the time a rather delicate argument of fintushel and stern relying on the observed presence of the homology sphere 2 3 7 x showed that certain donaldson invariants of x and its blow up x were nontrivial this distinguished x from the h cobordant manifold q in retrospect this was the rst nontrivial example of our theorem the result was a surprise the donaldson invariant which derives from the second homology had been localized on a contractible piece recently bizaca and gompf bg have shown that x is in fact dieomorphic to k3 allowing a more direct analysis of its donaldson invariant see e g qk or km they also nd an innite family of examples

on the scope of some formulas defining additive connectives in fuzzy logics in fuzzy sets and systems 149 2005 297 wang et al defined a new fuzzy logic called nmg they also introduced new formulas to define the additive connectives from multiplicative conjunction residuated implication and bottom in nmg however they did not study the scope of these formulas in the general framework of fuzzy logics this is the aim of this paper therefore we add the definability formulas to known fuzzy logics as new axioms following the method used in beyond two theory and applications of multiple valued logic 2003 251 and we obtain some families of logics presented in a simpler language finally we discuss the standard completeness of these new logics

a note on the ordinal sum theorem and its consequence for the construction of triangular norms in this paper the well known ordinal sum theorem of semigroups is generalized and applied to construct new families of triangular subnorms and triangular norms t norms among them one can find several new families of left continuous t norms too

monoidal t norm based logic towards a logic for left continuous t norms hajek s bl logic is the fuzzy logic capturing the tautologies of continuous t norms and their residua in this paper we investigate a weaker logic mtl which is intended to cope with the tautologies of left continuous t norms and their residua the corresponding algebraic structures mtl algebras are defined and completeness of mtl with respect to linearly ordered mtl algebras is proved besides several schematic extensions of mtl are also considered as well as their corresponding predicate calculi

a functional central limit theorem for strongly mixing sequences of random variables we prove a functional central limit theorem for a class of strongly mixing sequences of random variables stationarity is not assumed but the variances of the partial sums must grow linearly our theorem extends previous results by supplying sufficient conditions for the weak convergence of the partial sum process to the wiener process under less restrictive moment assumptions for instance if mathop sup limits n text ex n 2 log x n parallel 1 varepsilon 0 and the mixing rate is exponential then this functional c l t holds under the weaker assumption with e 0 the c l t may fail to hold and it is possible that the c l t is satisfied but the sequence of partial sum processes is not tight