homotopy self equivalences of 4 manifolds we establish a braid of interlocking exact sequences containing the group of homotopy self equivalences of a smooth or topological 4 manifold the braid is computed for manifolds whose fundamental group is finite of odd order

quantum bohmian model for financial market we apply methods of quantum mechanics for mathematical modeling of price dynamics at the financial market the hamiltonian formalism on the price price change phase space describes the classical like evolution of prices this classical dynamics of prices is determined by hard conditions natural resources industrial production services and so on these conditions are mathematically described by the classical financial potential v q where q q1 qn is the vector of prices of various shares but the information exchange and market psychology play important and sometimes determining role in price dynamics we propose to describe such behavioral financial factors by using the pilot wave bohmian model of quantum mechanics the theory of financial behavioral waves takes into account the market psychology the real trajectories of prices are determined through the financial analogue of the second newton law by two financial potentials classical like v q hard market conditions and quantum like u q behavioral market conditions

on the derived category of the classical godeaux surface abstract we construct an exceptional sequence of length 11 on the classical godeaux surface x which is the z 5 z quotient of the fermat quintic surface in p 3 this is the maximal possible length of such a sequence on this surface which has grothendieck group z 11 z 5 z in particular the result answers kuznetsov s nonvanishing conjecture which concerns hochschild homology of an admissible subcategory in the negative the sequence carries a symmetry when interpreted in terms of the root lattice of the simple lie algebra of type e 8 we also produce explicit nonzero objects in the right orthogonal to the exceptional sequence

s t fuzzy relational equations abstract studied are fuzzy relational equations with a general s t composition operator involving s and t norms basic properties of local and global interactivity in the proposed type of the equations are investigated a relevant optimization scheme illustrated with the aid of several detailed numerical examples is provided

fuzzy linear optimization in the presence of the fuzzy relation inequality constraints with max min composition in this paper we study the new linear objective function optimization with respect to the fuzzy relational inequalities defined by max min composition in which fuzzy inequality replaces ordinary inequality in the constraints fuzzy inequalities enable us to attain the optimal points that are better solutions than those resulting from the resolution of the similar problems with ordinary inequality constraints denoted by x o i in this paper we have presented an algorithm to generate such optimal solutions also two examples are given to illustrate the algorithm presented and some real application of this work

a black scholes schrodinger option price bit versus qubit abstract the celebrated black scholes differential equation provides for the price of a financial derivative the uncertainty environment of such option price can be described by the classical bit a system with two possible states this paper argues for the introduction of a different uncertainty environment characterized by the so called qubit we obtain an information based option price and discuss the differences between this option price and the classical option price

solutions of fuzzy relation equations based on continuous t norms this study is concerned with fuzzy relation equations with continuous t norms in the form atr b where a and b are the fuzzy subsets of x and y respectively email protected xxy is a fuzzy relation and t is a continuous t norm the problem is how to determine a from r and b first an if and only if condition of being solvable is presented novel algorithms are then presented for determining minimal solutions when x and y are finite the proposed algorithms generate all minimal solutions for the equations making them efficient solving procedures

exotic smooth structures on small 4 manifolds with odd signatures let m be 2n 1 mathbb cp 2 2n overline mathbb cp 2 for any integer n 1 we construct an irreducible symplectic 4 manifold homeomorphic to m and also an infinite family of pairwise non diffeomorphic irreducible non symplectic 4 manifolds homeomorphic to m we also construct such exotic smooth structures when m is mathbb cp 2 4 overline mathbb cp 2 or 3 mathbb cp 2 k overline mathbb cp 2 for k 6 8 10

directional dependence of random vectors in this paper we define and study several properties of the concept of multivariate directional dependence and study the new concept in terms of copulas and provide new measures of multivariate association based on directional dependence finally we show the relationships of directional dependence with other dependence concepts such as association and conditional dependence

a discussion on embedding the black scholes option pricing model in a quantum physics setting abstract in this paper we consider the implications of embedding the black scholes option pricing model within a quantum physical setting the option price is considered to be a state function and a potential function is found which allows the option price to satisfy the schrodinger differential equation once this arbitrage free potential function is obtained we argue for the construction of a so called arbitrage potential function this functional is instrumental in determining the existence of a financial state function we show the existence of an arbitrage free price when the potential function converges to one the existence of arbitrage hinges on the non zero value of the planck constant this constant is then linked to a parameter which regulates the probability of occurence of strategy paths we call this parameter the belief parameter we argue that it is the belief parameter which may indeed proxy arbitrage the outcome of this paper shows that the black scholes model can be captured within a quantum physical setting and that the advantages of doing so may indeed provide for a first step to include arbitrage in a natural way in an otherwise arbitrage free model

some concepts of negative dependence abstract the theory of positive dependence notions cannot yield useful results for some widely used distributions such as the multinomial dirichlet and the multivariate hypergeometric some conditions of negative dependence that are satisfied by these distributions and which have practical meaning are introduced preservation results for some of these concepts are derived useful inequalities for some widely used distributions are obtained results of mallows 1969 that apply to the multinomial distributions are extended to more distributions examples are listed author

to quantum averages through asymptotic expansion of classical averages on infinite dimensional space we study asymptotic expansions of gaussian integrals of analytic functionals on infinite dimensional spaces hilbert and nuclear frechet we obtain an asymptotic equality coupling the gaussian integral and the trace of the composition of scaling of the covariation operator of a gaussian measure and the second frechet derivative of a functional in this way we couple classical average given by an infinite dimensional gaussian integral and quantum average given by the von neumann trace formula we can interpret this mathematical construction as a procedure of dequantization of quantum mechanics we represent quantum mechanics as an asymptotic projection of classical statistical mechanics with infinite dimensional phase space this space can be represented as the space of classical fields so quantum mechanics is represented as a projection of prequantum classical statistical field theory

new constructions of diagonal patchwork copulas we present a method for constructing symmetric copulas which generalizes the diagonal patchwork construction of copulas procedure we also show how it is related to a new construction of a generalized farlie gumbel morgenstern distribution and to the copula transforms

interference of probabilities in the classical probabilistic framework the notion of context complex of physical conditions is basic in this paper we show that the main structures of quantum theory interference of probabilities born s rule complex probabilistic amplitudes hilbert state space representation of observables by operators are present in a latent form in the classical kolmogorov probability model however this model should be considered as a calculus of contextual probabilities in our approach it is forbidden to consider abstract context independent probabilities first context and then probability we start with the conventional formula of total probability for contextual conditional probabilities and then we rewrite it by eliminating combinations of incompatible contexts from consideration in this way we obtain interference of probabilities without to appeal to the hilbert space formalism or wave mechanics our contextual approach is important for demystification of quantum probabilistic formalism this approach gives the possibility to apply quantum like models in domains of science different from quantum theories e g in economics finance social sciences cognitive sciences psychology

finite group actions on kervaire manifolds abstract let m k 4 k 2 be the kervaire manifold a closed piecewise linear pl manifold with kervaire invariant 1 and the same homology as the product s 2 k 1 s 2 k 1 of spheres we show that a finite group of odd order acts freely on m k 4 k 2 if and only if it acts freely on s 2 k 1 s 2 k 1 if m k is smoothable then each smooth structure on m k admits a free smooth involution if k 2 j 1 then m k 4 k 2 does not admit any free top involutions free exotic pl involutions are constructed on m k 30 m k 62 and m k 126 each smooth structure on m k 30 admits a free z 2 z 2 action

the geography problem for 4 manifolds with specified fundamental group for any class m of 4 manifolds for instance the class m g of closed oriented manifolds with 1 m g for a fixed group g the geography of m is the set of integer pairs m m m m where and denote the signature and euler characteristic this paper explores general properties of the geography of m g and undertakes an extended study of m z n

direct and inverse problem in comparison of fuzzy data abstract discussed is the direct and inverse problem of comparison of two linguistic quantities specified as fuzzy sets relations in the same universe of discourse the proposed way of comparison makes use of some logical properties of connectives and implication operators stemming from the foundations of fuzzy sets a list of plausible equality indices is provided the inverse problem is formulated a set of its solutions is provided direct impacts of the discussed approach on development of fuzzy modelling are clearly indicated also it is pointed out how fuzzy sets of higher type or interval valued sets can be generated as a result of analysis of performance of any fuzzy model

homotopy invariants of nonorientable 4 manifolds we define a z 4 quadratic function on 2 for nonorientable 4 manifolds and show that it is a homotopy invariant we then use it to distinguish homotopy types of certain manifolds that arose from an analysis of toral action on nonorientable 4 manifolds

markov property in quantum logic a possible way of the markov property introduction within the framework of the orthomodular quantum logic which is commonly used as the calculus model for quantum mechanics is presented in this paper the presented work follows the logical line rather than any physical interpretation in the framework of quantum mechanics the basic algebraic structure which is used as a model for noncompatible random events is an orthomodular lattice on the orthomodular lattice a dynamical structure is introduced coupled with mappings which have similar properties as s n maps on the orthomodular lattice this construction leads to the definition of an l process with the markov property on the orthomodular lattice

geometrical analysis of physically allowed quantum cloning transformations for quantum cryptography the security of quantum key distribution qkd relies on the no cloning theorem which allows no to copy perfectly a quantum system an eavesdropping activity on the quantum channel perturbs the state of the quantum states which results in noise at the receiver the physical layer detection of the eavesdropping activity of the quantum channel requires tomography which is intractable in experiment an adequate and equivalent answer for the problem can be proposed through the logical layer we propose an efficient algorithmical tool to study the eavesdropping activity on the quantum channel and characterize the properties of a quantum cloning based attack for dv and cvqkd protocols the physically allowed quantum cloning transformations on a quantum system can be described in terms of information geometry we propose a computational geometrical method to analyze the cloning activity on the quantum channel and to characterize the noise properties the security analysis studies the dv discrete variable and cv continuous variable qkd schemes through the four state bb84 and six state dvqkd protocols and the two way cvqkd protocol the proposed geometrical method provides a useful tool to analyze the most powerful attacks against quantum cryptography and the effects of the physically allowed quantum cloning transformations

negative association of random variables with applications random variables x 1 cdots x k are said to be negatively associated na if for every pair of disjoint subsets a 1 a 2 of 1 2 cdots k operatorname cov lbrack f x 1 i in a 1 g x j j in a 2 rbrack leq 0 for all nondecreasing functions f g the basic properties of negative association are derived especially useful is the property that nondecreasing functions of mutually exclusive subsets of na random variables are na this property is shown not to hold for several other types of negative dependence recently proposed one consequence is the inequality p x i leq x i i 1 cdots k leq prod k 1p x i leq x i for na random variables x 1 cdots x k and the dual inequality resulting from reversing the inequalities inside the square brackets in another application it is shown that negatively correlated normal random variables are na other na distributions are the a multinomial b convolution of unlike multinomials c multivariate hypergeometric d dirichlet and e dirichlet compound multinomial negative association is shown to arise in situations where the probability measure is permutation invariant applications of this are considered for sampling without replacement as well as for certain multiple ranking and selection procedures in a somewhat striking example na and positive association representing quite strong opposing types of dependence are shown to exist side by side in models of categorical data analysis

system of fuzzy relation equations with inf composition complete set of solutions the problem of solvability of a system of equations with inf composition is considered on finite universes equations are expressed using operations of a bl algebra we study complete set of solutions of the respective system in the particular case one equation and in the general case in both cases various conditions of solvability are found and proved we characterize all maximal solutions and prove that under certain conditions each solution of the system an equation is less than or equal to a respective maximal one as a result we are able to characterize the complete set of solutions examples of single equations and their systems are considered and complete sets of solutions are found for each

lower solutions of systems of fuzzy equations lower solutions of a system of fuzzy equations are determined by lower solutions of each equation the result is applied to fuzzy relation equations so that they are decomposed to simple fuzzy relation equations

association of normal random variables and slepian s inequality abstract a simple extension of slepian s inequality is given which implies the original inequality and the result that positively correlated normal variables are associated author

quantumlike representation of extensive form games probabilistic aspects we consider an application of the mathematical formalism of quantum mechanics outside physics namely to game theory we present a simple game between macroscopic players say alice and bob or in a more complex form alice bob and cecilia which can be represented in the quantumlike ql way by using a complex probability amplitude game s wave function and noncommutative operators the crucial point is that games under consideration are so called extensive form games here the order of actions of players is important such a game can be represented by the tree of actions the ql probabilistic behavior of players is a consequence of incomplete information which is available to e g bob about the previous action of alice in general one could not construct a classical probability space underlying a ql game this can happen even in a ql game with two players in a ql game with three players bell s inequality can be violated the most natural probabilistic description is given by the so called co

copula and s map on a quantum logic a quantum logic is one of possible mathematical models for non compatible random events in this paper we introduce and study functions called ql copula and ql co copula on a quantum logic and we compare them with the classical definition of copula and co copula respectively finally we show several examples of these functions by means of an s map

linear representations of probabilistic transformations induced by context transitions by using straightforward frequency arguments we classify transformations of probabilities which can be generated by transition from one preparation procedure context to another there are three classes of transformations corresponding to statistical deviations of different magnitudes a trigonometric b hyperbolic c hyper trigonometric it is shown that not only quantum preparation procedures can have trigonometric probabilistic behaviour we propose generalizations of c linear space probabilistic calculus to describe non quantum trigonometric and hyperbolic probabilistic transformations we also analyse the superposition principle in this framework

algorithmic superactivation of asymptotic quantum capacity of zero capacity quantum channels the superactivation of zero capacity quantum channels makes it possible to use two zero capacity quantum channels with a positive joint capacity for their output currently we have no theoretical background to describe all possible combinations of superactive zero capacity channels hence there may be many other possible combinations in practice to discover such superactive zero capacity channel pairs we must analyze an extremely large set of possible quantum states channel models and channel probabilities there is still no extremely efficient algorithmic tool for this purpose this paper shows an efficient algorithmical method of finding such combinations our method can be a very valuable tool for improving the results of fault tolerant quantum computation and possible communication techniques over very noisy quantum channels

a pre quantum classical statistical model with infinite dimensional phase space we study the problem of correspondence between classical and quantum statistical models we show that contrary to a rather common opinion it is possible to construct a natural pre quantum classical statistical model the crucial point is that such a pre quantum classical statistical model is not the conventional classical statistical mechanics on the phase space r2n but its infinite dimensional analogue here the phase space h h where h is the real separable hilbert space the classical quantum correspondence is based on the taylor expansion of classical physical variables maps f r the space of classical statistical states consists of gaussian measures on having zero mean value and dispersion h the quantum statistical model is obtained as the limh 0 of the classical one all quantum states including so called pure states wavefunctions are simply gaussian fluctuations of the vacuum field 0 having dispersions of the planck magnitude

on the α migrativity of semicopulas quasi copulas and copulas in this paper we address the problem of a migrativity for a fixed a for semicopulas copulas and quasi copulas we introduce the concept of an a sum of semicopulas this new concept allows us to completely characterize a migrative semicopulas and copulas moreover a sums also provide a means to obtain a partial characterization of a migrative quasi copulas

generalized solvability criteria for fuzzy equations abstract recently e sanchez has given a necessary and sufficient condition for the existence of a solution of a fuzzy a x c with the extension of a given binary operation in the universe of discourse using many valued logic we generalize this result and get a characterization also of the cases if a x c has only nearly a solution additionally we consider fuzzy relation equations and get similar results

the wave equivalent of the black scholes option price an interpretation abstract we propose an interpretation of the wave equivalent of the black scholes option price we consider nelson s version of the brownian motion dynamical theories of brownian motion princeton university press princeton nj 1967 and we use this specific motion as an input to produce a black scholes pde with a risk premium

s norm aggregation of infinite collections abstract the aggregation of membership values by means of the iterate application of an s norm is of cardinal relevance for the development of any general theory of approximate reasoning which relies on a sup t model for relation composition here we present a definition of s norm aggregation for possibly infinite collections which can be demonstrated to generalize previous approaches consistently it provides a common framework in which classical sup t and finite s t compositions can be analyzed as well as other significant cases general properties of the s norm aggregation concept its specialization for the class of continuous s norms and its relationship with fuzzy measure theory are discussed

fuzzy relational structures the state of art fuzzy relational structures built with the aid of fuzzy sets and fuzzy relations constitute a fundamental class of constructs arising in fuzzy set theory they give rise to fuzzy relation equations in this paper we will develop the concepts of single and multilevel relational structures different logic operations will be discussed in detail aspects of the knowledge representation will be studied and illustrated with several schemes of applications

the orientation of yang mills moduli spaces and 4 manifold topology si x est une 4 variete lisse orientee fermee dont la forme intersection q h 2 x z torsion z est definie negative alors la forme est equivalente sur les entiers a la forme standard 1 1 1 soit x une 4 variete lisse orientee fermee avec les trois proprietes suivantes 1 h 1 x z n a pas de 2 torsion 2 la forme intersection q sur h 2 x torsion a une partie positive de rang 1 ou 2 3 la forme intersection est paire alors q est equivalente sur les entiers a une des formes 01 10 01 10 01 10

approximate solutions of fuzzy relational equations in the previous chs we have discussed various problems concerning solutions of fuzzy relation equations obviously an underlying assumption is that there exists a nonempty set of solutions a situation may occurr and indeed it is quite common in which no solution exists nevertheless even in this case one might be interested to obtain an approximate solution and know to which extent it can be viewed as a solution this stream of investigations is particularly interesting for applicational purposes contrary to the topics already discussed in the previous chs this is a field of research which has not been developed enough so far it concerns studies on solvability properties of fuzzy relation equations in this ch we shall try to answer by using several techniques the following basic question how difficult is it to attain a situation in which the system of equations has solutions and then how to measure this property

biconic aggregation functions we introduce a new method to construct aggregation functions these aggregation functions are called biconic aggregation functions with a given diagonal resp opposite diagonal section and their construction is based on linear interpolation on segments connecting the diagonal resp opposite diagonal of the unit square to the points 0 1 and 1 0 resp 0 0 and 1 1 subclasses of biconic aggregation functions such as biconic semi copulas biconic quasi copulas and biconic copulas are studied in detail

s map and tracial states the notion of s map introduced in quantum logics to define conditional expectations for non compatible events is studied in projection lattices of von neumann algebras it is shown that every tracial state gives rise to an s map and conversely every s map defines a tracial state

an efficient procedure for solving a fuzzy relational equation with max archimedean t norm composition in the literature a necessary condition for minimal solutions of a fuzzy relational equation with max product composition shows that each of its components is either zero or the corresponding component s value of the greatest solution in this paper we first extend this necessary condition to the situation with max archimedean triangular norm t norm composition based on this necessary condition we then propose rules to reduce the problem size so that the complete set of minimal solutions can be computed efficiently furthermore rather than work with the actual equations we employ a simple matrix whose elements capture all of the properties of the equations in finding the minimal solutions numerical examples with specific cases of the max archimedean t norm composition are provided to illustrate the procedure

processing in relational structures fuzzy relational equations abstract the paper provides an overview of methodology for processing fuzzy information in relational structures completed in terms of fuzzy relational equations the origin and the central role of relational calculus in general and fuzzy sets in particular is explained with special emphasis paid to its role and representation capabilities it is pointed out that fuzzy relational equations play a significant role as a platform for a uniform development of techniques in fuzzy sets many of the problems and frameworks developed in fuzzy sets so far can be easily translated into the language of fuzzy relational equations which immediately takes a significant advantage of their solid well developed formalisms techniques and clarity of exposition we will study the role of approximate solutions to fuzzy relational equations as a convenient tool to handle probabilistic type of uncertainty moreover those solutions can easily explain the origin and generate a way in which fuzzy sets of higher generality such as for instance type 2 sets interval valued sets can be algorithmically determined finally we study the role of equations in diverse fields of applications making use of an ample framework of general systems theory

fuzzy modelling fundamentals construction and evaluation abstract the paper is devoted to fundamental aspects of fuzzy modelling namely modelling articulated with the use of methodology of fuzzy sets open issues are addressed which summarize advantages of fuzzy models and point out some methodological deficiencies blurring existing approaches the problem of relevancy of fuzzy models and its direct impact on a suitable interpretation of derived results is studied in detail finally we analyze some particular fuzzy models developed in terms of relational equations

additions of interactive fuzzy numbers this paper provides an account of an approach to modeling unknown data by means of fuzzy set theory and addresses the problem of deriving the uncertainty on a sum of variables whose values lie within fuzzy intervals the first part is an extensive presentation of the theoretical background of the approach the extension principle is stated in terms of possibility of an event the concept of variable interaction is investigated at length section ii gives new results regarding the effective practical computation of additions of fuzzy numbers its originality lies in the introduction of interaction which enables to control the growth of uncertainty in calculations moreover the problem of computing mathematical expectations with fuzzy probabilities is solved the results derived in this paper can easily be used in decision problems where values of parameters or decision variables are not yet precisely fixed or assessed typical applications could be multicriteria optimization and decision making under uncertainty where fuzzy expected utilities can be obtained out of uncompletely assessed probabilities more generally fuzzy arithmetic can be an important tool for sophisticated computationally tractable sensitivity analysis in systems modeling computer aided design and operations research

on copulas and their diagonals we formulate the necessary and sufficient conditions for a function d 0 1 0 1 to be the diagonal section of a multivariate absolutely continuous copula moreover we provide some simple analytic formulas for copulas having given diagonal section or given distribution functions of order statistics

the black scholes pricing formula in the quantum context a natural explanation for extreme irregularities in the evolution of prices in financial markets is provided by quantum effects the lack of simultaneous observability of relevant variables and the interference of attempted observation with the values of these variables represent such effects these characteristics have been noted by traders and economists and appear intrinsic to market dynamics this explanation is explored here in terms of a corresponding generalization of the wiener process and its role in the black scholes merton theory the differentiability of the wiener process as a sesquilinear form on a dense domain in the hilbert space of square integrable functions over wiener space is shown and is extended to the quantum context this provides a basis for a corresponding generalization of the ito theory of stochastic integration an extension of the black scholes option pricing formula to the quantum context is deduced

contextual viewpoint to quantum stochastics we study the role of context complex of physical conditions in quantum as well as classical experiments it is shown that by taking into account contextual dependence of experimental probabilities we can derive the quantum rule for the addition of probabilities of alternatives thus we obtain quantum interference without applying the wave or hilbert space approach the hilbert space representation of contextual probabilities is obtained as a consequence of the elementary geometric fact cos theorem by using another fact from elementary algebra we obtain complex amplitude representation of probabilities finally we found contextual origin of noncommutativity of incompatible observables

piecewise linear aggregation functions based on triangulation we introduce a method to construct piecewise linear binary aggregation functions on the unit interval based on a triangulation of the unit square with one additional vertex we derive conditions under which such piecewise linear aggregation functions possess additional interesting properties such as idempotence symmetry lipschitz continuity and 2 monotonicity this construction method can also be used to approximate binary aggregation functions in this way copulas and quasi copulas are approximated by singular copulas

fuzzy system identification via probabilistic sets abstract the paper deals with the applications of probabilistic sets in system theory especially in system identification and the design of fuzzy logic controllers fuzzy systems described by means of fuzzy relational equations and fuzzy systems are discussed the identification procedure is based on some ideas of clustering techniques and probabilistic sets numerical examples using fuzzy and nonfuzzy data are used to illustrate the theory

the mackey gleason problem let a be a von neumann algebra with no direct summand of type i 2 and let p a be its lattice of projections let x be a banach space let m p a x be a bounded function such that m p q m p m q whenever p and q are orthogonal projections the main theorem states that m has a unique extension to a bounded linear operator from a to x in particular each bounded complex valued finitely additive quantum measure on p a has a unique extension to a bounded linear functional on a

quantum probability and financial market can the mathematical formalism of quantum mechanics and in particular quantum probability be applied outside of physics the answer is positive in this paper we apply methods of quantum mechanics for mathematical modelling of price dynamics of the financial market we propose to describe behavioral financial factors e g expectations of traders by using the pilot wave bohmian model of quantum mechanics on the one hand our bohmian model is a quantum like model for the financial market cf with works of w segal i e segal e haven e w piotrowski j sladkowski on the other hand since bohmian mechanics provides for the possibility to describe individual price trajectories it belongs to the domain of extended research on deterministic dynamics for financial assets our model emphasizes the complexity of the financial market the traditional description of price dynamics is completed by schrodinger s dynamics for the pilot wave of expectations of traders this is a kind of socio economic model for the financial market

surgery with finite fundamental group the relationship between the topology of manifolds and homotopy theory has been analysed by surgery 1 18 28 31 however the effectiveness of this analysis depends on being able to compute surgery obstructions in this paper we introduce a new technique for evaluating the weakly simple surgery obstructions for degree 1 normal maps of closed manifolds and apply it to oriented manifolds with finite fundamental group our main result is theorem a below let x dx be a finite poincare pair of dimension n and a top bundle over x which is stably fibre homotopy equivalent to the spivak normal fibre space v let m dm be a compact n dimensional manifold and let

surgery in cusp neighborhoods and the geography of irreducible 4 manifolds since its inception the theory of smooth 4 manifolds has relied upon complex surface theory to provide its basic examples this is especially true for simply connected 4 manifolds a longstanding conjecture held that every smooth simply connected closed 4 manifold is the connected sum of manifolds each admitting a complex structure with one of its orientations for this conjecture the 4 sphere was considered as the empty connected sum quite recently this was disproved by gompf and mrowka gm1 who produced infinite families of examples of 4 manifolds homeomorphic to the k3 surface and which admit no complex structure with either orientation the discovery of these dramatic counterexamples to the h cobordism theorem in dimension 4 was the most recent success in a long line of applications of donaldson invariants to the study of smooth structures on 4 manifolds beginning with donaldson s d4 and followed by fm1 ko ov1 ov2 which depended on donaldson s f invariant or a suitable generalization and fmm dk e2 eo1 mn2 sa using donaldson s polynomial invariant a common thread running through many of these counterexamples to the h cobordism conjecture is the process of logarithmic transformation which introduces multiple fibres in an elliptic surface in controlled situations this process will change the diffeomorphism type of a given elliptic surface while keeping its homotopy type fixed taking advantage of the complex structure on an elliptic surface this change can often be detected by using the relationship between anti self dual connections over a complex surface and stable holomorphic bundles d2 an alternative and more differential geometric

further relation equations with equality and difference composition operators in this ch we will introduce other composition operators which have a plausible logical interpretation they will be called equality and difference operator respectively we first define a notion of equality and difference of any two grades of membership of a fuzzy set and of a fuzzy relation in the sequel this concept will be utilized to form the respective composition operators and the related fuzzy equations afterwards we provide a method of resolution of these equations characterizing completely the set of the solutions all the fuzzy sets involved are defined on finite sets and with membership values in 0 1

posynomial geometric programming problem subject to max min fuzzy relation equations we discuss a class of posynomial geometric programming problem pgpf aimed at minimizing a posynomial subject to fuzzy relational equations with max min composition by introducing auxiliary variables we convert the pgpf into an equivalent programming problem whose objective function is a non decreasing function with an auxiliary variable we show that an optimal solution consists of a maximum feasible solution and one of the minimal feasible solutions by an equivalent programming problem in addition we introduce some rules for simplifying the problem then by using a branch and bound method and fuzzy relational equations fre path we present an algorithm to obtain an optimal solution to the pgpf finally numerical examples are provided to illustrate the steps of the procedure

topological triviality of smoothly knotted surfaces in 4 manifolds some generalizations of the fintushel stern rim surgery are known to produce smoothly knotted surfaces we show that if the fundamental groups of their complements are standard then these surfaces are topologically unknotted

a test of reason based and reluctance to think accounts of the disjunction effect the disjunction effect violates savage s sure thing principle that is if a is preferred over b regardless of whether relevant outcome x occurs then a should always be preferred over b l j savage the foundations of statistics new york wiley 1954 we tested reason based and reluctance to think accounts of the disjunction effect according to the former account the disjunction effect occurs when different reasons underlie the preference for a under x versus the preference for a under not x according to the latter account the disjunction effect is due to the failure to consider preferences when x is unknown we tested these accounts by varying the number of reasons underlying choices in the x and not x conditions consistent with the reason based account when only one reason was available the disjunction effect was reduced in addition we propose a new method of measuring the disjunction effect under different conditions based on the logic proposed by lambdin and burdsal 2007 c lambdin c burdsal the disjunction effect reexamined relevant methodological issues and the fallacy of unspecified percentage comparisons organizational behavior and human decision processes 103 2007 268 276

hidden variables joint probability and the bell inequalities it is shown that the following statements about a quantum correlation experiment are mutually equivalent 1 there is a deterministic hidden variables model for the experiment 2 there is a factorizable stochastic model 3 there is one joint distribution for all observables of the experiment returning the experimental probabilities 4 there are well defined compatible joint distributions for all pairs and triples of commuting and noncommuting observables 5 the bell inequalities hold

on a family of multivariate copulas for aggregation processes we introduce a family of multivariate copulas a special type of n ary aggregation operations depending on a univariate function this family is used in the construction of a special aggregation operation that satisfies a lipschitz condition several examples are provided and some statistical properties are studied