almost automorphic solutions for stochastic differential equations driven by levy noise abstract in this paper we are concerned with almost automorphic solutions for semilinear stochastic differential equations driven by levy noise on the hilbert space we present a new variant of gronwall s lemma which improves the variant of gronwall s lemma in kamenskii 2015 based on this new variant of gronwall s lemma suitable conditions on the coefficients we prove the existence and uniqueness of almost automorphic solution in distribution for some stochastic differential equations driven by levy noise on the hilbert space which improves and generalizes the results in liu 2014 subsequently by using this new variant of gronwall s lemma we investigate the existence and uniqueness of almost automorphic solution in distribution for stochastic differential equations driven by levy noise with markov switching processes under some weaker conditions in the end two examples are given to illustrate the theoretical results obtained in this paper

weak averaging of semilinear stochastic differential equations with almost periodic coefficients an averaging result is proved for stochastic evolution equations with highly oscillating coefficients this result applies in particular to equations with almost periodic coefficients the convergence to the solution of the averaged equation is obtained in distribution as in previous works by khasminskii and vrkoc this version corrects two minor errors from our paper published in j math anal appl 427 1 336 364 2015

fuzzy sets and residuated logic abstract the properties of a set theory rzf defined in a logic weaker than intuitionistic logic are investigated using natural models rzf is intended to act as a framework for fuzzy set theory more general and applicable than heyting valued structures such as topoi the theory rzf contains an interpretation of classical set theory and is consistent relative to this theory it is also a suitable theory for the expression of attributes of uncertainty and vagueness since a certain subclass of the sets definable in this theory are crisp or two valued and behave classically whereas sets in general obey only residuated logic of which the ukasiewicz semantics on 0 1 the real interval is a particular realisation

a note on kripke semantics for residuated logic abstract residuated logic is a suitable logical system for approximate reasoning and for the development of fuzzy mathematics residuated propositional logic rpc is shown to be a fragment of a well known substructural logic denoted by h bck using results for h bck kriple style semantics is described for rpc for which soundness and completeness theorems hold these results answer a question previously posed for rpc and situate rpc in the currently active research field of substructural logics

weighted pseudo almost automorphic functions and applications to abstract differential equations abstract this paper is concerned with weighted pseudo almost automorphic functions which are more general and complicated than weighted pseudo almost periodic functions using these properties we establish an existence and uniqueness theorem for pseudo almost automorphic mild solutions to semilinear differential equations in a banach space which extends known results

fuzzy sets and toposes towards higher order fuzzy logic abstract a series of paper which have appeared in fuzzy sets and systems over the last three years are reviewed in an expository manner the claims and counter claims made in them are dealt with some of the problems of representing knowledge in the first order predicate calculus are discussed briefly and a case is made for exposing the relationship between topoi and fuzzy mathematics with a view to making a true fuzzy logic both consistent complete and respectable the paper is an attempt to present the controversy to the non specialist and especially to practitioners in expert systems and artificial intelligence

weighted pseudo almost automorphic solutions for nonautonomous spdes driven by levy noise abstract in this paper we introduce the concept of weighted pseudo almost automorphy in distribution using the theory of evolution family and stochastic analysis method we establish the existence and uniqueness results of almost automorphic solutions in distribution and weighted pseudo almost automorphic solutions in distribution for some semilinear nonautonomous stochastic partial differential equations driven by levy noise when the coefficients of the equations satisfy some suitable conditions moreover we investigate the global exponentially stability of these solutions the results are generalizations of the results in wang and liu 32 chen and lin 11 and liu and sun 26

completing a symmetric 2 2 block matrix and its inverse abstract we consider the following completion problems suppose n1 n2 are nonnegative integers such that n 1 n 2 n 0 let a11 a12 a21 b22 be matrices with dimensions n1 n1 n1 n2 n2 n1 and n2 n2 respectively we determine necessary and sufficient conditions so that there exists an n2 n2 matrix a22 such that a a 11 a 21 a 12 a 22 and i a is nonsingular and symmetric and b22 is the lower right block of a partitioning of a 1 ii a is symmetric positive definite and b22 is the lower right block of a partitioning of a 1

almost periodic and almost automorphic solutions of linear differential difference equations without favard s separation condition ii abstract the well known favard s theorem states that the linear differential equation 1 x a t x f t with bohr almost periodic coefficients admits at least one bohr almost periodic solution if it has a bounded solution the main assumption in this theorem is the separation among bounded solutions of homogeneous equations 2 x b t x where b h a b b t lim n a t t n if there are bounded solutions which are non separated sometimes almost periodic solutions do not exist r johnson r ortega and m tarallo v zhikov and b levitan in this paper we prove that linear differential equation 1 with levitan almost periodic coefficients has a unique levitan almost periodic solution if it has at least one bounded solution and the bounded solutions of the homogeneous equation 3 x a t x are homoclinic to zero i e lim t t 0 for all bounded solutions of 3 if the coefficients of 1 are bohr almost periodic and all bounded solutions of all limiting equations 2 are homoclinic to zero then eq 1 admits a unique almost automorphic solution the analogue of this result for difference equations is also given we study the problem of existence of bohr levitan almost periodic solutions of eq 1 in the framework of general non autonomous dynamical systems cocycles

massera type theorem for almost automorphic solutions of functional differential equations of neutral type abstract in this work we study the existence of almost automorphic solutions for functional differential equations of neutral type we prove that the existence of a bounded solution on r implies the existence of an almost automorphic solution

tuning of fuzzy controller for an open loop unstable system a genetic approach abstract the design test and evaluation of an optimised fuzzy logic controller oflc is reported in this paper with the aid of genetic algorithms ga the rule base of an otherwise standard fuzzy logic controller flc is obtained this is achieved by deriving a tailor made encoding scheme initialisation crossover and mutation of rule table into strings of integers ga is implemented such that the existing knowledge of the system is utilised to increase the speed of optimisation the oflc is successfully applied to control an open loop unstable system the ball and beam balance system on a hardware test bed a kalman filter controller kfc and a manually tuned fuzzy logic controller mflc are also developed for the test bed and the performances of the three controllers are compared the experiment reveals that improved robustness with shorter design cycle can be achieved by integrating ga into an flc

almost periodic and almost automorphic solutions of linear differential equations the paper is dedicated to the study problem of existence of almost periodic respectively almost automorphic recurrent solutions of linear differential equations u t a t y u t f t y y y in banach space with almost periodic respectively almost automorphic recurrent coefficients where y r is a dynamical system on the metric space y in particular we prove that if the operator a y is positive and auto adjoint then for the equation 1 u t a t y u t 0 one of the following alternative is fulfilled i there exists a complete trajectory of 1 with constant positive norm ii the trivial solution of equation 1 is uniformly asymptotically stable this problem we investigate in the framework of general linear non autonomous dynamical system we apply our general results also for the functional differential equations and difference equations

the logic of tied implications part 1 properties applications and representation a conjunction t ties an implication operator a if the identity a a a b z a t a b z holds a a abdel hamid n n morsi associatively tied implications fuzzy sets and systems 136 2003 291 311 we study the class of tied adjointness algebras which are five connective algebras on two partially ordered sets in which the implications are tied by triangular norms this class contains besides residuated implications several other implications employed in fuzzy logic nevertheless we show that the algebraic inequalities of residuated algebras remain true for our tied implications but in forms that distribute roles over the five connectives of the algebra we apply the properties of tied implications to a generalized modus ponens inference scheme with two successive rules we prove its equivalence to a scheme with one compound rule when both schemata are interpreted by the compositional rule of inference and all connectives are taken from one tied adjointness algebra then we quote another application of this rich theory a notion of many valued rough sets which exhibit the basic mathematical behaviour of the rough sets of pawlak a comparator h is said to be prelinear if it satisfies h y z h z y 1 for all y z hajek we introduce prelinear tied adjointness algebras in which two comparators are prelinear we provide a representation of those algebras as subdirect products of tied adjointness chains on the lines of hajek s representation of bl algebras but our representations are more economical because we employ minimal prime filters on residuated lattices only rather than all prime filters

fuzzy real numbers as dedekind cuts with respect to a multiple valued logic abstract viewing fuzzy set theory as a model of set with respect to a given multiple valued logic we establish the dedekind macneille completion of a partially ordered l valued set contrary to other constructions in fuzzy set theory the completion is unique up to an order isomorphism specializing this situation to the set of all crisp rational numbers we obtain in a unique way the fuzzy dedekind real numbers

almost automorphic solutions for some evolution equations through the minimizing for some subvariant functional applications to heat and wave equations with nonlinearities in this work we study the existence of bounded and almost automorphic solutions for evolution equations in banach spaces we suppose that the linear part is the infinitesimal generator of a compact c0 semigroup of bounded linear operators and the nonlinear part is an almost automorphic function with respect to the second argument we give sufficient conditions ensuring the existence of an almost automorphic solution when there is at least one bounded solution on r we use the subvariant functional method to show that every k minimizing mild solution is compact almost automorphic applications are provided for both heat and wave equations with nonlinearities in several functional spaces

multiary α resolution principle for a lattice valued logic this paper focuses on resolution based automated reasoning theory in a lattice valued logic system with truth values that are defined in a lattice valued logical algebraic structure lattice implication algebras lias which essentially aims to extend the classical logic to handle automated deduction under an uncertain environment concretely we investigate a generalization of the known conjunctive normal form cnf in the classical logic representation that we call the generalized conjunctive normal form gcnf which aims to characterize the constants and implication connectives that are essentially different from the ones in classical logic we then extend the established resolution principle at a certain truth value level called resolution in this lattice valued logic to a more general form i e from binary resolution to multiary resolution the extension to multiary resolution starts from lattice valued propositional logic lp x while its theorems of both soundness and completeness are proved multiary resolution principle is then further established in the corresponding lattice valued first order logic lf x along with its soundness theorem lifting lemma and completeness theorem meanwhile an important result that multiary resolution principle in lf x can be equivalently transformed into that in lp x to some extent is obtained all these works will theoretically support the establishment of an automated reasoning algorithm and its implementation with further applications into automated deduction and decision making problems under uncertainty

job search and employment abstract a multistage search method based on fuzzy preference is used to analyze the processes of job search an employment decision based on fuzzy preference results in an exact choice the incorporation of fuzzy interval preference into employment decision however may lead to multiple choices which provides a theoretical justification for the existence of fuzzy supply of labor thus fuzziness in addition to randomness offers an explanation to wage dispersion

completion of an orthogonal projector and a related inverse mapping problem we study the completion problem for an orthogonal projector a of r n from knowledge of one or several of its columns as well as the related matrix inverse problem of finding an orthogonal projector a with ax y for two given n by k matrices x and y using geometric properties of orthogonal projections and of the singular value decomposition we derive theoretical and numerical solutions for these problems we give algorithms and test their matlab implementations

the logic of tied implications part 2 syntax an implication operator a is said to be tied if there is a binary operation t that ties a that is the identity a a a b z a t a b z holds for all a b z we aim at the construction of a complete predicate logic for prelinear tied adjointness algebras we realize this in three steps in the first step we establish a propositional calculus adjtpc complete for the class of all tied adjointness algebras on partially ordered sets without prelinearity and ignoring the lattice operations for that we supply a hilbert system based on seven axioms and one deduction rule modus ponens in the second and third steps we extend adjtpc to propositional and predicate calculi complete for prelinear tied adjointness algebras we apply a duality principle due to morsi in all three calculi through which we manage to cut down the number of proofs

almost automorphic solutions for stochastic differential equations driven by levy noise abstract we introduce the concepts of poisson square mean almost automorphy and almost automorphy in distribution under suitable conditions on the coefficients we establish the existence of solutions which are almost automorphic in distribution for some semilinear stochastic differential equations with infinite dimensional levy noise we further discuss the global asymptotic stability of these solutions finally to illustrate the theoretical results obtained in this paper we give several examples

a small set of axioms for residuated logic we show that a set of three axioms together with modus ponens suffices to build up a formal system for the class r of all quadruples l t j in which l is a partially ordered set with a top element and t is a triangular norm on l that has a residuated implication j we show that this r is not a variety

square mean pseudo almost automorphic process and its application to stochastic evolution equations abstract this paper introduces the concept of the square mean pseudo almost automorphy for a stochastic process also it introduces the properties on the completeness and the composition of the space that consists of such processes with appropriate settings and by virtue of the theory of the semigroups of the operators to an evolution family the banach fixed point theorem and the stochastic analysis techniques this paper investigates the existence the uniqueness and the global stability of the square mean pseudo almost automorphic solutions for a general class of stochastic evolution equations finally this paper provides an illustrative example to justify the practical usefulness of the established theoretical results

pseudo almost periodic solutions of some differential equations ii we first present some results about pseudo almost periodic functions then we use these results to show some theorems about existence and uniqueness of the pseudo almost periodic solutions of the linear and the quasi linear nonautonomous equations finally we set up some theorems of the existence of pseudo almost periodic solutions implying the existence of almost periodic solutions of general ordinary differential equation systems

formal frameworks for approximate reasoning abstract this paper discusses applications of a formal set theoretic foundation for fuzzy set theory 23 to problems of approximate and uncertain reasoning and also looks at other formalisms such as the classical alternative set theory 39 and its intuitionistic version 21 20 for uncertain reasoning formal definitions of these frameworks will be given many suggestions for semantic operations on values of formulae involving intermediate truth have been made 41 40 contain a survey of these there are two main problems how to reconcile the use of the linear order 0 1 as the value space when in reality degrees of truth are often incomparable and secondly within this simplified range of values to select operations which are both logically coherent with each other and intuitively reasonable we will derive general semantic constraints on operations which will motivate the formal frameworks that we define

on line fuzzy identification using genetic algorithms the design and implementation of an on line fuzzy identification method using genetic algorithms gas is reported in this paper in the proposed algorithm the rule table of a fuzzy system is first divided into several independent and much smaller fuzzy systems which in turn are encoded into separate bit strings for genetic operations a novel ga updating architecture is then proposed to search the optimal rule base of these fuzzy systems at each sample interval the performance of this identification algorithm is evaluated by simulation of a non linear system moreover an experiment on simple behavior learning of a mobile robot is also reported the results indicate an improvement in design cycle and convergence to the optimal rule base within a relatively short period of time

almost automorphic and weighted pseudo almost automorphic solutions of semilinear evolution equations abstract in this paper applying the theory of semigroups of operators to evolution family and banach fixed point theorem we prove the existence and uniqueness of an a almost automorphic weighted pseudo almost automorphic mild solution of the semilinear evolution equation x t a t x t f t x t in banach space under conditions

tableau method for residuated logic abstract residuated logic is a generalization of intuitionistic logic which does not assume the idempotence of the conjunction operator such generalized conjunction operators have proved important in expert systems in the area of approximate reasoning and in some areas of theoretical computer science here we generalize the intuitionistic tableau procedure and prove that this generalized tableau method is sound for the semantics the class of residuated algebras of residuated propositional calculus rpc since the axioms of rpc are complete for the semantics we may conclude that whenever a formula 0 is tableau provable it is deducible in rpc we present two different approaches for constructing residuated algebras which give us countermodels for some formulas which are not tableau provable the first uses the fact that the theory of residuated algebras is equational to construct quotients of free algebras the second uses finite algebras we end by discussing a number of open questions

quadratic forms in random variables theory and applications textbook for a one semester graduate course for students specializing in mathematical statistics or in multivariate analysis or reference for theoretical as well as applied statisticians confines its discussion to quadratic forms and second degree polynomials in real normal random vectors and matr

fuzzy on line identification of siso nonlinear systems abstract a new fuzzy on line identification algorithm for a single input single output continuous time nonlinear dynamic system is presented this method combines the conventional on line identification with fuzzy logic system the nonlinear system is approximated by a set of fuzzy rules that describe the local linear dynamic in each subspace formed by fuzzifying the input and output space the continuous time fuzzy input output model is identified on line by using the input and output measurements a fuzzy identification algorithm has been developed and a convergence analysis is carried out simulation studies have demonstrated that this fuzzy on line identifier can match the time varying nonlinear system within 5 accuracy

completing a matrix when certain entries of its inverse are specified abstract suppose a a 11 a 12 a 21 a 22 is an n n matrix where a 11 has order p q if a is nonsingular let a 1 have the transposed partitioning b 11 b 12 b 21 b 22 first we show that the nullities of a 11 and b 22 are equal the remainder of our paper deals with the following completion problem suppose m 1 m 2 n 1 n 2 are nonnegative integers such that m 1 m 2 n 1 n 2 n 0

propositional calculus under adjointness we develop a formal system for the class of all implications a and conjunctions k on partially ordered sets l with top elements 1 such that a and k are related by adjointness and they satisfy the neutrality principle that is 1 is their left identity element we call the resulting logic propositional calculus under adjointness abbreviated adjpc most algebraic theorems on those l a and k are inequalities in the posets l of truth values in consequence we have to find means for abstracting inequalities within syntax which must be free from partial truth values this is achieved by employing a further implication like adjoint h of a and k whereby the partial order of l coincides with the binary relation h 1 accordingly the semantical domain for adjpc should become the class of all such quintuples l a k h which we call adjointness algebras our axiom scheme for adjpc features seven axioms however it may be the case that no finite set of axioms can complete adjpc if inference is carried out by means of modus ponens mp alone this is because adjpc is too general it lacks some basic theorems of the more restricted logics such as residuated logic and intuitionistic logic as a result we have to adopt four inference rules for adjpc namely mp and three bits of the substitution theorem we deduce enough theorems and inferences in adjpc to delineate its basic structure this enables us to establish the completeness of adjpc for the semantical domain of adjointness algebras by means of a quotient algebra structure a lindenbaum type of algebra we also show how certain models can help disprove some incorrect inferences in adjpc we end by developing complete syntax with fewer axioms and inference rules for the smaller semantical domain of all adjointness algebras whose implications satisfy the exchange principle