anti periodic solutions for bam neural networks with time delays in the paper bidirectional associative memory neural networks with time delays are studied by using the fundamental solution matrix of coefficients and lyapunow function sufficient conditions are obtained for the existence and global exponential stability of the anti periodic solution of the model an example and numerical simulations are also given to illustrate the theoretical results

a note on existence of anti periodic and heteroclinic solutions for a class of second order odes abstract we discuss the existence of anti periodic solutions to the following second order differential equation q u t q by using fixed point theory together with the green s function for the anti periodic boundary value problem in the first part section 2 of the paper then in the next part section 3 we construct a kind of heteroclinic solution to some special cases of the equation above our method is variational in nature and is inspired by the ideas of rabinowitz and stredulinsky in p rabinowitz e stredulinsky on some results of moser and of bangert aihp anal nonlin 21 2004 673 688

exact solution and interfacial tension of the six vertex model with anti periodic boundary conditions we consider the six vertex model with anti periodic boundary conditions across a finite strip the row to row transfer matrix is diagonalized by the commuting transfer matrices method from the exact solution we obtain an independent derivation of the interfacial tension of the six vertex model in the anti ferroelectric phase the nature of the corresponding integrable boundary condition on the xxz spin chain is also discussed

guiding functions for generalized periodic problems and applications abstract in this paper developing the method of guiding functions for differential inclusions with a generalized periodic condition we obtain the existence theorem for such problems it is shown how the abstract result can be applied to the study of differential games and anti periodic problems

on a class of second order anti periodic boundary value problems of concern is the existence and uniqueness of anti periodic solutions to a class of abstract nonlinear second order differential equations the investigation relies on the theory of m accretive operators in banach or hilbert spaces examples of boundary value problems for ordinary and partial differential equations are also discussed

weighted pseudo almost periodic mild solutions of semilinear evolution equations with nonlocal conditions in this paper applying the theory of semigroups of operators to evolution families and banach fixed point theorem we prove the existence and uniqueness of the weighted pseudo almost periodic mild solution of the semilinear evolution equation x t a t x t f t x t with nonlocal conditions x 0 x 0 g x in banach space x under some suitable hypotheses

using one axiom to characterize rough set and fuzzy rough set approximations axiomatic approaches are important for understanding the concepts of rough set theory the properties of the approximation operators constructed in rough set theory are determined by a binary relation a linkage in the form of a necessary and sufficient condition between the constructive approach and an axiomatic system is established in this paper various classes of rough set algebras are characterized by different sets of axioms with no restriction on the cardinality of the universal set we use only one axiom to describe the approximation generated by the reflexive symmetric and transitive relations respectively in addition we characterize lower and upper approximations of the pawlak rough set with only one axiom we also study a similar problem in the context of fuzzy sets

analysis and control of differential inclusions with anti periodic conditions we deal with the optimal control of systems driven by differential inclusions with anti periodic conditions in banach spaces the operators in the differential inclusions describing the control system all depend on control variables by a solution of the control system we mean a trajectory control pair we first prove that for fixed control variables the set of solutions is non empty for the corresponding differential inclusion with anti periodic conditions we then show the functional topological properties of the set of solutions finally we investigate the existence of solutions to the optimal control problem these abstract results can be used to study optimal control systems of evolutionary hemi variational inequalities

existence of solutions for first order ordinary differential equations with nonlinear boundary conditions we present an existence theorem for nonlinear ordinary differential equations of first order with nonlinear boundary conditions the result includes for instance the initial value problem the final value problem and the antiperiodic boundary value problem the main novelty of the method lies in that it unifies different techniques for initial or boundary conditions

weighted pseudo almost periodic solutions of a class of abstract differential equations abstract for abstract linear functional differential equations with a weighted pseudo almost periodic forcing term we prove that the existence of a bounded solution on r implies the existence of a weighted pseudo almost periodic solution our results extend the classical theorem due to massera on the existence of periodic solutions for linear periodic ordinary differential equations to illustrate the results we consider the lotka volterra model with diffusion

weighted pseudo antiperiodic solutions for fractional integro differential equations in banach spaces in this paper we prove the existence of weighted pseudo antiperiodic mild solutions for fractional integro differential equations in the form d u t au t t a t s au s ds f t u t t r where f u is stepanov like weighted pseudo antiperiodic and a generates a resolvent family of bounded and linear operators on a banach space x a l loc 1 r and 0 here the fractional derivative is considered in the sense of weyl also we give a short proof to show that the vector valued space of stepanov like weighted pseudo antiperiodic functions is a banach space

weighted pseudo almost periodic solutions to some differential equations abstract the paper considers some new classes of functions called weighted pseudo almost periodic functions which implement in a natural fashion the classical pseudo almost periodic functions due to zhang properties of these weighted pseudo almost periodic functions are discussed including a composition result for weighted pseudo almost periodic functions the results obtained are subsequently utilized to study the existence and uniqueness of a weighted pseudo almost periodic solution to the heat equation with dirichlet conditions

analytic network process for pattern classification problems using genetic algorithms the analytic network process anp is a useful technique for multi attribute decision analysis mcda that employs a network representation to describe interrelationships between diverse attributes owing to effectiveness of the anp in allowing for complex interrelationships between attributes this paper develops an anp based classifier for pattern classification problems with interdependence or independence among attributes to deal with interdependence this study employs genetic algorithms gas to automatically determine elements in the supermatrix that are not easily user specified to find degrees of importance of respective attributes then with the relative importance for each attribute in the limiting supermatrix the current work determines the class label of a pattern by its synthetic evaluation experimental results obtained by the proposed anp based classifier are comparable to those obtained by other fuzzy or non fuzzy classification methods

the onset and end of the gunn effect in extrinsic semiconductors a hopf bifurcation analysis of the spontaneous current oscillation in direct current dc voltage biased extrinsic semiconductors is given for the classical model of the gunn effect in n gaas for semiconductor lengths l larger than a certain minimal value the steady state is linearly unstable for voltages in an interval phi alpha phi omega as l increases the branch of time periodic solutions bifurcating at simple eigenvalues when phi phi alpha turns from subcritical to supercritical and then back to subcritical again for very long semiconductors a quasi continuum of oscillatory modes bifurcates from the steady state at the onset of the instability the bifurcating branch is then described by a scalar reaction diffusion equation with cubic nonlinearity subject to antiperiodic boundary conditions on a subinterval of 0 l for the electron velocity curve we have considered the bifurcation is subcritical which may agree with experimental observations in n gaas an extension o

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

weighted pseudo almost periodic solutions to a neutral delay integral equation of advanced type abstract this paper studies suitable sufficient conditions to ensure the existence and uniqueness of weighted pseudo almost periodic solutions to a neutral delay integral equation of advanced type introduced by t a burton in the literature the abstract results are then utilized to characterize weighted pseudo almost periodic solutions to the well known logistic equation

almost periodic solutions to some semilinear non autonomous thermoelastic plate equations abstract the paper is concerned with the existence of almost periodic solutions to the so called semilinear thermoelastic plate systems for that the strategy consists of seeing these systems as a particular case of the semilinear parabolic evolution equations x t a t x t f t x t t r where a t for t r is a family of sectorial linear operators on a banach space x satisfying the so called acquistapace terreni conditions and f is a function defined on a real interpolation space x for 0 1 under some reasonable assumptions it will be shown that has a unique almost periodic solution we then make use of the previous result to obtain the existence and uniqueness of an almost periodic solution to the thermoelastic plate systems

existence results for quasilinear parabolic hemivariational inequalities abstract this paper is devoted to the periodic problem for quasilinear parabolic hemivariational inequalities at resonance as well as at nonresonance by use of the theory of multi valued pseudomonotone operators the notion of generalized gradient of clarke and the property of the first eigenfunction we build a landesman lazer theory in the nonsmooth framework of quasilinear parabolic hemivariational inequalities

existence and controllability for fractional evolution inclusions of clarke s subdifferential type in this paper by using the method of the measure of noncompactness the fixed points theorem of multivalued maps and the properties of clarke s subdifferential we give the existence result and controllability for the fractional evolution inclusions of clarke s subdifferential type in a separable reflexive banach space

decomposition of weighted pseudo almost periodic functions abstract first we show by constructing two counterexamples that the decomposition of weighted pseudo almost periodic functions is not unique in general then we prove that the decomposition of such functions is unique if p a p 0 x is translation invariant but not necessarily unique without the assumption moreover we give an example to show that the mean value under a certain weight may not exist for all almost periodic functions with these results we answer some fundamental questions on weighted pseudo almost periodic functions

a promethee based classification method using concordance and discordance relations and its application to bankruptcy prediction outranking relation theory has been widely used to study pattern classification here we propose a classification method with concepts from the flows used in promethee methods which are extensively applied in multi criteria decision aids promethee uses a flow generated on the basis of a preference index and measured by various preference functions for each criterion to represent the preference intensity for one pattern over another pattern however only criteria that are concordant with the preference contribute to a preference index in the present study the opinions from discordant criteria are also taken into account the proposed method newly defines an overall preference index using both concordance and discordance relations for ordinal sorting problems the final classification decision for a new pattern depends on its net flow the criteria weights are determined using a genetic algorithm based approach empirical results obtained for a real world problem regarding bankruptcy prediction demonstrate that the proposed method performs well compared to other well known classification methods

existence of anti periodic solutions for quasilinear parabolic hemivariational inequalities abstract in this paper we consider the problem of the existence of anti periodic solutions for quasilinear parabolic hemivariational inequalities with a pseudomonotone operator using regularized approximating and first eigenfunction methods and the surjectivity result we prove the existence of solutions for quasilinear parabolic hemivariational inequalities

existence in the large for nonlinear delay evolution inclusions with nonlocal initial conditions in this paper we provide a sufficient condition for the existence of c0 solutions for a class of nonlinear functional differential evolution equation of the form u t au t f t t r f t f t u t ut t r u t g u t t 0 where x is a real banach space a is the infinitesimal generator of a nonlinear compact semigroup f r x c 0 d a x is a nonempty convex and weakly compact valued multi function and g cb d a c 0 d a

existence of weighted pseudo anti periodic solutions to some non autonomous differential equations abstract in this paper we first introduce two new concepts called respectively weighted pseudo periodicity and weighted pseudo anti periodicity which generalize respectively the well known notions of periodicity and that of anti periodicity basic properties of these new functions are discussed furthermore the existence of weighted pseudo anti periodic solutions to some damped non autonomous second order differential equations will be investigated to illustrate our abstract results the existence of weighted pseudo anti periodic solutions to a plate like equation is discussed

an algorithmic approach for fuzzy inference to apply fuzzy logic two major tasks need to be performed the derivation of production rules and the determination of membership functions these tasks are often difficult and time consuming this paper presents an algorithmic method for generating membership functions and fuzzy production rules the method includes an entropy minimization for screening analog values membership functions are derived by partitioning the variables into the desired number of fuzzy terms and production rules are obtained from minimum entropy clustering decisions in the rule derivation process rule weights are also calculated this algorithmic approach alleviates many problems in the application of fuzzy logic to binary classification

weighted pseudo almost periodic functions and applications to evolution equations with delay in this paper we introduce a new class of vector valued weighted pseudo almost periodic functions and present some basic properties about these new functions moreover we obtain an new existence theorem of vector valued weighted pseudo almost periodic solution to the evolution equations x t ax t f t x t with delay in a banach space x

existence of anti periodic mild solutions for semilinear evolution equations in this paper we study the existence of anti periodic mild solutions for a class of semilinear evolution equations in banach spaces and extend some related results in this direction an example is given to illustrate our results

existence and uniqueness of anti periodic solutions for a kind of rayleigh equation with two deviating arguments abstract in this paper we use the leray schauder degree theory to establish new results on the existence and uniqueness of anti periodic solutions for a kind of rayleigh equation with two deviating arguments of the form x f t x t g 1 t x t 1 t g 2 t x t 2 t e t

existence of weighted pseudo almost periodic solutions to some classes of hyperbolic evolution equations this paper is concerned with the study of weighted pseudo almost periodic solutions to some classes of hyperbolic differential equations upon making some suitable assumptions the existence and uniqueness of a weighted pseudo almost periodic solution is obtained to illustrate our main result we study the existence of a weighted pseudo almost periodic solution to a system of partial differential equations arising in control systems described by abstract retarded functional differential equations with feedback control

effective algebraic degeneracy we show that for every smooth projective hypersurface x n 1 of degree d and of arbitrary dimension n 2 if x is generic then there exists a proper algebraic subvariety y x such that every nonconstant entire holomorphic curve f x has image f which lies in y as soon as its degree satisfies the effective lower bound d geqslant 2 n 5

anti periodic solutions to nonlinear evolution equations abstract we deal with anti periodic problems for nonlinear evolution equations with nonmonotone perturbations the main tools in our study are the maximal monotone property of the derivative operator with anti periodic conditions and the theory of pseudomonotone perturbations of maximal monotone mappings

fuzzy integral based perceptron for two class pattern classification problems the single layer perceptron with single output node is a well known neural network for two class classification problems furthermore the sigmoid or logistic function is usually used as the activation function in the output neuron a critical step is to compute the sum of the products of the connection weights with the corresponding inputs which indicates the assumption of additivity among individual variables unfortunately because the input variables are not always independent of each other an assumption of additivity may not be reasonable enough in this paper the inner product can be replaced with an aggregation value obtained by a useful fuzzy integral by viewing each of the connection weights as a value of a l fuzzy measure for the corresponding variable a genetic algorithm is then employed to obtain connection weights by maximizing the number of correctly classified training patterns and minimizing the errors between the actual and desired outputs of individual training patterns the experimental results further demonstrate that the proposed method outperforms the traditional single layer perceptron and performs well in comparison with other fuzzy or non fuzzy classification methods

existence of weighted pseudo almost periodic solutions to some classes of differential equations with sp weighted pseudo almost periodic coefficients abstract in this paper we introduce the concept of weighted pseudo almost periodicity in the sense of stepanov also called s p weighted pseudo almost periodicity and study its properties next we present a result on the existence of weighted pseudo almost periodic solutions to the n dimensional heat equation with s p weighted pseudo almost periodic coefficients

anti periodic solutions to a class of nonlinear differential equations in hilbert space abstract a broad class of nonlinear non monotone anti periodic boundary value problems in a hilbert space is considered as a preliminary step the existence uniqueness and continuous dependence upon data of anti periodic solutions to some first and second order evolution equations associated to odd noncoercive monotone operators is established applications of the theory to nonlinear partial differential equations are also discussed

initial boundary value problems and optimal control for nonautonomous parabolic systems a large class of linear nonautonomous parabolic systems in bounded domains is considered with control acting on the boundary through dirichlet or neumann conditions from the point of view of semigroup theory the results from rend sem mat univ padova 78 1987 pp 47 107 on fundamental solutions for abstract parabolic equations lecture notes in math vol 1223 springer verlag berlin heidelberg 1986 pp 1 11 on abstract homogeneous parabolic cauchy problems allow operators with varying domains and holder continuous coefficients to be handled a representation formula for solutions corresponding to square integrable control functions is derived and used to solve a linear quadratic regulator problem over finite time horizon by a direct study of the associated integral riccati equation

thom polynomials of morin singularities we prove a formula for thom polynomials of a d singularities in any codimension we use a combination of the test curve model of porteous and the localization methods in equivariant cohomology our formulas are independent of the codimension and are computationally effective up to d 6

fuzzy min max neural networks i classification a supervised learning neural network classifier that utilizes fuzzy sets as pattern classes is described each fuzzy set is an aggregate union of fuzzy set hyperboxes a fuzzy set hyperbox is an n dimensional box defined by a min point and a max point with a corresponding membership function the min max points are determined using the fuzzy min max learning algorithm an expansion contraction process that can learn nonlinear class boundaries in a single pass through the data and provides the ability to incorporate new and refine existing classes without retraining the use of a fuzzy set approach to pattern classification inherently provides a degree of membership information that is extremely useful in higher level decision making the relationship between fuzzy sets and pattern classification is described the fuzzy min max classifier neural network implementation is explained the learning and recall algorithms are outlined and several examples of operation demonstrate the strong qualities of this new neural network classifier

existence of solutions for anti periodic boundary value problems abstract by using schauder s fixed point theorem and the lower and upper solutions method we discuss the anti periodic boundary value problem for a class of second order differential equations some sufficient conditions for the existence of solutions are obtained

a handwritten numeral character classification using tolerant rough set proposes a data classification method based on the tolerant rough set that extends the existing equivalent rough set a similarity measure between two data is described by a distance function of all constituent attributes and they are defined to be tolerant when their similarity measure exceeds a similarity threshold value the determination of optimal similarity threshold value is very important for accurate classification so we determine it optimally by using the genetic algorithm ga where the goal of evolution is to balance two requirements such that 1 some tolerant objects are required to be included in the same class as many as possible and 2 some objects in the same class are required to be tolerant as much as possible after finding the optimal similarity threshold value a tolerant set of each object is obtained and the data set is grouped into the lower and upper approximation set depending on the coincidence of their classes we propose a two stage classification method such that all data are classified by using the lower approximation at the first stage and then the nonclassified data at the first stage are classified again by using the rough membership functions obtained from the upper approximation set we apply the proposed classification method to the handwritten numeral character classification problem and compare its classification performance and learning time with those of the feedforward neural network s backpropagation algorithm

pseudo almost automorphic mild solutions to nonautonomous differential equations and applications abstract in this paper we introduce a new concept of bi almost automorphic functions and obtain new existence and uniqueness theorems for pseudo almost automorphic mild solutions to several nonautonomous differential equations moreover two examples are given to illustrate the general theorems

existence of global invariant jet differentials on projective hypersurfaces of high degree let x subset mathbb p n 1 be a smooth complex projective hypersurface in this paper we show that if the degree of x is large enough then there exist global sections of the bundle of invariant jet differentials of order n on x vanishing on an ample divisor we also prove a logarithmic version effective in low dimension for the log pair mathbb p n d where d is a smooth irreducible divisor of high degree moreover these result are sharp i e one cannot have such jet differentials of order less than n

lattices in the cohomology of shimura curves we prove the main conjectures of breuil j reine angew math 2012 including a generalisation from the principal series to the cuspidal case and dembele j reine angew math 2012 subject to a mild global hypothesis that we make in order to apply certain r mathbb t theorems more precisely we prove a multiplicity one result for the mod p cohomology of a shimura curve at iwahori level and we show that certain apparently globally defined lattices in the cohomology of shimura curves are determined by the corresponding local p adic galois representations we also indicate a new proof of the buzzard diamond jarvis conjecture in generic cases our main tools are the geometric breuil mezard philosophy developed in emerton and gee j inst math jussieu 2012 and a new and more functorial perspective on the taylor wiles kisin patching method along the way we determine the tamely potentially barsotti tate deformation rings of generic two dimensional mod p representations generalising a result of breuil and mezard bull soc math de france 2012 in the principal series case

existence of anti periodic mild solutions to semilinear nonautonomous evolution equations abstract in this paper applying the theory of evolution family and schauder s fixed point theorem we prove the anti periodic mild solutions for semilinear nonautonomous evolution equations in banach space under conditions furthermore an example is given to illustrate our results

thom polynomials symmetries and incidences of singularities as an application of the generalized pontryagin thom construction rsz here we introduce a new method to compute cohomological obstructions of removing singularities i e thom polynomials t with the aid of this method we compute some sample results such as the thom polynomials associated to all stable singularities of codimension 8 between equal dimensional manifolds and some other thom polynomials associated to singularities of maps n n p n k for k 0 we also give an application by reproving a weak form of the multiple point formulas of herbert and ronga h ro2 as a byproduct of the theory we define the incidence class of singularities which the author believes may turn to be an interesting useful and simple tool to study incidences of singularities

evolutionary variational hemivariational inequalities existence and comparison results we consider an evolutionary quasilinear hemivariational inequality under constraints represented by some closed and convex subset our main goal is to systematically develop the method of sub supersolution on the basis of which we then prove existence comparison compactness and extremality results the obtained results are applied to a general obstacle problem we improve the corresponding results in the recent monograph s carl v k le d motreanu nonsmooth variational problems and their inequalities comparison principles and applications springer monogr math springer new york 2007

weighted pseudo almost periodic solutions for some partial functional differential equations abstract in this work we give sufficient conditions for the existence and uniqueness of a weighted pseudo almost periodic solution for some partial functional differential equations to illustrate our main result we study the existence of a weighted pseudo almost periodic solution for some diffusion equation with delay

finding useful fuzzy concepts for pattern classification using genetic algorithm in this paper a fuzzy classifier is treated as a fuzzy information retrieval system to construct such a system a fuzzy data mining method is employed to determine useful fuzzy concepts subsequently each of the classes and patterns can be represented by a fuzzy set of useful fuzzy concepts from the viewpoint of fuzzy information retrieval a pattern can be categorized into one class if there exists a maximum degree of similarity between them the genetic algorithm ga whose objective is to find a compact set consisting of useful fuzzy concepts with high classification capability is further employed to automatically determine parameter specifications that are not easily specified by users to evaluate classification performance of the proposed method computer simulations are performed on some well known classification problems demonstrating that the generalization ability of the proposed method is comparable to other fuzzy classification methods

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

rough set approach to incomplete numerical data rough set theory has been applied successfully in many fields however classical rough set model can only deal with complete and symbolic data sets some researchers have proposed extended rough set models to handle incomplete data while others proposed extensions of classical rough set models to deal with numerical data however there exist many data which contain numerical attributes and missing values simultaneously we propose in this paper an extended rough set model i e tolerance fuzzy rough set model to deal with this type of data characterized with numerical attributes and missing values that is incomplete numerical data discernibility matrices and discernibility functions for incomplete numerical information systems and incomplete numerical decision systems are defined to compute reducts or relative reducts meanwhile the relationship between the proposed tolerance fuzzy rough set model and the tolerance rough set model is also examined it is shown that the tolerance fuzzy rough set model is an extension of the tolerance rough set model finally uncertainty measurement is also investigated it is suggested that the proposed tolerance fuzzy rough set model provide an optional approach to incomplete numerical data

forecasting time series with genetic fuzzy predictor ensemble this paper proposes a genetic fuzzy predictor ensemble gfpe for the accurate prediction of the future in the chaotic or nonstationary time series each fuzzy predictor in the gfpe is built from two design stages where each stage is performed by different genetic algorithms ga the first stage generates a fuzzy rule base that covers as many of training examples as possible the second stage builds fine tuned membership functions that make the prediction error as small as possible these two design stages are repeated independently upon the different partition combinations of input output variables the prediction error will be reduced further by invoking the gfpe that combines multiple fuzzy predictors by an equal prediction error weighting method applications to both the mackey glass chaotic time series and the nonstationary foreign currency exchange rate prediction problem are presented the prediction accuracy of the proposed method is compared with that of other fuzzy and neural network predictors in terms of the root mean squared error rmse

antiperiodic solutions of semilinear integrodifferential equations in banach spaces abstract we are concerned in this paper with the existence of antiperiodic mild solutions of some semilinear integrodifferential equations in a banach space we study further properties of antiperiodic functions including a new composition theorem and introduce the new concept of asymptotically antiperiodic functions

rough sets and boolean reasoning abstract in this article we discuss methods based on the combination of rough sets and boolean reasoning with applications in pattern recognition machine learning data mining and conflict analysis

existence results for some damped second order volterra integro differential equations abstract in this paper we make a subtle use of operator theory techniques and the well known schauder fixed point principle to establish the existence of pseudo almost automorphic solutions to some second order damped integro differential equations with pseudo almost automorphic coefficients in order to illustrate our main results we will study the existence of pseudo almost automorphic solutions to a structurally damped plate like boundary value problem

on the existence of anti periodic solutions to a nonlinear evolution equation associated with odd subdifferential operators the existence of anti periodic solutions hence also that of periodic solutions to the nonlinear parabolic type evolution equation ddt u t u t f t u t 0 t r is shown under the assumptions that the subdifferential operator is odd and that f t t r is a family of monotone operators satisfying the anti periodicity condition f t t v f t v v d f t hence f t t v f t v v d d f t t r for a fixed t r here coerciveness of is not assumed an application to a heat equation is given without assuming boundedness of the domain of rxn

rudiments of rough sets abstract worldwide there has been a rapid growth in interest in rough set theory and its applications in recent years evidence of this can be found in the increasing number of high quality articles on rough sets and related topics that have been published in a variety of international journals symposia workshops and international conferences in recent years in addition many international workshops and conferences have included special sessions on the theory and applications of rough sets in their programs rough set theory has led to many interesting applications and extensions it seems that the rough set approach is fundamentally important in artificial intelligence and cognitive sciences especially in research areas such as machine learning intelligent systems inductive reasoning pattern recognition mereology knowledge discovery decision analysis and expert systems in the article we present the basic concepts of rough set theory and point out some rough set based research directions and applications

anti periodic solutions for semilinear evolution equations in this paper we use the homotopy method to establish the existence and uniqueness of anti periodic solutions for the nonlinear anti periodic problem a t x bx f t a e t r x t t x t where a t x is a nonlinear map and b is a bounded linear operator from r n to r n sufficient conditions for the existence of the solution set are presented also we consider the nonlinear evolution problems with a perturbation term which is multivalued we show that for this problem the solution set is nonempty and weakly compact in w 1 2 i r n for the case of convex valued perturbation and prove the existence theorems of anti periodic solutions for the nonconvex case all illustrative examples are provided

a composition theorem for weighted pseudo almost automorphic functions and applications abstract in this paper we establish a composition theorem for weighted pseudo almost automorphic functions under a weaker lipschitz condition our composition theorem generalizes some known results moreover the existence and uniqueness of pseudo almost automorphic solutions for abstract semilinear evolution equations are studied

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

extremal solutions of quasilinear parabolic inclusions with generalized clarke s gradient abstract in this paper we consider an initial boundary value problem for a parabolic inclusion whose multivalued nonlinearity is characterized by clarke s generalized gradient of some locally lipschitz function and whose elliptic operator may be a general quasilinear operator of leray lions type recently extremality results have been obtained in case that the governing multivalued term is of special structure such as multifunctions given by the usual subdifferential of convex functions or subgradients of so called dc functions the main goal of this paper is to prove the existence of extremal solutions within a sector of appropriately defined upper and lower solutions for quasilinear parabolic inclusions with general clarke s gradient the main tools used in the proof are abstract results on nonlinear evolution equations regularization comparison truncation and special test function techniques as well as tools from nonsmooth analysis

approximations and uncertainty measures in incomplete information systems there are mainly two methodologies dealing with uncertainty measurement issue in rough set theory pure rough set approach and information theory approach pure rough set approach is based on the concepts of accuracy roughness and approximation accuracy proposed by pawlak information theory approach is based on shannon s entropy or its variants several authors have extended the information theory approach into incomplete information systems however there are few studies on extending the pure rough set approach to incomplete information systems this paper focuses on constructing uncertainty measures in incomplete information systems by pure rough set approach three types of definitions of lower and upper approximations and corresponding uncertainty measurement concepts including accuracy roughness and approximation accuracy are investigated theoretical analysis indicates that two of the three types can be used to evaluate the uncertainty in incomplete information systems experiments on incomplete real life data sets have been conducted to test the two selected types the first type and the third type of uncertainty measures results show that the two types of uncertainty measures are effective

second order differential variational inequalities involving anti periodic boundary value conditions abstract this paper deals with a new class of second order nonlinear differential variational inequalities firstly we study the properties of a solution set for a variational inequality by using the kkm technique and a monotonicity property then we prove the existence of solutions to a second order nonlinear differential variational inequality with anti periodic boundary value conditions not assuming the lipschitz continuity of the nonlinear term our approaches which are essentially different from previous research methods in differential variational inequalities are based on the topological degree theory and the filippov implicit function lemma

existence results for some higher order evolution equations with operator coefficients abstract in this paper we study and obtain the existence of c r pseudo almost automorphic solutions to some higher order differential equations with operator coefficients whose forcing is c s pseudo almost automorphic we next use these abstract results to study the existence of c r pseudo almost automorphic solutions to some second order differential equations in hilbert space which among other things model the so called linear beam equation

linear dimensionality reduction using relevance weighted lda the linear discriminant analysis lda is one of the most traditional linear dimensionality reduction methods this paper incorporates the inter class relationships as relevance weights into the estimation of the overall within class scatter matrix in order to improve the performance of the basic lda method and some of its improved variants we demonstrate that in some specific situations the standard multi class lda almost totally fails to find a discriminative subspace if the proposed relevance weights are not incorporated in order to estimate the relevance weights of individual within class scatter matrices we propose several methods of which one employs the evolution strategies

existence of weighted pseudo almost periodic solutions to some classes of nonautonomous partial evolution equations abstract in this paper under acquistapace terreni conditions we make extensive use of interpolation spaces and exponential dichotomy techniques to obtain the existence of weighted pseudo almost periodic solutions to some classes of nonautonomous partial evolution equations applications include the existence of weighted pseudo almost periodic solutions to a nonautonomous heat equation with gradient coefficients