variable threshold concept lattices in this paper the definition of a variable threshold concept lattice is introduced based on a galois connection three kinds of variable threshold concept lattices in which diverse requirements of knowledge discovery can be satisfied by adjusting a threshold are defined the number of formal concepts in a variable threshold concept lattice is far less than that in a fuzzy concept lattice the three kinds of variable threshold concept lattices are constructed between two crisp sets between a crisp set and a fuzzy set and between a fuzzy set and a crisp set their properties are analogous to that of the classical concept lattices and can be induced by the fuzzy concept lattice

finite surface discretization for incompressible navier stokes equations and coupled conservation laws abstract we present a new finite surface discretization fsd aiming at the incompressible navier stokes equations nse and other coupled conservation laws this discretization defines the velocities as surfaced averaged values living on the faces of the pressure volumes in which the mass is set to be conserved consequently the calculation of the mass balance on these control volumes is exact which allows more accurate information to be kept in the velocity field and produces a very accurate prediction of the pressure in the next time step the proposed discretization reduces the stencil size of the poisson equation in the projection method compared to the finite volume and finite difference discretizations due to highly accurate mass conservation the compact sixth order approximation of fsd can be used with an explicit fourth order pressure treatment this property greatly reduces the cost and complexity of the implementation we present the discrete evolution equation of the surface averaged velocities together with the enforcement of mass conservation and the solution procedure for the pressure the approximation of the nse under this new discretization uses a combination of finite difference and finite volume methods the proposed method is validated using standard laminar test cases we identify the conditions under which a fourth order pressure treatment can support the sixth order and eighth order approximations of the convection term using fourier analysis the performance of the method is evaluated on turbulent channel flows up to friction reynolds number of 950 the quantitative relationships between the accuracy of the solution and grid size are identified we present two performance indices for comparison with other methods at the error level of 1 per mille the proposed method is 28 times faster than the classic second order scheme

an efficient compact difference scheme for solving the streamfunction formulation of the incompressible navier stokes equations recently a new paradigm for solving the steady navier stokes equations using a streamfunction velocity formulation was proposed by gupta and kalita m m gupta j c kalita a new paradigm for solving navier stokes equations streamfunction velocity formulation j comput phys 207 2005 52 68 which avoids difficulties inherent in the conventional streamfunction vorticity and primitive variable formulations it is discovered that this formulation can reached second order accurate and obtained accuracy solutions with little additional cost for a couple of fluid flow problems in this paper an efficient compact finite difference approximation named as five point constant coefficient second order compact 5pcc soc scheme is proposed for the streamfunction formulation of the steady incompressible navier stokes equations in which the grid values of the streamfunction and the values of its first derivatives velocities are carried as the unknown variables the derivation approach is simple and can be easily used to derive compact difference schemes for other similar high order elliptic differential equations numerical examples including the lid driven cavity flow problem and a problem of flow in a rectangular cavity with the hight width ratio of 2 are solved numerically to demonstrate the accuracy and efficiency of the newly proposed scheme the results obtained are compared with ones by different available numerical methods in the literature the present scheme not only shows second order accurate but also proves more effective than the existing second order compact scheme of the streamfunction formulation in the aspect of computational cost

some convergence results on quadratic forms for random fields and application to empirical covariances limit theorems are proved for quadratic forms of gaussian random fields in presence of long memory we obtain a non central limit theorem under a minimal integrability condition which allows isotropic and anisotropic models we apply our limit theorems and those of ginovian j contemp math anal 34 2 1 15 to obtain the asymptotic behavior of the empirical covariances of gaussian fields which is a particular example of quadratic forms we show that it is possible to obtain a gaussian limit when the spectral density is not in l 2 therefore the dichotomy observed in dimension d 1 between central and non central limit theorems cannot be stated so easily due to possible anisotropic strong dependence in d 1

an application of the seasonal fractionally differenced model to the monetary aggregates abstract in this article three significant variables used by the u s federal reserve as targets to shape monetary policy the monetary aggregates m1 m2 and m3 are examined using a seasonal fractionally differenced model the sample autocorrelation functions of these monetary variables exhibit a decay pattern at the seasonal lags that is typical of a fractional model the seasonal fractionally differenced model is found to remove a great deal of the autocorrelation at the seasonal lags especially when a series is extended by splicing together earlier monetary data some monte carlo evidence as to the efficacy of this technique is presented finally one year ahead out of sample forecasts of m1 are made using both the box jenkins airline model and the seasonal fractionally differenced model

a multi level conceptual data reduction approach based on the lukasiewicz implication starting from fuzzy binary data represented as tables in the fuzzy relational database in this paper we use fuzzy formal concept analysis to reduce the tables size to only keep the minimal rows in each table without losing knowledge i e association rules extracted from reduced databases are identical at given precision level more specifically we develop a fuzzy extension of a previously proposed algorithm for crisp data reduction without loss of knowledge the fuzzy galois connection based on the lukasiewicz implication is mainly used in the definition of the closure operator according to a precision level which makes data reduction sensitive to the variation of this precision level

relationship between generalized rough sets based on binary relation and covering rough set theory is a powerful tool for dealing with uncertainty granularity and incompleteness of knowledge in information systems this paper systematically studies a type of generalized rough sets based on covering and the relationship between this type of covering based rough sets and the generalized rough sets based on binary relation firstly we present basic concepts and properties of this kind of rough sets then we investigate the relationships between this type of generalized rough sets and other five types of covering based rough sets the major contribution in this paper is that we establish the equivalency between this type of covering based rough sets and a type of binary relation based rough sets through existing results in binary relation based rough sets we present axiomatic systems for this type of covering based lower and upper approximation operations in addition we explore the relationships among several important concepts such as minimal description reduction representative covering exact covering and unary covering in covering based rough sets investigation of this type of covering based will benefit to our understanding of other types of rough sets based on covering and binary relation

formal concept analysis via multi adjoint concept lattices several fuzzifications of formal concept analysis have been proposed to deal with uncertain information in this paper we focus on concept lattices under a multi adjoint paradigm which enriches the language providing greater flexibility to the user in that he she can choose from a number of different connectives multi adjoint concept lattices are shown to embed different fuzzy extensions of concept lattices found in the literature the main results of the paper being the representation theorem of this paradigm and the embedding of other well known approaches

a minimum distance estimator for long memory processes this paper considers a minimum distance estimator mde of the differencing para meter of the fractionally integrated white noise model the mde minimizes the differ ence between sample and population autocorrelations the paper presents calculations of asymptotic variances to examine the efficiency of the mde relative to that of the mle for values of the differencing parameter less than l 4 the mde is consistent and asymptotically normal and the asymptotic variance of the mde using the first n auto correlations approaches that of the mle as n increases however there is a substantial efficiency loss if low order autocorrelations are omitted this implies that a non parametric treatment of short run dynamics will involve a substantial loss of efficiency

on the topological properties of fuzzy rough sets this paper is devoted to the discussion of the relationship between fuzzy rough set models and fuzzy topologies on a finite universe the tc axiom for fuzzy topology is proposed it is proved that the set of all lower approximation sets based on a reflexive and transitive fuzzy relation consists of a fuzzy topology which satisfies tc axiom and conversely a fuzzy topology which obey tc axiom is just the set of all lower approximation sets under a reflexive and transitive fuzzy relation that is to say there exists a one to one correspondence between the set of all reflexive and transitive fuzzy relations and the set of all fuzzy topologies which satisfy tc axiom

attribute reduction in decision theoretic rough set models rough set theory can be applied to rule induction there are two different types of classification rules positive and boundary rules leading to different decisions and consequences they can be distinguished not only from the syntax measures such as confidence coverage and generality but also the semantic measures such as decision monotocity cost and risk the classification rules can be evaluated locally for each individual rule or globally for a set of rules both the two types of classification rules can be generated from and interpreted by a decision theoretic model which is a probabilistic extension of the pawlak rough set model as an important concept of rough set theory an attribute reduct is a subset of attributes that are jointly sufficient and individually necessary for preserving a particular property of the given information table this paper addresses attribute reduction in decision theoretic rough set models regarding different classification properties such as decision monotocity confidence coverage generality and cost it is important to note that many of these properties can be truthfully reflected by a single measure c in the pawlak rough set model on the other hand they need to be considered separately in probabilistic models a straightforward extension of the c measure is unable to evaluate these properties this study provides a new insight into the problem of attribute reduction

generalized fuzzy rough sets this paper presents a general framework for the study of fuzzy rough sets in which both constructive and axiomatic approaches are used in constructive approach a pair of lower and upper generalized approximation operators is defined the connections between fuzzy relations and fuzzy rough approximation operators are examined in axiomatic approach various classes of fuzzy rough approximation operators are characterized by different sets of axioms axioms of fuzzy approximation operators guarantee the existence of certain types of fuzzy relations producing the same operators

bias in the sample autocorrelations of fractional noise summary the autocorrelation function of fractional noise when the difference parameter is positive is quite distinctive however for time series of moderate length this pattern is unlikely to be seen in the sample autocorrelations which are severely biased when the process mean is unknown

the detection and estimation of long memory in stochastic volatility abstract we propose a new time series representation of persistence in conditional variance called a long memory stochastic volatility lmsv model the lmsv model is constructed by incorporating an arfima process in a standard stochastic volatility scheme strongly consistent estimators of the parameters of the model are obtained by maximizing the spectral approximation to the gaussian likelihood the finite sample properties of the spectral likelihood estimator are analyzed by means of a monte carlo study an empirical example with a long time series of stock prices demonstrates the superiority of the lmsv model over existing short memory volatility models

high re solutions for incompressible flow using the navier stokes equations and a multigrid method the vorticity stream function formulation of the two dimensional incompressible navierstokes equations is used to study the effectiveness of the coupled strongly implicit multigrid csi mg method in the determination of high re fine mesh flow solutions the driven flow in a square cavity is used as the model problem solutions are obtained for configurations with reynolds number as high as 10 000 and meshes consisting of as many as 257 x 257 points for re 1000 the 129 x 129 grid solution required 1 5 minutes of cpu time on the amdahl 470 v 6 computer because of the appearance of one or more secondary vortices in the flow field uniform mesh refinement was preferred to the use of one dimensional gridclustering coordinate transformations the past decade has witnessed a great deal of progress in the area of computational fluid dynamics developments in computer technology hardware as well as in advanced numerical algorithms have enabled attempts to be made towards analysis and numerical solution of highly complex flow problems for some of these applications the use of simple iterative techniques to solve the navier stokes equations leads to a rather slow convergence rate for the solutions the solution convergence rate can be seriously affected if the coupling among the various governing differential equations is not properly honored either in the interior of the solution domain or at its boundaries the rate of convergence is also generally strongly dependent on such problem parameters as the reynolds number the mesh size and the total number of computational points this has led several researchers to examine carefully the recently emerging multigrid mg technique as a useful means for enhancing the convergence rate of iterative numerical methods for solving discretized equations at a number of computational grid points so large as to be considered impractical previously

concept lattices and conceptual knowledge systems abstract concept lattice is the central notion of formal concept analysis a new area of research which is based on a set theoretical model for concepts and conceptual hierarchies this model yields not only a new approach to data analysis but also methods for formal representation of conceptual knowledge these methods are outlined on three levels first basics on concept lattices are explained starting from simple data contexts which consist of a binary relation between objects and attributes indicating which object has which attribute on the second level conceptual relationships are discussed for data matrices which assign attribute values to each of the given objects finally a mathematical model for conceptual knowledge systems is described this model allows us to study mathematically the representation inference acquisition and communication of conceptual knowledge

long term memory in stock market prices a test for long term memory that is robust to short range dependence is developed it is a modification of the r s statistic and the relevant asymptotic sampling theory is derived via functional central limit theory contrary to previous findings when applied to daily and monthly stock returns indexes over several time periods this test yields no evidence of long range dependence once short range dependence is accounted for monte carlo experiments show that the modified r s test has power against at least two specific models of long term memory suggesting that models with short range dependence may adequately capture the behavior of historical stock returns copyright 1991 by the econometric society

a new algebraic structure for formal concept analysis formal concept analysis fca originally proposed by wille 39 is an important theory for data analysis and knowledge discovery concept lattice is the core of the mathematical theory of formal concept analysis to address the requirements of real word applications concept lattice has been extended to many other forms from the theoretical point of view and possible applications in this paper with the aim of deriving the mathematical properties of formal concepts from the point of algebra we propose a new algebra system for the formal context under the frame of the proposed system some interesting properties of formal concepts are explored which could be applied to explore concept hierarchy and ontology merging

generalized rough sets based on relations rough set theory has been proposed by pawlak as a tool for dealing with the vagueness and granularity in information systems the core concepts of classical rough sets are lower and upper approximations based on equivalence relations this paper studies arbitrary binary relation based generalized rough sets in this setting a binary relation can generate a lower approximation operation and an upper approximation operation but some of common properties of classical lower and upper approximation operations are no longer satisfied we investigate conditions for a relation under which these properties hold for the relation based lower and upper approximation operations

numerical simulation of 2d square driven cavity using fourth order compact finite difference schemes abstract fourth order compact finite difference schemes are employed with multigrid techniques to simulate the two dimensional square driven cavity flow with small to large reynolds numbers the governing navier stokes equation is linearized in streamfunction and vorticity formulation the fourth order compact approximation schemes are coupled with fourth order approximations for velocities and vorticity boundaries numerical solutions are obtained for square driven cavity flow at high reynolds numbers and are compared with solutions obtained by other researchers using other approximation methods

higher order solutions of square driven cavity flow using a variable order multi grid method a new higher order method is devised for the numerical simulation of square driven cavity flows the spatial derivatives of the navier stokes equations are discretized by means of the modified differential quadrature mdq method the resulting system of ordinary differential equations odes in time is then integrated by the classical fourth order runge kutta gill rkg scheme the elliptic poisson equation is solved by means of a new variable order multi grid method the numerical simulations of the square driven cavity flows are carried out with spatial order of accuracy up to 10th order the results suggest that the higher order solutions are more reliable than the well known results obtained by ghia et al

formal concept analysis based on the topology for attributes of a formal context formal concept analysis fca concerns the hierarchical structures induced by a binary relation between a pair of sets it is widely applied in data analysis information retrieval and knowledge discovery within the framework of fca computing all formal concepts is the main challenge due to its exponential complexity it has be proved that all formal concepts is a closure system on objects hence the closure operator on objects are general used to generate all formal concepts of a formal context in the lexicographic tree approach a base on objects is used to generate extensions of all formal concepts and construct the formal concept lattice inspired from the approach we concentrate a base on attributes and generate intensions of all formal concepts in this paper to this end we firstly analyze an example the lexicographic tree approach is used to generate all formal concepts from the time complexity point of view we present that it is not trivial to generate the base on attributes by a simple symmetrical way from the methods based on objects then we deduce a set valued mapping from attributes to the power set of attributes in a formal context and define a binary relation on attributes by the set valued mapping using the binary relation on attributes we construct an approximation space and a topology for attributes respectively and obtain a base for the topology we prove that intensions of all formal concepts are included in the topology for attributes this means that the base can be used to generate intensions of all formal concepts of the formal context and construct the formal concept lattice more general our results represent relationships and the hierarchical structures among attributes of the formal context we present some typical applications in which the topology for attributes and the base for the topology are applied for association rules discovery from a formal context and linguistic concept analysis

differentiating intraday seasonalities through wavelet multi scaling it is well documented that strong intraday seasonalities may induce distortions in the estimation of volatility models these seasonalities are also the dominant source for the underlying misspecifications of the various volatility models therefore an obvious route is to filter out the underlying intraday seasonalities from the data in this paper we propose a simple method for intraday seasonality extraction that is free of model selection parameters which may affect other intraday seasonality filtering methods our methodology is based on a wavelet multi scaling approach which decomposes the data into its low and high frequency components through the application of a non decimated discrete wavelet transform it is simple to calculate does not depend on a particular model selection criterion or model specific parameter choices the proposed filtering method is translation invariant has the ability to decompose an arbitrary length series without boundary adjustments is associated with a zero phase filter and is circular being circular helps to preserve the entire sample unlike other two sided filters where data loss occurs from the beginning and the end of the studied sample

clt and other limit theorems for functionals of gaussian processes conditions for the clt for non linear functionals of stationary gaussian sequences are discussed with special references to the borderline between the clt and the non clt examples of the non clt for such functionals with the norming factor sqrt n are given

modeling persistence in hydrological time series using fractional differencing the class of autoregressive integrated moving average arima time series models may be generalized by permitting the degree of differencing d to take fractional values models including fractional differencing are capable of representing persistent series d 0 or short memory series d 0 the class of fractionally differenced arima processes provides a more flexible way than has hitherto been available of simultaneously modeling the long term and short term behavior of a time series in this paper some fundamental properties of fractionally differenced arima processes are presented methods of simulating these processes are described estimation of the parameters of fractionally differenced arima models is discussed and an approximate maximum likelihood method is proposed the methodology is illustrated by fitting fractionally differenced models to time series of streamflows and annual temperatures

noncentral limit theorems for quadratic forms in random variables having long range dependence we study the weak convergence in d lbrack 0 1 rbrack of the quadratic form sum lbrack nt rbrack j 1 sum lbrack nt rbrack k 1 a j k h m x j h m x k adequately normalized here a s infty s infty is a symmetric sequence satisfying sum a s infty h m is the m th hermite polynomial and x j j geq 1 is a normalized gaussian sequence with covariances r k sim k d l k as k rightarrow infty where 0 d 1 and l is slowly varying we prove that for all m geq 1 the limit is brownian motion when 1 2 d 1 and it is the non gaussian rosenblatt process when 0 d 1 2

a rational high order compact difference method for the steady state stream functionvorticity formulation of the navierstokes equations a rational high order compact rhoc finite difference fd method on the nine point stencil is proposed for solving the steady state two dimensional navierstokes equations in the stream functionvorticity form the resulting system of algebra equations can be solved by using the point successive over or under relaxation sor iteration numerical experiments involving two linear and two nonlinear problems with their analytical solutions and two flow problems including the lid driven cavity and backward facing step flows are carried out to validate the performance of the newly proposed method numerical solutions of the driven cavity problem with different grid mesh sizes maximum being 513513 for reynolds numbers ranging from 0 to 17500 are obtained and compared with some of the accurate results available in the literature

topological approaches to covering rough sets rough sets a tool for data mining deal with the vagueness and granularity in information systems this paper studies covering based rough sets from the topological view we explore the topological properties of this type of rough sets study the interdependency between the lower and the upper approximation operations and establish the conditions under which two coverings generate the same lower approximation operation and the same upper approximation operation lastly axiomatic systems for the lower approximation operation and the upper approximation operation are constructed

approaches to the representations and logic operations of fuzzy concepts in the framework of axiomatic fuzzy set theory ii in this paper the representations of fuzzy concepts based on raw data have been investigated within the framework of afs axiomatic fuzzy set theory first a brief review of afs theory is presented and a completely distributive lattice the e i algebra is proposed secondly two kinds of e i algebra representations of fuzzy concepts are derived in detail in order to represent the membership functions of fuzzy concepts in the interval 0 1 the norm of afs algebra is defined and studied finally the relationships of various representations with their advantages and drawbacks are analyzed

asymptotic distributions of the sample mean autocovariances and autocorrelations of long memory time series we derive the asymptotic distributions of the sample mean autocovariances and autocorrelations for a time series whose autocovariance function has the powerlaw decay 0 o 1 as the results differ in important respects from the corresponding results for short memory processes whose autocovariance functions are absolutely summable for long memory processes the variances of the sample mean and of the sample autocovariances and autocorrelations for 0 12 are not of asymptotic order n 1 when 0 12 the asymptotic distributions of the sample autocovariances and autocorrelations are not normal

how much information does dependence between wavelet coefficients contain abstractthis article is motivated by several articles that propose statistical inference where the independence of wavelet coefficients for both short as well as long range dependent time series is assumed we focus on the sample variance and investigate the influence of the dependence between wavelet coefficients and this statistic to this end we derive asymptotic distributional properties of the sample variance for a time series that is synthesized ignoring some or all dependence between wavelet coefficients we show that the second order properties differ from the those of the true time series whose wavelet coefficients have the same marginal distribution except in the independent gaussian case this holds true even if the dependency is correct within each level and only the dependence between levels is ignored in the case of sample autocovariances and sample autocorrelations at lag one we indicate that first order properties are erroneous in a second step we investigate several nonparametric b

steady viscous flow in a triangular cavity by efficient numerical techniques abstract accurate and efficient calculations of the flow inside a triangular cavity are presented for high reynolds numbers the navier stokes equations expressed in a stream function and vorticity formulation are solved numerically using finite differences on a transformed geometry second order numerical boundary conditions are derived and newton s iteration is employed to solve the nonlinear system resulting from the finite difference discretization aside from solving the equilateral triangular cavity problem we have also been able to compute numerical solutions for scalene triangular cavity problems our coarse mesh results for the equilateral triangular cavity problem are compared with finer mesh results in the literature and the agreement is good

some simple properties of sums of random variables having long range dependence the higher order moments and cumulants of sums of a special case of random variables having long range dependence are investigated tensor methods are used to simplify the calculations the limiting form of the second and third cumulants as the number of variables added becomes large is studied by analytical and numerical methods the implications are discussed for the existence of non gaussian limits of sums of random quantities of finite variance and long range dependence

empirical study of arfima model based on fractional differencing abstract in this paper we studied the long term memory of hong kong hang sheng index using mrs analysis established arfima model for it and detailed the procedure of fractional differencing furthermore we compared the arfima model built by this means with the one that took first order differencing as an alternative the result showed that if doing so much useful information of time series would be lost the forecast formula of arfima model was corrected according to the method of fractional differencing and was employed in the empirical study it was illustrated that the forecast performance of arfima model was not as good as we expected since the arfima model was ineffective in forecasting hang sheng index the certainty of this conclusion was proposed from two different aspects