vertex operators of uq gl n n and highest weight representations of uq gl 2 2 we determine the exchange relations of the level one q vertex operators of the quantum affine superalgebra uq gl n n we study in detail the level one irreducible highest weight representations of uq gl 2 2 and compute the characters and supercharacters associated with these irreducible modules

a method for training finite mixture models under a fuzzy clustering principle in this paper we establish a novel regard towards fuzzy clustering showing it provides a sound framework for fitting finite mixture models we propose a novel fuzzy clustering type methodology for finite mixture model fitting effected by utilizing a regularized form of the fuzzy c means fcm algorithm and introducing a proper dissimilarity functional for the algorithm with respect to the probabilistic properties of the model being treated we apply the proposed methodology in a number of popular finite mixture models and the corresponding expressions of the fuzzy model fitting algorithm are derived we examine the efficacy of our novel approach in both clustering and classification applications of benchmark data sets and we demonstrate the advantages of the proposed approach over maximum likelihood

a quantum analog of the z algebra we define a natural quantum analog for the z algebra and which we refer to as the zq algebra by modding out the heisenberg algebra from the quantum affine algebra uq sl 2 with level k we discuss the representation theory of this zq algebra in particular we exhibit its reduction to a group algebra and to a tensor product of a group algebra with a quantum clifford algebra when k 1 and k 2 and thus we recover the explicit constructions of uq sl 2 standard modules as achieved by frenkel jing and bernard respectively moreover for arbitrary nonzero level k we show that the explicit basis for the simplest z generalized verma module as constructed by lepowsky and primc is also a basis for its corresponding zq module i e it is invariant under the q deformation for generic q we expect this zq algebra associated with uq sl 2 at level k to play the role of a dynamical symmetry in the off critical zk statistical models

parallel adaptive finite element euler flow solver for rotary wing aerodynamics we discuss the development of a code for the automated reliable numerical simulation of rotor aerodynamics the code performs all the stages of the analysis finite element solution error indication mesh adaptation in a parallel multiple instruction multiple data environment making use of efficient scalable parallel algorithms the main features of all the building blocks of the implemented approach are detailed and discussed the capabilities and performance characteristics of the parallel automated adaptive procedure are demonstrated with regard to subsonic and transonic compressible flow problems in particular different hovering rotor problems are analyzed

twisted quantum affinizations and their vertex representations in this paper we generalize drinfeld s twisted quantum affine algebras to construct twisted quantum algebras for all simply laced generalized cartan matrices and present their vertex representation realizations

graded tetrahedral finite element meshes vertices in the body centred cubic bcc lattice are used to create a tetrahedral spatial decomposition with this spatial decomposition an octree approach is combined with delaunay triangulations to decompose solids into tetrahedral finite element meshes solids must have their surfaces triangulated and the vertices in the triangulation are finite element nodes local densities of interior tetrahedra are controlled by the densities of surface triangles accuracy of the decomposition into finite elements depends on the accuracy of the surface triangulation which can be constructed with state of the art computer aided design systems

vertex operator representation of some quantum tori lie algebras we are defining the trigonometric lie subalgebras in bar x infty bar a infty bar b infty bar c infty bar d infty which are the natural generalization of the well known sin lie algebra the embedding formulas into bar x infty are introduced these algebras can be considered as some lie algebras of quantum tori an irreducible representation ofa b series of trigonometric lie algebras is constructed special cases of the trigonometric lie factor algebras which can be considered as a quantum preserving lie algebra structure deformation of the kac moody algebras are considered

vertex operators and symmetric functions an algorithm for the calculation of q dependent spin characters of the symmetric group is given with an explicit example of s4 a method for constructing the q analogue of the vertex operators is developed a 1 1 correspondence between the space v of twisted q vertex operators and the ring of q deformed symmetric functions lambda x zq q t is established and a mapping from v to lambda x zq q t is defined a number of relevant theorems are given

vertex operators for twisted quantum affine algebras we construct explicitly the q vertex operators intertwining operators for the level one modules v i of the classical quantum affine algebras of twisted types using interacting bosons where i 0 1 for a 2 n 1 i 0 for d 3 i 0 n for d 2 1 and i n for a 2 n a perfect crystal graph for d 3 4 is constructed as a by product

staggered polarization of vertex models with u_q widehat sl n symmetry in this paper we give an explicit formula for level 1 vertex operators related to u q widehat sl n as operators on the fock spaces we derive also their commutation relations as an application we calculate with the vector representation of u q widehat sl n thereby extending the recent work on the staggered polarization of the xxz model

unsupervised optimal fuzzy clustering this study reports on a method for carrying out fuzzy classification without a priori assumptions on the number of clusters in the data set assessment of cluster validity is based on performance measures using hypervolume and density criteria an algorithm is derived from a combination of the fuzzy k means algorithm and fuzzy maximum likelihood estimation the unsupervised fuzzy partition optimal number of classes algorithm performs well in situations of large variability of cluster shapes densities and number of data points in each cluster the algorithm was tested on different classes of simulated data and on a real data set derived from sleep eeg signal

plethysms replicated schur functions and series with applications to vertex operators specializations of schur functions are exploited to define and evaluate the schur functions s x and plethysms s s x for any integer real or complex plethysms are then used to define pairs of mutually inverse infinite series of schur functions m and l specified by arbitrary partitions these are used in turn to define and provide generating functions for formal characters s of certain groups h thereby extending known results for orthogonal and symplectic group characters each of these formal characters is then given a vertex operator realization first in terms of the seriesm m 0 and various l dual to l and then more explicitly in the exponential form finally the replicated form of such vertex operators are written down the characters of the orthogonal and symplectic groups have been found by schur 34 and weyl 35 respectively the method used is transcendental and depends on integration over the group manifold these characters however may be obtained by purely algebraic methods this algebraic method would seem to offer a better prospect of successful application to other restricted groups than the method of group integration littlewood d e 1944 phil trans r soc london ser a 239 809 392 pacs numbers 02 10 v 02 10 de 02 20 a 02 20 hj mathematics subject classification 05e05 17b69 11e57 16w30 20e22 33d52 43a40 1751 8113

consideration of constraints within the finite element method by means of matrix operators the following paper describes the incorporation of different constraints into a finite element system by means of matrix operators in conjunction with consecutive corresponding transformations instead of increasing the number of equations as e g the lagrange multiplier method10 14 does the matrix operator method yields a set of reduced magnitude which can be solved more efficiently the method will be developed for two classes of constraints i stiff coupling of previously known subdomains and ii contact problem between two bodies the assembly rules to obtain the system matrices are deduced an application is given by a three dimensional example of structural analysis in mechanical engineering

γ conformal algebras conformal algebra is an axiomatic description of the operator product expansion of chiral fields with simple poles at finitely many points we classify these algebras and their representations in terms of lie algebras and their representations with an action of the group to every conformal algebra and a character of we associate a lie algebra generated by fields with the ope with simple poles examples include twisted affine kac moody algebras the sin algebra which is a conformal analogue of the general linear algebra and its analogues the algebra of pseudodifferential operators on the circle etc

essential boundary conditions and multi point constraints in finite element analysis the application of boundary conditions and other constraints to the stiffness matrix and load vector is an integral part of any finite element code this process is usually trivial but can present difficulties to the point where some codes disallow certain combinations of commonly occurring boundary conditions a general approach to this problem is presented and applied to representative examples necessary and sufficient conditions are obtained under which constraints can be applied sequentially bounds are obtained for the condition number of the reduced system showing it is essentially the same as for the original problem

mixtures of probabilistic principal component analyzers principal component analysis pca is one of the most popular techniques for processing compressing and visualizing data although its effectiveness is limited by its global linearity while nonlinear variants of pca have been proposed an alternative paradigm is to capture data complexity by a combination of local linear pca projections however conventional pca does not correspond to a probability density and so there is no unique way to combine pca models therefore previous attempts to formulate mixture models for pca have been ad hoc to some extent in this article pca is formulated within a maximum likelihood framework based on a specific form of gaussian latent variable model this leads to a well defined mixture model for probabilistic principal component analyzers whose parameters can be determined using an expectationmaximization algorithm we discuss the advantages of this model in the context of clustering density modeling and local dimensionality reduction and we demonstrate its application to image compression and handwritten digit recognition

adapting broyden method to handle linear constraints imposed via lagrange multipliers various non linear equation solvers are adapted to handle linear constraints via the lagrange multiplier technique this adaptation process turns out to be quite straightforward for newton raphson methods and rank two quasi newton methods bfgs and dfp but rather more involved for broyden method in fact two broyden methods can be obtained the standard one and a modified one better adapted to the lagrange multiplier environment some numerical examples are used to assess the relative performance of the various adapted solvers these tests illustrate the superiority of the modified broyden method over the standard one

level one highest weight representation of uq sl n 1 and bosonization of the multicomponent super t j model we study the level one irreducible highest weight representations of the quantum affine superalgebra uq sl n 1 and calculate their characters and supercharacters we obtain bosonized q vertex operators acting on the irreducible uq sl n 1 modules and derive the exchange relations satisfied by the vertex operators we give the bosonization of the multicomponent super t j model by using the bosonized vertex operators

trace construction of a basis for the solution space of sln qkz equation the trace of intertwining operators over the level one irreducible highest weight modules of the quantum affine algebra of type a n 1 1 is studied it is proved that the trace function gives a basis of the solution space of the qkz equation at a generic level the highest highest matrix elements of the composition of intertwining operators are explicitly determined as rational functions up to an overall scalar function the integral formula for the trace is presented

vertex operators arising from the homogeneous realization for we use the underlying fock space for the homogeneous vertex operator representation of the affine lie algebra to construct a family of vertex operators as an application an irreducible module for an extended affine lie algebra of type a n 1 coordinatized by a quantum torus q of 2 variables or 3 variables is obtained moreover this module turns out to be a highest weight module which is an analog of the basic module for affine lie algebras

from a gaussian mixture model to nonadditive fuzzy systems this work explores how a kind of probabilistic system namely the gaussian mixture model gmm can be translated to an additive fuzzy system we will prove the mathematical equivalence between the conditional mean of a gmm and the defuzzified output of a generalized fuzzy model gfm the relationship between a gmm and a gfm and the conditions for gmm to gfm translation will be made explicit in the form of theorems the work will then extend to special cases of the gfm specifically the mamdani larsen and takagi sugeno fuzzy models the possibility of reverse translation that is from a gfm to a gmm will also be discussed finally we will consider the generality of a gmm specifically how it can approximate other distribution functions

fuzzy semi supervised co clustering for text documents in this paper we propose a new heuristic semi supervised fuzzy co clustering algorithm ss hfcr for categorization of large web documents in this approach the clustering process is carried out by incorporating some prior knowledge in the form of pair wise constraints provided by users into the fuzzy co clustering framework each constraint specifies whether a pair of documents must or cannot be clustered together moreover we formulate the competitive agglomeration cost function which is also able to make use of prior knowledge in the clustering process the experimental studies on a number of large benchmark datasets demonstrate the strength and potentials of ss hfcr in terms of accuracy stability and efficiency compared with some of the recent popular semi supervised clustering approaches

fuzzy gaussian mixture models in this paper in order to improve both the performance and the efficiency of the conventional gaussian mixture models gmms generalized gmms are firstly introduced by integrating the conventional gmms and the active curve axis gmms for fitting non linear datasets and then two types of fuzzy gaussian mixture models fgmms with a faster convergence process are proposed based on the generalized gmms inspired from the mechanism of fuzzy c means fcms which introduces the degree of fuzziness on the dissimilarity function based on distances one is named as probability based fgmms defining the dissimilarity as the multiplicative inverse of probability density function and the other is distance based fgmms which define the dissimilarity function focusing the degree of fuzziness only on the distances between points and component centres different from fcms both of the proposed dissimilarity functions are based on the exponential function of the distance the fgmms are compared with the conventional gmms and the generalized gmms in terms of the fitting degree and convergence speed the experimental results show that the proposed fgmms not only possess the non linearity to fit datasets with curve manifolds but also have a much faster convergence process saving more than half computational cost than gmms

a possibilistic clustering approach toward generative mixture models generative mixture models mms provide one of the most popular methodologies for unsupervised data clustering mms are formulated on the basis of the assumption that each observation derives from belongs to a single cluster however in many applications data may intuitively belong to multiple classes thus rendering the single cluster assignment assumptions of mms irrelevant furthermore even in applications where a single cluster data assignment is required the induced multinomial allocation of the modeled data points to the clusters derived by a mm imposing the constraint that the membership probabilities of a data point across clusters sum to one makes mms very vulnerable to the presence of outliers in the clustered data sets and renders them ineffective in discriminating between cases of equal evidence or ignorance to resolve these issues in this paper we introduce a possibilistic formulation of mms possibilistic clustering is a methodology that yields possibilistic data partitions with the obtained membership values being interpreted as degrees of possibility compatibilities of the data points with respect to the various clusters we provide an efficient maximum likelihood fitting algorithm for the proposed model and we conduct an objective evaluation of its efficacy using benchmark data

vertex representations of quantum affine algebras we construct vertex representations of quantum affine algebras of ade type which were first introduced in greater generality by drinfeld and jimbo the limiting special case of our construction is the untwisted vertex representation of affine lie algebras of frenkel kac and segal our representation is given by means of a new type of vertex operator corresponding to the simple roots and satisfying the defining relations in the case of the quantum affine algebra of type a we introduce vertex operators corresponding to all the roots and determine their commutation relations this provides an analogue of a chevalley basis of the affine lie algebra unk n in the basic representation

null vectors in integrable field theory the form factor bootstrap approach allows to construct the space of local fields in the massive restricted sine gordon model this space has to be isomorphic to that of the corresponding minimal model of conformal field theory we describe the subspaces which correspond to the verma modules of primary fields in terms of the commutative algebra of local integrals of motion and of a fermion neveu schwarz or ramond depending on the particular primary field the description of null vectors relies on the relation between form factors and deformed hyper elliptic integrals the null vectors correspond to the deformed exact forms and to the deformed riemann bilinear identity in the operator language the null vectors are created by the action of two operators linear in the fermion and quadratic in the fermion we show that by factorizing out the null vectors one gets the space of operators with the correct character in the classical limit using the operators and we obtain a new very compact description of the kdv hierarchy we also discuss a beautiful relation with the method of whitham

regularized linear fuzzy clustering and probabilistic pca mixture models fuzzy c means fcm type fuzzy clustering approaches are closely related to gaussian mixture models gmms and em like algorithms have been used in fcm clustering with regularized objective functions especially fcm with regularization by kullback leibler information klfcm is a fuzzy counterpart of gmms in this paper we propose to apply probabilistic principal component analysis pca mixture models to linear clustering following a discussion on the relationship between local pca and linear fuzzy clustering although the proposed method is a kind of the constrained model of klfcm the algorithm includes the fuzzy c varieties fcv algorithm as a special case and the algorithm can be regarded as a modified fcv algorithm with regularization by k l information numerical experiments demonstrate that the proposed clustering algorithm is more flexible than the maximum likelihood approaches and is useful for capturing local substructures properly

vertex operator of for level one in this paper we give the explicit formulae of vertex operators of u q b l 1 for level one as operators on the fock space meanwhile we point out that the free field realization by one fermionic field and l bosonic fields of highest weight module with highest weight lambda l has two irreducible modules