spectral parameter dependent approach to quantized algebra its multiparameter deformations and their q oscillator realizations yang baxterization of faddeev reshetikhin takhtajan algebra 1989 leading to quantum ybe is considered for a class of r matrices which satisfy hecke relations the authors apply such construction of the gl n case together with its multiparameter deformations revealing the connection between frt relations and the extended trigonometric sklyanin algebra new realizations of frt algebra through q oscillator modes are presented and their potential importance in the context of quantum integrable models is discussed a multiparametrized r matrix with the inclusion of spectral parameter is constructed as a by product

the universal r matrix for u_q rm sl 3 and beyond ther matrices for the quantised lie algebrasa n are constructed through the quantum double procedure given by drinfel d 6 the case ofu q sl 3 is thoroughly analysed initially to demonstrate the more subtle points of the calculation the ease of the calculation fora n is very dependent on a choice of generators for the borel subalgebrau q b and its dual and a certain ordering imposed on these generators which is related to the length of a certain word in the weyl group

artificial boundary conditions for two dimensional incompressible viscous flows around an obstacle abstract in this paper we consider numerical simulation of incompressible viscous flow around an obstacle in velocity pressure formulation two horizontal straight line artificial boundaries are introduced and the original flow is approximated by a flow in an infinite channel with slip boundary condition on the wall then two vertical segment artificial boundaries are introduced to limit the channel to a bounded computational domain in the region of the channel between the vertical boundaries and infinity the velocity of the flow is almost a constant vector in which the navier stokes equations can be linearised by oseen equations and thus a general solution can be derived by using separation of variables artificial boundary conditions on the vertical segments are then designed by imposing the continuity of velocity and normal stress therefore the original problem is reduced to a boundary value problem on a bounded computational domain numerical example shows that our artificial boundary conditions are very effective

artificial boundary conditions for incompressible navier stokes equations a well posed result abstract numerical simulation of two dimensional incompressible viscous flows around an obstacle is considered two horizontal straight line artificial boundaries are introduced and the original flow is approximated by a flow in an infinite channel with slip boundary condition on the wall then two vertical segment artificial boundaries are introduced and a series of approximate artificial boundary conditions on them are derived by imposing the continuity of velocity and the normal stress thus the original problem is reduced to a problem defined in a bounded computational domain the well posedness of the reduced problem is proved the finite element approximation of this problem is given and error estimates are obtained furthermore numerical examples show the accuracy and efficiency of our artificial boundary conditions

asymptotic boundary conditions for dissipative waves general theory an outstanding issue in the computational analysis of time dependent problems is the imposition of appropriate radiation boundary conditions at artificial boundaries accurate conditions are developed which are based on the asymptotic analysis of wave propagation over long ranges employing the method of steepest descents dominant wave groups are identified and simple approximations to the dispersion relation are considered in order to derive local boundary operators the existence of a small number of dominant wave groups may be expected for systems with dissipation estimates of the error as a function of domain size are derived under general hypotheses leading to convergence results some practical aspects of the numerical construction of the asymptotic boundary operators are also discussed

a direct formulation for sparse pca using semidefinite programming given a covariance matrix we consider the problem of maximizing the variance explained by a particular linear combination of the input variables while constraining the number of nonzero coefficients in this combination this problem arises in the decomposition of a covariance matrix into sparse factors or sparse principal component analysis pca and has wide applications ranging from biology to finance we use a modification of the classical variational representation of the largest eigenvalue of a symmetric matrix where cardinality is constrained and derive a semidefinite programming based relaxation for our problem we also discuss nesterov s smooth minimization technique applied to the semidefinite program arising in the semidefinite relaxation of the sparse pca problem the method has complexity o n 4 sqrt log n epsilon where n is the size of the underlying covariance matrix and epsilon is the desired absolute accuracy on the optimal value of the problem

a universal non quasitriangular quantization of the heisenberg group a new universal r matrix for the quantum heisenberg algebra h 1 q is obtained by imposing the analyticity in the deformation parameter despite the non quasitriangularity of this hopf algebra the quantum group induced from it coincides with the quasitriangular deformation already known

shannon kotel nikov mappings in joint source channel coding this paper deals with lossy joint source channel coding for transmitting memoryless sources over awgn channels the scheme is based on the geometrical interpretation of communication by kotel nikov and shannon where amplitudecontinuous time discrete source samples are mapped directly onto the channel using curves or planes the source and channel spaces can have different dimensions and thereby achieving either compression or error control depending on whether the source bandwidth is smaller or larger than the channel bandwidth we present a general theory for 1 n and m 1 dimension changing mappings and provide two examples for a gaussian source and channel where we optimize both a 2 1 bandwidth reducing and a 1 2 bandwidth expanding mapping both examples show high spectral efficiency and provide both graceful degradation and improvement for imperfect channel state information at the transmitter

suq 3 corepresentations and bivariate q krawtchouk polynomials the matrix elements of unitary suq 3 corepresentations which are analogs of the symmetric powers of the natural representation are shown to be the bivariate q krawtchouk orthogonal polynomials thus providing an algebraic interpretation of these polynomials in terms of quantum groups the matrix elements of unitary suq 3 corepresentations which are analogs of the symmetric powers of the natural representation are shown to be the bivariate q krawtchouk orthogonal polynomials thus providing an algebraic interpretation of these polynomials in terms of quantum groups

an open boundary condition for the computation of the steady incompressible navier stokes equations abstract we design a new boundary condition on the stream function at outflow for the steady incompressible navier stokes equations written in the stream function vorticity formulation by using a fourier transform in the direction perpendicular to the flow our open boundary condition is compared to the dirichlet and neumann boundary conditions by computing the flow past an ellipse of excentricity 50 our boundary condition proves to be the most accurate and thus the most time saving

decomposable principal component analysis in this paper we consider principal component analysis pca in decomposable gaussian graphical models we exploit the prior information in these models in order to distribute pca computation for this purpose we reformulate the pca problem in the sparse inverse covariance concentration domain and address the global eigenvalue problem by solving a sequence of local eigenvalue problems in each of the cliques of the decomposable graph we illustrate our methodology in the context of decentralized anomaly detection in the abilene backbone network based on the topology of the network we propose an approximate statistical graphical model and distribute the computation of pca

duality for the matrix quantum group glp q 2 c it is shown that the algebra up q dual to glp q 2 c is isomorphic to u pq 1 2 sl 2 c z as a commutation algebra where z is a subalgebra central in up q the subalgebra z is a hopf subalgebra of up q while the commutation subalgebra u pq 1 2 sl 2 c is not a hopf subalgebra

convergence rate of some domain decomposition methods for overlapping and nonoverlapping subdomains three iterative domain decomposition methods are considered simultaneous updates on all subdomains additive schwarz method flow directed sweeps and double sweeps by using some techniques of formal language theory we obtain a unique criterion of convergence for the three methods the convergence rate is a function of the criterion and depends on the algorithm

compact matrix pseudogroups the compact matrix pseudogroup is a non commutative compact space endowed with a group structure the precise definition is given and a number of examples is presented among them we have compact group of matrices duals of discrete groups and twisted deformed su n groups the representation theory is developed it turns out that the tensor product of representations depends essentially on their order the existence and the uniqueness of the haar measure is proved and the orthonormality relations for matrix elements of irreducible representations are derived the form of these relations differs from that in the group case this is due to the fact that the haar measure on pseudogroups is not central in general the corresponding modular properties are discussed the haar measures on the twistedsu 2 group and on the finite matrix pseudogroup are found

error bounds for the finite element approximation of an incompressible material in an unbounded domain in this paper we design high order local artificial boundary conditions and present error bounds for the finite element approximation of an incompressible elastic material in an unbounded domain the finite element approximation is formulated in a bounded computational domain using a nonlocal approximate artificial boundary condition or a local one in fact there are a family of nonlocal approximate artificial boundary conditions with increasing accuracy and computational cost and a family of local ones for a given artificial boundary our error bounds indicate how the errors of the finite element approximations depend on the mesh size the terms used in the approximate artificial boundary condition and the location of the artificial boundary numerical examples of an incompressible elastic material outside a circle in the plane is presented numerical results demonstrate the performance of our error bounds

artificial boundary conditions for the linear advection diffusion equation a family of artificial boundary conditions for the linear advection diffusion equation with small viscosity is developed well posedness for the associated initial boundary value problem is analyzed the error produced by truncating the domain is estimated numerical results are presented 1 introduction when computing the solution of a partial differential equation in an unbounded domain one often introduces artificial boundaries in order to limit the computational cost these boundaries must be chosen not too far from the domain of interest therefore the boundary conditions must be good approxima tions to the so called transparent i boundary condition i e such ithat the solution of the problem in the bounded domain is equal to the solution in the original domain the transparent boundary condition is usually an integral relation in time and space between u and its normal derivative on the boundary which makes it impractical from a numerical point of view one must approximate this relation to get local boundary conditions they are often called absorbing or artificial boundary conditions this question is of crucial interest in such different areas as geophysics plasma physics fluid dynamics 1 2 3 and the use of such conditions is now classical in geophysics our interest for the linear advection diffusion equation comes from the navier stokes equation but it arises also in other fields as for example meteorology 6 the incompressible navier stokes equation can be written as

colored quantum universal enveloping algebras we define some new algebraic structures termed colored hopf algebras by combining the coalgebra structures and antipodes of a standard hopf algebra set h corresponding to some parameter set q with the transformations of an algebra isomorphism group g herein called color group such transformations are labeled by some color parameters taking values in a color set c we show that various classes of hopf algebras such as almost cocommutative coboundary quasitriangular and triangular ones can be extended into corresponding colored algebraic structures and that colored quasitriangular hopf algebras in particular are characterized by the existence of a colored universal r matrix satisfying the colored yang baxter equation the present definitions extend those previously introduced by ohtsuki which correspond to some substructures in those cases where the color group is abelian we apply the new concepts to construct colored quantum universal enveloping algebras of both semisimple and nonsemisimple lie algebras considering several examples with fixed or varying parameters as a by product some of the matrix representations of colored universal r matrices derived in the present paper provide new solutions of the colored yang baxter equation which might be of interest in the context of integrable models

reduced dimension linear transform coding of distributed correlated signals with incomplete observations we study the problem of optimal reduced dimension linear transform coding and reconstruction of a signal based on distributed correlated observations of the signal in the mean square estimation context this involves finding the optimal signal representation based on multiple incomplete or only partial observations that are correlated in particular this leads to the study of finding the optimal karhunen loeve basis based on the censored observations the problem has been considered previously by gastpar dragotti and vetterli in the context of jointly gaussian random variables based on using conditional covariances in this paper we derive the estimation results in the more general setting of second order random variables with arbitrary distributions using entirely different techniques based on the idea of innovations we explicitly solve the single transform coder case give a characterization of optimality in the multiple distributed transform coders scenario and provide additional insights into the structure of the problem

dimensionality reduction for distributed estimation in the infinite dimensional regime distributed estimation of an unknown signal is a common task in sensor networks the scenario usually envisioned consists of several nodes each making an observation correlated with the signal of interest the acquired data is then wirelessly transmitted to a fusion center that aims at estimating the desired signal within a prescribed accuracy motivated by the obvious processing limitations inherent to such distributed infrastructures we seek to find efficient compression schemes that account for limited available power and communication bandwidth in this paper we propose a transform based approach to this problem where each sensor provides the fusion center with a low dimensional approximation of its local observation by means of a suitable linear transform under the mean squared error criterion we derive the optimal solution to apply at one sensor assuming all else being fixed this naturally leads to an iterative algorithm whose optimality properties are exemplified using a simple though illustrative correlation model the stationarity issue is also investigated under restrictive assumptions we then provide an asymptotic distortion analysis as the size of the observed vectors becomes large our derivation relies on a variation of the toeplitz distribution theorem which allows us to provide a reverse ldquowater fillingrdquo perspective to the problem of optimal dimensionality reduction we illustrate with a first order gauss markov model how our findings allow for the computation of analytical closed form distortion formulas that provide an accurate estimation of the reconstruction error obtained in the finite dimensional regime

nonlocal artificial boundary conditions for the incompressible viscous flow in a channel using spectral techniques in this paper the numerical simulation of the steady incompressible viscous flow in a no slip channel is considered a sequence of approximate nonlocal artificial boundary conditions on a given segment artificial boundary is derived by a system of linearized navier stokes equations and spectral techniques then the original problem is reduced to a boundary value problem in a bounded computational domain the numerical examples show that these artificial boundary conditions are very effective and are also more accurate than dirichlet and neumann boundary conditions which are often used in the engineering literature

linear coherent decentralized estimation we consider the distributed estimation of an unknown vector signal in a resource constrained sensor network with a fusion center due to power and bandwidth limitations each sensor compresses its data in order to minimize the amount of information that needs to be communicated to the fusion center in this context we study the linear decentralized estimation of the source vector where each sensor linearly encodes its observations and the fusion center also applies a linear mapping to estimate the unknown vector signal based on the received messages we adopt the mean squared error mse as the performance criterion when the channels between sensors and the fusion center are orthogonal it has been shown previously that the complexity of designing the optimal encoding matrices is np hard in general in this paper we study the optimal linear decentralized estimation when the multiple access channel mac is coherent for the case when the source and observations are scalars we derive the optimal power scheduling via convex optimization and show that it admits a simple distributed implementation simulations show that the proposed power scheduling improves the mse performance by a large margin when compared to the uniform power scheduling we also show that under a finite network power budget the asymptotic mse performance when the total number of sensors is large critically depends on the multiple access scheme for the case when the source and observations are vectors we study the optimal linear decentralized estimation under both bandwidth and power constraints we show that when the mac between sensors and the fusion center is noiseless the resulting problem has a closed form solution which is in sharp contrast to the orthogonal mac case while in the noisy mac case the problem can be efficiently solved by semidefinite programming sdp

optimal dimensionality reduction of sensor data in multisensor estimation fusion when there exists the limitation of communication bandwidth between sensors and a fusion center one needs to optimally precompress sensor outputs sensor observations or estimates before the sensors transmission in order to obtain a constrained optimal estimation at the fusion center in terms of the linear minimum error variance criterion or when an allowed performance loss constraint exists one needs to design the minimum dimension of sensor data this paper will answer the above questions by using the matrix decomposition pseudo inverse and eigenvalue techniques

reduced dimension linear transform coding of correlated signals in networks a model called the linear transform network ltn is proposed to analyze the compression and estimation of correlated signals transmitted over directed acyclic graphs dags an ltn is a dag network with multiple source and receiver nodes source nodes transmit subspace projections of random correlated signals by applying reduced dimension linear transforms the subspace projections are linearly processed by multiple relays and routed to intended receivers each receiver applies a linear estimator to approximate a subset of the sources with minimum mean squared error mse distortion the model is extended to include noisy networks with power constraints on transmitters a key task is to compute all local compression matrices and linear estimators in the network to minimize end to end distortion the nonconvex problem is solved iteratively within an optimization framework using constrained quadratic programs qps the proposed algorithm recovers as special cases the regular and distributed karhunen loeve transforms klts cut set lower bounds on the distortion region of multi source multi receiver networks are given for linear coding based on convex relaxations cut set lower bounds are also given for any coding strategy based on information theory the distortion region and compression estimation tradeoffs are illustrated for different communication demands e g multiple unicast and graph structures

coding for errors and erasures in random network coding the problem of error control in random linear network coding is considered a ldquononcoherentrdquo or ldquochannel obliviousrdquo model is assumed where neither transmitter nor receiver is assumed to have knowledge of the channel transfer characteristic motivated by the property that linear network coding is vector space preserving information transmission is modeled as the injection into the network of a basis for a vector space v and the collection by the receiver of a basis for a vector space u a metric on the projective geometry associated with the packet space is introduced and it is shown that a minimum distance decoder for this metric achieves correct decoding if the dimension of the space v capu is sufficiently large if the dimension of each codeword is restricted to a fixed integer the code forms a subset of a finite field grassmannian or equivalently a subset of the vertices of the corresponding grassmann graph sphere packing and sphere covering bounds as well as a generalization of the singleton bound are provided for such codes finally a reed solomon like code construction related to gabidulin s construction of maximum rank distance codes is described and a sudan style ldquolist 1rdquo minimum distance decoding algorithm is provided

absorbing boundary conditions for the wave equation and parallel computing absorbing boundary conditions have been developed for truncating unbounded computational domains to bounded ones the authors investigate the use of absorbing boundary conditions in domain decomposition algorithms for the wave equation moreover they optimize the absorbing boundary conditions in order to obtain a good performance of the schwarz waveform relaxation algorithm the analysis given is confirmed by numerical experiments

on theq commutations inuq n at roots of one abstract let e be a root of one and g a semisimple lie algebra with triangular decomposition g n h n letu e resp ures e be the nonrestricted resp restricted quantum enveloping algebra of n we prove that fract u eis a quantum weyl field we then give a description of the e center ofu e letufin ebe the finite part ofures e via the drinfeld correspondence theufin e covariant space of a weyl module is e central in case g s l n this enables us to describe this space in terms of semistandard young tableaux

the artificial boundary conditions for incompressible materials on an unbounded domain in this paper we consider the numerical simulations of the incompressible materials on an unbounded domain in frak r 2 a series of artificial boundary conditions at a circular artificial boundary for solving incompressible materials on an unbounded domain is given then the original problem is reduced to a problem on a bounded domain which be solved numerically by a mixed finite element method the numerical example shows that our artificial boundary conditions are very effective

spectral extension of the quantum group cotangent bundle the structure of a cotangent bundle is investigated for quantum linear groups gl q n and sl q n using a q version of the cayley hamilton theorem we construct an extension of the algebra of differential operators on sl q n otherwise called the heisenberg double by spectral values of the matrix of right invariant vector fields we consider two applications for the spectral extension first we describe the extended heisenberg double in terms of a new set of generators the weyl partners of the spectral variables calculating defining relations in terms of these generators allows us to derive sl q n type dynamical r matrices in a surprisingly simple way second we calculate an evolution operator for the model of the q deformed isotropic top introduced by a alekseev and l faddeev the evolution operator is not uniquely defined and we present two possible expressions for it the first one is a riemann theta function in the spectral variables the second one is an almost free motion evolution operator in terms of logarithms of the spectral variables the relation between the two operators is given by a modular functional equation for the riemann theta function

an application of nonlocal external conditions to viscous flow computations we are looking for a steady state solution of an external flow problem originally formulated on an unbounded domain our case is a 2d viscous compressible flow past a finite body airfoil we truncate the original domain by introducing a finite grid around the airfoil and integrate the navier stokes equations on this grid with the help of a finite volume code which involves a multigrid pseudo time iteration technique for achieving a steady state to integrate the navier stokes equations on a finite subregion of an original domain only we supplement the numerical algorithm by special nonlocal artificial boundary conditions formulated on an external boundary of the finite computational domain these artificial boundary conditions are based on the difference potentials method proposed by v s ryaben kii we compare the results provided by the nonlocal conditions with those obtained from the standard external conditions which are based on locally one dimensional characteristic analysis at inflow and extrapolation at outflow it turns out that the nonlocal artificial boundary conditions accelerate the convergence by about a factor of 3 as well as allow one to shrink substantially the computational domain without loss of accuracy

symmetric pairs for quantized enveloping algebras abstract let be an involution of a semisimple lie algebra g let g denote the fixed lie subalgebra and assume the cartan subalgebra of g has been chosen in a suitable way we construct a quantum analog of u g which can be characterized as the unique subalgebra of the quantized enveloping algebra of g which is a maximal right coideal that specializes to u g

universal r matrix of reductive lie algebras and quantum integrable systems from its colour representation the universal r matrix intertwining between the coproduct structures related to the universal deformations of reductive lie algebras has been found in an explicit form using twisting a possible colour representation of this r matrix and its application to the integrable systems are shown using the example of a deformed gl n algebra

polynomial time algorithms for multicast network code construction the famous max flow min cut theorem states that a source node s can send information through a network v e to a sink node t at a rate determined by the min cut separating s and t recently it has been shown that this rate can also be achieved for multicasting to several sinks provided that the intermediate nodes are allowed to re encode the information they receive we demonstrate examples of networks where the achievable rates obtained by coding at intermediate nodes are arbitrarily larger than if coding is not allowed we give deterministic polynomial time algorithms and even faster randomized algorithms for designing linear codes for directed acyclic graphs with edges of unit capacity we extend these algorithms to integer capacities and to codes that are tolerant to edge failures

absorbing boundary conditions for diffusion equations summary we construct and analyse a family of absorbing boundary conditions for diffusion equations with variable coefficients curved artifical boundary and arbitrary convection it relies on the geometric identification of the dirichlet to neumann map and rational interpolation of z 1 2 in the complex plane the boundary conditions are stable accurate and practical for computations

the standard complex of quantum enveloping algebras we consider quantized derivation representations of hopf algebras in some associative algebras the algebra of quantized differential operators of bialgebra representations which are special representations by derivations are constructed for the quantum enveloping algebras of lie algebras associated with the root systems and we define a deformation of the exterior algebra of forms and by applying the above results it is shown that the quantized adjoint representation of induces a bialgebra representation of in the resulting algebra of differential operators is a deformation of the standard koszul complex of lie algebras it admits an exterior derivative which is in particular a module morphism hence cohomology groups of relative to some module can be constructed

a q heisenberg algebra and a contact metric structure the actions for two q heisenberg algebras are constructed by extending a contact metric structure of a heisenberg group manifold to the corresponding line bundle the author obtains the q heisenberg algebras under a canonical quantization and regularization also the q parameter is shown to be the regularizing parameter

a rank metric approach to error control in random network coding the problem of error control in random linear network coding is addressed from a matrix perspective that is closely related to the subspace perspective of rotter and kschischang a large class of constant dimension subspace codes is investigated it is shown that codes in this class can be easily constructed from rank metric codes while preserving their distance properties moreover it is shown that minimum distance decoding of such subspace codes can be reformulated as a generalized decoding problem for rank metric codes where partial information about the error is available this partial information may be in the form of erasures knowledge of an error location but not its value and deviations knowledge of an error value but not its location taking erasures and deviations into account when they occur strictly increases the error correction capability of a code if mu erasures and delta deviations occur then errors of rank t can always be corrected provided that 2t les d 1 mu delta where d is the minimum rank distance of the code for gabidulin codes an important family of maximum rank distance codes an efficient decoding algorithm is proposed that can properly exploit erasures and deviations in a network coding application where n packets of length m over f q are transmitted the complexity of the decoding algorithm is given by o dm operations in an extension field f qn

distributed state estimation with dimension reduction preprocessing system state estimation relies heavily on the measurements with the advance of sensing technology the ability to measure is no longer a bottleneck in many systems and more and more researchers now focus on the rich information setting i e big data however although information never hurts it does not help unconditionally how to make the most of it depends on whether we can process the data efficiently in some systems the inherent constraint such as the bandwidth and cost makes it necessary to reduce the dimension of the measurement before further processing the problem that the raw measurements are first preprocessed to reduce size and then used for estimation is addressed in this paper it is shown that there is a lower bound on the size of the preprocessed data such that if the size is beyond the bound there exists a closed form estimator design that the linear minimum mean square estimation can be obtained moreover we propose an algorithm that is guaranteed to converge to a stationary point to design an estimator in the conditions that the lower bound cannot be reached besides convergence the proposed algorithm guarantees bounded performance loss compared with the global optimal solution under some additional conditions finally simulation results in three different applications are shown to demonstrate the effectiveness of the proposed algorithm

vector fields on complex quantum groups using previous results we construct theq analogues of the left invariant vector fields of the quantum enveloping algebra corresponding to the complex lie algebras of typean 1 bn cn anddn these quantum vector fields are functionals over the complex quantum groupa in the special casea1 it is shown that this hopf algebra coincides withuqsl 2

the distributed karhunen loeve transform the karhunen loeve transform klt is a key element of many signal processing and communication tasks many recent applications involve distributed signal processing where it is not generally possible to apply the klt to the entire signal rather the klt must be approximated in a distributed fashion this paper investigates such distributed approaches to the klt where several distributed terminals observe disjoint subsets of a random vector we introduce several versions of the distributed klt first a local klt is introduced which is the optimal solution for a given terminal assuming all else is fixed this local klt is different and in general improves upon the marginal klt which simply ignores other terminals both optimal approximation and compression using this local klt are derived two important special cases are studied in detail namely the partial observation klt which has access to a subset of variables but aims at reconstructing them all and the conditional klt which has access to side information at the decoder we focus on the jointly gaussian case with known correlation structure and on approximation and compression problems then the distributed klt is addressed by considering local klts in turn at the various terminals leading to an iterative algorithm which is locally convergent sometimes reaching a global optimum depending on the overall correlation structure for compression it is shown that the classical distributed source coding techniques admit a natural transform coding interpretation the transform being the distributed klt examples throughout illustrate the performance of the proposed distributed klt this distributed transform has potential applications in sensor networks distributed image databases hyper spectral imagery and data fusion

numerical radiation boundary conditions for unsteady transonic flow a family of numerical boundary conditions for far field computational boundaries in calculations involving unsteady transonic flow is devised these boundary conditions are developed in a systematic fashion from general principles both numerical and analytic comparisons with other currently used methods are given

casimir operators of uq sl 3 the q deformed casimir operators of u sl 3 are constructed using the hopf algebra structure and the fundamental representation of uq sl 3

distributed estimation using reduced dimensionality sensor observations we derive linear estimators of stationary random signals based on reduced dimensionality observations collected at distributed sensors and communicated to a fusion center over wireless links dimensionality reduction compresses sensor data to meet low power and bandwidth constraints while linearity in compression and estimation are well motivated by the limited computing capabilities wireless sensor networks are envisioned to operate with and by the desire to estimate random signals from observations with unknown probability density functions in the absence of fading and fusion center noise ideal links we cast this intertwined compression estimation problem in a canonical correlation analysis framework and derive closed form mean square error mse optimal estimators along with coordinate descent suboptimal alternatives that guarantee convergence at least to a stationary point likewise we develop estimators based on reduced dimensionality sensor observations in the presence of fading and additive noise at the fusion center nonideal links performance analysis and corroborating simulations demonstrate the merits of the novel distributed estimators relative to existing alternatives

singularly perturbed problems in partial differential equations a survey this survey paper contains a surprisingly large amount of material on singularly perturbed partial differential equations and indeed can serve as an introduction to some of the ideas and methods of the singular perturbation theory starting from prandtl s work a large amount of work has been done in the area of singular perturbations this paper limits its coverage to some standard singular perturbation models considered by various workers and the methods developed by numerous researchers after 1980 2000 in this review we have covered singularly perturbed partial differential equations about odes the survey has already been done by us see m k kadalbajoo k c patidar appl math comput 130 2002 457 510

relating the approaches to quantised algebras and quantum groups this paper constructs two representations of the quantum groupu q g by exploiting its quotient structure and the quantum double construction here the quantum group is taken as the dual to the quantised algebrau q g a one parameter deformation of the universal enveloping algebra of the lie algebra g as in drinfel d 6 and jimbo 10 from the two representations the hopf structure of the quantised algebrau q g is reexpressed in a matrix format this is the very structure given by faddeev et al 7 in their approach to defining quantum groups and quantised algebras via the quantisation of the function space of the associated lie group to g

characteristic relations for quantum matrices the general algebraic properties of the algebras of vector fields over the quantum linear groups glq n and slq n are studied these quantum algebras appear to be quite similar to the classical matrix algebra in particular the quantum analogues of the characteristic polynomial and characteristic identity are obtained for them the q analogues of the newton relations connecting two different generating sets of central elements of these algebras the determinant like and trace like ones are derived this allows one to express the q determinant of quantized vector fields in terms of their q traces

mixed finite element method and high order local artificial boundary conditions for exterior problems of elliptic equation the mixed finite element method is used to solve the exterior elliptic problem with high order local artificial boundary conditions new unknowns are introduced to reduce the order of the derivatives to two this leads to an equivalent mixed variational problem such that the normal finite element can be used and special finite elements are no longer needed on the adjacent layer of the artificial boundary error estimates are obtained for some local artificial boundary conditions with prescribed order numerical examples are presented and the results demonstrate the effectiveness of this method

steady viscous flow past a circular cylinder up to reynolds number 600 viscous flow past a circular cylinder becomes unstable around reynolds number re 40 with a numerical technique based on newton s method and made possible by the use of a supercomputer steady but unstable solutions have been calculated up to re 600 it is found that the wake bubble region with recirculating flow grows in length approximately linearly with re the width increases like re12 up to re 300 at which paint a transition to linear increase with re begins at the highest reynolds numbers we reached the wake resembles a pair of translating uniform vortices both touching the center line the cylinder moving in front with the same speed supplies the vorticity required to balance diffusion

quantization of lie group and algebra of g2 type in the faddeev reshetikhin takhtajan approach based on the quantized universal enveloping que algebras a quantization of the automorphism group of some nonassociative algebras is given in the formulation employing noncommuting matrix entries a quantum group of g2 type included in this scheme is studied in detail in the faddeev reshetikhin takhtajan frt approach also in the formulation employing noncommuting matrix entries the que algebra of g2 type is reconstructed through the pairing induced by the r matrix between the quantum group and the que algebra