jordanian deformation of sl 2 as a contraction of its drinfeld jimbo deformation we introduce a contraction procedure for obtaining the jordanian deformation of sl 2 from its drinfeld jimbo deformation to be specific we obtain slh 2 its differential geometry and its star product from their q deformed counterparts we also present a transformation of the generators of uq sl 2 which in a limit yield the generators of uh sl 2

an r matrix approach to the quantization of the euclidean group e 2 the r matrices for two different deformations of the euclidean group e 2 calculated in a two dimensional representation are used to determine the deformed hopf algebra of the representative functions the duality of the latter with the initial quantum algebras is explicitly proved and the relationship between the two quantum groups is discussed and clarified

multiparametric quantum gl 2 lie bialgebras quantum r matrices and non relativistic limits multiparametric quantum deformations of gl 2 are studied through a complete classification of gl 2 lie bialgebra structures from these the non relativistic limit leading to harmonic oscillator lie bialgebras is implemented by means of a contraction procedure new quantum deformations of gl 2 together with their associated quantum r matrices are obtained and other known quantizations are recovered and classified several connections with integrable models are outlined

moving mesh methods in multiple dimensions based on harmonic maps in practice there are three types of adaptive methods using the finite element approach namely the h method p method and r method in the h method the overall method contains two parts a solution algorithm and a mesh selection algorithm these two parts are independent of each other in the sense that the change of the pdes will affect the first part only however in some of the existing versions of the r method also known as the moving mesh method these two parts are strongly associated with each other and as a result any change of the pdes will result in the rewriting of the whole code in this work we will propose a moving mesh method which also contains two parts a solution algorithm and a mesh redistribution algorithm our efforts are to keep the advantages of the r method e g keep the number of nodes unchanged and of the h method e g the two parts in the code are independent a framework for adaptive meshes based on the hamilton schoen yau theory was proposed by dvinsky in this work we will extend dvinsky s method to provide an efficient solver for the mesh redistribution algorithm the key idea is to construct the harmonic map between the physical space and a parameter space by an iteration procedure each iteration step is to move the mesh closer to the harmonic map this procedure is simple and easy to program and also enables us to keep the map harmonic even after long times of numerical integration the numerical schemes are applied to a number of test problems in two dimensions it is observed that the mesh redistribution strategy based on the harmonic maps adapts the mesh extremely well to the solution without producing skew elements for multi dimensional computations

on a family of symmetric polynomials abstract in this paper we provide two simple approaches to the explicit expression of a family of symmetric polynomials introduced and studied in milovanovic and cvetkovic j math anal appl 311 2005 191 thereby improving on their observations

simulation of laminar vortex shedding flow past cylinders using a coupled bem and fem model abstract this paper describes a novel computational model developed to simulate laminar vortex shedding flows past circular cylinders in 2d incompressible viscous flows in external flow fields the model based on unsteady 2d navier stokes equations in primitive variables is able to solve the infinite boundary value problems by extracting the boundary effects on a specified finite computational domain using the projection method the external flow field is simulated using the boundary element method bem by solving a pressure poisson equation that assumes the pressure as zero at the infinite boundary the momentum equation of the flow motion is solved using the three step finite element method fem the present model is applied to simulate vortex shedding flow past a single circular cylinder and flow past two cylinders in which one act as a control cylinder for low reynolds number flows for both the cases the time development of the flow towards periodic vortex shedding are illustrated by streamline pictures the simulation results are compared with experimental data and other numerical models and found to be very reasonable and satisfactory

a penalization method to take into account obstacles in incompressible viscous flows from the navier stokes brinkman model a penalization method has been derived by several authors to compute incompressible navier stokes equations around obstacles in this paper convergence theorems and error estimates are derived for two kinds of penalization the first one corresponds to l 2 penalization inducing a darcy equation in the solid body the second one corresponds to a h 1 penalization and induces a brinkman equation in the body numerical tests are performed to confirm the efficiency and accuracy of the method

nested cartesian grid method in incompressible viscous fluid flow in this work the local grid refinement procedure is focused by using a nested cartesian grid formulation the method is developed for simulating unsteady viscous incompressible flows with complex immersed boundaries a finite volume formulation based on globally second order accurate central difference schemes is adopted here in conjunction with a two step fractional step procedure the key aspects that needed to be considered in developing such a nested grid solver are proper imposition of interface conditions on the nested block boundaries and accurate discretization of the governing equations in cells that are with block interface as a control surface the interpolation procedure adopted in the study allows systematic development of a discretization scheme that preserves global second order spatial accuracy of the underlying solver and as a result high efficiency accuracy nested grid discretization method is developed herein the proposed nested grid method has been widely tested through effective simulation of four different classes of unsteady incompressible viscous flows thereby demonstrating its performance in the solution of various complex flow structure interactions the numerical examples include a lid driven cavity flow and pearson vortex problems flow past a circular cylinder symmetrically installed in a channel flow past an elliptic cylinder at an angle of attack and flow past two tandem circular cylinders of unequal diameters for the numerical simulations of flows past bluff bodies an immersed boundary ib method has been implemented in which the solid object is represented by a distributed body force in the navier stokes equations the main advantages of the implemented immersed boundary method are that the simulations could be performed on a regular cartesian grid and applied to multiple nested block cartesian structured grids without any difficulty through the numerical experiments the strength of the solver in effectively accurately simulating various complex flows past different forms of immersed boundaries is extensively demonstrated in which the nested cartesian grid method was suitably combined together with the fractional step algorithm to speed up the solution procedure

canonical structure in so 4 q and relations to e 3 q and so 3 1 q starting with the su 2 q su 2 q basis and using q cg coefficients the closest possible q deformation of the classical canonical gelfand zetlin formalism is constructed explicitly for so 4 q simple introduction of q brackets for each factor of the classical matrix elements valid for su n q is shown to need significant and unexpected modifications for so n q even when n 4 contraction to e 3 q and continuation to so 3 1 q are studied making explicit the possibilities and the problems that arise periodic representations for q a root of unity are commented upon briefly

two parametric extension of h deformation of gr 1 1 the two parametric quantum deformation of the algebra of coordinate functions on the supergroup gl 1 1 via a contraction of glp q 1 1 is presented related differential calculus on the quantum superplane is introduced

an immersed boundary method with formal second order accuracy and reduced numerical viscosity a formally second order accurate immersed boundary method is presented and tested in this paper we apply this new scheme to simulate the flow past a circular cylinder and study the effect of numerical viscosity on the accuracy of the computation by comparing the numerical results with those of a first order method the numerical evidence shows that the new scheme has less numerical viscosity and is therefore a better choice for the simulation of high reynolds number flows with immersed boundaries

an adaptive formally second order accurate version of the immersed boundary method like many problems in biofluid mechanics cardiac mechanics can be modeled as the dynamic interaction of a viscous incompressible fluid the blood and a visco elastic structure the muscular walls and the valves of the heart the immersed boundary method is a mathematical formulation and numerical approach to such problems that was originally introduced to study blood flow through heart valves and extensions of this work have yielded a three dimensional model of the heart and great vessels in the present work we introduce a new adaptive version of the immersed boundary method this adaptive scheme employs the same hierarchical structured grid approach but a different numerical scheme as the two dimensional adaptive immersed boundary method of roma et al a multilevel self adaptive version of the immersed boundary method ph d thesis courant institute of mathematical sciences new york university 1996 an adaptive version of the immersed boundary method j comput phys 153 2 1999 509 534 and is based on a formally second order accurate i e second order accurate for problems with sufficiently smooth solutions version of the immersed boundary method that we have recently described b e griffith c s peskin on the order of accuracy of the immersed boundary method higher order convergence rates for sufficiently smooth problems j comput phys 208 1 2005 75 105 actual second order convergence rates are obtained for both the uniform and adaptive methods by considering the interaction of a viscous incompressible flow and an anisotropic incompressible viscoelastic shell we also present initial results from the application of this methodology to the three dimensional simulation of blood flow in the heart and great vessels the results obtained by the adaptive method show good qualitative agreement with simulation results obtained by earlier non adaptive versions of the method but the flow in the vicinity of the model heart valves indicates that the new methodology provides enhanced boundary layer resolution differences are also observed in the flow about the mitral valve leaflets

universal r matrix for non standard quantum a universal r matrix for the non standard jordanian quantum deformation of is presented a family of solutions of the quantum yang baxter equation is obtained from some finite dimensional representations of this lie bialgebra quantization of

direct numerical simulation of flow past elliptic cylinders flow over elliptic cylinders can be considered prototypical of flow over a range of bluff bodies since the geometry allows one to study the effect of both thickness and angle of attack on the flow field therefore a careful study of this flow should provide valuable insight into the phenomenon of unsteady separation and the structure of bluff body wakes with this in mind a spectral collocation technique has been developed to simulate the full three dimensional incompressible flow over elliptic cylinders and unlike spectral element and spectral multidomain techniques here the flow is solved in a single domain the equations are discretized on a body fitted elliptic cylindrical grid and properties of the metric associated with this coordinate system are used to solve the governing equations in an efficient manner key issues including the inflow and outflow boundary conditions and time discretization are discussed in detail with the hope that this will facilitate future simulations of similar flows finally we present results of two and three dimensional simulations for a range of flow and geometric parameters the results are compared with available experimental data and it is found that important quantities like strouhal numbers and drag coefficients match well with established values

on the positivity of symmetric polynomial functions part i general results abstract we prove that a real symmetric polynomial inequality of degree d 2 holds on r n if and only if it holds for elements with at most d 2 distinct non zero components which may have multiplicities we establish this result by solving a cauchy problem for ordinary differential equations involving the symmetric power sums this implies the existence of a special kind of paths in the minimizer of some restriction of the considered polynomial function in the final section extensions of our results to the whole space r n are outlined the main results are theorems 5 1 and 5 2 with corollaries 2 1 and 5 2 and the corresponding results for r n from the last subsection part ii will contain a discussion on the ordered vector space h d n in general as well as on the particular cases of degrees d 4 and d 5 finite test sets for positivity in the homogeneous case and other sufficient criteria

the three dimensional euclidean quantum group e 3 q and its r matrix a contraction procedure starting from so 4 q is used to determine the quantum analog e 3 q of the three dimensional euclidean group and the structure of its representations a detailed analysis of the contraction of the r matrix is then performed and its explicit expression has been found the classical limit of r is shown to produce an integrable dynamical system by means of the r matrix the pseudogroup of the noncommutative representative functions is considered it will finally be shown that a further contraction made on e 3 q produces the two dimensional galilei quantum group and this in turn can be used to give a new realization of e 3 q and e 2 1 q

h deformation of gr 2 the h deformation of functions on the grassmann matrix group gr 2 is presented via a contraction of as an interesting point we have seen that in the case of the h deformation both r matrices of and are the same

a conservative finite volume method for incompressible navierstokes equations on locally refined nested cartesian grids a second order accurate finite volume method is developed for the solution of incompressible navierstokes equations on locally refined nested cartesian grids numerical accuracy and stability on locally refined nested cartesian grids are achieved using a finite volume discretization of the incompressible navierstokes equations based on higher order conservation principles i e in addition to mass and momentum conservation kinetic energy conservation in the inviscid limit is used to guide the selection of the discrete operators and solution algorithms hanging nodes at the interface are virtually slanted to improve the pressurevelocity projection while the other parts of the grid maintain an orthogonal cartesian grid topology the present method is straight forward to implement and shows superior conservation of mass momentum and kinetic energy compared to the conventional methods employing interpolation at the interface between coarse and fine grids

the gamma poincare quantum group from quantum group contraction we propose a contraction of the de sitter quantum group leading to a poincare quantum group in any dimensions the method relies on the coaction of the de sitter quantum group on a non commutative space and the deformation parameter q is sent to one the bicrossproduct structure of this gamma poincare quantum group is exhibited and shown to be dual to the one of the kappa poincare hopf algebra at least in two dimensions

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

three dimensional quantum groups from contractions of su 2 q contractions of lie algebras and of their representations are generalized to define new quantum groups an explicit and complete exposition is made for the one dimensional heisenberg h 1 q and the two dimensional euclidean quantum group e 2 q obtained by contracting su 2 q

quantumsu 2 ande 2 groups contraction procedure in 3 it was shown in the framework of deformed enveloping algebras that quantumsu 2 ande 2 groups are related by the contraction procedure we consider the same problem on thec level as a result we find a number of formulae coupling the comultiplications in quantumsu 2 ande 2 in particular we show that the comultiplications in both groups are implemented by partial isometries an unexpected feature of quantume 2 is discovered and the corresponding strange behavior of quantumsu 2 is described

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

an effective explicit pressure gradient scheme implemented in the two level non staggered grids for incompressible navier stokes equations in this paper an improved two level method is presented for effectively solving the incompressible navier stokes equations this proposed method solves a smaller system of nonlinear navier stokes equations on the coarse mesh and needs to solve the oseen type linearized equations of motion only once on the fine mesh level within the proposed two level framework a prolongation operator which is required to linearize the convective terms at the fine mesh level using the convergent navier stokes solutions computed at the coarse mesh level is rigorously derived to increase the prediction accuracy this indispensable prolongation operator can properly communicate the flow velocities between the two mesh levels because it is locally analytic solution convergence can therefore be accelerated for the sake of numerical accuracy momentum equations are discretized by employing the general solution for the two dimensional convection diffusion reaction model equation the convective instability problem can be simultaneously eliminated thanks to the proper treatment of convective terms the converged solution is thus very high in accuracy as well as in yielding a quadratic spatial rate of convergence for the sake of programming simplicity and computational efficiency pressure gradient terms are rigorously discretized within the explicit framework in the non staggered grid system the proposed analytical prolongation operator for the mapping of solutions from the coarse to fine meshes and the explicit pressure gradient discretization scheme which accommodates the dispersion relation preserving property have been both rigorously justified from the predicted navier stokes solutions

d 3 real quantum conformal algebra using the equivalence of o 3 2 with d 3 conformal algebras we describe the d 3 quantum conformal algebra by the q deformed cartan weyl basis of a real hopf algebra uq o 3 2 with mod q mod 1 the universal r matrix written in terms of d 3 conformal generators is investigated the hopf subalgebras of uq o 3 2 and their quasitriangularity are discussed the analogies with d 4 quantum conformal algebra are pointed out

an adaptive version of the immersed boundary method a computational setting for the immersed boundary method employing an adaptive mesh refinement is presented enhanced accuracy for the method is attained locally by covering an immersed boundary vicinity with a sequence of nested progressively finer rectangular grid patches which dynamically follow the immersed boundary motion the set of equations describing the interaction between a non stationary viscous incompressible fluid and an immersed elastic boundary is solved by coupling a projection method specially designed for locally refined meshes to an implicit formulation of the immersed boundary method the main contributions of this work concern the formulation and the implementation of a multilevel self adaptive version of the immersed boundary method on locally refined meshes this approach is tested for a particular two dimensional model problem for which no significant difference is found between the solutions obtained on a mesh refined locally around the immersed boundary and on the associated uniform mesh built with the resolution of the finest level

two parameter nonstandard deformation of 2 2 matrices we introduce a two parameter deformation of 2 2 matrices without imposing any condition on the matrices and give the universal r matrix of the nonstandard quantum group which satisfies the quantum yang baxter relation although in the standard two parameter deformation the quantum determinant is not central in the nonstandard case it is central we note that the quantum group thus obtained is related to the quantum supergroup glp q 1 1 by a transformation

contraction of the gr s quantum group to its nonstandard analog and corresponding colored quantum groups the quantum group gr s provides a realization of the two parameter quantum glp q 2 which is known to be related to the two parameter nonstandard glh h 2 group via the contraction method we apply the contraction procedure to gr s and obtain a new jordanian quantum group gm k furthermore we provide a realization of glh h 2 in terms of gm k the contraction procedure is then extended to the colored quantum group glr 2 to yield a new jordanian quantum group glm 2 both gr s and gm k are then generalized to their colored versions which in turn provide similar realizations of glr 2 and glm 2

on some nonlinear extensions of the angular momentum algebra deformations of the lie algebras so 4 so 3 1 and e 3 that leave their so 3 subalgebra undeformed and preserve their coset structure are considered it is shown that such deformed algebras are associative for any choice of the deformation parameters their casimir operators are obtained and some of their unitary irreducible representations are constructed for vanishing deformation the unitary irreducible representations of the deformed algebras transform into those of the corresponding lie algebras that contain each of the so 3 unitary irreducible representations at most once it is also proved that similar deformations of the lie algebras su 3 sl 3 r and of the semidirect sum of an abelian algebra t 5 and so 3 do not lead to associative algebras

the quantum group glh 2 among all quantum group structures on the space mat 2 of 2 by 2 matrices how many have a central quantum determinant so that one can define quantum sl 2 out of quantum gl 2 up to isomorphism there are two such structures glq 2 and glh 2 the former is well known the latter is described in this letter

differential geometry of glp q 1 1 we introduce a construction of the differential calculus on the quantum supergroup glp q 1 1 we obtain two differential calculi respectively associated with the left and the right cartan maurer one forms we also obtain the quantum superalgebra of glp q 1 1 although all of the structures we obtain are derived without an r matrix they nevertheless can be expressed using an r matrix

a ghost cell immersed boundary method for flow in complex geometry an efficient ghost cell immersed boundary method gcibm for simulating turbulent flows in complex geometries is presented a boundary condition is enforced through a ghost cell method the reconstruction procedure allows systematic development of numerical schemes for treating the immersed boundary while preserving the overall second order accuracy of the base solver both dirichlet and neumann boundary conditions can be treated the current ghost cell treatment is both suitable for staggered and non staggered cartesian grids the accuracy of the current method is validated using flow past a circular cylinder and large eddy simulation of turbulent flow over a wavy surface numerical results are compared with experimental data and boundary fitted grid results the method is further extended to an existing ocean model mitgcm to simulate geophysical flow over a three dimensional bump the method is easily implemented as evidenced by our use of several existing codes

quantum structure of the motion groups of the two dimensional cayley klein geometries a simultaneous and global scheme of quantum deformation is defined for the set of algebras corresponding to the groups of motions of the two dimensional cayley klein geometries their central extensions are also considered under this unified pattern in both cases some fundamental properties characterizing the classical ck geometries as the existence of a set of commuting involutions contractions and dualities relationships remain in the quantum version

differential geometry of glh 1 1 we construct a differential calculus on the quantum supergroup glh 1 1 and obtain the h deformed superalgebra of glh 1 1

a q schrodinger algebra its lowest weight representations and generalized q deformed heat schrodinger equations we construct a q deformation of the centrally extended schrodinger algebra and an algebraic representation theory through lowest weight representations we use verma modules over calculate their singular vectors and factorize the verma modules by submodules built on the singular vectors we also give a realization of with q difference operators and obtain a polynomial realization of the lowest weight representations and an infinite family of q difference equations which may be called generalized q deformed heat schrodinger equations we also apply our methods to the on shell q schrodinger algebra proposed by floreanini and vinet

deformed minkowski spaces classification and properties using general but simple covariance arguments we classify the quantum minkowski spaces for dimensionless deformation parameters this requires a previous analysis of the associated lorentz groups which reproduces a previous classification by woronowicz and zakrzewski as a consequence of the unified analysis presented we give the commutation properties the deformed and central length element and the metric tensor for the different spacetime algebras

a cell centered adaptive projection method for the incompressible euler equations we present an algorithm to compute adaptive solutions for incompressible flows using block structured local refinement in both space and time this method uses a projection formulation based on a cell centered approximate projection which allows the use of a single set of cell centered solvers because of refinement in time additional steps are taken to accurately discretize the advection and projection operators at grid refinement boundaries using composite operators which span the coarse and refined grids this ensures that the method is approximately freestream preserving and satisfies an appropriate form of the divergence constraint

regular article an accurate cartesian grid method for viscous incompressible flows with complex immersed boundaries a cartesian grid method has been developed for simulating two dimensional unsteady viscous incompressible flows with complex immersed boundaries a finite volume method based on a second order accurate central difference scheme is used in conjunction with a two step fractional step procedure the key aspects that need to be considered in developing such a solver are imposition of boundary conditions on the immersed boundaries and accurate discretization of the governing equation in cells that are cut by these boundaries a new interpolation procedure is presented which allows systematic development of a spatial discretization scheme that preserves the second order spatial accuracy of the underlying solver the presence of immersed boundaries alters the conditioning of the linear operators and this can slow down the iterative solution of these equations the convergence is accelerated by using a preconditioned conjugate gradient method where the preconditioner takes advantage of the structured nature of the underlying mesh the accuracy and fidelity of the solver is validated by simulating a number of canonical flows and the ability of the solver to simulate flows with very complicated immersed boundaries is demonstrated

generalization of the h deformation to higher dimensions we construct glh 3 from glq 3 by a singular map we show that there exist two singular maps which map glq 3 to new quantum groups we also construct their r matrices and will show that although the maps are singular their r matrices are not then we generalize these singular maps to the case gl n and for cn series

the euclidean hopf algebra u q e n and its fundamental hilbert space representations the euclidean hopf algebra uq en dual of fun rnq soq 1 n is constructed by realizing it as a subalgebra of the differential algebra diff rnq on the quantum euclidean space rnq in fact the previous realization g fiore commun math phys 169 475 500 1995 of uq 1 so n is extended within diff rnq through the introduction of q derivatives as generators of q translations the fundamental hilbert space representations of uq en turn out to be of highest weight type and rather simple lattice regularized versions of the classical ones the vectors of a basis of the singlet i e zero spin irrep can be realized as normalizable functions on rnq going to distributions in the limit q 1

a cell centered adaptive projection method for the incompressible navier stokes equations in three dimensions we present a method for computing incompressible viscous flows in three dimensions using block structured local refinement in both space and time this method uses a projection formulation based on a cell centered approximate projection combined with the systematic use of multilevel elliptic solvers to compute increments in the solution generated at boundaries between refinement levels due to refinement in time we use an l0 stable second order semi implicit scheme to evaluate the viscous terms results are presented to demonstrate the accuracy and effectiveness of this approach

a cartesian grid embedded boundary method for the heat equation on irregular domains we present an algorithm for solving the heat equation on irregular time dependent domains it is based on the cartesian grid embedded boundary algorithm of johansen and colella j comput phys 147 2 60 85 for discretizing poisson s equation combined with a second order accurate discretization of the time derivative this leads to a method that is second order accurate in space and time for the case where the boundary is moving we convert the moving boundary problem to a sequence of fixed boundary problems combined with an extrapolation procedure to initialize values that are uncovered as the boundary moves we find that in the moving boundary case the use of crank nicolson time discretization is unstable requiring us to use the l sub 0 stable implicit runge kutta method of twizell gumel and arigu

bounds on elementary symmetric functions abstract tight bounds on an elementary symmetric function are established under the assumption that the values of the elementary symmetric functions of lower orders are given the explicit form of the inverse hankel moment matrix leads to inequalities for moments and for elementary symmetric polynomials

inhomogeneous quantum groups related to two dimensional quantum planes we propose a simple and compact method for deriving quantum groups acting on manin s q and h planes using this method we classify all the rigid motions of the two dimensional quantum planes requiring that these inhomogenous transformations preserve differential structure of the quantum plane we obtain two distinct inhomogenous quantum groups for the q plane and one previously unknown inhomogenous quantum group for the h plane iglh h 2

jordanian quantum algebra h sl n via contraction method and mapping using a contraction procedure developed earlier we construct in the first part of the present paper the jordanian quantum hopf algebra h sl 3 which has a remarkably simple coalgebraic structure and contains the jordanian algebra h sl 2 obtained by ohn as a hopf subalgebra a nonlinear map between the quantum h sl 3 and the classical sl 3 algebras is then established and the universal h matrix of the h sl 3 algebra is given in the second part we give the higher dimensional jordanian algebras h sl n for all n the universal h matrix of the h sl n algebra is also given

hopf superalgebra contractions and r matrix for fermions different contractions are applied to the quantum superalgebra ospq 1 mod 2 in the first of them the graded analogue s hq 1 of the one dimensional heisenberg quantum algebra is obtained and its r matrix explicitly calculated in the second contraction a z2 graded version of the q oscillator is proposed and finally the supersymmetric two dimensional euclidean quantum algebra s eq 2 is found

a conservative adaptive projection method for the variable density incompressible navier stokes equations in this paper we present a method for solving the equations governing time dependent variable density incompressible flow in two or three dimensions on an adaptive hierarchy of grids the method is based on a projection formulation in which we first solve advection diffusion equations to predict intermediate velocities and then project these velocities onto a space of approximately divergence free vector fields our treatment of the first step uses a specialized second order upwind method for differencing the nonlinear convection terms that provides a robust treatment of these terms suitable for inviscid and high reynolds number flow density and other scalars are advected in such a way as to maintain conservation if appropriate and free stream preservation our approach to adaptive refinement uses a nested hierarchy of logically rectangular girds with simultaneous refinement of the girds in both space and time the integration algorithm on the grid hierarchy is a recursive procedure in which coarse grids are advanced in time fine grids are advanced multiple steps to reach the same time as the coarse grids and the data at different levels are then synchronized the single grid algorithm is described briefly but the emphasis here is on the time stepping procedure for the adaptive hierarchy numerical examples are presented to demonstrate the algorithms s accuracy and convergence properties and illustrate the behavior of the method an additional example demonstrates the performance of the method on a more realistic problem namely a three dimensional variable density shear layer

on the biparametric quantum deformation of gl 2 gl 1 we study the biparametric quantum deformation of gl 2 gl 1 and exhibit its cross product structure we derive explicitly the associated dual algebra i e the quantized universal enveloping algebra employing the r matrix procedure this facilitates construction of a bicovariant differential calculus which is also shown to have a cross product structure finally a jordanian analog of the deformation is presented as a cross product algebra

irreducible decomposition for tensor product representations of jordanian quantum algebras tensor products of irreducible representations of the jordanian quantum algebras and are considered for both the highest weight finite dimensional representations of and the lowest weight infinite dimensional ones of it is shown that tensor product representations are reducible and that the decomposition rules to irreducible representations are exactly the same as those of corresponding lie algebras

multistability and symmetry breaking in the two dimensional flow around a square cylinder we use numerical methods to study two dimensional flow passing a square cylinder at low reynolds numbers and observe period 1 and 3 vortices behind the cylinder at the same reynolds number re when re increases from a small number to a critical value re c approximately equal to 320 the system could change from bistability which maintains the spatial symmetry to tristability which breaks the spatial symmetry our results suggest many interesting problems for further studies

a projection method for locally refined grids a numerical method for the solution of the two dimensional euler equatons for incompressible flow on locally refined grids is presented the method is a second order godunov projection method adapted from bell colella and glaz second order accuracy of the numerical method in time and space is established through numerical experiments the main contributions of this work concern the formulation and implementation of a projection for refined grids a discussion of the adjointness relation between gradient and divergence operators for a refined grid mac projection is presented and a refined grid approximate projection is developed an efficient multigrid method which exactly solves the projection is developed and a method for casting certain approximate projections as mac projections on refined grids is presented

lie bialgebra contractions and quantum deformations of quasi orthogonal algebras lie bialgebra contractions are introduced and classified a non degenerate coboundary bialgebra structure is implemented into all pseudo orthogonal real algebras so p q starting from the one corresponding to so n 1 it allows us to introduce a set of lie bialgebra contractions which leads to lie bialgebras of quasi orthogonal algebras this construction is explicitly given for n 2 3 4 all lie bialgebra contractions studied in this paper define hopf algebra contractions for the drinfel d jimbo deformations uzso p q they are explicitly used to generate new non semisimple quantum algebras as it is the case for the euclidean poincare and galilean algebras

an approach to local refinement of structured grids structured grids can be refined locally by adding line segments these are notionally made into complete grid lines by filling the remainder of the line with blanks a discretization scheme is adapted to this type of grid by adding interpolation points to complete differencing stencils the navier stokes equations are solved by the artificial compressibility approach examples show the efficacy of the method

a stencil adaptive algorithm for finite difference solution of incompressible viscous flows in this paper a solution adaptive algorithm is presented for the simulation of incompressible viscous flows the framework of this method consists of an adaptive local stencil refinement algorithm and 3 points central difference discretization the adaptive local stencil refinement is designed in such a manner that 5 points symmetric stencil is guaranteed at each interior node so that conventional finite difference formula can be easily constructed everywhere in the domain thus high efficiency and accuracy of central difference scheme can be ultimately enjoyed together with the solution adaptive property the adaptive finite difference method has been tested by three numerical examples to examine its performance in the two dimensional problems the numerical examples include poisson equation moving interface problem and a lid driven incompressible flow problem it was found that the multigrid approach can be efficiently combined with solution adaptive algorithm to speed up the convergence rate