high reynolds number separated flow solutions using navier stokes and approximate equations simulation d ecoulements laminaires faiblement decolles incompressibles stationnaires a nombre de reynolds eleve on montre qu un code bien concu peut resoudre les equations completes de navier stokes et les equations de vorticite parabolisees avec la meme vitesse de convergence on resoud egalement les equations de couche limite sous forme vorticite fonction de courant

young invariant decomposition of spin interacting operators the young invariant decomposition of totally symmetric spin interacting operators is examined from the viewpoint of outer product isoscalar factors of the symmetric group the coefficients required for the decomposition of oneand two body operators are constructed and given explicitly the formalism enables a separate treatment of the spatial and spin parts of the matrix elements of the spin interacting operators

symmetric green s functions on complete manifolds on demontre d une facon constructive que l operateur de laplace admet une fonction de green symetrique g x y sur une variete de riemann complete

sharp estimates for capacities and applications to symmetric diffusions we give sharp estimates for the capacity of compact setf x wherex is the state space of a strongly regular dirichlet form of diffusion type these estimates are in terms of the reference measurem and the caratheodory metric onx for instance cap 0 f leqq left mathop smallint limits 0 infty frac dr v r right 1 leqq 2 left mathop smallint limits 0 infty frac r dr v r right 1 wherev r m 0 x f r from these estimates one easily obtains lower estimates for the green function as well as sharp criteria for polarity and for recurrence the latter we apply to the question of hitting the nodal set 0 for the process associated with the operator delta 2 tfrac nabla varphi varphi nabla and to recurrence questions for divergence form operators a ond n witha a ij which degenerate at d

function theory random paths and covering spaces pour des varietes de riemann connexes m on etudie la relation entre la theorie de fonction harmonique sur m les proprietes statistiques des chemins aleatoires sur m et la structure geometrique globale de m

analytic and geometric background of recurrence and non explosion of the brownian motion on riemannian manifolds we provide an overview of such properties of the brownian motion on complete non compact riemannian manifolds as recurrence and non explosion it is shown that both properties have various analytic characterizations in terms of the heat kernel green function liouville properties etc on the other hand we consider a number of geometric conditions such as the volume growth isoperimetric inequalities curvature bounds etc which are related to recurrence and non explosion

coupling coefficient for the symmetric and unitary groups two recursion formulae are deduced for the construction of inner and outer product isoscalar factors respectively for the symmetric group by which the corresponding coupling coefficients can be easily obtained a formula for the evaluation of the isoscalar factor for the subgroup chain u n contains implies u n 1 is proposed based on the relation between the outer product coupling coefficient for the standard basis of the symmetric group and clebsch gordan coefficient for the canonical basis of the unitary group the calculation procedures are presented and the properties of those coefficients are investigated

hardy littlewood theory for semigroups soit t t t 0 un semi groupe symetrique sousmarkovien et soit n 2 alors on a les proprietes equivalentes a dim t t n b il existe c 2 0 s t t t f c 2 t n 2 f 1 f l 1 x t 0 en fait a b meme dans le cas n 2

instability of the liouville property for quasi isometric riemannian manifolds and reversible markov chains on montre par un exemple que la propriete de liouville n est pas un invariant quasi isometrique des varietes de riemann et des chaines de markov reversibles

on the parabolic kernel of the schrodinger operator etude des equations paraboliques du type q x t t u x t 0 sur une variete riemannienne generale introduction estimations de gradients inegalites de harnack majorations et minorations des solutions fondamentales equation de la chaleur et noyau de green operateur de schrodinger

gaussian upper bounds for the heat kernels of some second order operators on riemannian manifolds abstract we describe a method of obtaining gaussian upper bounds on heat kernels which unifies and improves recent results for hypoelliptic operators in divergence form and for laplace beltrami operators on complete riemannian manifolds

an incremental block line gauss seidel method for the navier stokes equations a block line gauss seidel lgs method is developed for solving the incompressible and compressible navier stokes equations in two dimensions the method requires only one block tridiagonal solution process per iteration and is consequently faster per step than the linearized block adi methods results are presented for both incompressible and compressible separated flows in all cases the proposed block lgs method is more efficient than the block adi methods furthermore for high reynolds number weakly separated incompressible flow in a channel which proved to be an impossible task for a block adi method solutions have been obtained very efficiently by the new scheme

the theory of angular momenta and higher su n symmetries the authors discuss interrelations between generating invariants gi for the reduction pi mi 1 d pi to d on 1 of the m fold tensor product of su n irreducible representations irreps d pi and polynominal bases of the su m irreps d on 1j om n 1 ok 0 0 0 k times a realisation of the su m irrep d oj om 3 bases is given in terms of gi for su 2 coupling wigner coefficients as a byproduct an expression is obtained for su 2 6 j symbols in terms of only two wigner coefficients the authors also discuss some possibilities of the analysis involved in solving the wigner biedenharn problem construction of orthonormal sets of the wigner coefficients for su n groups n or 3

multiplicity free wigner coefficients for semisimple lie groups i the u n pattern calculus this is the first paper in a series of two dedicated to a new algebraic determination of the multiplicity free reduced wigner coefficients for the lie groups u n and o n the approach employed enables a direct nonrecursive derivation of reduced wigner coefficients the absolute value squared of the reduced wigner coefficients is expressed as a rational polynomial function numerator polynomial divided by denominator polynomial whose weyl group symmetries are seen to fall out naturally in our approach from the transformation properties of polynomial functions determined by casimir invariants a unified treatment of the composition laws of reduced wigner coefficients and the evaluation of their associated denominator polynomials is presented which applies to both u n and o n an explicit formula for the numerator polynomials of u n is also derived the numerator polynomials for the orthogonal groups will be given in the second paper of the series

comparison of iterative and direct solution methods for viscous flow problems coles d the law of the wake in the turbulent boundary layer journal of fluid mechanics vol 1 feb 1956 pp 191 226 dechow r mittlere geschwindigkeit und reynoldscher spannungstensor in der dreidimensionalen turbulenten wandgrenzschicht vor einem stehenden zylinder dissertation technische hochschule karlsruhe federal republic of germany 1976 johnston j p on the three dimensional turbulent boundary layer generated by secondary flow transactions ofasme journal of basic engineering vol 82 march 1960 pp 233 248 miiller u r messung von reynoldsschen spannungen und zeitlich gemittelten geschwindigkeiten in einer dreidimensionalen grenzschicht mit nichtverschwindenden druckgradienten dissertation rheinisch westfalische technische hochschule aachen federal republic of germany march 1979 pfeil h and sticksel w influence of the pressure gradient on the law of the wall aiaa journal vol 20 1982 pp 434 436 pfeil h and miiller t a velocity profile model for two dimensional zero pressure gradient transitional boundary layers aiaa journal to be published

new perspective on the u n wigner racah calculus ii elementary reduced wigner coefficients for u n for pt i see ibid vol 20 no 9 p 2241 50 1987 exploiting the powerful formalism of the vector coherent state theory expounded in part i the group theoretical content of the complementarity principle and a novel interpretation of the operator pattern of biedenharn and louck the authors rederive in a simple fashion all u n u n 1 reduced wigner coefficients for the elementary u n tensors

range of fluctuation of brownian motion on a complete riemannian manifold we investigate the escape rate of the brownian motion w x t on a complete noncompact riemannian manifold assuming that the manifold has at most polynomial volume growth and that its ricci curvature is bounded below we prove that dist w x t x ct log t for all large t with probability 1 on the other hand if the ricci curvature is nonnegative and the volume growth is at least polynomial of the order n 2 then formula math again for all large t with probability 1 where e 0

classification selection rules and symmetry properties of the clebsch gordan coefficients of symmetric group new analytical expressions for clebsch gordan coefficients cgcs of symmetric group are formulated based on the racah factorization lemma as examples cgcs for the coupling f 1 1 f 1 1 and f 1 1 f 2 2 are tabulated we have introduced a new technique called the clebsch gordan sequences cgss cgss provide a partial understanding of vanishing of cgcs and an explanation of new symmetry properties of multiplicity free cgcs

uniqueness of ϕ minimal hypersurfaces in warped product manifolds abstract we show that generalized minimal graphs in a warped product with density over a parabolic manifold are fibers under appropriate conditions on the density the proof employs appropriate test functions

difference equations isoperimetric inequality and transience of certain random walks the difference laplacian on a square lattice in rn has been stud ied by many authors in this paper an analogous difference operator is studied for an arbitrary graph it is shown that many properties of the laplacian in the continuous setting e g the maximum principle the harnack inequality and cheeger s bound for the lowest eigenvalue hold for this difference oper ator the difference laplacian governs the random walk on a graph just as the laplace operator governs the brownian motion as an application of the theory of the difference laplacian it is shown that the random walk on a class of graphs is transient the random walks we consider are defined as follows let k be a connected graph i e a one dimensional simplicial complex for a vertex x e k let m x denote the number of edges emanating from x the probability that a particle moves from x to another vertex y e k is l m x if x and y are connected by an edge and it is zero otherwise as observed by courant friedrichs and lewy cfl for the case of a square lattice in the plane this random walk is intimately related to the difference analog of the laplacian

a probabilistic approach to martin boundaries for manifolds with ends we use martingale methods and coupling arguments to prove results of li and tam 1987 and donnelly 1986 characterizing positive and bounded harmonic functions respectively on certain manifolds with ends

spinor group and its restrictions a realization of the spinor algebra of the rotation group so n n 2n or 2n 1 in the covering algebra of u 2n is exploited to obtain explicit representation matrices for the so n generators in the basis adapted to the subgroup chain so n u n u n 1 u 1 as a special case the computation of matrices of u n representations characterized by a k column young tableau is reduced to the evaluation of at most k box totally symmetric representations of u 2n

the structure of phi stable minimal hypersurfaces in manifolds of nonnegative p scalar curvature suppose n n g is an n dimensional riemannian manifold with a given smooth measure m the p scalar curvature is defined as p g r m infty g r g 2 delta g rm log phi nabla g rm log phi g 2 where dm phi dvol g and r g is the scalar curvature of n n g in this paper under a technical assumption on phi we prove that phi stable minimal oriented hypersurface in the three dimensional manifold with nonnegative p scalar curvature must be conformally equivalent to either the complex plane mathbb c or the cylinder mathbb r times mathbb s 1

on the symmetry properties of outer product reduction the symmetry properties of outer product coupling coefficients for the symmetric group and of clebsch gordan coefficients for the unitary group and of the corresponding isoscalar factors are discussed a simple rule is given for determination of a phase factor of outer reduction symmetry of sn and u n the rule is provided with a relationship between the phase factor of a young diagram with its subdiagrams

new perspective on the u n wigner racah calculus i vector coherent state theory and construction of gel fand bases using a vector coherent state theory it is shown that the construction of gel fand bases for the unitary group is particularly simple the very specific rules for construction of the states greatly facilitate the subsequent computation of matrix elements of the generators of the u n lie algebra

a liouville property for schrodinger operators 6 examples 27 6 1 thick and thin sets in r 27 6 2 big and small measures in r 29 6 3 a scattered measure in r which is big 31 6 4 counter example to theorem 1 2 32 6 5 counter example to theorem 5 2 34 6 6 harmonic functions with the third boundary condition 35

uniqueness of l 1 solutions for the laplace equation and the heat equation on riemannian manifolds on deduit une hypothese geometrique optimale sur une variete de riemann complete qui assure des proprietes d unicite pour des solutions l 1 de l equation de laplace et de la chaleur

large time behavior of the heat equation on complete manifolds with non negative ricci curvature sur une variete de riemann complete m on considere le noyau de la chaleur h x y t qui resout l equation de la chaleur t f x t 0 sur mx 0 avec la donnee initiale f x 0 f x en posant f x t m h x y t f y dy

symmetric markov chains in ℤ d how fast can they move consider a reversible markov chain x n which takes values in a subset of d if the steps of the chain are uniformly bounded and the invariant measure satisfies a mild regularity condition varopoulos carne and kesten have obtained estimates on p x n x text 0 lambda n 1 2 which exhibit a gaussian tail in but blow up as n following kesten s approach we derive bounds which are uniform in n in some special cases our main result however is an example which shows that in general the estimates of varopoulos carne and kesten are essentially best possible