The Reissner-Mindlin plate theory models a thin plate with thickness t. The condition number of finite element approximations of this model deteriorates badly as the thickness t of the plate converges to 0. In this thesis, we develop an overlapping domain decomposition method for the Reissner-Mindlin plate model discretized by Falk-Tu elements with a convergence rate which does not deteriorate ...

We introduce a quasisymmetric generalization of Berele and Regev’s hook Schur functions and prove that these new quasisymmetric hook Schur functions decompose the hook Schur functions in a natural way. In this paper we examine the combinatorics of the quasisymmetric hook Schur functions, providing analogues of the RobinsonSchensted-Knuth algorithm and a generalized Cauchy Identity. Résumé. Nous...

Recently a new basis for the Hopf algebra of quasisymmetric functions QSym, called quasisymmetric Schur functions, has been introduced by Haglund, Luoto, Mason, van Willigenburg. In this paper we extend the definition of quasisymmetric Schur functions to introduce skew quasisymmetric Schur functions. These functions include both classical skew Schur functions and quasisymmetric Schur functions ...

We use Hopf algebras to prove a version of the Littlewood–Richardson rule for skew Schur functions, which implies a conjecture of Assaf and McNamara. We also establish skew Littlewood–Richardson rules for Schur P and Q-functions and noncommutative ribbon Schur functions, as well as skew Pieri rules for k-Schur functions, dual k-Schur functions, and for the homology of the affine Grassmannian of...

In the present paper, we first prove the logarithmic convexity of the elementary function b x −a x x , where x 6= 0 and b > a > 0. Basing on this, we then provide a simple proof for Schur-convex properties of the extended mean values, and, finally, discover some convexity related to the extended mean values.

In [20] the connections between the Schur algorithm, the Wall’s continued fractions and the orthogonal polynomials are revisited and used to establish some nice convergence properties of the sequence of Schur functions associated with a Schur function. In this report, we generalize some of Krushchev’s results to the case of a multipoint Schur algorithm, that is a Schur algorithm where all the i...