We introduce normal coordinates on the infinite dimensional group G introduced by Connes and Kreimer in their analysis of the Hopf algebra of rooted trees. We study the primitive elements of the algebra and show that they are generated by a simple application of the inverse Poincaré lemma, given a closed left invariant 1-form onG. For the special case of the ladder primitives, we find a second ...

In this paper, we consider the boundedness of the Libera operator on Dirichlet spaces in terms of the Schur test. Moreover, we get its point spectrum and norm.

Inhomogeneous lattice paths are introduced as ordered sequences of rectangular Young tableaux thereby generalizing recent work on the Kostka polynomials by Nakayashiki and Yamada and by Lascoux, Leclerc and Thibon. Motivated by these works and by Kashiwara’s theory of crystal bases we define a statistic on paths yielding two novel classes of polynomials. One of these provides a generalization o...

It was recently shown by R. Souam and E. Toubiana [33] that the (non constantly curved) Berger spheres do not contain totally umbilic surfaces. Nevertheless in this article we show, by perturbative arguments, that all analytic metrics su ciently close to the round metric g0 on S possess generalized totally umbilic 2-spheres, namely critical points of the conformal Willmore functional ∫ Σ |A◦|2 ...

Recent work of A. Postnikov shows that cylindric skew Schur functions, which are a generalisation of skew Schur functions, have a strong connection with a problem of considerable current interest: that of finding a combinatorial proof of the non-negativity of the 3-point Gromov-Witten invariants. After explaining this motivation, we study cylindric skew Schur functions from the point of view of...

and Applied Analysis 3 holds in Di ∩ Dj , then f a1, a2, . . . , an ≥ ≤ f A a , A a , . . . , A a 1.7 for all a a1, a2, . . . , an ∈ D, with equality if only if a1 a2 · · · an. Proof. If n 2, then Theorem 1.2 follows from Lemma 1.1 and l |a1 − a2|/2. We assume that n ≥ 3 in the next discussion. Without loss of generality, we only prove the case of ∂f/∂xi > ∂f/∂xj with i / j. If a1 a2 · · · an, ...

By the properties of Schur-convex function, Schur geometrically convex function and Schur harmonically convex function, Schur-convexity, Schur geometric and Schur harmonic convexities of the dual form for a class of symmetric functions are simply proved. As an application, several inequalities are obtained, some of which extend the known ones. Mathematics subject classification (2010): 26D15, 0...

An important problem in algebraic combinatorics is finding expansions of products of symmetric functions as sums of symmetric functions. Schur functions form a well-known basis for the ring of symmetric functions. The Littlewood-Richardson rule was introduced to expand the product of two Schur functions as a positive sum of Schur functions. Remmel and Whitney introduced an algorithmic way to fi...

In this paper, using the properties of Schur-convex function, Schur-geometrically convex function and Schur-harmonically convex function, we provide much simpler proofs of the Schur-convexity, Schur-geometric convexity and Schur-harmonic convexity for a composite function of the complete symmetric function.

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 ...