We show that a large class of right-angled Artin groups (in particular, those with planar complementary defining graph) can be embedded quasi-isometrically in pure braid groups and in the group Diff(D2, ∂D2, vol) of area preserving diffeomorphisms of the disk fixing the boundary (with respect to the L2-norm metric); this extends results of Benaim and Gambaudo who gave quasi-isometric embeddings...

Consider the Laplacian in a bounded domain in Rd with general (mixed) homogeneous boundary conditions. We prove that its eigenfunctions are ‘quasi-orthogonal’ on the boundary with respect to a certain norm. Boundary orthogonality is proved asymptotically within a narrow eigenvalue window of width o(E1/2) centered about E, as E → ∞. For the special case of Dirichlet boundary conditions, the norm...

In this paper, we show how by a very simple modification of bivariate spline discrete quasi-interpolants, we can construct a new class of quasi-interpolants, which have remarkable properties such as high order of regularity and polynomial reproduction. More precisely, given a spline discrete quasi-interpolation operator Qd, which is exact on the space Pm of polynomials of total degree at most m...

The completion A[τ ] of a locally convex ∗-algebra A[τ ] with not jointly continuous multiplication is a ∗-vector space with partial multiplication xy defined only for x or y ∈ A0, and it is called a topological quasi ∗-algebra. In this paper two classes of topological quasi ∗-algebras called strict CQ-algebras and HCQ-algebras are studied. Roughly speaking, a strict CQ-algebra (resp. HCQ-algeb...

This paper shows that there is a correspondence between quasi-exactly solvable models in quantum mechanics and sets of orthogonal polynomials {Pn}. The quantum-mechanical wave function is the generating function for the Pn(E), which are polynomials in the energy E. The condition of quasi-exact solvability is reflected in the vanishing of the norm of all polynomials whose index n exceeds a criti...

We consider the one-dimensional quantum harmonic oscillator perturbed by a linear operator which is polynomial of degree $2$ in $(x,-{\rm i}\partial_x)$, with coefficients quasi-periodically depending on time. By establishing reducibility results, we describe growth Sobolev norms. In particular, $t^{2s}-$polynomial ${\mathcal H}^s-$norm observed this model if original time quasi-periodic equati...

There were elucidated mechanisms maintenance stability Internal Energy and Internal Medium as an organism as well as cells an organism in norm and in quasi-stationary pathologic states. These mechanisms are exerted by three levels of regulative mechanism: highest level regulation, high level regulation and low level regulation. Also, cells from all sections of an organism (blood, lymph, neuroly...