We prove Lieb-Robinson bounds for systems defined on infinite dimensional Hilbert spaces and described by unbounded Hamiltonians. In particular, we consider harmonic and certain anharmonic lattice systems.

We prove sharp Lieb-Thirring inequalities for Schrödinger operators with potentials supported on a hyperplane and we show how these estimates are related to LiebThirring inequalities for relativistic Schrödinger operators.

We present short and elementary proofs of two theorems of Huckaba and Marley, while generalizing them at the same time to the case of a module. The theorems concern a characterization of the depth of the associated graded ring of a Cohen-Macaulay module, with respect to a Hilbert filtration, in terms of the Hilbert coefficient e1. As an application, we derive bounds on the higher Hilbert coeffi...

A new coefficient bound is established for factoring univariate polynomials over the integers. Unlike an overall bound, the new bound limits the size of the coefficients of at least one irreducible factor of the given polynomial. The single-factor bound is derived from the weighted norm introduced in Beauzamy et al. (1990) and is almost optimal. Effective use of this bound in p-adic lifting res...

Abstract The main objective of this paper is to obtain necessary and sufficient condition for a subclass of uniformly convex functions and corresponding subclass of starlike functions with fixed second coefficient defined by Carlson and Shaffer operator for the function f(z) in UCT (α, β). Furthermore, we obtain extreme points, distortion bounds and closure properties for f(z) in UCT (α, β) by ...

In the book Boolean Function Complexity by Stasys Jukna [7], two lower bound techniques for Tree-like Cutting Plane proofs (henceforth, “Tree-CP proofs”) using Karchmer-Widgerson type communication games (henceforth, “KW games”) are presented: The first, applicable to Tree-CP proofs with bounded coefficients, translates Ω(t) deterministic lower bounds on KW games to 2 logn) lower bounds on Tree...

Abstract. For elliptic interface problems in two and three dimensions, this paper studies a priori and residual-based a posteriori error estimations for the Crouzeix–Raviart nonconforming and the discontinuous Galerkin finite element approximations. It is shown that both the a priori and the a posteriori error estimates are robust with respect to the diffusion coefficient, i.e., constants in th...

We define a new subclass of univalent function based on Salagean differential operator and obtained the initial Taylor coefficients using the techniques of Briot-Bouquet differential subordination in association with the modified sigmoid function. Further we obtain the classical Fekete-Szego inequality results.

we give sharp upper bounds on the zagreb indices and lower bounds on the zagreb coindices of chemical trees and characterize the case of equality for each of these topological invariants.

We present a posteriori error bounds for reduced basis approximations of parabolic partial differential equations involving (i) a nonaffine dependence on the parameter and (ii) a nonlinear dependence on the field variable. The method employs the Empirical Interpolation Method in order to construct “affine” coefficient-function approximations of the “nonaffine” (or nonlinear) parametrized functi...