Let X be a normed linear space, x ∈ X an element of norm one, and ε > 0 and δ(x,ε) the local modulus of convexity of X . We denote by ρ(x,ε) the greatest ρ≥ 0 such that for each closed linear subspace M of X the quotient mapping Q : X → X/M maps the open ε-neighbourhood of x in U onto a set containing the open ρ-neighbourhood of Q(x) in Q(U). It is known that ρ(x,ε) ≥ (2/3)δ(x,ε). We prove that...

We prove that for any semi-Dirichlet form (ε, D(ε)) on a measurable Lusin space E there exists a Lusin topology with the given σ-algebra as the Borel σ-algebra so that (ε, D(ε)) becomes quasi–regular. However one has to enlarge E by a zero set. More generally a corresponding result for arbitrary L-resolvents is proven.

We study Chebyshev filter diagonalization as a tool for the computation of many interior eigenvalues of very large sparse symmetric matrices. In this technique the subspace projection onto the target space of wanted eigenvectors is approximated with high-order filter polynomials obtained from a regularized Chebyshev expansion of a window function. After a short discussion of the conceptual foun...

Numerical methods for strongly oscillatory and singular functions are given in this paper. We present an alternative numerical solution for of oscillatory integrals of the general form Where and are smooth functions in the interval [a, b]. Also ε ω and . In order to achieve this goal and avoid singularity, the mentioned integral is solved by the modified moments using interpolating at the Cheby...

We give new constructions of two classes algebraic code families that are efficiently list decodable with small output size from a fraction 1-R-ε adversarial errors, where R is the rate code, for any desired positive constant ε. The alphabet depends only ε and nearly optimal. first class codes obtained by folding algebraic-geometric using automorphisms underlying function field. second restrict...

We show that s-term DNF formulas can be learned under the uniform distribution in quasi-polynomial time with statistical queries of tolerance Ω(ε/s). The tolerance improves on the known tolerance Ω(ε/s) and is optimal with respect to its dependence on the error parameter ε. We further consider the related model of learning with proper distance queries and show that DNF formulas can be learned u...

The complexity (quasi-metric) space was introduced in [23] to study complexity analysis of programs. Recently, it was introduced in [22] the dual complexity (quasi-metric) space, as a subspace of the function space [0,+∞)ω. Several quasi-metric properties of the complexity space were obtained via the analysis of its dual. We here show that the structure of a quasi-normed semilinear space provid...

Construction of subspace codes with good parameters is one of the most important problems in random network coding. In this paper we present first a generalization of the concept of cyclic subspaces codes and further we show that the usual methods for constructing cyclic subspace codes over finite fields works for m-quasi cyclic codes, namely the subspaces polynomials and Frobenius mappings.

We present a subspace projection technique to conduct large-scale Kohn-Sham density functional theory calculations using higher-order spectral finite-element discretization. The proposed method treats both metallic and insulating materials in a single framework, and is applicable to both pseudopotential as well as all-electron calculations. The key ideas involved in the development of this meth...

This paper introduces q-series for a curve singularity (C, 0) in the affine space (Cn, 0) via subspace arrangements. These q-series are certain multivariable generating functions whose coefficients are the characteristic polynomials of subspace arrangements associated with the singularity (C, 0) at various orders; the q is the variable in the characteristic polynomials of the subspace arrangeme...