In this paper, will be presented the concept of Borel sets and Baire on normal topological spaces locally compact as new types λ – system study basic characteristics related to each them obtain results them.

We resolve two open problems on Kronecker coefficients g(λ,μ,ν) of the symmetric group. First, we prove that for partitions λ,μ,ν with fixed Durfee square size, grow at most polynomially. Second, show maximal g(λ,λ,λ) self-conjugate λ superexponentially. also give applications to explicit special cases.

The aim of this paper is to establish density properties in Lp spaces the span powers functions {ψλ:λ∈Λ}, Λ⊂N spirit Müntz-Szász Theorem. As almost never achieved, we further investigate and a modulation {ψλ,ψλeiαt:λ∈Λ}. Finally, Theorem for translates cosines {cosλ⁡(t−θ1),cosλ⁡(t−θ2):λ∈Λ}. Under some arithmetic restrictions on θ1−θ2, show that equivalent condition Λ conjecture those are not ne...

The goal of this paper is to study the performance Thresholding Greedy Algorithm (TGA) when we increase size greedy sums by a constant factor λ⩾1. We introduce so-called λ-almost and λ-partially bases. case λ=1 gives us classical definitions almost (strong) partially show that basis if only it for all (some) However, each λ>1, there exists an unconditional but not 1-partially greedy. Furthermor...

The independent set polynomial is important in many areas of combinatorics, computer science, and statistical physics. For every integer Δ≥2, the Shearer threshold value λ⁎(Δ)=(Δ−1)Δ−1/ΔΔ. It known that for λ<−λ⁎(Δ), there are graphs G with maximum degree Δ whose polynomial, evaluated at λ, most 0. Also, no such any λ>−λ⁎(Δ). This paper motivated by computational problem approximating when λ<−λ...