We consider the vertex cover problem with multiple coverage constraints in hypergraphs. In this problem, we are given a hypergraph \(G=(V,E)\) maximum edge size f, cost function \(w: V\rightarrow {\mathbb {Z}}^+\), and subsets \(P_1,P_2,\ldots ,P_r\) of E along covering requirements \(k_1,k_2,\ldots ,k_r\) for each subset. The objective is to find minimum subset S V such that, \(P_i\), at least...

This paper separately evaluates the effects of inclination and asymmetry solar coronal loops on resonant absorption kink magnetohydrodynamic (MHD) oscillations. We modelled a typical loop by straight axisymmetric cylindrical magnetic flux tube filled with cold plasma. solved dispersion relation numerically for different values longitudinal mass density stratification. show that, in inclined asy...

NbSe$_3$ and monoclinic-TaS$_3$ ($m$-TaS$_3$) are quasi-1D metals containing three different types of chains undergoing two charge density wave (CDW) Peierls transitions at T$_{P_1}$ T$_{P_2}$. The nature these is discussed on the basis first-principles DFT calculation their electron-hole Lindhard response function. As a result stronger inter-chain interactions Fermi surface (FS) function consi...

The groups mentioned in the title are certain matrix of infinite size over a finite field $\mathbb F_q$. They built from classical and at same time they similar to reductive $p$-adic Lie groups. In present paper, we initiate study invariant measures for coadjoint action these infinite-dimensional We examine first group $\mathbb{GLB}$, topological completion inductive limit $\varinjlim GL(n, \ma...

Abstract We study the integrability of 2D Hamiltonian systems $$H_\mu =\frac{1}{2}(p_1^2+p_2^2) + \omega (p_1q_2-p_2q_1) -\tfrac{\mu }{r}+ V(q_1,q_2)$$ H μ = 1 2 ( ...

Let $\lambda$ denote the Liouville function. We show that, as $X \rightarrow \infty$, $$\int_{X}^{2X} \sup_{\substack{P(Y)\in \mathbb{R}[Y]\\ deg(P)\leq k}} \Big | \sum_{x \leq n x + H} \lambda(n) e(-P(n)) |\ dx = o ( X H)$$ for all fixed $k$ and $X^{\theta} H X$ with $0 < \theta 1$ but arbitrarily small. Previously this was only established $k 1$. obtain result a special case of corresponding ...

In dimensions n ≥ 2 n\ge 2 we obtain alttext="u...

Let Γ ⊂ Q ¯ × $\Gamma \subset \overline{\mathbb {Q}}^{\times }$ be a finitely generated multiplicative group of algebraic numbers. α 1 , … r ∈ $\alpha _1,\ldots ,\alpha _r\in {Q}}^\times$ numbers which are $\mathbb {Q}$ -linearly independent and let ε > 0 $\epsilon >0$ given real number. One the main results that we prove in this article is as follows: There exist only many tuples ( u q p ) Z +...