let$ p_{n}(x)= sum_{i=0}^{n} a_{i}x^{i}$ be a random algebraicpolynomial, where $a_{0},a_{1}, cdots $ is a sequence of independent random variables belong to the domain of attraction of the normal law. thus $a_j$'s for $j=0,1cdots $ possesses the characteristic functions $exp {-frac{1}{2}t^{2}h_{j}(t)}$, where $h_j(t)$'s are complex slowlyvarying functions.under the assumption that th...

‎a $(p‎,‎q)$ graph $g$ is said to have a $k$-odd mean‎ ‎labeling $(k ge 1)$ if there exists an injection $f‎ : ‎v‎ ‎to {0‎, ‎1‎, ‎2‎, ‎ldots‎, ‎2k‎ + ‎2q‎ - ‎3}$ such that the‎ ‎induced map $f^*$ defined on $e$ by $f^*(uv) =‎ ‎leftlceil frac{f(u)+f(v)}{2}rightrceil$ is a‎ ‎bijection from $e$ to ${2k - ‎‎‎1‎, ‎2k‎ + ‎1‎, ‎2k‎ + ‎3‎, ‎ldots‎, ‎2‎ ‎k‎ + ‎2q‎ - ‎3}$‎. ‎a graph that admits $k$...

Let $A$ be a limsup random fractal with indices $\gamma_1, ~\gamma_2 ~$and $\delta$ on $[0,1]^d$. We determine the hitting probability $\mathbb{P}(A\cap G)$ for any analytic set $G$ condition $(\star)$$\colon$ $\dim_{\rm H}(G)>\gamma_2+\delta$, where H}$ denotes Hausdorff dimension. This extends correspondence of Khoshnevisan, Peres and Xiao [10] by relaxing that $P_n$ choosing each dyadic hype...

Abstract In this paper, we investigate algebraic, differential and asymptotic properties of polynomials $p_n(x)$ that are orthogonal with respect to the complex oscillatory weight $w(x)=\mathrm {e}^{\mathrm {i}\omega x}$ on interval $[-1,1]$, where $\omega>0$. We also related quantities such as Hankel determinants recurrence coefficients. prove existence $p_{2n}(x)$ for all values $\omeg...

In this paper, we show that Bandwidth is hard for the complexity class W[t] all \(t\in \mathbf{N}\), even caterpillars with hair length at most three. As intermediate problem, introduce Weighted Path Emulation problem: given a vertex-weighted path \(P_N\) and integer M, decide if there exists mapping of vertices to \(P_M\), such adjacent are mapped or equal vertices, total weight pre-image vert...

A“scheduled” arrival process is one in which the nth scheduled for time n, but instead occurs at \(n+\xi _n\) , where \(\xi _j\)’s are i.i.d. We describe here behavior of a single server queue fed by such traffic processing times deterministic. A particular focus on perturbations with Pareto-like tails finite mean. obtain tail approximations steady-state workload both cases critically loaded an...

This is the second paper in a series which we develop machine learning (ML) moment closure models for radiative transfer equation (RTE). In our previous work \cite{huang2021gradient}, proposed an approach to directly learn gradient of unclosed high order moment, performs much better than itself and conventional $P_N$ closure. However, ML model \cite{huang2021gradient} not able guarantee hyperbo...

In this paper, the author studied skeletal congruences θ^* of a distributive nearlattice S, where * represents pseudocomplement. Then described θ(I)^*, θ(I) is smallest congruence S containing n-ideal I as class and showed that I^+ n-kernel θ(I)^*. established following fundamental results: When n an upper element has shown n-kernels are precisely those n-ideals which intersection relative anni...