let $k$ be a positive integer. a subset $s$ of $v(g)$ in a graph $g$ is a $k$-tuple total dominating set of $g$ if every vertex of $g$ has at least $k$ neighbors in $s$. the $k$-tuple total domination number $gamma _{times k,t}(g)$ of $g$ is the minimum cardinality of a $k$-tuple total dominating set of $g$. if$v(g)=v^{0}={v_{1}^{0},v_{2}^{0},ldots ,v_{n}^{0}}$ and $e(g)=e_{0}$, then for any in...

Let D be a digraph, V (D) and A(D) will denote the sets of vertices and arcs of D, respectively. A (k, l)-kernel N of D is a k-independent set of vertices (if u, v ∈ N , u 6= v, then d(u, v), d(v, u) ≥ k) and l-absorbent (if u ∈ V (D) − N then there exists v ∈ N such that d(u, v) ≤ l). A k-kernel is a (k, k − 1)-kernel. Quasi-transitive, right-pretransitive and left-pretransitive digraphs are g...

A t-intersecting constant dimension subspace code C is a set of k-dimensional subspaces in projective space \(\mathrm {PG}(n,q)\), where distinct intersect exactly t-dimensional subspace. classical example such the sunflower, all pass through same t-space. The sunflower bound states that if \(|C| > \left( \frac{q^{k + 1} - q^{t 1}}{q \right) ^2 1\). In this article we will look at case \(t=0\) ...

В даній статті для комплексної алгебри Лі sl3 запропонована явна формула знаходження кратності ваги незвідного зображення Γλ, яке визначається старшою вагою λ = (a,b). Множина всіх ваг Λ такого утворює групове кільце Z[Λ] з мультиплікативним базисом e(μ),μ ∈ Λ. Характер Char Γλ є елементом Z[Λ], коефіцієнти якого і шуканими кратностями. Головна ідея обчислень полягає у специфікації базису e(μ) ...

We study the following learning problem with dependent data: Observing a trajectory of length $n$ from stationary Markov chain notation="LaTeX">$k$ states, goal is to predict next state. For notation="LaTeX">$3 \leq k O(\sqrt {n})$ , ...

Let V ⊆ [n] be a k-element subset of [n]. The uniform distribution on the 2k strings from {0, 1}n that are set to zero outside is called an (n, k)-zero-fixing source. An ϵ-extractor for sources mapping F: → 1}m, some m, such F(X) ϵ-close in statistical distance 1}m every source X. Zero-fixing were introduced by Cohen and Shinkar [7] connection with previously studied extractors bit-fixing sourc...

A subset S of nodes in a graph G is k-connected m-dominating set ((k , m)-cds) if the subgraph G[S] induced by and every $$v \in V {\setminus } S$$ has at least m neighbors S. In k -Connected -Dominating Set m)-CDS) problem, goal to find minimum weight (k, m)-cds node-weighted graph. For $$m \ge k$$ we obtain following approximation ratios. unit disk graphs improve ratio $$O(k \ln k)$$ Nutov (I...

A bstract We have extracted the ratio | V ub |/| cb from a combined study of available inputs on $$ \overline{B}\to \left(\pi, \rho, \omega \right){\ell}^{-}{\overline{\nu}}_{\ell } B ¯ → π ρ ω </mm...

K-means—and the celebrated Lloyd’s algorithm—is more than clustering method it was originally designed to be. It has indeed proven pivotal help increase speed of many machine learning, data analysis techniques such as indexing, nearest-neighbor search and prediction, compression and, lately, inference with kernel machines. Here, we introduce an efficient extension K-means, dubbed QuicK-means, t...