Let H = (V, E) be a hypergraph, where V is set of vertices and E non-empty subsets called edges. If all edges have the same cardinality r, then an r-uniform hypergraph; if consists r-subsets V, complete denoted by $$K_n^r$$ , n |V|. A hypergraph H′ (V′, E′) subhypergraph V′ ⊆ E′ E. The edge-connectivity minimum edge F such that − not connected, F). An k-edge-maximal every has at most k, but for...

‎let $x=left(‎ ‎begin{array}{llll}‎ ‎ x_1 & ldots & x_{n-1}& x_n‎ ‎ x_2& ldots & x_n & x_{n+1}‎ ‎end{array}right)$ be the hankel matrix of size $2times n$ and let $g$ be a closed graph on the vertex set $[n].$ we study the binomial ideal $i_gsubset k[x_1,ldots,x_{n+1}]$ which is generated by all the $2$-minors of $x$ which correspond to the edges of $g.$ we show that...

the aim of this article is to extend the study of the lorentz transformation of order (m,n) from m=1 and n>=1 to all m,n>=1, obtaining algebraic structures called a bi-gyrogroup and a bi-gyrovector space. a bi-gyrogroup is a gyrogroup each gyration of which is a pair of a left gyration and a right gyration. a bi-gyrovector space is constructed from a bi-gyrocommutative bi-gyrogroup that admits ...

Given a minimal model of an elliptic curve, $E/K$, over finite extension, $K$, ${\mathbb Q}_{p}$ for any rational prime, $p$, and point $P \in E(K)$ infinite order, we determine precisely $\min \left( v \phi_{n}(P) \right), \psi_{n}^{2}(P) \right) \right)$, where $v$ is normalised valuation on $K$ $\phi_{n}(P)$ $\psi_{n}(P)$ are polynomials arising from multiplication by $n$ this the curve.

‎Let $X=left(‎ ‎begin{array}{llll}‎ ‎ x_1 & ldots & x_{n-1}& x_n\‎ ‎ x_2& ldots & x_n & x_{n+1}‎ ‎end{array}right)$ be the Hankel matrix of size $2times n$ and let $G$ be a closed graph on the vertex set $[n].$ We study the binomial ideal $I_Gsubset K[x_1,ldots,x_{n+1}]$ which is generated by all the $2$-minors of $X$ which correspond to the edges of $G.$ We show that $I_G$ is Cohen-Macaula...

In many markets, sellers must spend resources to learn the costs of providing goods/services. This paper considers consumer searches in such markets. The findings show that: (i) even with ex ante identical consumers and sellers, there is price dispersion equilibrium, (ii) despite minimal search costs, it could be optimal just two (iii) number can increase sellers' information costs. Cherchez mo...

В статье рассматриваются однородные функции, имеющие вид $\theta \left(\tau \right)\left|t\right|^{\alpha },$ гдепорядок однородности $\alpha >-n$, а \left(\tau\right)$ - функция на единичной сфере $S^{n-1}=\left\{t{\in}R^n, \left|t\right|=1\right\}$. При вычислении преобразования Лапласа этих функций с носителем востром конусе необходимо получить их явное представление. Это достигается сумм...

The clique-chromatic number of a graph is the minimum colors required to assign its vertex set so that no inclusion maximal clique monochromatic. McDiarmid, Mitsche, and Prałat proved binomial random G n , 1 2 $G\left(n,\frac{1}{2}\right)$ at most + o ( ) log $\left(\frac{1}{2}+o(1)\right){\mathrm{log}}_{2}n$ with high probability (whp). Alon Krivelevich showed it greater than 2000 $\frac{1}{20...

The solution $x_n\left(t\right)$, $n=1,2,$ of the \textit{initial-values} problem is reported \textit{autonomous} system $2$ coupled first-order ODEs with \textit{homogeneous cubic polynomial} right-hand sides, \begin{eqnarray} \dot{x}_n = c_{n1} \left(x_1\right)^3 + c_{n2}\left( x_1\right)^2 x_2 c_{n3} x_1 \left(x_2\right)^2+c_{n4} \left(x_2\right)^3\ ,\quad n=1,2\ , \nonumber \end{eqnarray} w...