For fixed $r\geq 3$ and $n$ divisible by $r$, let ${\mathcal H}={\mathcal H}^r_{n,M}$ be the random $M$-edge $r$-graph on $V=\{1,\ldots ,n\}$; that is, H}$ is chosen uniformly from $M$-subsets of K}:={V \choose r}$ ($:= \{\mbox{$r$-subsets $V$}\}$). Shamir's Problem (circa 1980) asks, roughly, for what $M=M(n)$ likely to contain a perfect matching (that $n/r$ disjoint $r$-sets)? In 2008 Johan...

Abstract We prove asymptotic formulas for the complex coefficients of $$(\zeta q;q)_\infty ^{-1}$$ ( ζ q ; ) ∞ - 1 , where $$\zeta $$ is a ...

The current paper studied the concept of right n-derivation satisfying certified conditions on semigroup ideals near-rings and some related properties. Interesting results have been reached, most prominent which are following: Let M be a 3-prime left near-ring A_1,A_2,…,A_n nonzero M, if d is satisfies following conditions,d(u_1,u_2,…,(u_j,v_j ),…,u_n )=0 ∀ 〖 u〗_1 〖ϵA〗_1 ,u_2 〖ϵA〗_2,…,u_j,v_j ϵ...

In this paper, we study additive properties of finite sets lattice points on spheres in three and four dimensions. Thus, given d , m ? N $d,m \in \mathbb {N}$ let A $A$ be a set ( x 1 ? ) Z $(x_1, \dots x_d) {Z}^d$ satisfying 2 + = $x_1^2 x_{d}^2 m$ . When 4 $d=4$ prove threshold breaking bounds for the energy that is, show there are at most O ? | / 3 ? 2766 $O_{\epsilon }(m^{\epsilon }|A|^{2 1...

Abstract In this paper, we introduce and study the numerical semigroups generated by $$\{a_1, a_2, \ldots \} \subset {\mathbb {N}}$$ { a 1 , 2 … } ⊂ N <...

We analyze the Next-to-minimal supersymmetric standard model with Grand unification boundary conditions under current theoretical and experimental constraints. compute mass spectrum of focus on three lightest particles in Higgs sector (two CP-even scalars, $h_1, h_2$, one CP-odd, $a_1$). The reduced couplings such particles, singlet-doublet components, their branching ratios to bosons, cross-se...

The rare decay $B\rightarrow A\gamma$, with $A$ representing axial-vector mesons such as $K_1 (1270),\; K_1 (1400),\; b_1(1300),\; a_1(1260)$, is studied at next-to-leading order (NLO) in soft collinear effective theory (SCET). large outgoing meson energy encourages the study of an appropriate factorization scheme that separates factorizable and non-factorizable parts systematically. We have an...

Let $$A_n=(a_1,a_2,\ldots ,a_n)$$ and $$B_n=(b_1,b_2,\ldots ,b_n)$$ be nonnegative integer sequences with $$A_n\le B_n$$ . The purpose of this note is to give a good characterization such that every sequence $$\pi =(d_1,d_2,\ldots d_n)$$ even sum \pi \le graphic. This solves forcible version problem posed by Niessen generalizes the Erdős–Gallai theorem.