We study unconventional decays of the top-quark and the top-squark in the framework of SUSY models with broken R-parity. The model under study is the MSSM with an additional bilinear term that breaks R-parity. In this model the top-squark behaves similar to a third generation leptoquark. We demonstrate that existing Tevatron data on the top give rise to restrictions on the SUSY parameter space....

We are concerned with the first-order differential system of form $$\left\{ \begin{array}{ll} u'(t)+a(t)u(t)=\lambda b(t) f(v(t-\tau(t))), &t\in\mathbb{R},\\ v'(t)+a(t)v(t)=\lambda b(t)g(u(t-\tau(t))), \end{array} \right. $$ where $\lambda\in\mathbb{R}$~is a parameter. $a,b\in C(\mathbb{R},[0,+\infty))$ two $\omega$-periodic functions such that $\int_0^\omega a(t)\text{d}t>0$,~$\int_0^\omega b(...

‎Let $tau$ be a subgroup functor and $H$ a $p$-subgroup of a finite group $G$‎. ‎Let $bar{G}=G/H_{G}$ and $bar{H}=H/H_{G}$‎. ‎We say that $H$ is $Phi$-$tau$-quasinormal in $G$ if for some $S$-quasinormal subgroup $bar{T}$ of $bar{G}$ and some $tau$-subgroup $bar{S}$ of $bar{G}$ contained in $bar{H}$‎, ‎$bar{H}bar{T}$ is $S$-quasinormal in $bar{G}$ and $bar{H}capbar{T}leq bar{S}Phi(bar{H})$‎. ‎I...

In this paper, we define a new, special second order cone as type-$k$ cone. We focus on the case of $k=2$, which can be viewed SOCO with an additional {\em complicating variable}. For new problem, develop necessary prerequisites, based previous work for traditional SOCO. then primal-dual interior point algorithm solving type-2 conic optimization (SOCO) family kernel functions suitable finally d...

we describe under various conditions abelian subgroups of the automorphism‎ ‎group $mathrm{aut}(t_{n})$ of the regular $n$-ary tree $t_{n}$‎, ‎which are‎ ‎normalized by the $n$-ary adding machine $tau =(e‎, ‎dots‎, ‎e,tau )sigma _{tau‎ ‎}$ where $sigma _{tau }$ is the $n$-cycle $left( 0,1‎, ‎dots‎, ‎n-1right) $‎. ‎as‎ ‎an application‎, ‎for $n=p$ a prime number‎, ‎and for $n=4$‎, ‎we prove that...

Let $H$ be a bialgebra. $\sigma: H\otimes H\to A$ linear map, where $A$ is left $H$-comodule coalgebra, and an algebra with $H$-weak action $\triangleright$. $\tau: B$ $B$ right $\triangleleft$. In this paper, we improve the necessary conditions for two-sided crossed product $A\#^{\sigma} H~{^{\tau}\#} smash coproduct coalgebra $A\times H\times to form bialgebra (called double biproduct) such t...

A natural variant of Lehmer’s conjecture that the Ramanujan $$\tau $$ -function never vanishes asks whether, for any given integer $$\alpha , there exist $$n \in \mathbb {Z}^+$$ such (n) = \alpha . series recent papers excludes many integers as possible values using theory primitive divisors Lucas numbers, computations points on curves, and congruences (n)$$ We synthesize these results methods ...

In this paper, we study the existence of normalized solutions to following nonlinear Choquard equation with exponential growth \begin{align*} \left\{ \begin{aligned} &-\Delta u+\lambda u=(I_{\alpha}\ast F(u))f(u), \quad \hbox{in }\mathbb{R}^{2},\\ &\int_{\mathbb{R}^{2}}|u|^{2}dx=a^{2}, \end{aligned} \right. \end{align*} where $a>0$ is prescribed, $\lambda\in \mathbb{R}$, $\alpha\in(0,2)$, $I_{\...