An element $a$ in a ring $R$ is very clean in case there exists‎ ‎an idempotent $ein R$ such that $ae = ea$ and either $a‎- ‎e$ or $a‎ + ‎e$ is invertible‎. ‎An element $a$ in a ring $R$ is very $J$-clean‎ ‎provided that there exists an idempotent $ein R$ such that $ae =‎ ‎ea$ and either $a-ein J(R)$ or $a‎ + ‎ein J(R)$‎. ‎Let $R$ be a‎ ‎local ring‎, ‎and let $sin C(R)$‎. ‎We prove that $Ain K_...

Abstract We have identified the decay modes of $$D_s^+ \rightarrow \pi ^+ K^{*+} K^{*-} , K^{*0} \bar{K}^{*0}$$ D s + → π K ∗ <mml:m...

Let $M_R$ be a module with $S=End(M_R)$. We call a submodule $K$ of $M_R$ annihilator-small if $K+T=M$, $T$ a submodule of $M_R$, implies that $ell_S(T)=0$, where $ell_S$ indicates the left annihilator of $T$ over $S$. The sum $A_R(M)$ of all such submodules of $M_R$ contains the Jacobson radical $Rad(M)$ and the left singular submodule $Z_S(M)$. If $M_R$ is cyclic, then $A_R(M)$ is the unique ...

We extend the notion of singular vectors to context Diophantine approximation real numbers with elements a totally number field K. For $$m\ge 1$$ , we establish version Dani’s correspondence in fields and prove that under class ‘friendly measures’ $$K_S^m$$ set has measure zero. Here S is Archimedean valuations K $$K_S$$ product completions $$\sigma (K)$$ \in S$$ . On other hand, show existence...

let $m_r$ be a module with $s=end(m_r)$. we call a submodule $k$ of $m_r$ annihilator-small if $k+t=m$, $t$ a submodule of $m_r$, implies that $ell_s(t)=0$, where $ell_s$ indicates the left annihilator of $t$ over $s$. the sum $a_r(m)$ of all such submodules of $m_r$ contains the jacobson radical $rad(m)$ and the left singular submodule $z_s(m)$. if $m_r$ is cyclic, then $a_r(m)$ is the unique ...

Based on an $e^{+}e^{-}$ collision data sample corresponding to integrated luminosity of 2.93 $\mathrm{fb}^{-1}$ collected with the BESIII detector at $\sqrt{s}=3.773 \mathrm{GeV}$, first amplitude analysis singly Cabibbo-suppressed decay $D^{+}\to K^+ K_S^0 \pi^0$ is performed. From analysis, $K^*(892)^+ K_S^0$ component found be dominant a fraction $(57.1\pm2.6\pm4.2)\%$, where uncertainty st...

Using the in-viscid two-field reduced MHD model, a new analytical theory is developed to unify Hahm-Kulsrud-Taylor (HKT) linear solution and Rutherford quasi-linear regime. Adopting approach, we obtain closed system of equations for plasma response in static slab geometry. An integral form obtained forced magnetic reconnection, uniformly valid throughout entire regimes from HKT solution. In par...

The extinction law from $0.9$ to $8$ microns in the inner $3\times3$ deg$^2$ of Milky Way is measured using data VISTA Variables Via Lactea, GLIMPSE and WISE. Absolute ratios are found by requiring that observed red clump density peaks at GRAVITY collaboration distance Galactic centre. When combined with selective bulge giant colour-colour diagrams, we find an $A_Z:A_Y:A_J:A_H:A_{K_s}:A_{W1}:A_...