the rings considered in this article are  commutative  with identity which admit at least two  nonzero annihilating ideals. let $r$ be a ring. let $mathbb{a}(r)$ denote the set of all annihilating ideals of $r$ and let $mathbb{a}(r)^{*} = mathbb{a}(r)backslash {(0)}$. the annihilating-ideal graph of $r$, denoted by $mathbb{ag}(r)$  is an undirected simple graph whose vertex set is $mathbb{a}(r)...

In the $B^+\to D^+ D^-K^+$ decay, LHCb has reported observation of open-charm exotic states $X_{0,1}^0\equiv X_{0,1}(2900)^0$ with four different quark flavors~$(ud\bar s \bar c)$, where subscripts (0,1) denote spins. To confirm discovery, we propose $\Lambda_b\to \Sigma_c^{0(++)} X_{0,1}^{\prime\,0(--)}$ in final state interaction, $X_{0,1}^{\prime\,0(--)}$ $s u\bar d c$ ($ds\bar u c$) are new...

We present a search for the dark photon $A^{\prime}$ in $B^0 \to A^{\prime} A^{\prime}$ decays, where subsequently decays to $e^+ e^-$, $\mu^+ \mu^-$, and $\pi^+ \pi^-$. The is performed by analyzing $772 \times 10^6$ $B\overline{B}$ events collected Belle detector at KEKB e^-$ energy-asymmetric collider $\Upsilon (4S)$ resonance. No signal found mass range $0.01~\mathrm{GeV}/c^2 \le m_{A^{\pri...

We study the charmless two-body decays of $B\to {\bf B}_n \overline{\bf B}_n^\prime$ with $B = ( B^+ , B^0 B^0_s)$ and ${\bf B}_n^{(\prime)}$ low-lying octet baryons. The factorizable amplitudes are calculated by modified bag model, while nonfactorizable ones extracted from experimental data $SU(3)_F$ flavor symmetry. able to explain all current measurements provide predictions on decay branchi...

In this research, we develop some differential subordination results involving harmonic means of $f_{b}(z),f_{b}(z)+zf_{b}^{\prime}(z)$ and $f_{b}(z)+\frac{zf_{b}^{\prime}(z)}{f_{b}(z)},$ where $f_{b}(z)=\frac{z}{\left(1-z^{n}\right) ^{b}},$ $b\geq0;n\in\mathbb{N}=1,2,3...$ is an $n$-fold symmetric Koebe type functions defined in the unit disk with $f_{b}(0)=0,f_{b}^{\prime}(z)\neq0.$ By using ...

We examine the computably enumerable (c.e.) degrees of prime models of complete atomic decidable (CAD) theories. A structure has degree d if d is the degree of its elementary diagram. We show that if a CAD theory T has a prime model of c.e. degree c, then T has a prime model of strictly lower c.e. degree b, where, in addition, b is low (b′ = 0′). This extends Csima’s result that every CAD theor...

In this paper, we introduce a new generalization of weakly prime ideals called $I$-prime. Suppose $R$ is a commutative ring with identity and $I$ a fixed ideal of $R$. A proper ideal $P$ of $R$ is $I$-prime if for $a, b in R$ with $ab in P-IP$ implies either $a in P$ or $b in P$. We give some characterizations of $I$-prime ideals and study some of its properties.  Moreover, we give conditions  ...