in this paper, we introduce a method by which we can find a close connection between the set of prime $z$-ideals of $c(x)$ and the same of $c(y)$, for some special subset $y$ of $x$. for instance, if $y=coz(f)$ for some $fin c(x)$, then there exists a one-to-one correspondence between the set of prime $z$-ideals of $c(y)$ and the set of prime $z$-ideals of $c(x)$ not containing $f$. moreover, c...

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...

Given the recent investigation of Clause Management Systems (CMSs) for Artificial Intelligence applications, there is an urgent need for art efficient incremental method for generating prime implicants. Given a set of clauses 5 c, a set of prime implicants 1I of ~ and a clause C, the problem can be formulated as finding the set of prime implicaate for II t.J {C). Intuitively, the property of im...

In this paper we defined prime ideal and maximal ideal and proved several properties of these. We have discussed the space of prime ideals of a C-algebra A with respect to the hull-kernel topology, which is called the prime spectrum of A and denoted by Spec A. It is also proved that Spec A is a T0 space.

in a previous paper, the second author established that, given finite fields $f < e$ and certain subgroups $c leq e^times$, there is a galois connection between the intermediate field lattice ${l mid f leq l leq e}$ and $c$'s subgroup lattice. based on the galois connection, the paper then calculated the irreducible, complex character degrees of the semi-direct product $c rtimes {rm gal} (e/f)$...