For a connected reductive group $G$ defined over $\mathbb{F}_q$ and equipped with the induced Frobenius endomorphism $F$, we study relation among following three $\mathbb{Z}$-algebras: (i) $\mathbb{Z}$-model $\mathsf{E}_G$ of algebras Gelfand-Graev representations $G^F$; (ii) Grothendieck $\mathsf{K}_{G^\ast}$ category $G^{\ast F^\ast}$ $\overline{\mathbb{F}_q}$ (Deligne-Lusztig dual side); (ii...

We show that a ring is a Krull ring if and only if every nonzero regular prime ideal contains a t-invertible prime ideal if and only if every proper regular principal ideal is quasi-equal to a product of prime ideals.

Exposure of Venezuelan equine encephalomyelitis (VEE) virus (at -70 C) to 6 x 10 r gamma-radiation (Co) resulted in loss of lethality for young adult mice and guinea pigs, and loss of capacity to produce plaques or cytopathic effects in tissue culture. The suckling mouse was more sensitive for detecting live virus in radiated suspensions than was the adult mouse or guinea pig. Live virus was de...

The concepts of a prime ideal of a distributively generated (d.g.) nearring R, a prime d.g. near-ring and an irreducible R-group are introduced1). The annihilating ideal of an irreducible R-group with an R-generator is a prime ideal. Consequently we define a prime ideal to be primitively prime if it is the annihilating ideal of such an R-group, and a d.g. near-ring to be a primitively prime nea...

Let $$G = (V,E)$$ be a connected simple graph of order p and size q. A G is called local antimagic if admits labeling. bijection $$f \colon E \to \{1,2,\ldots,q\}$$ labeling for any two adjacent vertices $$u$$ $$v$$ , we have $$f^+(u) \ne f^+(v)$$ where \sum_{e\in E(u)} f(e)$$ $$E(u)$$ the set edges incident to . Thus, induces proper vertex coloring assigned color $$f^+(v)$$ The chromatic numbe...

Using Galois theory, we explicitly construct (in all complex dimensions $$g\ge 2$$ ) an infinite family of simple $$g$$ -dimensional tori $$T$$ that enjoy the following properties: $$\bullet$$ Picard number is $$0;$$ in particular, algebraic dimension $$0$$ ; if $$T^\vee$$ dual , then $$\mathrm{Hom}(T,T^\vee)=\{0\}$$ automorphism group $$\mathrm{Aut}(T)$$ isomorphic to $$\{\pm 1\} \times \mathb...

Bound states in the continuum (BIC) are highly confined, nonradiative modes that can exist open structures, despite their potential compatibility and coupling with radiation spectrum, may give rise to resonances arbitrary large lifetimes. Here, we study this phenomenon layered materials featuring epsilon-near-zero constituents. Specifically, outline a systematic procedure synthesize quasi-BIC a...

Let $R$ be a commutative ring. The purpose of this article is to introduce a new class of ideals of R called weakly irreducible ideals. This class could be a generalization of the families quasi-primary ideals and strongly irreducible ideals. The relationships between the notions primary, quasi-primary, weakly irreducible, strongly irreducible and irreducible ideals, in different rings, has bee...