We prove that $D_n(3)$, where $ngeq6$ is even, is uniquely determined by its prime graph. Also, if $G$ is a finite group with the same prime graph as $D_4(3)$, then $Gcong D_4(3), B_3(3), C_3(3)$ or $G/O_2(G)cong {rm Aut}({}^2B_2(8))$.

We establish a duality between the quantum wave vector spectrum and the eigenmodes of the classical Liouvillian dynamics for integrable billiards. Signatures of the classical eigenmodes appear as peaks in the correlation function of the quantum wave vector spectrum. A semiclassical derivation and numerical calculations are presented in support of the results. These classical eigenmodes can be o...

Much is known about the adele ring of an algebraic number field from perspective harmonic analysis and class theory. However, its ring-theoretical aspects are often ignored. Here, we present a description prime spectrum this study some topological properties these ideals. We also how they behave under separable extensions base give indication can be applied in rings not fields.

Due to the increased usage of wireless communications in personal, commercial, and governmental capacities, efficient spectrum utilization has become a prime topic of interest. The Federal Communications Commission (FCC) governs spectrum usage and allocates specific ranges to licensed users. However, some spectrum ranges are overcrowded, while some are under-utilized. The overcrowded spectrum r...

The purpose of this paper is to study topological properties both the set all $k$-prime ideals and congruences for any commutative semiring with zero identity. We first prove that spectrum, i.e. equipped Zariski topology a spectral space, then homeomorphic spectrum respect their topologies.

Many observations about coalgebras were inspired by comparable situations for algebras. Despite the prominent role of prime algebras, the theory of a corresponding notion for coalgebras was not well understood so far. Coalgebras C over fields may be called coprime provided the dual algebra C∗ is prime. This definition, however, is not intrinsic it strongly depends on the base ring being a field...