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 $G/O_2(G)cong {rm Aut}({}^2B_2(8))$.

Quantum mechanical systems whose symmetry is given by $\mathbb{Z}_2^3$-graded version of superconformal algebra are introduced. This done finding a realization Lie superalgebra in terms standard and the Clifford algebra. The allows us to map many models quantum mechanics (SCQM) their extensions. It observed that for simplest SCQM with $\mathfrak{osp}(1|2)$ there exist two inequivalent Applying ...

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.

We describe which topological spaces can arise as the prime spectrum of a commutative monoid, in the spirit of Hochster’s thesis.

As known to us all, it is challenging to monitor wideband signals in frequency domain due to the restriction of hardware. Several practical sampling schemes, such as multicoset sampling and the modulated wideband converter (MWC), have been proposed. In this work, a co-prime array (CA) based modulated wideband converter (MWC) spectrum sensing method is suggested. Our proposed method has the same...

We define the spectrum of a tensor triangulated category K as the set of so-called prime ideals, endowed with a suitable topology. In this very generality, the spectrum is the universal space in which one can define supports for objects of K. This construction is functorial with respect to all tensor triangulated functors. Several elementary properties of schemes hold for such spaces, e.g. the ...