In this paper, for an odd prime p, the differential spectrum of the power function x pk+1 2 in Fpn is calculated. For an odd prime p such that p ≡ 3 mod 4 and odd n with k|n, the differential spectrum of the power function x pn+1 pk+1 + p n −1 2 in Fpn is also derived. From their differential spectrums, the differential uniformities of these two power functions are determined. We also find some...

In this paper a bijection between the set of prime ideals of a Leavitt path algebra L K (E) and a certain set which involves maximal tails in E and the prime spectrum of K[x, x −1 ] is established. Necessary and sufficient conditions on the graph E so that the Leavitt path algebra L K (E) is primitive are also found.

The frequency of occurrence of prime numbers at unit number spacing intervals exhibits selfsimilar fractal fluctuations concomitant with inverse power law form for power spectrum generic to dynamical systems in nature such as fluid flows, stock market fluctuations, population dynamics, etc. The physics of long-range correlations exhibited by fractals is not yet identified. A recently developed ...

Let S0 (p) denote the sphere spectrum localized at an odd prime p. Then we have the first beta element β1 ∈ π2p2−2p−2(S (p)), whose cofiber we denote by W . We also consider a generalized Smith-Toda spectrum Vr characterized by BP∗(Vr) = BP∗/(p, vr 1). In this note, we show that an element of π∗(Vr ∧W ) gives rise to a beta element of homotopy groups of spheres. As an application, we show the e...

Let $R$ be a commutative ring with identity and $M$ be a unitary$R$-module. The primary-like spectrum $Spec_L(M)$ is thecollection of all primary-like submodules $Q$ such that $M/Q$ is aprimeful $R$-module. Here, $M$ is defined to be RSP if $rad(Q)$ isa prime submodule for all $Qin Spec_L(M)$. This class containsthe family of multiplication modules properly. The purpose of thispaper is to intro...

Let G be a finite group and let $GK(G)$ be the prime graph of G. We assume that $n$ is an odd number. In this paper, we show that if $GK(G)=GK(B_n(p))$, where $ngeq 9$ and $pin {3,5,7}$, then G has a unique nonabelian composition factor isomorphic to $B_n(p)$ or $C_n(p)$ . As consequences of our result, $B_n(p)$ is quasirecognizable by its spectrum and also by a new proof, the ...

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

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.