Solutions of the congruence $a^{p-1} \equiv 1 \pmod {p^r}$

Soliton-like Solutions of the Complex Non-linear Klein-Gordon Systems in 1 + 1 Dimensions

In this paper, we present soliton-like solutions of the non-linear complex Klein-Gordon systems in 1+1 dimensions. We will use polar representation to introduce three different soliton-like solutions including, complex kinks (anti-kinks), radiative profiles, and localized wave-packets. Complex kinks (anti-kinks) are topological objects with zero electrical charges. Radiative profiles are object...

On the nature of solutions of the difference equation $mathbf{x_{n+1}=x_{n}x_{n-3}-1}$

We investigate the long-term behavior of solutions of the difference equation[ x_{n+1}=x_{n}x_{n-3}-1 ,, n=0 ,, 1 ,, ldots ,, ]noindent where the initial conditions $x_{-3} ,, x_{-2} ,, x_{-1} ,, x_{0}$ are real numbers.  In particular, we look at the periodicity and asymptotic periodicity of solutions, as well as the existence of unbounded solutions.

Organ-specific distribution of AP-1 in AP-1 luciferase transgenic mice during the maturation process.

Activator protein-1 (AP-1), a dimeric complex consisting of proteins encoded by the jun and fos gene families, is a transcription factor induced by a variety of signals including those eliciting proliferation, differentiation, and neoplastic transformation. Although AP-1 has been widely studied in the last decade, physiological levels of AP-1 in different tissues are unclear. In the present stu...

Characterization of $G_2(q)$, where $2 < q equiv 1(mod 3)$ by order components

In this paper we will prove that the simple group $G_2(q)$, where $2 < q equiv 1(mod3)$ is recognizable by the set of its order components, also other word we prove that if $G$ is a finite group with $OC(G)=OC(G_2(q))$, then $G$ is isomorphic to $G_2(q)$.

NF- B and AP-1 Connection: Mechanism of NF- B-Dependent Regulation of AP-1 Activity