We say that a positive integer $d$ is special number of degree $n$ if for every $m$, there exist nonzero integers $a,b,c$ such $m=a^n+b^n-dc^n$. In this paper, we investigate some necessary conditions on existing $n$.

Up to now, various empty carbon fullerenes with different magic number "n", such as C10, Cow Cm, Cso,Cis** Cm and so on. have been obtained. The calix[n]arenes are a class of chalice-like rnacrocyclicmolecules that have attracted widespread attention as complex molecules with liquid crystal behaviors.These classes of compounds are cyclic ohgomers synthessid by condensation of a para-alkylated p...

background: telomerase activity increases in cancer cells. bcl-2 is an antiapoptotic factor that its concentration grows in many cancer cells including hepatocellular carcinoma cells. in this study, an attempt was made to investigate the effects of a new synthetic compound, platinum azidothymidine (pt-azt) on treatment of rats with hepatocellular carcinoma (hcc) and to compare its effects with ...

let$ p_{n}(x)= sum_{i=0}^{n} a_{i}x^{i}$ be a random algebraicpolynomial, where $a_{0},a_{1}, cdots $ is a sequence of independent random variables belong to the domain of attraction of the normal law. thus $a_j$'s for $j=0,1cdots $ possesses the characteristic functions $exp {-frac{1}{2}t^{2}h_{j}(t)}$, where $h_j(t)$'s are complex slowlyvarying functions.under the assumption that th...

One of the most important challenges in information networks is to gather data from a larger set nodes smaller nodes. This can be done via use concentrator architecture connection topology. paper proof-of-concept that demonstrates quantum-based controller large interconnection asymptotically perform this task faster. We specifically present quantum algorithms for routing concentration assignmen...

In this research paper, we found both numerical and analytical solutions for the effect of chemical reaction on unsteady, incompressible, viscous fluid flow past an exponentially accelerated vertical plate with heat absorption and variable temperature in a magnetic field. The flow problem is governed by a system of coupled non-linear partial differential equations with suitable boundary conditi...