The static power consumprion is analysed with taking into account reverse biased p_n jun;ti; current and MOSFET leakage current. The p_n junction reverse current is assessed as a sum of saturation I, and generation I*.n .o,r,fon"nrr. fl. donrinant leakage cument of MId structirc for deep s,ubmigro.n technologies is subthrc_sholA .rrrcnt I,"u [2], thus this. is the only con'lponcnt considc.rcd. ...

An r-dynamic coloring of a graph G is proper such that every vertex in V(G) has neighbors at least $\min\{d(v),r\}$ different color classes. The chromatic number denoted as $\chi_r (G)$, the k coloring. In this paper we obtain central graph, middle total line para-line and sub-division comb $P_n\odot K_1$ by $C(P_n\odot K_1), M(P_n\odot T(P_n\odot L(P_n\odot P(P_n\odot K_1)$ $S(P_n\odot respect...

We obtain a lower bound for $$\#\{x/2<p_n\leq x \colon\, \, p_n\equiv\dots\equiv p_{n+m}\equiv a\pmod{q}$$ , $$p_{n+m} - p_n\leq y\}$$ where $$p_n$$ is the $$n$$ th prime.

In this paper we prove that all pure Artin braid groups $$P_n$$ ( $$n\ge 3$$ ) have the $$R_\infty $$ property. order to obtain result, analyse naturally induced morphism $${\text {Aut}}\left( {P_n}\right) \longrightarrow {\text {\Gamma _2 (P_n)/\Gamma _3(P_n)}\right) which turns out factor through a representation $$\rho :S_{{n+1}} . We can then use theory of symmetric show any automorphism $$...

Let $P_n(y_1,\ldots,y_n):= \prod_{1\leq i<j\leq n}\left( 1 -\frac{y_i}{y_j}\right) $ and $P_n:= \sup_{(y_1,\ldots,y_n)}P_n(y_1,\ldots,y_n) where the supremum is taken over $n$-ples $(y_1,\ldots,y_n)$ of real numbers satisfying $0 <|y_1| < |y_2|< \cdots |y_n|$. We prove that $P_n \leq 2^{\lfloor n/2\rfloor}$ for every $n$, i.e., we extend to all $n$ bound Pohst proved $n\leq 11$. As a consequenc...

Abstract Let $x_1, \dots , x_n$ be $n$ independent and identically distributed real-valued random variables with mean zero, unit variance, finite moments of all remaining orders. We study the polynomial $p_n$ having roots at x_n$. prove that for $\ell \in \mathbb{N}$ fixed as $n \rightarrow \infty $, $(n-\ell )-$th derivative $p_n^{}$ behaves like a Hermite polynomial: $x$ in compact interval, ...