1389 with u(w; s) = jwj1u(^ w; s) where ^ w = w=jwj1. For any w 2 R 2 and s 2 f0; 1g; jz(w;s)j 1 6jwj 1. We now turn our attention to signals w(k) 2 l n 1 and w(t) 2 L n 1 , and to distinguish them from vectors in R n we will use boldface type.

Explicit formulae for τ ′ r(L(p, q)) and τ(L(p, q)) are obtained for all L(p, q). There are three systems of invariants of Witten-type for closed oriented 3manifolds: 1. {τr(M), r ≥ 2; τ ′ r(M), r odd ≥ 3}, where τr was defined by Reshetikhin and Turaev [1], and τ ′ r was defined by Kirby-Melvin [2] 2. {Θr(M,A), r ≥ 1,whereA is a 2r-th primitive root of unity} defined by Blanchet, Habegger, Mas...

In this letter, we investigate the cosmic expansion scenario of universe in framework $f(R,L_m)$ gravity theory. We consider a non-linear model, specifically, $f(R,L_m)=\frac{R}{2}+L_m^n + \beta$, where $n$ and $\beta$ are free model parameters. Then derive motion equations for flat FLRW obtain exact solution corresponding field equations. estimate best fit ranges parameters by using updated $H...

On the basis of molecular genetic analysis intron-1 nuclear serum albumin gene (SAI-1) were identified 177 individuals Pelophylax esculentus complex 9 localities Belgorod. Two types population systems R and RE identified. Pure populations L-type, E-type LE-type as well P. lessonae not