Let R = Zq + uZq, where q = p and u = 0. In this paper, some structural properties of cyclic codes and quasi-cyclic (QC) codes over the ring R are considered. A QC code of length ln with index l over R is viewed both as in the conventional row circulant form and also as an R[x]/(x − 1)-submodule of GR(R, l)[x]/(x − 1), where GR(R, l) is the Galois extension ring of degree l over R. A necessary ...

Rosa persica with a distinctive red eye is a good candidate for addition to the breeding pool of roses. In order to optimize micropropagation of R. persica, three culture media (MS, QL and VS) were compared. The maximum growth rate was observed in the VS medium. Addition of FeEDTA (Fe: 65.4 mg/l), calcium gluconate (Cg: 2.7 g/l) and Gamborg vitamins (B5) instead of VS vitamins, alone or in comb...

The d i s s i p a t i o n o f mechanical energy i n g l a s s e s of t h e " f a s t ion conductor" type (AgI-AgP03, AgI-Ap,B02 and AgC1-CsI) has been s t u d i e d us ing a Rheovibron mechanical ana lyze r i n t h e temperature range -190 t o 200°C. I n most cases a s i n g l e l o s s peak a t low temperature is found f o r fixed-frequency scans . The peak temperature almost co inc ides wi th...

Let v and ω be the velocity and the vorticity of the a suitable weak solution of the 3D Navier-Stokes equations in a space-time domain containing z0 = (x0, t0), and Qz0,r = Bx0,r×(t0−r 2, t0) be a parabolic cylinder in the domain. We show that if v × ω |ω| ∈ L γ,α x,t (Qz0,r) or ω × v |v| ∈ L γ,α x,t (Qz0,r), where L γ,α x,t denotes the Serrin type of class, then z0 is a regular point for v. Th...

In t h i s paper we cons ide r a . spec i f i c type of l o g i c programs ca l led recursive-schema programs and show t h a t the c l ass of r ecu rs i ve -schema programs has s u f f i c i e n t e x p r e s s i v e c a p a b i l i t y , which provides an a l t e r n a t i v e simple proof fo r the resultby Tarnlund concerning the computat ional power of Horn c lause programs. F u r t h e r , ...

Let $\mathcal{L} = -\partial_x^2 - V(x) \partial_y^2$ be the Grushin operator on $\mathbb{R}^2$ with coefficient $V : \mathbb{R} \to [0,\infty)$. Under sole assumptions that $V(-x) \simeq xV'(x)$ and $x^2 |V''(x)| \lesssim V(x)$, we prove a spectral multiplier theorem of Mihlin--H\"ormander type for $\mathcal{L}$, whose smoothness requirement is optimal independent $V$. The assumption second de...