Let p be a prime number and Zp be the cyclic group of order p. A coloring of Zp is called rainbow–free with respect to a certain equation, if it contains no rainbow solution of the equation, that is, a solution whose elements have pairwise distinct colors. In this paper we describe the structure of rainbow–free 3–colorings of Zp with respect to all linear equations on three variables. Consequen...

The ideals of the ring Zp are {0} and pZp, n ≥ 0. From this it follows that Zp is a discrete valuation ring, a principal ideal domain with exactly one maximal ideal, namely pZp; Zp is the valuation ring of Qp with the valuation vp. For n ≥ 1, Zp/pZp is isomorphic as a ring with Z/pZ. |x|p = p−vp(x), dp(x, y) = |x− y|p. With the topology induced by the metric dp, Qp is a locally compact abelian ...

BACKGROUND The human egg coat, zona pellucida (ZP), is composed of four glycoproteins designated as zona pellucida glycoprotein-1 (ZP1), -2 (ZP2), -3 (ZP3) and -4 (ZP4) respectively. The zona proteins possess the archetypal 'ZP domain', a signature domain comprised of approximately 260 amino acid (aa) residues. In the present manuscript, attempts have been made to delineate the functional signi...

Although zomepirac (ZP) and tolmetin (TM) induce anaphylactic reactions and form reactive acyl glucuronides, a direct link between the two events remains obscure. We report herein that, in addition to acyl glucuronidation, both drugs are subject to oxidative bioactivation. Following incubations of ZP with human liver microsomes fortified with NADPH and glutathione (GSH), a metabolite with an MH...

The far-infrared properties of spruce wood are examined with a terahertz time-domain spectrometer. The solid wood is shown to exhibit both birefringence and diattenuation. The birefringence properties are sufficient for construction of a quarter-wave plate operating at 0.36 THz, and a half-wave plate operating at 0.71 THz. The origin of the birefringence is attributed to preferential fiber orie...

let $p$ be an analytic function defined on the open unit disc $mathbb{d}$ with $p(0)=1.$ the conditions on $alpha$ and $beta$ are derived for $p(z)$ to be subordinate to $1+4z/3+2z^{2}/3=:varphi_{c}(z)$ when $(1-alpha)p(z)+alpha p^{2}(z)+beta zp'(z)/p(z)$ is subordinate to $e^{z}$. similar problems were investigated for $p(z)$ to lie in a region bounded by lemniscate of bernoulli $|w^{2}-1...

The zona pellucida (ZP) is the spherical layer that surrounds the mammalian oocyte. The physical hardness of this layer plays a crucial role in fertilization and is largely unknown because of the lack of appropriate measuring and modelling methods. The aim of this study is to measure the biomechanical properties of the ZP of human/mouse ovum and to test the hypothesis that Young's modulus of th...

Mitotic apparatus (MA) were isolated from sea-urchin zygotes using glycerol-dimethyl-sulphoxide. Cold treatment had no effect on MA birefringence when MA were in isolation medium, but caused a 10-15% reduction of MA birefringence when MA were in quarter-strength isolation medium. Pressure treatment also caused a reduction in MA birefringence, but the cold and pressure treatments were not additi...

Throughout this paper, let p be a fixed odd prime number. The symbol, Zp, Qp and Cp denote the ring of p-adic integers, the field of p-adic rational numbers and the completion of algebraic closure of Qp. Let N be the set of natural numbers and Z+ = N ∪ {0}. As well known definition, the p-adic absolute value is given by |x|p = p−r where x = p t s with (t, p) = (s, p) = (t, s) = 1. When one talk...