For a monochrome layer $x$ of opacity $0\le o_x\le1 $ placed on another monochrome layer of opacity 1, the result given by the standard formula is $$\small\Pi\left({\bf C}_\varphi\right)=1+\sum_{n=1}^2\left(2-n-(-1)^no_{\chi(\varphi+1)}\right)\left(\chi(n+\varphi-1)-o_{\chi(n+\varphi-1)}\right),$$ the formula being of course explained in detail in this paper. We will eventually deduce a very si...

In this paper, we introduce the notions of fuzzy $alpha$-Geraghty contraction type mapping and fuzzy $beta$-$varphi$-contractive mapping and establish some interesting results on the existence and uniqueness of fixed points for these two types of mappings in the setting of fuzzy metric spaces and non-Archimedean fuzzy metric spaces. The main results of our work generalize and extend some known ...

In this work we study the monodromy group of covers $\varphi \circ \psi$ curves \linebreak $\mathcal{Y}\xrightarrow {\quad {\psi}} \mathcal{X} \xrightarrow \varphi} \mathbb{P}^{1}$, where $\psi$ is a $q$-fold cyclic \'etale cover and $\varphi$ totally ramified $p$-fold cover, with $p$ $q$ different prime numbers odd. We show that Galois $\mathcal{G}$ closure $\mathcal{Z}$ form $ \mathcal{G} = \...

For a fixed graph $H$, the reconfiguration problem for $H$-colourings (i.e. homomorphisms to $H$) asks: given a graph $G$ and two $H$-colourings $\varphi$ and $\psi$ of $G$, does there exist a sequence $f_0,\dots,f_m$ of $H$-colourings such that $f_0=\varphi$, $f_m=\psi$ and $f_i(u)f_{i+1}(v)\in E(H)$ for every $0\leq i<m$ and $uv\in E(G)$? If the graph $G$ is loop-free, then this is the equiva...

(3) JC'C' and (3) JHNHα couplings are related to the intervening backbone torsion angle ${\varphi }$ by standard Karplus equations. Although these couplings are known to be affected by parameters other than ${\varphi }$, including H-bonding, valence angles and residue type, experimental results and quantum calculations indicate that the impact of these latter parameters is typically very small....

Emulsions of water in as-recovered native crude oils of diverse geographical origin evidently possess some common morphological features. At low volume fractions varphi of water, the viscosity behavior of emulsions is governed by the presence of flocculated clusters of water droplets, whereas characteristic tight gels, composed of visually monodisperse small droplets, are responsible for the vi...

The purpose of this paper is to present a best proximity point theorems through rational expression for a combination of contraction condition, Kannan and Chatterjea nonlinear cyclic contraction in what we call MT-K and MT-C rational cyclic contraction. Some best proximity point theorems for a mapping satisfy these conditions have been established in metric spaces. We also give some examples to...

In this paper, we prove some common fixed point theorems for co-cyclic weak contractions in compact metric spaces. Keywords—Cyclic weak contraction, Co-cyclic weak contraction, Co-cyclic representation, Common fixed point.

The purpose of this study was to determine whether cyclic guanosine monophosphate inhibits contraction through inhibition of phosphatidylinositol hydrolysis. Sodium nitroprusside and atriopeptin II, agents which activate soluble and particulate guanylate cyclase, respectively, inhibited norepinephrine-induced contraction and accumulation of inositol monophosphate, a measure of phosphatidylinosi...