The category of the title is called $mathcal{W}$. This has all free objects $F(I)$ ($I$ a set). For an object class $mathcal{A}$, $Hmathcal{A}$ consists of all homomorphic images of $mathcal{A}$-objects. This note continues the study of the $H$-closed monoreflections $(mathcal{R}, r)$ (meaning $Hmathcal{R} = mathcal{R}$), about which we show ({em inter alia}): $A in mathcal{A}$ if and  only if...

Let $\Omega\subset\mathbb{R}^2$ be a smooth bounded domain with $0\in\partial\Omega$. In this paper, we prove that for any $\beta\in(0,1)$, the supremum $$\sup_{u\in W^{1,2}(\Omega), \int_\Omega u dx=0, \int_\Omega|\nabla u|^2dx\leq1}\int_\Omega \frac{e^{2\pi(1-\beta) u^2}}{|x|^{2\beta}}dx$$ is finite and can attained. This partially generalizes well-known work of Alice Chang Paul Yang (J. Diff...

Abstract We consider a Lévy process Y ( t ) that is not continuously observed, but rather inspected at Poisson( $\omega$ moments only, over an exponentially distributed time $T_\beta$ with parameter $\beta$ . The focus lies on the analysis of distribution running maximum such inspection up to , denoted by $Y_{\beta,\omega}$ Our main result decomposition: we derive remarkable distributional equa...

Intuitionistic Fuzzy Modal Operator was defined by Atanassov in cite{at3}in 1999. In 2001, cite{at4}, he introduced the generalization of thesemodal operators. After this study, in 2004, Dencheva cite{dencheva} definedsecond extension of these operators. In 2006, the third extension of thesewas defined in cite{at6} by Atanassov. In 2007,cite{gc1}, the authorintroduced a new operator over Intuit...

The class A PSE-4 beta-lactamase was used for studying the importance of amino acids in the omega (Omega) loop and its interactions for hydrolysis of beta-lactam antibiotics. By cassette mutagenesis, we replaced the amino acids 163-179 Omega loop in PSE-4 with TEM-1, SHV-1 and Streptomyces albus G beta-lactamase Omega loops. Phenotypic analysis of Escherichia coli recombinants expressing the Om...

"We get a new multiplicity result for gradient systems. Here is very particular corollary: Let $\Omega\subset {\bf R}^n$ ($n\geq 2$) be smooth bounded domain and let $\Phi:{\bf R}^2\to R}$ $C^1$ function, with $\Phi(0,0)=0$, such that $$\sup_{(u,v)\in R}^2}\frac{|\Phi_u(u,v)|+|\Phi_v(u,v)|}{1+|u|^p+|v|^p}<+\infty$$ where $p>0$, $p=\frac{2}{n-2}$ when $n>2$.\\ Then, every convex set $S\...

‎We define hyperbolic harmonic $omega$-$alpha$-Bloch space‎ ‎$mathcal{B}_omega^alpha$ in the unit ball $mathbb{B}$ of ${mathbb R}^n$ and‎ ‎characterize it in terms of‎ ‎$$frac{omegabig((1-|x|^2)^{beta}(1-|y|^2)^{alpha-beta}big)|f(x)-f(y)|}{[x,y]^gamma|x-y|^{1-gamma}‎},$$ where $0leq gammaleq 1$‎. ‎Similar results are extended to‎ ‎little $omega$-$alpha$-Bloch and Besov spaces‎. ‎These obtained‎...

Cholangiocarcinoma is a highly malignant neoplasm of the biliary tree. It has a high rate of mortality, and currently, there is no effective chemoprevention and treatment. This study was designed to investigate the potential effect of omega 3 polyunsaturated fatty acids (omega 3-PUFA) on human cholangiocarcinoma cell growth and to determine their mechanisms of actions. Treatment of three human ...