Let $A(G)$ be the adjacency matrix and $D(G)$ diagonal of vertex degrees a simple connected graph $G$. Nikiforov defined $A_{\alpha}(G)$ convex combinations as $A_{\alpha}(G)=\alpha D(G)+(1-\alpha)A(G)$, for $0\leq \alpha\leq 1$. If $ \rho_{1}\geq \rho_{2}\geq \dots \geq \rho_{n}$ are eigenvalues (which we call $\alpha$-adjacency $G$), \alpha $-adjacency energy $G$ is $E^{A_{\alpha}}(G)=\sum_{i...

In this paper, we are concerned with the fractional and higher order H\'{e}non-Hardy type equations \begin{equation*} (-\Delta)^{\frac{\alpha}{2}}u(x)=f(x,u(x)) \,\,\,\,\,\,\,\,\,\,\,\, \text{in} \,\,\, \mathbb{R}^{n}, \mathbb{R}^{n}_{+} \text{or} \Omega \end{equation*} $n>\alpha$, $0<\alpha<2$ or $\alpha=2m$ $1\leq m<\frac{n}{2}$. We first consider typical case $f(x,u)=|x|^{a}u^{p}$ $a\in(-\al...

In the model of randomly perturbed graphs we consider union a deterministic graph $\mathcal{G}_\alpha$ with minimum degree $\alpha n$ and binomial random $\mathbb{G}(n,p)$. This was introduced by Bohman, Frieze, Martin for Hamilton cycles their result bridges gap between Dirac's theorem results Pósa Korshunov on threshold in this note extend $\mathcal{G}_\alpha\cup\mathbb{G}(n,p)$ to sparser $\...

background: premature ejaculation (pe) is the most common sexual disorder in men and studies reported prevalence up to 30% (1, 2). pe is not a life-threatening medical condition but it influences the quality of life (qol). objectives the aim of this study was to compare the efficiency, and safety of alpha blocker drugs in the treatment of patients with premature ejaculation (pe). additionally w...

There is an extensive literature on the asymptotic order of Sudler's trigonometric product $P_N (\alpha) = \prod_{n=1}^N |2 \sin (\pi n \alpha)|$ for fixed or "typical" values $\alpha$. In present paper we establish a structural result, which given $\alpha$ characterizes those $N$ $P_N(\alpha)$ attains particularly large values. This characterization relies coefficients in its Ostrowski expansi...

In 2013, Huczynska, Mullen, Panario and Thomson introduced the concept of k-normal elements: an element $$\alpha \in {\mathbb {F}}_{q^n}$$ is over $${\mathbb {F}}_q$$ if greatest common divisor polynomials $$g_{\alpha }(x)= \alpha x^{n-1}+\alpha ^qx^{n-2}+\cdots +\alpha ^{q^{n-2}}x+\alpha ^{q^{n-1}}$$ $$x^n-1$$ in {F}}_{q^n}[x]$$ has degree k, generalizing normal elements (normal usual sense 0-...

In this paper, the new notions of ``belongingness ($in_{gamma}$)"and ``quasi-coincidence ($q_delta$)"  of a fuzzy point with a fuzzyset are  introduced. By means of this new idea, the  concept of$(alpha,beta)$-fuzzy $n$-ary subhypergroup of an $n$-aryhypergroup is given, where $alpha,betain{in_{gamma}, q_{delta},in_{gamma}wedge q_{delta}, ivq}$,  andit is shown that, in 16 kinds of $(alpha,beta...