In this work we set up the generating function of ultimate time survival probability $\varphi(u+1)$, where $$\varphi(u)=\mathbb{P}\left(\sup_{n\geqslant 1}\sum_{i=1}^{n}\left(X_i-\kappa\right)<u\right)$$ and $u\in\mathbb{N}_0,\,\kappa\in\mathbb{N}$, random walk $\left\{\sum_{i=1}^{n}X_i,\,n\in\mathbb{N}\right\}$ consists independent identically distributed variables $X_i$, which are non-negativ...

A well-known result of Ajtai Komlós, Pintz, Spencer, and Szemerédi (J. Combin. Theory Ser. 32 (1982), 321–335) states that every k $$ -graph H on n vertices, with girth at least five, average degree t − 1 {t}^{k-1} contains an independent set size c ( log ) / cn{\left(\log t\right)}^{1/\left(k-1\right)}/t for some > 0 c>0 . In this paper we show the same can be found under weaker conditions all...

The ‘midpoint’ approximation to the integral $$\int_0^1 f $$ is $${M_n}\left( \right) = {1 \over n}\sum\limits_{r 1}^n \left( {{{2r - 1} {2n}}} \right)$$ .

We say that G → ( F , H ) $$ G\to \left(F,H\right) if, in every edge coloring c : E { 1 2 } c:E(G)\to \left\{1,2\right\} we can find either a 1-colored copy of or 2-colored . The well-known states the threshold for property n p G\left(n,p\right)\to is equal to − / m {n}^{-1/{m}_2\left(F,H\right)} where {m}_2\left(F,H\right) given by = max e J v + ⊆ ≥ {m}_2\left(F,H\right):= \max \left\{\frac{e(...

In this paper, we deal with quasilinear Keller–Segel systems indirect signal production, u t = ∇ · ( + 1 ) m − v , x ∈ Ω > 0 Δ μ w $$ \left\{\begin{array}{ll}{u}_t&#x0003D;\nabla \cdotp \left({\left(u&#x0002B;1\right)}&#x0005E;{m-1}\nabla u\right)-\nabla \left(u\nabla v\right),& x\in \Omega, t>0,\\ {}0&#x0003D;\Delta v-\mu (t)&#x0002B;w,& {}{w}_t&#x0002B;w&#x0003D;u,& t>0,\end{array}\right. com...

background: venoarterial extracorporeal membrane oxygenation (ecmo) provides systemic arterial support without directly unloading the left heart, which causes an elevated left ventricular (lv) pressure. the aim of the present study was to investigate the adjunctive application of the impella device for lv unloading in patients during ecmo. methods: this retrospective cohort study included patie...

OBJECTIVES To describe our preferred method of right laparoscopic live donor nephrectomy (LDN) using a retroperitoneoscopic approach to determine the indications for, and overall rate of, right LDN and to compare the donor and recipient early outcomes of right retroperitoneal LDN to those of left transperitoneal LDN in a consecutive single-institution series. METHODS At our institution, LDN f...

For the Cauchy problem$$ {\displaystyle \begin{array}{c}{L}_1u\equiv Lu+\left(b,\nabla u\right)+ cu-{u}_t=0,\kern0.5em \left(x,t\right)\in D,\\ {}u\left(x,0\right)={u}_0(x),\kern1em x\in {\mathbb{R}}^N,\end{array}} $$for a nondivergent parabolic equation with growing lower-order term in half-space \( \overline{D}={\mathbb{R}}^N\times \left[0,\left.\infty \right)\right. \), N ≥ 3, we prove suffi...

The coupling reaction mechanisms of the Rh(iii)-catalyzed redox-neutral C7-selective aryl C-H functionalization of indolines with alkynes and alkenes have been theoretically investigated with the aid of the density functional theory (DFT) calculations. Our calculation results indicate that the active catalyst in this system is the cationic species [Cp*Rh(OAc)]+ (2cat) instead of the neutral spe...