It is known that if the Gaussian curvature function along each meridian on a surface of revolution $(\mathbb{R}^{2}, dr^{2} + m(r)^{2} d\theta^{2})$ decreasing, then cut locus point $\theta^{-1} (0)$ empty or subarc opposite (\pi)$. Such called von Mangoldt's revolution. A generalized Mangoldt For example, m_0(r)^{2} d\theta^{2})$, where $m_{0}(x) = x/(1 x^{2})$, has same structure as above and...

In this paper, we define the almost uniform convergence and the almost everywhere convergence for cone-valued functions with respect to an operator valued measure. We prove the Egoroff theorem for Pvalued functions and operator valued measure θ : R → L(P, Q), where R is a σ-ring of subsets of X≠ ∅, (P, V) is a quasi-full locally convex cone and (Q, W) is a locally ...

This study was performed to evaluate the alterations of glomerular filtration barrier characteristics following acute renal ischemia-reperfusion (I/R). Ischemia was induced in anesthetized rats by unilateral renal artery occlusion for either 20 or 60 min, followed by reperfusion during 20 or 60 min, respectively, with the contralateral kidney serving as control. Sieving coefficients (theta) wer...

Let Σg,r be a compact oriented surface of genus g with r boundary components. We determine the abelianization of the symmetric mapping class group M̂(g,r)(p2) of a double unbranched cover p2 : Σ2g−1,2r → Σg,r using the Riemann constant, Schottky theta constant, and the theta multiplier. We also give lower bounds of the abelianizations of some finite index subgroups of the mapping class group.

We consider minimal graphs $$u = u(x,y) > 0$$ over unbounded domains $$D \subset R^2$$ bounded by a Jordan arc $$\gamma $$ on which . prove sort of reverse Phragmén-Lindelöf theorem showing that if D contains sector $$\begin{aligned} S_{\lambda }=\{(r,\theta )=\{-\lambda /2<\theta<\lambda /2\},\quad \pi <\lambda \le 2\pi , \end{aligned}$$ then the rate growth is at most $$r^{\pi /\lambda }$$

We have obtained the exact-order estimates for some approximative characteristics of Sobolev classes $$ {\mathbbm{W}}_{p,\alpha}^r and Nikоl’skii–Besov {\mathbbm{B}}_{p,\theta}^r periodic functions one several variables in norm space B∞,1. Properties linear operators realizing orders best approximation {\mathbbm{B}}_{\infty, \theta}^r this by trigonometric polynomials generated a set harmonics ...

A new London-Eyring-Polanyi-Sato (LEPS) potential energy surface (PES) is used in the O + CH(4) --> OH + CH(3) reaction via the quasiclassical trajectory method (QCT). Comparing with the experiments and the former ab initio calculations, the new LEPS PES describes the actual potential energy surface of the O + CH(4) reaction successfully. The four polarization dependent "generalized" differenti...

To construct the rotation curve of Galaxy, classical Cepheids with proper motions, parallaxes and line-of-sight velocities from Gaia DR2 Catalog are used in large part. The working sample formed literature data contains about 800 estimates their age. We determined that linear velocity Galaxy at a solar distance is $V_0=240\pm3$~km s$^{-1}$. In this case, Sun to axis found be $R_0=8.27\pm0.10$~k...

We prove the reducibility of 1-D quantum harmonic oscillators in $\mathbb R$ perturbed by a quasi-periodic time potential $V(x,\omega t)$ under following conditions, namely there is $C>0$ such that \begin{equation*} |V(x,\theta)|\le C,\quad|x\partial_xV(x,\theta)|\le C,\quad\forall~(x,\theta)\in\mathbb R\times\mathbb T_\sigma^n. \end{equation*} The corresponding perturbation matrix $(P_i^j(\the...