Convergence of ray sequences of Padé approximants for 2 f 1(a, 1; c; z), (c > a > 0)

The Padé table of ₂ F ₁(a, 1; c; z) is normal for c > a > 0 (cf. [4]). For m ≥ n - 1 and c ? Z^-, the denominator polynomial Q _mn (z) in the [m/n] Padé approximant P _mn (z)/Q _mn (z) for ₂ F ₁(a, 1; c; z) and the remainder term Q _mn (z)₂ F ₁(a, 1; c; z)-P_mn (z) were explicitly evaluated by Padé (cf. [2], [6] or [9]). We show that for c > a > 0 and m ≥ n - 1, the poles of P_mn (z)/Q_mn (z) lie on the cut (1,∞). We deduce that the sequence of approximants P_mn (z)/Q_mn (z) converges to ₂ F ₁(a, 1; c; z) as m → ∞, n/m → ρ with 0 < ρ ≤ 1, uniformly on compact subsets of the unit disc |z| < 1 for c > a > 0.     

关于一类波方程的非线性本征值问题的注记

本文推广[1]中关于问题[Ⅰ] 的无穷多对本征值,本征函数存在性定理到p>2的情形.当p=2时,所考虑的空间是Hilbert空间,可利用相应线性算子的本征函数展开;当p>2时,我们的工作空间是Banach空间.我们利用空间L~p和其对偶空间L~p(?)上的Hausdorff-Young不等式对泛函数估值,从而证明了相应的定理.     

The Extensions of Gravitational Soliton Solutions with Real Poles

We analyse vacuum gravitationalsoliton solutions with real poles in thecosmological context. It is well known that thesesolutions contain singularities on certain nullhypersurfaces. Using a Kasner seed solution, we demonstrate thatthese may contain thin sheets of null matter or may besimple coordinate singularities, and we describe anumber of possible extensions through them.     

Virtual Screening in Search for a Chemical Probe for Angiotensin-Converting Enzyme 2 (ACE2)

We elaborate new models for ACE and ACE2 receptors with an excellent prediction power compared to previous models. We propose promising workflows for working with huge compound collections, thereby enabling us to discover optimized protocols for virtual screening management. The efficacy of elaborated roadmaps is demonstrated through the cost-effective molecular docking of 1.4 billion compounds. Savings of up to 10-fold in CPU time are demonstrated. These developments allowed us to evaluate ACE2/ACE selectivity in silico, which is a crucial checkpoint for developing chemical probes for ACE2.     

三硝基均苯三酚金属(Li,Na, K,Mg)化合物的快速热分解

利用温度快速跃升傅立叶变换红外(T-jump/FTIR)原位分析技术对三硝基均苯三酚(TNPG, 2,4,6-三硝基-1,3,5-苯三酚)的锂、钠、钾、镁金属盐的快速热分解反应过程进行了系统研究. 确定了三硝基均苯三酚系列化合物快速热分解过程产生的可挥发金属化合物的类型, 得到了快速热分解过程主要红外活性气体产物的种类、分布及浓度随时间的变化关系曲线, 提出了其快速热分解方程式. 利用计算机模拟方法, 采用REAL程序对三硝基均苯三酚系列化合物的燃烧性能(燃烧产物和燃烧温度等参数)进行了计算, 与T-jump/FTIR分析技术得到的实验结果进行比较分析和讨论.