有界凸圆型域上的准凸映照

本文研究星形映照的一类子族——有界凸圆型城上的准凸映照,并讨论了它与星形映照及凸映照的关系,建立其与凸映照同形的增长定理和掩盖定理．     

一类函数方程的Cm解的存在性和惟一性

本文讨论了较为广泛的一类函数方程G（x,f(x),f^2(H2(x,f(x)),…,f^n(Hn(x,f(x),…,f^n-1(x))))=0, 对任x∈J.其中n≥,J为实数轴R 的连通闭子集,G∈C^m(J^n 1,R),Hk∈C^m(J^k,R),k=2,…,n.对任一个整数m≥0,本文在较弱的条件下讨论下该方程的C^m解的存在性和惟一性。     

Global and uniform convergence of subspace correction methods for some convex optimization problems

This paper gives some global and uniform convergence estimates for a class of subspace correction (based on space decomposition) iterative methods applied to some unconstrained convex optimization problems. Some multigrid and domain decomposition methods are also discussed as special examples for solving some nonlinear elliptic boundary value problems.

     

Method for studying boundary value problems with nonlinear boundary conditions

A constructive approach to the determination of an approximate solution of a boundary value problem with nonlinear boundary conditions g[z (0), z (T)]=0 is proposed. Existence of the exact solution is proved, and error estimates for the constructed approximate solution are provided.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 7, pp. 951–957, July, 1990.     

汽车尾气颗粒物的STXM和NEXAFS研究

为了研究汽车尾气颗粒物的结构和氮的种态,使用扫描透射X射线显微成像(STXM)技术研究了桑塔纳3000和高尔汽车尾气颗粒物.STXM表明单颗粒物的粒径为500nm,颗粒物质量分布不均匀,有中间空洞.比较汽车尾气颗粒物和(NH4)2SO4和NaNO3中N的1sX射线近边吸收精细结构谱(NEXAFS),铵盐在406eV有显著的σ*吸收峰,有肩部结构;汽车尾气颗粒物和NaNO3中N的近边吸收谱在412eV和418.5eV有明显的σ吸收峰;(NH4)2SO4中N的近边吸收谱在413.5eV和421.8eV更宽的σ吸收峰.硝酸盐是汽车尾气颗粒物中的N化学种态的主要存在形式.在395—418eV能量范围内对桑塔纳3000汽车尾气颗粒物进行堆栈扫描,经过主成分分析和聚类分析,发现其表层主要为硝酸盐,内部有少量铵盐.     

On the convergence of hybrid polynomial approximation to higher derivatives of rational curves

In this paper, we derive the bounds on the magnitude of l  th (l=2,3)$(l=2,3)$ order derivatives of rational Bézier curves, estimate the error, in the _L∞$L_{\infty }$ norm sense, for the hybrid polynomial approximation of the l  th (l=1,2,3)$(l=1,2,3)$ order derivatives of rational Bézier curves. We then prove that when the hybrid polynomial approximation converges to a given rational Bézier curve, the l  th (l=1,2,3)$(l=1,2,3)$ derivatives of the hybrid polynomial approximation curve also uniformly converge to the corresponding derivatives of the rational curve. These results are useful for designing simpler algorithms for computing tangent vector, curvature vector and torsion vector of rational Bézier curves.     

Distortion theorem for Bloch mappings on the unit ball <Emphasis Type="Italic">ℬ</Emphasis><Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>

In this paper, we obtain a version of subordination lemma for hyperbolic disk relative to hyperbolic geometry on the unit disk D. This subordination lemma yields the distortion theorem for Bloch mappings f ∈ H（B^n） satisfying ｜｜f｜｜0 = 1 and det f＇（0） = α ∈ （0, 1], where｜｜f｜｜0 = sup{（1 - ｜z｜^2 ）n＋1/2n det（f＇（z））[1/n ： z ∈ B^n}. Here we establish the distortion theorem from a unified perspective and generalize some known results. This distortion theorem enables us to obtain a lower bound for the radius of the largest univalent ball in the image of f centered at f（0）. When a = 1, the lower bound reduces to that of Bloch constant found by Liu. When n = 1, our distortion theorem coincides with that of Bonk, Minda and Yanagihara.     

Balancing the Rate of Cluster Growth and Etching for Gram‐Scale Synthesis of Thiolate‐Protected Au25 Nanoclusters with Atomic Precision

We report a NaOH‐mediated NaBH₄ reduction method for the synthesis of mono‐, bi‐, and tri‐thiolate‐protected Au₂₅ nanoclusters (NCs) with precise control of both the Au core and thiolate ligand surface. The key strategy is to use NaOH to tune the formation kinetics of Au NCs, i.e., reduce the reduction ability of NaBH₄ and accelerate the etching ability of free thiolate ligands, leading to a well‐balanced reversible reaction for rapid formation of thermodynamically favorable Au₂₅ NCs. This protocol is facile, rapid (≤3 h), versatile (applicable for various thiolate ligands), and highly scalable (>1 g Au NCs). In addition, bi‐ and tri‐thiolate‐protected Au₂₅ NCs with adjustable ratios of hetero‐thiolate ligands were easily obtained. Such ligand precision in molecular ratios, spatial distribution and uniformity resulted in richly diverse surface landscapes on the Au NCs consisting of multiple functional groups such as carboxyl, amine, and hydroxy. Analysis based on NMR spectroscopy revealed that the hetero‐ligands on the NCs are well distributed with no ligand segregation. The unprecedented synthesis of multi‐thiolate‐protected Au₂₅ NCs may further promote the practical applications of functional metal NCs.     

Synthesis and Antiviral Bioactivity of Novel 2‐Substituted Methlthio‐5‐(4‐Amino‐2‐Methylpyrimidin‐5‐yl)‐1,3,4‐Thiadiazole Derivatives

A series of novel 2‐substituted methlthio‐5‐(4‐amino‐2‐methylpyrimidin‐5‐yl‐)‐1,3,4‐thiadiazole derivatives were synthesized, characterized and evaluated for antiviral activities against tobacco mosaic virus (TMV). The preliminary biological results indicated that most compounds exhibit excellent antiviral activity against TMV in vivo. Among these compounds, compounds 9c , 9i , and 9p displayed the similar curative effect against TMV (EC₅₀ = 287.05–322.47 µg/mL) to that of the commercial agent Ningnanmycin (EC₅₀ = 301.83 µg/mL). In particular, compound 9d demonstrated the best curative effect against TMV (EC₅₀ = 266.21 µg/mL), which was better than that of commercial Ningnanmycin.     

Triticonazole enantiomers: Separation by supercritical fluid chromatography and the effect of the chromatographic conditions

Enantiomeric pairs of triticonazole have been successfully separated by supercritical fluid chromatography coupled with a tris(3,5‐dimethylphenylcarbamoyl) cellulose‐coated chiral stationary phase in this work. The effects of co‐solvent, dissolution solvent, flow rate, backpressure, and column temperature have been studied in detail with respect to retention, selectivity, and resolution of triticonazole. As indicated, the co‐solvents mostly affected the retention factors and resolution, due to the different molecular structure and polarity. In addition, the dissolution solvents, namely, chloromethanes and alcohols, have been also important for enantioseparation because of the different interaction with stationary phase. Higher flow rate and backpressure led to faster elution of the triticonazole molecules, and the change of column temperature showed slight effect on the resolution of triticonazole racemate. Moreover, a comparative separation experiment between supercritical fluid chromatography and high performance liquid chromatography revealed that chiral supercritical fluid chromatography gave the 3.5 times value of R_s/t_R2 than high performance liquid chromatography, which demonstrated that supercritical fluid chromatography had much higher separation efficiency.