Existence of best simultaneous approximations in Lp(S,Σ,X)

Let $(S,\Sigma ,\mu )$ be a complete positive $\sigma$-finite measure space and let $X$ be a Banach space. We are concerned with the proximinality problem for the best simultaneous approximations to two functions in $L_p(S,\Sigma ,X)$. Let ${\Sigma }_0$ be a sub-$\sigma$-algebra of $\Sigma$ and $Y$ a nonempty locally weakly compact convex subset of $X$ such that $\overline{\mathrm{span}Y}$ and its dual have the Radon–Nikodym property. We prove that $L_p(S,{\Sigma }_0,Y)$ is $N$-simultaneous proximinal in $L_p(S,\Sigma ,X)$ (with the additional assumption that $(S,\Sigma ,\mu )$ be finite for the case when $p=1$). Furthermore, for the special case when ${\Sigma }_0=\Sigma$, we show that the assumption that the dual of $\overline{\mathrm{span}Y}$ has the Radon–Nikodym property can be removed.     

Facile Synthesis of Functional Poly(methyltriazolylcarboxylate)s by Solvent-and Catalyst-free Butynoate-Azide Polycycloaddition

The copper-catalyzed and metal-free azide-alkyne click polymerizations have become efficient tools for polymer synthesis. However,the 1,3-dipolar polycycloadditions between internal alkynes and azides are rarely employed to construct functional polymers. Herein, the polycycloadditions of dibutynoate(1) and tetraphenylethene-containing diazides(2) were carried out at 100 °C for 12 h under solvent-and catalyst-free conditions, producing soluble poly(methyltriazolylcarboxylate)s(PMTCs) with high molecular weights in high yields. The resultant polymers were thermally stable with 5% weight loss temperatures up to 377 °C. The PMTCs showed aggregation-induced emission(AIE)properties. They could work as fluorescent sensors for detecting explosive with high sensitivity, and generate two-dimensional fluorescent photopatterns with high resolution. Furthermore, their triazolium salts could be utilized for cell-imaging applications.     

C60的氧化反应研究

在C60的甲苯或二氯苯溶液中通入O3,通过改变O3的吸收量及反应时间可得到两种氧化产物,一种产物在有机溶剂及水中均不溶,但经性水解后得到水溶性产物,其红外光谱与C60羟基化合物相似,在长时间通O3条件下,得到水溶性的C60氧化产物,用变温红外光谱、XPS、元素分析、热谱和质谱研究了氧化产物的可能结构,发现生成的C60氧化产物对热不稳定,随着温度升高,有CO2,CO和H2O放出。     

差速离心结合蛋白质组学技术研究受镉盐胁迫后的牙鲆肝差异蛋白质

人工构建镉盐污染源,选用差速离心结合双向凝胶电泳(2D-PAGE)法,高效提取、分离和筛选牙鲆(Paralichthys olivaceus, PO)受镉盐胁迫后的肝脏全蛋白和差异蛋白质.实验结果表明: 选用直接裂解法提取牙鲆肝(PO liver POL)全蛋白质且用2D-PAGE分离,可获得约800个蛋白斑点,其中镉盐诱导了11个差异蛋白斑点.以相对离心力为1000×g、12000×g和100000 ×g 的差速离心法,分别制备了3种沉淀蛋白和1种胞浆蛋白,称为POL组分Ⅰ、POL组分Ⅱ、POL组分Ⅲ和POL组分Ⅳ(胞浆蛋白),蛋白斑点数目分别为380、550、500和850个,总计2280个,明显高于直接裂解法.比较分析法发现,差速离心结合2D-PAGE分离技术可获得牙鲆肝脏受镉盐胁迫后表达的54个差异蛋白质,并适合于用肽质量指纹(peptide mass fingerprint,PMF)图谱技术鉴定.本实验所建立的差速离心结合蛋白质组学技术可高效提取、分离和鉴定组织全蛋白或差异蛋白,并能有效地筛选出蛋白指示物.     

Strong convergence of an iterative method for nonexpansive and accretive operators

Let X be a Banach space and A an m-accretive operator with a zero. Consider the iterative method that generates the sequence {xn} by the algorithm xn+1=αnu+(1−αn)Jrnxn, where {αn} and {rn} are two sequences satisfying certain conditions, and Jr denotes the resolvent ⁻¹(I+rA) for r>0. Strong convergence of the algorithm {xn} is proved assuming X either has a weakly continuous duality map or is uniformly smooth.     

Strong convergence of modified Mann iterations for asymptotically nonexpansive mappings and semigroups

The Mann iterations for nonexpansive mappings have in general only weak convergence in a Hilbert space. We modify an iterative method of Mann's type introduced by Nakajo and Takahashi [Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups, J. Math. Anal. Appl. 279 (2003) 372–379] for nonexpansive mappings and prove strong convergence of our modified Mann's iteration processes for asymptotically nonexpansive mappings and semigroups.     

Iterative Algorithms for Nonlinear Operators

Iterative algorithms for nonexpansive mappings and maximal monotoneoperators are investigated. Strong convergence theorems areproved for nonexpansive mappings, including an improvement ofa result of Lions. A modification of Rockafellar’s proximalpoint algorithm is obtained and proved to be always stronglyconvergent. The ideas of these algorithms are applied to solvea quadratic minimization problem.     

过氧多酸盐[NBu4]3[M(O2)W5O18]的合成及表征

过渡金属过氧化合物是一类性能良好的催化剂,在有机合成中得到广泛的应用[1,2].过氧多酸催化过氧化氢氧化有机物的反应,近年来倍受重视[3～5].     

Hydrothermal Synthesis of Al-Doped ZnO with a Novel Cactus Microstructure and Their Gas Sensitivity Research

Russian Journal of Applied Chemistry - Al-Doped ZnO (AZO) nanocrystals with a novel cactus morphology have been successfully synthesized by a facile and efficient hydrothermal method. The crystal...