A characterization of ∗-isomorphism on factor von Neumann algebras北大核心CSCD

Let H and K be complex Hilbert spaces. Let A and B be two factor von Neumann algebras acting on H and K respectively. A characterization of ∗-isomorphism between A and B is given. Let Φ: A → B be a bijection. If Φ(A∗B + B∗A) = Φ(A)∗Φ(B) + Φ(B)∗Φ(A) for all A,B ∈ A, then Φ is a linear or a conjugate linear ∗-isomorphism. ©, 2015, Chinese Academy of Sciences. All right reserved.     

Computing the Approximation Error for Neural Networks with Weights Varying on Fixed Directions

We obtain a sharp lower bound estimate for the approximation error of a continuous function by single hidden layer neural networks with a continuous activation function and weights varying on two fixed directions. We show that for a certain class of activation functions this lower bound estimate turns into equality. The obtained result provides us with a method for direct computation of the approximation error. As an application, we give a formula, which can be used to compute instantly the approximation error for a class of functions having second order partial derivatives.     

Synthesis of 3,3-disubstituted oxetane building blocks

The synthesis of two different sets of 3,3-disubstituted oxetane building blocks is described. These molecules can be usefully incorporated in more complex structures to modulate their metabolic and physicochemical properties. The synthetic pathways are general and could be exploited for the synthesis of many other related derivatives.     

Concise synthesis of Bacillusanthracis exosporium tetrasaccharide via two-stage activation of allyl glycosyl donor strategy

A highly efficient glycosylation protocol recently developed in our laboratory has been utilized in the short synthesis of the tetrasaccharide 1, an antigen important to the development of carbohydrate-based diagnostic tools and vaccines against anthrax. The protocol employs allyl glycosides as building blocks and improves the overall synthetic efficiency.     

线性约束两分块非凸优化的ADMM-SQP算法

基于乘子交替方向法(ADMM)和序列二次规划(SQP)方法思想, 致力于研究线 性约束两分块非凸优化的新型高效算法. 首先, 以SQP思想为主线, 在其二次规划(QP)子问题的求解中引入ADMM思想, 将QP分解为两个相互独立的小规模QP求解. 其次, 借助增广拉格朗日函数和Armijo线搜索产生原始变量新迭代点. 最后, 以显式解析式更新对偶变量. 因此, 构建了一个新型ADMM-SQP算法. 在较弱条件下, 分析了算法通常意义下的全局收敛性, 并对算法进行了初步的数值试验.     

T∞-测度分解定理的进一步讨论

在对T∞-测度做进一步研究的基础上,得到了(有限或无限)T∞-测度的Hahn分解定理和Jordan分解定理。同时,用一种新方法证明了有限T∞-测度的Lebesgue分解定理。此外,还得到了一些类似于经典测度的结论。     

Which sets are images of disk-algebra functions?

We give a characterization of those compact sets in the plane with finitely many holes that are images of disk-algebra functions. We also show that the image of the closed unit disk via a polynomial is, in general, not polynomially convex.     

正规六边形和更广泛具有正规结构的Banach 空间

假设Ｘ是一个实Ｂａｎａｃｈ空间，Ｓ（Ｘ）是单位球面。作者引进了一个新的几何参数（Ｈ（Ｘ），讨论了Ｈ（Ｘ）和Ｎｅｕｍａｎｎ－Ｊｏｒｄａｎ常数ＣＮＪ（Ｘ）Ｒ 性质以及Ｈ（Ｘ）和其他几何常数的关系，本文主要结果是：Ｈ（Ｘ）〈２或ＣＮＪ（Ｘ）〈４／５一致正规结构。     

Sol-gel polymerization of silylated amino acids around a protein template yields selective biomimetic imprints

The development of artificial receptors able to selectively recognize a target protein is of particular interest in separation, diagnostics, and therapeutics fields. Herein, we disclose a method to prepare biomimetic and functionalized protein imprints in biocompatible conditions avoiding any protein denaturation. For that purpose, a set of different hybrid silylated amino acid derivatives were synthesized and used without tetraethyl orthosilicate to prepare our molecularly imprinted polymers, allowing to reduce to a minimum of the silicon amount, in order to obtain imprints made almost entirely of amino acids to mimic paratope surfaces of antibodies. Such functional building blocks were polymerized on the surface of magnetic silica nanoparticles at pH 8.5 in ultrapure water in the presence of two globular proteins: cytochrome C or lysozyme. The resulting imprinted hybrid materials were evaluated for their adsorption capacity, specificity, and selectivity by quartz-crystal microbalance with dissipation and magnetic enzyme-linked immunosorbent assay (ELISA) assays. High imprinting factors of 8.7 were measured for these biomimetic hybrid materials (corresponding to approximately 4000 and 450 ng of protein per cm² immobilized on molecularly imprinted polymers and non-imprinted polymer nanoparticles, respectively), representing a significant breakthrough in sol-gel-based molecular imprinting materials. Moreover, competition experiments performed by magnetic ELISA (mELISA) show very good specificity of our imprints at the usual concentrations of ELISA measurements.