Dual subspaces of operators

In this note we introduce some new constructions of dual spaces of operators, which are, of course, at the same time, operator spaces in the sense of Pisier (2003) [12]. We exemplify the utility of these constructs by establishing, in this more general setting, a curious and little known result from the theory of dual algebras, namely from Chevreau and Pearcy (1991) [11].     

向量组线性相关性的教学方法与技巧

向量组线性相关性是线性代数教学中的一项重要内容．由于概念比较抽象、定理难以理解,因此一直是线性代数教学环节中的一项难点．通过对向量组线性相关性的定义以及判断方法进行了形象的描述,建立向量组线性相关性与矩阵、线性方程组之间的关系,有利于学生理解向量组线性相关性的真正内涵与简便求解方法．     

基于NIR高光谱成像技术的长枣虫眼无损检测

为了研究快速识别虫眼枣与正常枣的有效方法,利用特征波长主成分分析法结合波段比算法进行虫眼枣识别。首先,利用NIR高光谱成像系统采集130个长枣(50个正常、80个虫眼枣)图像,提取并分析不同类型长枣特征区域的平均光谱曲线,对970~1 670 nm范围内的光谱数据进行主成分分析,确定7个特征波长(990,1 028,1 109,1 160,1 231,1 285,1 464 nm)。然后,对长枣图像做主成分分析,选择PC2图像进行虫眼识别,虫眼与正常枣的识别率分别为67.5%、100%。为了进一步提高虫眼枣的识别率,采用波段比(R1231/R1109)对未识别的虫眼枣进行再次识别,识别率提高到90%。结果表明,基于NIR高光谱成像技术的检测方法对虫眼枣识别是可行的,同时也为多光谱成像技术应用于在线检测长枣品质提供了理论依据。     

Ellagitannin Digestion in Moth Larvae and a New Dimeric Ellagitannin from the Leaves of Platycarya strobilacea

Ellagitannins (ETs) are plant polyphenols with various health benefits. Recent studies have indicated that the biological activities of ETs are attributable to their degradation products, including ellagic acid and its gut microflora metabolites, such as urolithins. Insect tea produced in the Guangxi region, China, is made from the frass of moth larvae that feed on the ET-rich leaves of Platycarya strobilacea. Chromatographic separation of the Guangxi insect tea showed that the major phenolic constituents are ellagic acid, brevifolin carboxylic acid, gallic acid, brevifolin, and polymeric polyphenols. Chemical investigation of the feed of the larvae, the fresh leaves of P. strobilacea, showed that the major polyphenols are ETs including pedunculagin, casuarictin, strictinin, and a new ET named platycaryanin E. The new ET was confirmed as a dimer of strictinin having a tergalloyl group. The insect tea and the leaves of P. strobilacea contained polymeric polyphenols, both of which were shown to be composed of ETs and proanthocyanidins by acid hydrolysis and thiol degradation. This study clarified that Guangxi insect tea contains ET metabolites produced in the digestive tract of moth larvae, and the metabolites probably have higher bioavailabilities than the original large-molecular ETs of the leaves of P. strobilacea.     

The Rings of Witt Vectors for Noncommutative Rings with Some Rich Structure

In this article, for a noncommutative ring A with some rich structure, we define a ring of Witt vectors with coefficients in A, which is noncommutative unless A is commutative.     

Schmidt modes and entanglement

Motivated by their frequent use in quantum mechanical studies of entanglement, we give a brief overview of Schmidt modes and Schmidt decompositions of two-particle wave functions. We discuss methods of their derivation and include a little-known approach used in the original work by E. Schmidt [Math. Annalen, 63 (1906), 433]. This employs the bipartite wave function itself rather than the more complicated two-party reduced density matrix. As an illustration, Schmidt modes for two-photon polarisation qutrits are derived in a general form. The derivation is accompanied by a series of simple examples with special choices of parameters. Relationships between Schmidt modes, polarisation Stokes vectors and entanglement are also discussed.     

Biodegradable polymers in gene‐silencing technology

Small interfering RNAs (siRNAs) technology has shown great promise as a new class of therapeutics invention for treatment of cancer and other diseases. siRNA has been used extensively in blocking various genes and is presently being evaluated as a therapeutic for cancer and viral disease. Despite the excitement about this remarkable biological process for sequence specific gene regulation, the major limitations against the use of siRNAs‐based therapeutics are their rapid degradation by serum nuclease, poor cellular uptake, and rapid renal clearance following systemic delivery, off‐target effects, and induction of immune responses. Many researchers have tried to overcome these limitations with developing nuclease‐resistant chemically modified siRNAs and variety of synthetic and natural biodegradable lipids and polymers for siRNA delivery to enhance efficacy and safety profiles. An ideal siRNAs‐based delivery system must be clinically suitable, safe, and effective. This review discuss the recent progress of biodegradable polymers in siRNA delivery technology.     

Total Synthesis,Stereochemical Assignment,and Field‐Testing of the Sex Pheromone of the Strepsipteran Xenos peckii

The sex pheromone of the endoparasitoid insect Xenos peckii (Strepsiptera: Xenidae) was recently identified as (7E,11E)‐3,5,9,11‐tetramethyl‐7,11‐tridecadienal. Herein we report the asymmetric synthesis of three candidate stereostructures for this pheromone using a synthetic strategy that relies on an sp³–sp² Suzuki–Miyaura coupling to construct the correctly configured C7‐alkene function. Comparison of ¹H NMR spectra derived from the candidate stereostructures to that of the natural sex pheromone indicated a relative configuration of (3R*,5S*,9R*). Chiral gas chromatographic (GC) analyses of these compounds supported an assignment of (3R,5S,9R) for the natural product. Furthermore, in a 16‐replicate field experiment, traps baited with the synthetic (3R,5S,9R)‐enantiomer alone or in combination with the (3S,5R,9S)‐enantiomer captured 23 and 18 X. peckii males, respectively (mean±SE: 1.4±0.33 and 1.1±0.39), whereas traps baited with the synthetic (3S,5R,9S)‐enantiomer or a solvent control yielded no captures of males. These strong field trapping data, in combination with spectroscopic and chiral GC data, unambiguously demonstrate that (3R,5S,9R,7E,11E)‐3,5,9,11‐tetramethyl‐7,11‐tridecadienal is the X. peckii sex pheromone.