一般状态空间跳过程的不可约性

本文研究了一般状态空间跳过程的ψ-不可约性.利用与马氏链类似的方法,得到了最大不可约测度及其性质,推广了离散时间一般状态空间马氏链的结果,作为应用,给出了C∈E+的充分条件.最后,证明了跳过程、骨架链、跳跃链和预解链的ψ-不可约是等价的.     

The isometric extension problem between unit spheres of two separable Banach spaces

In this article, we use some analytic and geometric characters of the smooth points in a sphere to study the isometric extension problem in the separable or reflexive real Banach spaces. We obtain that under some condition the answer to this problem is affirmative.     

Universal C*-algebras defined by completely bounded unital homomorphisms

Suppose A is a unital C*-algebra and r 1.In this paper,we define a unital C*-algebra C_(cb)*(A,r) and a completely bounded unital homomorphism α_r:A → C_(cb)*(A,r)with the property that C_(cb)*(A,r)=C*(α_r(A))and,for every unital C*-algebra B and every unital completely bounded homomorphism φ:A→ B,there is a(unique)unital *-homomorphism π:C_(cb)*(A,r)→B such thatφ=πoα_r.We prove that,if A is generated by a normal set {t_λ:λ∈Λ},then C_(cb)*(A,r)is generated by the set {α_r(t_λ):λ∈Λ}.By proving an equation of the norms of elements in a dense subset of C_(cb)*(A,r)we obtain that,if Β is a unital C*-algebra that can be embedded into A,then C_(cb)*(B,r)can be naturally embedded into C(cb)*(A,r).We give characterizations of C_(cb)*(A,r)for some special situations and we conclude that C_(cb)*(A,r)will be "nice" when dim(A)≤ 2 and "quite complicated" when dim(A)≥ 3.We give a characterization of the relation between K-groups of A and K-groups of C_(cb)*(A,r).We also define and study some analogous of C_(cb)*(A,r).     

Copper-mediated cyanation reactions

Aryl nitriles can be efficiently synthesized through transition-metal-mediated cyanation of aryl halides, arenes, aryl boronic acids, and so on. Among those most commonly used transition-metals, copper catalysts are surely much more inexpensive and easier to handle, compared to any other metal catalysts. Considering the high-efficiency of copper catalysts in the activation of C–X, C–H, and C–B bond as well as in the formation of C–CN bond, this Letter summarizes various copper-mediated cyanations based on the different kinds of cyanide reagents, such as metal cyanides, potassium hexacyanoferrate(II), acetone cyanohydrins, DDQ, AIBN, benzyl cyanide, malononitrile, nitromethane, and DMF. Our group’s recent contributions to this area are also demonstrated.     

Two Coordination Polymers Constructed from 5‐(4‐Pyridyl)‐1H‐tetrazole Ligands with Different Organic Carboxylates: Structure and Luminescence Properties

Two coordination polymers (CPs), namely, [Cu(Hptz)₂(Hhba)₂]_n ( 1 ) [Hptz = 5‐(4‐pyridyl)‐1H‐tetrazole, H₂hba = 2‐hydroxybenzoic acid] and [Zn₃(ptz)₂(hpa)₂]_n ( 2 ) (H2hpa = 2‐hydroxy‐2‐phenylacetic acid), were synthesized by solvothermal reactions. Both complexes were characterized by elemental analysis, infrared spectroscopy, powder X‐ray diffraction, thermogravimetric analysis, and single‐crystal X‐ray diffraction analysis. Compound 1 exhibits a 2D (4,4) network, where each layer connects to four adjacent layers to construct a 3D supramolecular framework. Compound 2 has a 3D framework structure composed of 1D SUBs, which are formed by both carboxyl and tetrazole groups. The complexes represent two rare examples of CPs constructed from Hptz and organic carboxyl acid ligands. Complex 2 exhibits intense, red‐shifted emissions in the visible region at room temperature.     

Three New Coordination Compounds with Neodymium Based on Tetrazole Containing Carboxylic Acid Ligands

Reactions of three tetrazole containing carboxylic acid ligands, namely, Hpztza, Htzpya, and Hpytza [Hpztza = 5‐(2‐pyrazinyl)tetrazole‐2‐acetic acid, Htzpya = 3‐(5‐tetrazolyl)pyridine‐1‐acetic acid, Hpytza = 5‐(3‐pyridyl)tetrazole‐2‐acetic acid] with NdCl₃ · 6H₂O under hydrothermal conditions, afforded the complexes [Nd(pztza)₂(H₂O)₆] · pztza · 3H₂O ( 1 ), [Nd₂(tzpya)₂(H₂O)₁₂]Cl₄ · 2H₂O ( 2 ), and [Nd(pytza)₂Cl(H₂O)₂] ( 3 ). The compounds were structurally characterized by elemental analysis, IR spectroscopy and single‐crystal X‐ray diffraction. X‐ray diffraction analyses revealed that compound 1 displays a mononuclear structure, 2 shows a dinuclear structure, and 3 features a 1D polymeric chain structure via pytza as linker. Furthermore, the luminescent properties investigated at room temperature in the solid state show that compound 2 has an obvious decrease in its luminescence, when compared to the ligand.     

A rapid and effective method for silver staining of PCR products separated in polyacrylamide gels

With the development of molecular quantitative genetics, particularly, genetic linkage map construction, quantitative trait loci mapping or genes fine mapping and association analysis etc., more and more PCR products separated in polyacrylamide gels need to be silver‐stained. However, conventional silver‐staining procedures are complicated and time‐consuming as they require a lot of preparation and handling of several solutions prior to use. In this study, a simple and rapid protocol for silver staining of PCR products was developed. The number of steps was reduced compared to conventional protocols, thus achieving detection of PCR products in 7 min, saving time and resources. Fixation and staining solution and developing solution in present staining procedure allowed a reutilization for 12 and 8 times, respectively, reducing the cost greatly. Meanwhile, the sensitivity was significantly improved with the improved method and the minimum of 0.097 ng/μL of DNA amount can be detected in denaturing polyacrylamide gel. The protocol developed in this study will facilitate the development of molecular quantitative genetics.     

Genetic profile characterization and population study of 21 autosomal STR in Chinese Kazak ethnic minority group

Short tandem repeat loci have been recognized as useful tools in the routine forensic application and in recent decades, more and more new short tandem repeat (STR) loci have been constantly discovered, studied, and applied in forensic caseworks. In this study, we investigated the genetic polymorphisms of 21 STR loci in the Kazak ethnic minority as well as the genetic relationships between the Kazak ethnic minority and other populations. Allelic frequencies of 21 STR loci were obtained from 114 unrelated healthy Kazak individuals in the Ili Kazak Autonomous Prefecture, Xinjiang Uigur Autonomous Region of China. We observed a total of 159 alleles in the group with the allelic diversity values ranging from 0.0044 to 0.5088. The highest polymorphism was found at D19S433 locus and the lowest was found at D1S1627. Statistical analysis of the generated data indicated no deviation from Hardy–Weinberg equilibriums at all 21 STR loci. In order to estimate the population differentiation, allelic frequencies of all STR loci of the Kazak were compared with those of other neighboring populations using analysis of molecular variance method. Statistically significant differences were found between the studied population and other populations at 2–7 STR loci. A neighbor‐joining tree was constructed based on allelic frequencies of the 21 STR loci and phylogenetic analysis indicates that the Kazak has a close genetic relationship with the Uigur ethnic group. The present results may provide useful information for forensic sciences and population genetics studies, and can also increase our understanding of the genetic background of this group. The present findings showed that all the 21 STR loci are highly genetically polymorphic in the Kazak group, which provided valuable population genetic data for the genetic information study, forensic human individual identification, and paternity tests.