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.     

Numerical discretization-based kernel type estimation methods for ordinary differential equation models

We consider the problem of parameter estimation in both linear and nonlinear ordinary differential equation(ODE) models. Nonlinear ODE models are widely used in applications. But their analytic solutions are usually not available. Thus regular methods usually depend on repetitive use of numerical solutions which bring huge computational cost. We proposed a new two-stage approach which includes a smoothing method(kernel smoothing or local polynomial fitting) in the first stage, and a numerical discretization method(Eulers discretization method, the trapezoidal discretization method,or the Runge–Kutta discretization method) in the second stage. Through numerical simulations, we find the proposed method gains a proper balance between estimation accuracy and computational cost.Asymptotic properties are also presented, which show the consistency and asymptotic normality of estimators under some mild conditions. The proposed method is compared to existing methods in term of accuracy and computational cost. The simulation results show that the estimators with local linear smoothing in the first stage and trapezoidal discretization in the second stage have the lowest average relative errors. We apply the proposed method to HIV dynamics data to illustrate the practicability of the estimator.     

Highly unsaturated pyranone derivatives from the basidiomycete Junghuhnianitida

Four new highly unsaturated pyranone derivatives A–D (1–4), together with one known compound 5 (−)-nitidon were isolated from cultures of the fungus Junghuhnianitida. Planar structures of the new compounds were elucidated on the basis of extensive NMR spectroscopic and mass spectrometric analyses. Absolute configurations of the new compounds were determined on the basis of biosynthetic considerations and quantum chemistry theory. Compound 1 exhibited almost the same cytotoxic activities as cis-platin.     

A Low‐dimensional Viologen/Iodoargentate Hybrid [(BV)2­(Ag5I9)]n: Structure,Properties, and Theoretical Study

A new low‐dimensional benzyl viologen/iodoargentate hybrid, [(BV)₂(Ag₅I₉)]_n ( 1 ) (BV²⁺ = benzyl viologen) was prepared. In 1 , (Ag₆I₉)_n^2– chain exhibits a new type of one‐dimensional chain constructed from vertex‐sharing of Ag₅I₁₀ units, and its two‐dimensional layer structure was constructed from C–H ··· I hydrogen bonds. Strong luminescence at 404 nm can be detected in 1 . DFT calculation suggests that 1 displays a reduced bandgap, which is led by a more dispersed LUMO band of BV²⁺ compared with MV²⁺ in [MV(Ag₂I₄)]_n.     

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.     

Characterization of size‐segregated aerosols using ToF‐SIMS imaging and depth profiling

Size‐segregated particles were collected with a ten‐stage micro‐orifice uniform deposit impactor from a busy walkway in a downtown area of Hong Kong. The surface chemical compositions of aerosol samples from each stage were analyzed using time‐of‐flight secondary ion mass spectrometry (ToF‐SIMS) operated in the static mode. The ToF‐SIMS spectra of particles from stage 2 (5.6–10 µm), stage 6 (0.56–1 µm), and stage 10 (0.056–0.1 µm) were compared, and the positive ion spectra from stage 2 to stage 10 were analyzed with principal component analysis (PCA). Both spectral analysis and PCA results show that the coarse‐mode particles were associated with inorganic ions, while the fine particles were associated with organic ions. PCA results further show that the particle surface compositions were size dependent. Particles from the same mode exhibited more similar surface features. Particles from stage 2 (5.6–10 µm), stage 6 (0.56–1 µm), and stage 10 (0.056–0.1 µm) were further selected as representatives of the three modes, and the chemical compositions of these modes of particles were examined using ToF‐SIMS imaging and depth profiling. The results reveal a non‐uniform chemical distribution from the outer to the inner layer of the particles. The coarse‐mode particles were shown to contain inorganic salts beneath the organics surface. The accumulation‐mode particles contained sulfate, nitrate, ammonium salts, and silicate in the regions below a thick surface layer of organic species. The nucleation‐mode particles consisted mainly of soot particles with a surface coated with sulfate, hydrocarbons, and, possibly, fullerenic carbon. The study demonstrated the capability of ToF‐SIMS depth profiling and imaging in characterizing both the surface and the region beneath the surface of aerosol particles. It also revealed the complex heterogeneity of chemical composition in size and depth distributions of atmospheric particles. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

Novel cytotoxic nine-membered macrocyclic polysulfur cembranoid lactones from the soft coral Sinularia sp.

One novel nine-membered macrocyclic polysulfur cembranoid lactone, sinulariaoid A (1); three new multioxygenated cembranoids, sinulariaoid B (2), sinulariaoid C (3), sinulariaoid D (4); and four known cembranoids, capilloloid (5), dihydrosinularin (6), sinularin (7), and dihydrosinuflexolide (8) were isolated from the soft coral Sinularia sp. collected off of Sanya Bay in the South China Sea. Their stereochemical structures were determined on the basis of extensive spectroscopic methods, including single crystal X-ray diffraction analysis. Sinulariaoid A (1) is the first reported nine-membered macrocyclic polysulfur cembranoid from soft coral. The cytotoxic activities of compounds 1–8 were determined in four human cancer cell lines (HepG2, HepG2/ADM, MCF-7, and MCF-7/ADM). Of these, sinulariaoid A (1) exhibited the most potent anticancer activity in vitro, and its cytotoxicity in HepG2/ADM was more potent than in the other three cell lines. Furthermore, it was found that sinulariaoid A (1) induced apoptosis, and its selective toxicity toward HepG2/ADM cells was not related to P-glycoproteins.