Theoretical IR,Raman and NMR spectra of 1,2- and 1,3-dimethylenecyclobutane

Equilibrium geometries, rotational constants, harmonic vibrational frequencies, infrared intensities, Raman activities, and ¹H and ¹³C NMR spectra were calculated for 1,2-dimethylenecyclobutane and its less stable isomer 1,3-dimethylenecyclobutane by using MP2, DFT (B3PW91), and RHF theoretical methods involving the 6-311++G⁷ basis set.The properties calculated theoretically have been compared with the experimental values. The internal coordinates defined for both isomers were used in the potential energy distribution (PED) analysis. The theoretical vibrational and NMR spectra form the basis to differentiate particular compounds in reaction mixture.     

具非负曲率完备非紧曲面的几何性质

本文证明了单连通完备非紧具非负曲率之曲面的任一测地线γ：[0,+∞)→M均趋于∞处这一几何性质,指出了一般的高维流形不具有此性质.本文还证明了单连通完备非紧具非负曲率的曲面的割迹与第一共轭轭迹是一致的;并且讨论了一般高维流形的共轭点与测地线的关系.     

k-Regular partitions and overpartitions with bounded part differences

Recently, partitions with fixed or bounded difference between largest and smallest parts have attracted a lot of attention. In this paper, we provide both analytic and combinatorial proofs of the generating function for k-regular partitions with bounded difference kt between largest and smallest parts. Inspired by Franklin’s result, we further find a new proof of the generating function for overpartitions with bounded part differences by using Dousse and Kim’s results on (q, z)-overGaussian polynomials.

     

Comparison of Immobilization Modes in pH-Sensitive Phase Separation Immunoassay

Three immobilization modes of antigen to the polymers in the pH‐sensitive phase separation immunoassay were investigated and compared. The results showed that the immobilization mode in the presence of N‐ethyl‐N′‐(3‐dimethylaminopropyl)carbodiimide hydrochloride (EDCI) rendered the most desirable results. The immobilization efficiencies and immunological reaction activities of immobilized antigen of this mode were improved over the other two modes. The novel immobilization mode by EDCI was used in the pH‐sensitive phase separation immunoassay for rabbit IgG (Ag). In the competitive immunoassay, immobilized Ag and the standard Ag (or sample) competed for binding to a horseradish peroxidase labeled antibody at 37°C in a homogeneous format. After changing the pH to separate the polymer‐immune complex, the complex precipitate was re‐dissolved and determined by coupling with the color reaction of hydrogen peroxide and o‐phenylenediamine. The linear range of this determination was between 100–1400 ng/mL. Compared to the traditional enzyme‐linked immunosorbent assays (ELISA) using the same reactants, the proposed method was quiet fast (the time decreased from 100?120 to 30 min) and showed similar sensitivity, i.e., 6.0 ng/mL.     

A note on maximal commutators with rough kernels

This paper gives a characterization of compactness for maximal commutators with rough kernels in weighted Lebesgue spaces, which is new and interesting even in un-weighted cases. Meanwhile, a new characterization of weighted boundedness for such operators is also established.     

Extinction and permanence in delayed stage-structure predator–prey system with impulsive effects

Based on the classical stage-structured model and Lotka–Volterra predator–prey model, an impulsive delayed differential equation to model the process of periodically releasing natural enemies at fixed times for pest control is proposed and investigated. We show that the conditions for global attractivity of the ‘pest-extinction’ (‘prey-eradication’) periodic solution and permanence of the population of the model depend on time delay. We also show that constant maturation time delay and impulsive releasing for the predator can bring great effects on the dynamics of system by numerical analysis. As a result, the pest maturation time delay is considered to establish a procedure to maintain the pests at an acceptably low level in the long term. In this paper, the main feature is that we introduce time delay and pulse into the predator–prey (natural enemy-pest) model with age structure, exhibit a new modelling method which is applied to investigate impulsive delay differential equations, and give some reasonable suggestions for pest management.     

扩散 Cantor 集的最小Hausdorff 测度

In this paper, we construct a scattered Cantor set having the value 1/2 of log2/log3- dimensional Hausdorff measure. Combining a theorem of Lee and Baek, we can see the value 21 is the minimal Hausdorff measure of the scattered Cantor sets, and our result solves a conjecture of Lee and Baek.     

龙岩煤不同宏观煤岩组分的颗粒及其燃烧性质实验研究

用浮选法分选出3个密度档、代表不同宏观岩相的龙岩煤颗粒，进行工业分析、元素分析和煤岩分析；并进一步通过扫描电镜结合压汞实验分析颗粒的结构，通过热天平实验研究不同宏观煤岩组分的燃烧性质。结果表明，(1)龙岩煤颗粒的煤岩主要由镜质组组成。其中，亮煤富含镜质组，密度相对较低，挥发分极少、固定碳高达80％以上；暗煤富含矿物质成分，密度极高但含碳量却很少，热值很低，接近于原煤中的矸石。灰煤中惰性组的量是三种岩相中最多的，其工业分析性质与原煤接近；(2)龙岩煤颗粒结构致密，密度在1.6g/cm3以上。颗粒中绝大多数孔隙的孔径在1μm以下。其中亮煤颗粒表面光洁致密，内部孔隙以亚微孔(0.01μm<d<0.10μm)居多，大孔径较少，比表面积较大；暗煤颗粒的表面孔隙较发达，内部结构相对较蓬松，颗粒中细孔、微孔、亚微孔都存在；而灰煤颗粒中的孔隙最不发达，以超微孔(d<0.01μm)为主；(3)不同宏观煤岩组分龙岩煤的着火温度相近，约580℃；但燃尽温度相差较大：亮煤最高，大于800℃；暗煤最低，两者相差约100℃；(4) 龙岩煤不同宏观煤岩颗粒的反应性按亮煤、煤(混煤)、灰煤、暗煤依次递减，亮煤的反应性最好，暗煤的反应性最差。     

Laser photolysis of interaction of poly-guanylic acid (5′) with anthraquinone-2-sulfonate

The electron transfer reaction between triplet anthraquinone-2-sulfonate and poly- guanylic acid (5′) in CH3CN-H2O (97:3) has been investigated by 248 nm (KrF) laser flash photolysis. The transient absorption spectra and kinetics obtained from the interaction of triplet anthraquinone-2-sulfonate and poly[G] demonstrate that the primary ionic radical pair, radical cation of poly[G] and radical anion of anthraquinone-2-sulfonate have been detected simultaneously. The free energy changes in the process of the electron transfer were also calculated.