G可积函数的Lebesgue可测性

Botsko在连续和可导的知识基础上推广了Riemann积分,得到了一种新的积分,称为G积分．G积分既不同于Riemann积分也不同于Lebesgue积分．本文通过对G积分的研究,得到了G可积函数一定Lebesgue可测,从而有界G可积函数一定Lebesgue可积;同时我们还证明了这两个积分值相等．     

Computational insight into asymmetric uranyl‐salophen coordinated with α, β‐unsaturated aldehydes and ketones

The study of the catalytic activity and activation mechanism of asymmetric uranyl‐salophens with α, β‐unsaturated aldehydes or α, β‐unsaturated ketones, is a research hotspot. In this paper, the complexes of the uranyl–salophen(U‐S) modified by unilateral benzene, coordinated with cyclohexenone, cyclopentenone and acrolein, were investigated using density functional theory calculations at the level of B3LYP/6‐311G(d, p) basis set. The results showed that the uranyl‐salophen(U‐S) weakened the large π bond between C = C and C = O of the α, β‐unsaturated aldehydes and ketones, making the unsaturated aldehydes and ketones activated. In addition, the molecular‐recognition selectivity of the asymmetrical uranyl‐salophen for cyclohexenone and cyclopentenone were much higher than for acrolein.     

A new epidemic model of computer viruses

This paper addresses the epidemiological modeling of computer viruses. By incorporating the effect of removable storage media, considering the possibility of connecting infected computers to the Internet, and removing the conservative restriction on the total number of computers connected to the Internet, a new epidemic model is proposed. Unlike most previous models, the proposed model has no virus-free equilibrium and has a unique endemic equilibrium. With the aid of the theory of asymptotically autonomous systems as well as the generalized Poincare–Bendixson theorem, the endemic equilibrium is shown to be globally asymptotically stable. By analyzing the influence of different system parameters on the steady number of infected computers, a collection of policies is recommended to prohibit the virus prevalence.     

Determination of the standard molar enthalpy of formation of the ternary complex of neodymium with vitamin B3 and 8-hydroxylquinoline by microcalorimetry

A novel solid ternary complex, [Nd(C₆H₄NO₂)₂·C₉H₆NO·2H₂O], was synthesized in a water bath (333.15 K) by three kinds of reagents: neodymium chloride, vitamin B3 (C₆H₅NO₂), and 8-hydroxylquinoline (C₉H₇NO). Its composition and structure were characterized by elemental analysis, IR spectra, UV spectra, molar conductance, and thermogravimetric analysis. During the process of coordination, C₆H₅NO₂ was bidentate-coordinated with Nd³⁺ in the form of an acidic group by removing the proton; hydroxyl oxygen atom and heterocyclic nitrogen atom of C₉H₇NO formed a chelate ring. Particularly, in this article, a thermochemical cycle in the calorimetric solvent (V _HCl:V _DMF:V _EtOH = 3:1:1) was designed on the basis of Hess’s law. At 298.15 K, the dissolution enthalpies of the reactants and products were determined by a advanced solution–reaction isoperibol microcalorimeter, respectively. According to the above results and relevant literature data, the standard molar enthalpy of formation of [Nd(C₆H₄NO₂)₂·C₉H₆NO·2H₂O], was estimated to be $ \Updelta_{f} H_{m}^{\Uptheta} $ [[Nd(C₆H₄NO₂)₂·C₉H₆NO·2H₂O(s)], 298.15 K] = ?(2,129.1 ± 2.5) kJ mol^?1.     

Analysis of ginseng root and leaf by multiple columns and detections liquid chromatography

Abstract

A multiple columns and detections liquid chromatography system, including size exclusion chromatography (SEC) and reversed phase liquid chromatography (RPLC), for the analysis of macromolecules and micromolecules in ginseng root and leaf was developed. The columns were connected by two switching valves. Macromolecules were separated on a SEC column (TSK gel SuperMultipore PW-H column, 6?mm× 150?mm, 8?μm) by isocratic elution of 50?mM ammonium acetate aqueous solution, 0.3?mL/min of flow rate and detected by evaporative light scattering detection (ELSD). Micromolecules were analyzed on a Poroshell RP column (Agilent Poroshell 120?SB-Aq column, 4.6?mm × 50?mm, 2.7 µm) with gradient elution of water and acetonitrile, 0.6?mL/min of flow rate and detected by ultraviolet detection (UV). As a result, in the macromolecules chromatogram of ginseng root sample showed two main peaks while only one major peak for ginseng leaf. For micromolecules analysis, 17 compounds (3 nucleosides + 14 saponins) and 17 compounds (3 nucleosides + 1 flavonoid + 13 saponins) were found in ginseng root and leaf, respectively. The developed method is helpful for the quality evaluation of ginseng root and leaf.     

Wigner function of coherent state of N components

In this paper, we study the Wigner function of coherent state of N components, especially two components and three components. This function consists of two terms： the Gaussian term and the interference term with the negativity. The first term comprises N Gaussian surfaces evenly centred on a circle of radius ｜β｜ = ｜α｜ with a separate angle of 2π/N, and the second term is composed of 1/2N（N - 1） Gaussian-cosine surfaces evenly centred in a circular region of radius ｜β｜ 〈 ｜α｜. Here, a is the eigenvalue of the annihilation operator α, and β is a variable in some complex space in which the Wigner function is defined. We have proved that the essential condition to eliminate the negativity of the Wigner function is that the mean photon count of the coherent state is equal to that of the Glouber coherent state.     

具时滞的Hopfield网络周期解的指数稳定性

The paper is devoted to periodic attractor of delayed Hopfield neural networks with time-varying.By constructing Lyapunov functionals and using inequality techniques,some new sufficient criteria are obtained to guarantee the existence and global exponential stability of periodic attractor.Our results improve and extend some existing ones in[13～14].One example is also worked out to demonstrate the advantages of our results.     

Parameter space of the Rulkov chaotic neuron model

The parameter space of the two dimensional Rulkov chaotic neuron model is taken into account by using the qualitative analysis, the co-dimension 2 bifurcation, the center manifold theorem, and the normal form. The goal is intended to clarify analytically different dynamics and firing regimes of a single neuron in a two dimensional parameter space. Our research demonstrates the origin that there exist very rich nonlinear dynamics and complex biological firing regimes lies in different domains and their boundary curves in the two dimensional parameter plane. We present the parameter domains of fixed points, the saddle-node bifurcation, the supercritical/subcritical Neimark–Sacker bifurcation, stability conditions of non hyperbolic fixed points and quasiperiodic solutions. Based on these parameter domains, it is easy to know that the Rulkov chaotic neuron model can produce what kinds of firing regimes as well as their transition mechanisms. These results are very useful for building-up a large-scale neuron network with different biological functional roles and cognitive activities, especially in establishing some specific neuron network models of neurological diseases.