On nearly parallel G2-structures

A nearly parallel G₂-structure on a seven-dimensional Riemannian manifold is equivalent to a spin structure with a Killing spinor. We prove general results about the automorphism group of such structures and we construct new examples. We classify all nearly parallel G₂-manifolds with large symmetry group and in particular all homogeneous nearly parallel G₂-structures.     

The differential equation satisfied by a plane curve of degree n

Eliminating the arbitrary coefficients in the equation of a generic plane curve of order n by computing sufficiently many derivatives, one obtains a differential equation. This is a projective invariant. The first one, corresponding to conics, has been obtained by Monge. Sylvester, Halphen, Cartan used invariants of higher order. The expression of these invariants is rather complicated, but becomes much simpler when interpreted in terms of symmetric functions.     

Differential subordinations concerning starlike functions

Denote byS ^* (⌕), (0≤⌕<1), the family consisting of functionsf(z)=z+a ₂z²+...+a_nzⁿ+... that are analytic and starlike of order ⌕, in the unit disc ⋎z⋎<1. In the present article among other things, with very simple conditions on μ, ⌕ andh(z) we prove the f’(z) (f(z)/z)^μ−1<h(z) implies f∈S^*(⌕). Our results in this direction then admit new applications in the study of univalent functions. In many cases these results considerably extend the earlier works of Miller and Mocanu [6] and others.     

用定义求解高等数学中的有关问题

应用导数的定义，为分段函数的分界点提供了一种行之有效的求导方法，利用微分的定义判断函数在分界点及其他特殊点的可微性，运用定和分的定义求一类特殊类型的极限．     

Enthalpies of sorption of linear hydrocarbons (C2–C8) and chloroderivatives of methane and ethylene on the surface of hydrotalcite

Differential molar adsorption enthalpies (DMAE) were determined by gas chromatographic measurements of specific retention volume of vapors on the surface of two forms of Mg–Al hydrotalcite. A linear dependence of the DMAE on the number of the carbon atoms in hydrocarbons was observed for both form of hydrotalcite. The dependence of the differential molar adsorption enthalpies on the number of chlorine atoms in organic molecules is discussed. A linear dependence of DMAE on the molecular weight of chloroderivatives of methane and ethylene on the basic form in an order monochloromethane < dichloromethane < trichloromethane or vinylidene chloride < 1,1-dichloroethylene < trichloroethylene was found.     

Surjectivity and fixed points of relaxed dissipative multifunctions. Differential inclusions approach

One from the most important properties of accretive and monotone operators is the existence of zeros and surjectivity. In the paper we introduce relaxed variants of dissipative, accretive and monotone operators. Using essentially the properties of the solution set of appropriate differential inclusions we study the existence of zeros of such operators. As corollaries the existence of fixed points of relaxed contractive and relaxed nonexpansive multifunctions are obtained.     

鸟嘌呤和次黄嘌呤的铜络合物的吸附作用和伏安特性研究

本文研究了鸟瞟呤(Gua)和次黄嘌呤(Hxa)铜络合物在悬汞电极(HMDE)上的吸附作用和电极反应机理,溶液中形成的1:1络合物有强烈吸附性,通过分子结构的比较,推断出Cu~(2+)与Gua和Hxa的咪唑环N(7)和外环氧O(6)原子结合形成封闭的五元环。嘌呤环的π-电子有使分子呈平面吸附的趋势,但是Gua络合物分子优先取“倾斜”定向;随着表面吸附浓度增加,Hxa络合物分子存在从“平面”向“垂直”的再定向作用。本文测定了单层吸附浓度、包含的电量和每个分子占据的面积。络合物吸附得到S形等温线,它与Frumkin吸附等温线接近。本文还列出有关吸附参数B、a、△G_A~O和θ~*的计算结果。     

Electrooxidation of carbo/thiocarbohydrazide and their hydrazone derivatives at a glassy carbon electrode

Electrochemical oxidation of thio/carbohydrazide and their hydrazone derivatives Benzaldehyde thiocarbohydrazone [BTCH] diacetylene thiocarbohydrazone [DATCH] have been studied in Brit-ton Robinson buffer in aqueous and nonaqueous media at a glassy carbon electrode. The effects of pH, sweep rate, concentration, temperature and surfactants have been studied. The complex bis (carbo/thiocabohydrazide) Zn(II) chloride was also subjected to voltammetric analysis in order to understand the reactivity both in free and metal bound states. The reaction conditions were optimized for the determination of above compounds in micrograms quantities by differential pulse voltammetry, analytical utility of this investigation is also highlighted.     

The variational Lyapunov function and strict stability theory for differential systems

In this paper, we investigate strict stability of differential systems by variational Lyapunov function. We obtain some sufficient conditions and comparison theorems.     

Measurement of small-signal and large-signal responses of packaged laser modules at high temperature

In this paper, the pulsed injection method is extended to measure the chip temperature of various packaged laser modules, such as the DFB laser modules, the FP laser modules, and the EML laser modules. An optimal injection condition is obtained by investigating the dependence of the lasing wavelength on the width and period of the injection pulse in a relatively wide temperature range. The small-signal frequency responses and large-signal performances of packaged laser modules at different chip temperature are measured. The adiabatic small-signal modulation characteristics of packaged LD are first extracted. In the large-signal measurement, the effects of chip temperature, bias current and driving signal on the performances of the laser modules are discussed. It has been found that the large-signal performances of the EML modules depend on the different red-shift speeds of the DFB and EAM sections as chip temperature varying, and the optimal characteristics may be achieved at higher temperature.