GENERALIZATION OF STEINER FORMULAFOR THE HOMOTHETIC MOTIONS ONTHE PLANAR KINEMATICS

The Steiner formula and the mixture area formula given by M(U|¨)ller were expressed under the one-parameter closed planar homothetic motions in the complex sense . Also, using the generalization of Steiner formula, the result of Holditch theorem for homothetic motions is got. In the case of the homothetic scale h≡1 the results given by M(U|¨)ller are obtained as a special case.     

ON CERTAIN CLASS OF MEROMORPHIC FUNCTIONS WITH POSITIVE COEFFICIENTS

In the present investigation we define a new class of meromorphic functions on the punctured unit disk △*:= {z ∈ C : 0 < |z| < 1} by making use of the generalized Dziok-Srivastava operator H l m [α1 ]. Coefficient inequalities, growth and distortion inequalities, as well as closure results are obtained. We also establish some results concerning the partial sums of meromorphic functions and neighborhood results for functions in new class.     

On double sine and cosine transforms,Lipschitz and Zygmund classes

We consider complex-valued functions f ∈ L 1 (R+2),where R +:= [0,∞),and prove sufficient conditions under which the double sine Fourier transform f ss and the double cosine Fourier transform f cc belong to one of the two-dimensional Lipschitz classes Lip(α,β) for some 0 α,β≤ 1;or to one of the Zygmund classes Zyg(α,β) for some 0 α,β≤ 2.These sufficient conditions are best possible in the sense that they are also necessary for nonnegative-valued functions f ∈ L 1 (R+2).     

Synthesis and characterisation of coating polyurethane cationomers containing fluorine built-in hard urethane segments

Polyurethane cationomers were synthesised in the reaction of 4,4’-methylenebis(phenyl isocyanate) with polyoxyethylene glycol (M?= 2,000) or poly(tetrafluoroethyleneoxide-co-difluoromethylene oxide) α,ω-diisocyanate and N-methyl diethanolamine. Amine segments were built-in to the urethane-isocyanate prepolymer in the reaction with 1-bromobutane or formic acid, and then they were converted to alkylammonium cations. The obtained isocyanate prepolymers were then extended in the aqueous medium that yielded stable aqueous dispersions which were applied on the surfaces of test poly(tetrafluoroethylene) plates. After evaporation of water, the dispersions formed thin polymer coatings. ¹H, ¹³C NMR and IR spectral methods were employed to confirm chemical structures of synthesised cationomers. Based on ¹H NMR and IR spectra, the factors κ and α were calculated, which represented the polarity level of the obtained cationomers. The DSC, wide angle X-ray scattering and atom force microscopy methods were employed for the microstructural assessment of the obtained materials. Changes were discussed in the surface free energy and its components, as calculated independently according to the method suggested by van Oss–Good, in relation to chemical and physical structures of cationomers as well as morphology of coating surfaces obtained from those cationomers. Fluorine incorporated into cationomers (about 30%) contributed to lower surface free energy values, down to about 15 mJ/m². That was caused by gradual weakening of long-range interactions within which the highest share is taken by dispersion interactions.     

不同状态方程对固体介质中斜激波反射的影响

相比气体,固体介质在高压下的状态方程更为复杂,形式也多种多样.现有关于固体介质中激波反射的理论研究,一般直接采用某种状态方程,缺乏对采用不同状态方程得到的结果的对比.本项工作采用激波极曲线的理论分析方法,选择4种不同组合形式的状态方程(一次冲击激波采用线性的冲击波速度与粒子速度关系式,二次冲击激波采用Gr(u|¨)neisen状态方程;一次冲击和二次冲击激波均采用冲击波速度与粒子速度关系式:一次冲击激波采用线性冲击波速度与粒子速度关系式,二次冲击激波采用刚性气体状态方程;以及一次冲击激波和二次冲击激波均采用刚性气体状态方程),研究固体介质中的斜激波反射,比较了采用不同组合形式的状态方程对反射激波波后压力的影响.利用量纲分析方法讨论了简化状态方程达到较高精度的条件.此外,用ANSYS/LS-DYNA软件,对激波极曲线理论给出的结果进行了验证.本项工作可为固体介质中激波反射问题状态方程的选取提供一定的指导.     

GENERALIZED CIRCLES AND THEIR CONFORMAL MAPPING IN A SUBSPACE OF A WEYL SPACE

The authors give the necessary and sufficient conditions for a generalized circle in a Weyl hypersurface to be generalized circle in the enveloping Weyl space. They then obtain the neccessary and sufficient conditions under which a generalized concircular transformation of one Weyl space onto another induces a generalized transformation oil its subspaces. Finally, it is shown that any totally geodesic or totally umbilical hypersurface of a generalized concircularly flat Weyl space is also generalized concircularly flat.     

Generalized Supersymmetric Perturbation Theory

Using the basic ingredient of supersymmetry, a simple alternative approach is developed to perturbation theory in one-dimensional non-relativistic quantum mechanics. The formulae for the energy shifts and wavefunctions do not involve tedious calculations which appear in the available perturbation theories. The model applicable in the same form to both the ground state and excited bound states, unlike the recently introduced supersymmetric perturbation technique which, together with other approaches based on logarithmic perturbation theory, are involved within the more general framework of the present formalism.     

评介《半导体光谱和光学性质》一书(第2版)

这是一本由一位令人敬重的中国学者撰写的光学性质方面的经典著作 .其第一版是 1992年问世的 ,有里程碑标志意义 ,是第一本有关半导体光学性质的论著 .其写作定位的读者群是相关科学和技术领域内的研究生和科研工作者 .当时论著已涉猎了多方面的丰富内容 ,但其中仅有一章讨论量子阱光学性质 (该领域的最新研究成就 ,译者注补 ) .书的印刷质量按西方的标准看来是相当差的 ,书的后面缺少主题索引 .在第二版中作者对第一版的论述内容作了极其重要的 (significantly)拓展 .新增加了一章 ,并在其他各章中新添加了若干小节 .例如 ,在第一章中增添…     

Analytical evaluation of the derivatives used in equilibrium calculations

The derivatives of the total concentrations and other measured quantities with respect to the formation constants are calculated in general by a numerical method using finite increments. It is shown in this paper that these values can be calculated analytically, whereby the disadvantages of numerical differentiation may be avoided. The use of this method gives the possibility of writing faster programs for the calculation of the stability constants, based on the SCOGS and LETAGROP principle, without as large a memory requirement as in the LEAST and MINIQUAD programs.     

Ring-opening Polymerization of Chloromethyl Thiirane with Catalytic Systems Composed of Lanthanide Compound and Ethyl Aluminum Sesquichloride

Thering-openingpolymerinahonofchloromethylthiirane(CMT)wasfirstcatriedoutinl952.lLater,itwasfoundthatcahoniccatalystSH,SO','CF3SO3H,andBF,.OEt2'couldpolymerizeCMTbutwithoutdefndtedataofmolecularweightandcatalghcefficiency.Anioincinihators,suchasKOHandNaNH2,areineffechve.2OrganocomPoundsbasedoncadminIn,zinc,andaluIninmcanconvertCMTtoviscousoil.2TwocomPonentZiegler-NattampecatalystsbasedonneodyIninmtris(2-ethylhexylphosphonate),Nd(Pzoo)s,andtriisobutylaluIninUmeAlitedhighactivity…