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.     

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.     

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…     

用分子运动论推导理想气体绝热定律

与通常单独从热力学推导相反，本文证 明了如何从麦克斯韦－玻尔兹曼（或其他任 意）速度分布假设推导理想气体绝热定律．文 中还讨论了导致单体粘滞性（ｏ ｎｅ－ｂｏｄｙｖｉｓｃｏｓｉｔｙ）的高阶效应，给出了适合于低年级 的更简单的绝热定律的推导．     

Ultraviolet up-conversion luminecence of noncrystalline HOP_5O_(l4) induced by 532nm pulsed laser

This paper reports the ultraviolet up-conversion luminescence of the noncrystalline HoP_5O_(14) at room temperature induced by 532nm pulsed laser for the first time and gives some simple analysis.