The upper and lower second order directional derivatives of a sup-type function

The purpose of this paper is to give a formula for expressing the second order directional derivatives of the sup-type functionS(x) = sup{f(x, t); t T} in terms of the first and second derivatives off(x, t), whereT is a compact set in a metric space and we assume thatf, f/x and ² f/x ² are continuous on ⁿ × T. We will give a geometrical meaning of the formula. We will moreover give a sufficient condition forS(x) to be directionally twice differentiable.     

One-dimensional harmonic lattice caricature of hydrodynamics: Second approximation

The long-time behavior of an infinite chain of coupled harmonic oscillators is studied. In addition to a limiting hydrodynamic (Euler-type) equation, the next approximation is investigated. The corresponding equation is derived.     

超高真空中银表面垂直谐波电流的实验测量

在超高真空的条件下,测量了清洁、自由银表面产生的光学二次谐波随基波电矢量与入射面之间夹角(?)的变化,从而通过理论公式,求得由Rudnick和Stern引入的,用于衡量垂直面电流密度的唯象参数a的值,在入射基频光波长为1.064μm时,被测定为-4.0±0.8.     

Zur Theorie der Chiralitätsfunktionen

The Algebraic Theory of Chirality Functions is derived by means of exclusively qualitative considerations. Hence, the significance of quantitative results is questionable. Moreover the construction of “Näherungsansätze” (”Approximation-Ansatz”), which may be interpreted as semiempirical methods, is achieved on the basis of plausibility and mathematical simplicity. Since physical arguments are not included, the consistency or inconsistency of “Näherungsansätze” with experimental results do not justify direct physical conclusions.     

超球坐标下原子、分子体系的变分计算：—氦原子和氢负离子基态

应用超球会标表示氦原子和氢负离子的薛定谔方程，将二电子原子在三维空间中的运动转化为单电子原子在六维空间中受广义库仑力作用的运动，我们给出了六维空间广义角动量算符的本征值与本征函数，并以此本征函数微基构造超球波函数，得到超球径微分方程，以广义Laguerre 多项式表示超球径波函数，运用密度矩阵和线性变分法得到非正交基下超球径波函数满足的久期方程，最后求得能量和波函数，计算结果与精确的计算符合良好。     

薄层扫描法测定冬眠过程中刺猬活性组织酶的周期变化

薄层扫描法测定冬眠过程中刺猬活性组织酶的周期变化冯金城（天津师范大学天津３０００７４）孙金生（天津水产研究所天津３００２２１）１前言为了跟踪观察刺猬在冬眠过程中体内乳酸脱氢酶的周期性变化，利用薄层扫描仪测定了其相关的组织同工酶的差异。实践证明，此法简...     

Second‐harmonic response of a series of chiral polyesters: A joint experimental and theoretical study

A series of polyesters with π‐conjugated donor–acceptor segments was synthesized by the condensation of azobenzene‐4,4′‐dicarbonylchloride with 1,4:3,6‐dianhydro‐D‐sorbitol ([α] = + 42.5°) and biphenolic chromophores, bis(4‐hydroxyphenylazo)‐2,2′‐dinitrodiphenylmethane and bis(4‐hydroxyphenylazo)‐2,2′‐dinitrodiphenylsulfone. The polymers were characterized by spectral methods (IR, ultraviolet–visible, and NMR), thermal methods (thermogravimetry and differential scanning calorimetry), wide‐angle X‐ray scattering, and polarimetry. The polymers containing isosorbide units were optically active and crystalline. They exhibited glass‐transition temperature values between 100 and 160 °C and were stable up to 400 °C. The second‐harmonic generation (SHG) efficiency of the polymers was experimentally verified by a powder‐reflection technique with 2‐methyl‐4‐nitroaniline as a reference. The SHG efficiencies of the polymers were compared to those of the chromophores and explained as a function of the percentage of chiral composition. The hyperpolarizability β values were also determined by a two‐level model solvatochromic method and computational methods. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 2868–2877, 2002     

Synthesis and Structure of the New Ammonium Indium Phosphate (NH4)In(OH)PO4

A new ammonium indium phosphate (NH₄)In(OH)PO₄ was prepared by hydrothermal reaction in the In₂O₃-NH₄H₂PO₄-NH₃/OH system (T=200°C, autogenous pressure, 7 days). The formula (NH₄)In(OH)PO₄ was determined on the basis of chemical and thermal analysis (TG/DSC), X-ray powder diffraction and IR-spectroscopy. (NH₄)In(OH)PO₄ crystallizes in the tetragonal system with space group P4₃2₁2 (No. 96); a=9.4232(1) Å, c=11.1766(1) Å, V=992.45(2) ų; Z=8. The crystal structure was refined by the Rietveld method (R_w=6.35%, R_p=5.10%). The second-harmonic generation study confirmed that structure of (NH₄)In(OH)PO₄ does not have a center of symmetry. The cis-InO₄(OH)₂ octahedra form helical chains, parallel to the c-axis. The In-O-In bonds are nearly equidistant. The chains are interconnected by phosphate tetrahedra and create tunnels containing the NH₄⁺ ions along the c-axis. (NH₄)In(OH)PO₄ is isostructural with RbIn(OH)PO₄.     

Second-order nonlinear optical properties of side-chain liquid crystalline polymers studied by second harmonic generation from thin films

The two independent elements of the second-order nonlinear optical susceptibility tensor of a range of contact poled, donor–acceptor substitued side-chain polymers are reported. The susceptibilities were measured by second harmonic generation from thin films, typically less than 0.5 μm thick, at a fundamental wavelength of 1064 nm. The largest value was χ = 2.64 pm/V which is three times greater than the χ value of KDP and was measured in a nitrobenzylidene side chain, polyhydroxystyrene polymer with an eleven unit alkyl chain spacer attaching the side group to the backbone. Typical susceptibility values obtained were χ～0.3 pm/V and X⁽²⁾₃₃～1 pm/V. The coherence lengths of the materials, which lay in the range 4–12 μm, were measured at 1064 nm by the maker fringe technique using thick, wedge-shaped samples.     

Contracted polarization functions for B to Ar

Using optimal exponents for B through Ne given by Dunning and those for Al through Ar by Woon and Dunning, d-type contracted polarization functions (2d/1d), (3d/1d), and (3d/2d) are generated from natural orbitals of atomic single and double excitation configuration interaction (SDCI) calculations, where the numbers before and after the slash are those of the primitive and contracted Gaussian type functions. The resulting contracted functions are tested on N₂ and P₂ molecules by self-consistent field and SDCI calculations, which clarify characteristics of the present polarization functions. Received: 5 June 1997 / Accepted: 20 August 1997