WKB-type approximations for second-order differential equations in -algebras

Rigorous asymptotic approximations of the WKB (or Liouville-Green) type are obtained for a basis of solutions to in the framework of -algebras. Both cases and are included, thus generalizing the classical theory for scalar equations developed by F.W.J. Olver to matrix as well as to infinite-dimensional equations.

     

A global pinching theorem for compact surfaces inS 3 with constant mean curvature

LetM be a compact minimal surface inS ³. Y. J. Hsu^[5] proved that if S₂22, thenM is either the equatorial sphere or the Clifford torus, whereS is the square of the length of the second fundamental form ofM, ·₂ denotes theL ²-norm onM. In this paper, we generalize Hsu's result to any compact surfaces inS ³ with constant mean curvature.Supported by NSFH.     

Thermal decomposition of transition metal carboxylates

Thermal solid-phase decomposition of anhydrous copper(ii) formate has been studied at 120–180 ° The rate of gas evolution during the decomposition depends on the depth of conversion and can be presented as the sum of first-order reaction rates and the rate of the autocatalytic process (a second-order reaction). The evolution of the solid phase during thermolysis has been observed by optical microscopy. The decomposition of copper formate is a complex topochemical process, a combination of homogeneous and heterogeneous transformations and dispersion of large crystals.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. l, pp. 72–76, January, 1996.     

Reaction of 2,6-dibenzylidenecyclohexanone with phosphorus pentachloride: Triple functionalization of the isosemiquinoid system

The reaction of 2,6-dibenzylidenecyclohexanone with PCl₅ occursvia the sequential stages of desoxychlorination and substitutional phosphorylation to form (after oxidation, methoxylation, and hydrolysis on the surface of the chromatographic SiO₂ adsorbent) organophosphorus products of the 1-(a-chloro-, a-hydroxy-, or -alkoxy)benzyl-2-chloro-3-(-(dimethylphosphoryl)benzylidene)cyclobex-1-ene series.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 441–443, February, 1996.     

A predictive model for impact response of viscoelastic polymers in drop tests

We show for the first time that a classical Hookean viscoelastic constitutive law for rubbery materials can predict the impact forces and deflections measured with a commercial drop tester when a mass, or tup with a flat impacting surface is dropped onto a flat pad of commercial impact-absorbing rubber. The viscoelastic properties of the rubber, namely the relaxation times and strengths, are obtained by a standard rheological linear-oscillatory test, and the equation of momentum transfer is then solved, using these measured parameters, assuming a uniaxial deflection of the pad during the impact. Good agreement between measured and predicted forces and deflections is obtained for a series of various drop heights, tup masses, impact areas, and pad thicknesses, as long as the deflection of the pad relative to its thickness is small or modest (<50% or so), and as long as the area of the pad is less than or equal to that of the tup. When the pad area is greater than the tup, forces are higher than predicted, unless an empirical factor is introduced to account for the nonuniaxial stretching of the ring of material that extends outside of the impact area. These results imply that the impact-absorbing properties of a rubbery polymeric material can be assessed by simply examining the material's linear viscoelastic spectrum.     

不共轴光学系统自动优化中的有关问题

描述不共轴光学系统计算机优化中坐标变换与逆变换、“入瞳”与光线坐标、像面基准与质量函数定义的一致性问题。     

Surface modified precipitated calcium carbonates at a high degree of dispersion

Calcium carbonates of different degrees of surface hydrophobicity were obtained when sorbic acid or polyoxyethylene glycol were present during the precipitation. In the presence of trace amounts of divalent cations carbonates with high surface hydrophilicity and improved monodisperse character are obtained. Surface modification of the calcium carbonates by several proadhesive compounds can markedly improve the chemical affinity of the carbonates to polymers. Very effective are isostearoyl titanate and two polyoxyethylene compounds. Precipitated calcium carbonates modified with 2 to 3 percent (wt/wt) of isostearoyl titanate increased the tensile strenght of butadiene-styrene rubber by approximately 100%. Polyurethane is only strengthened when 30 wt/wt of a filler are introduced independently of the type proadhesive compounds. The best strength and hysteresis of polyurethanes are obtained with calcium carbonate modified with 2 percent (wt/wt) of polyoxyethylene glycol.     

Fubini theorem for anticipating stochastic integrals in Hilbert space

Let (X,l,) be a measure space, letW be a cylindrical Hilbert-Wiener process, and let be an anticipating integrable process-valued function onX. We prove, under natural assumptions on, that there exists a measurable version Y_x,x X, of the anticipating integral of(x) such that the integral _x Y_x(dx) is a version of the anticipating integral of _X (x)(dx). We apply this anticipating Fubini theorem to study solutions of a class of stochastic evolution equations in Hilbert space.     

An application of the generalized alternating polynomials to the numerical solution of Fredholm integral equations

Generalized alternating polynomials have been introduced by the author earlier. In the present paper their indirect analogue is constructed for numerical solution of the Fredholm linear integral equations. Although the proposed method is a particular case of the general projection scheme, its valuable feature is the presence of a sequence of parameters, which, for sufficiently smooth kernels and inhomogeneous terms, serves as an indicator of the quality of approximation.     

Electronic control of stereoselectivity. 20. Crystal and molecular structure of the ferrocene derived from tricyclo[5.2.1.02,6]Deca-2,5,8-triene

Reaction of the isodicyclopentadienide anion and its dehydro congener with Fe(II) leads to a stereochemically homogeneous ferrocene derivative in each instance. Through chemical correlation and X-ray analysis, above-plane complexation is established for both halves within the two sandwich compounds.