SAPO－5，－11和－34分子筛模板剂的脱除及其结构的热致变化

用水热法合成了ＳＡＰＯ－５，－１１和－３４硅磷酸铝类分子筛。并对经不同温度焙烧处理的样品进行表征，结果表明：分子筛中模块剂的热分解过程与其结构和孔大小有较大的关系。在ＳＡＰＯ－５和ＳＡＰＯ－３４分子筛中，外部联接的Ｔ－Ｏ－Ｔ键的反对称伸缩振动峰（１２４０ｃｍ~（－１）－１０３８ｃｍ~（－１））和其对称伸缩振动（７３４ｃｍ~（－１）－６００ｃｍ~（－１））及双环的变形振动（６００－５００ｃｍ~（－１））的吸收峰对样品的结晶度比较敏感。但在ＳＡＰＯ－１１中，分子筛骨架中Ｔ－Ｏ－Ｔ反对称伸缩振动（１２２５ｃｍ~（－１）和１０３８ｃｍ~（－１））随结晶度的下降而基本保持不变，但内四面体（ＴＯ_４）的对称伸缩振动，反对称伸缩振动峰及Ｔ－Ｏ弯曲振动峰随样品焙烧温度的升高而减弱并分裂。红外吸收带向低频方向移动。ＳＥＭ－ＥＤＡＸ结果表明：随样品焙烧温度的升高，结晶度下降，分子筛晶形变得不规则，晶面越来越粗糙，但结晶度的下降并非由于其中ＰＯ_４四面体的热分解所引起，而是由外部联结的Ｔ－Ｏ－Ｔ键的断裂，双环被破坏及骨架元素间的重排所引起。     

Darstellung und Strukturen einiger N-(Tri-t-butoxysilyl)anilin-Derivate

Formation and Structures of N-(tri-t-butoxysilyl)aniline Compounds Para-substituted N-(tri-t-butoxysilyl)anilines (t-BuO)₃SiNRC₄H₄X-p, R = H, CH₃, with substituents of high electron affinity (X = CN, NO₂) were prepared by a one-pot reaction of tri-t-butoxychlorsilane, potassium t-butanolate and substituted anilines. Corresponding compounds with substituents of low electron affinity (X = OMe, H) preferably were prepared by metalation of anilines with sodium amide. Four crystal structures were determined. N-(tri-t-butoxysilyl)-p-nitro-aniline, N-methyl-(N-tri-t-butoxysilyl)-p-nitroaniline and N-(tri-t-butoxysilyl)-p-cyanoaniline crystallize at 298 K monoclinically, N-(tri-t-butoxysilyl)aniline crystallizes orthorhombically.     

Invariant manifolds and global error estimates of numerical integration schemes applied to stiff systems of singular perturbation type -- Part I: RK-methods

Summary. For implicit RK-methods applied to singularly perturbed systems of ODEs it is shown that the resulting discrete systems preserve the geometric properties of the underlying ODE. This invariant manifold result is used to derive sharp bounds on the global error of RK-solutions. Received August 26, 1993 / Revised version received May 10, 1994     

Kneser-type oscillation criteria for self-adjoint two-term differential equations

It is proved that the even-order equationy ⁽²ⁿ⁾ +p(t)y=0 is (n,n) oscillatory at 34.gif" alt="infin" align="MIDDLE" border="0"> if

BV periodic solutions of an evolution problem associated with continuous moving convex sets

This paper is concerned with BV periodic solutions for multivalued perturbations of an evolution equation governed by the sweeping process (or Moreau's process). The perturbed equation has the form –DuN _C (t)(u(t))+F(t,u(t)), whereC is a closed convex valued continuousT-periodic multifunction from [0,T] to ^d ,N ^C (t)(u(t)) is the normal cone ofC(t) atu(t),F: [0,T]× ^{d d} is a compact convex valued multifunction and Du is the differential measure of the periodic BV solutionu. Several existence results for this differential inclusion are stated under various assumptions on the perturbationF.     

On some properties of solutions of second-order linear functional differential equations

The properties of solutions of the equationu″(t) =p ₁(t)u(τ₁(t)) +p ₂(t)u′(τ₂(t)) are investigated wherep _i :a, + W34;[→R (i=1,2) are locally summable functions τ₁ :a, + W34;[→R is a measurable function, and τ₂ :a, + W34;[→R is a nondecreasing locally absolutely continuous function. Moreover, τ _i (t) ≥t (i = 1,2),p ₁(t)≥0,p ₂ ² (t) ≤ (4 - ɛ)τ ₂ ^′ (t)p ₁(t), ɛ =const > 0 and 343j33ln456/11290_2006_Article_BF02317679_TeX2GIFIE1.gif" alt=" $$\int {_a^{ + \infty } } (\tau _1 (t) - t)p_1 (t)dt< + \infty $$ " align="middle" border="0"> . In particular, it is proved that solutions whose derivatives are square integrable on [α,+W34;] form a one-dimensional linear space and for any such solution to vanish at infinity it is necessary and sufficient that 343j33ln456/11290_2006_Article_BF02317679_TeX2GIFIE2.gif" alt=" $$\int {_a^{ + \infty } } tp_1 (t)dt = + \infty $$ " align="middle" border="0"> .     

Oscillatory criteria for nonlinearnth-order differential equations with quasiderivatives

Sufficient conditions are given for the existence of oscillatory proper solutions of a differential equation with quasiderivativesL _n y=f(t,L ₀ y, ..., L _n–1 y) under the validity of the sign conditionf(t,x ₁ ,...,x _n )x ₁0,f(t,0,x ₂ ,...,x _n )=0 on ₊ x ⁿ .     

Nonselfadjoint spectral problems for linear pencilsN-λP of ordinary differential operators with λ-linear boundary conditions: Completeness results

We study nonselfadjoint spectral problems for ordinary differential equationsN(y)–P(y)=0 with -linear boundary conditions where the orderp of the differential operatorP is less than the ordern ofN. The present paper addresses the question of the completeness of the eigenfunctions and associated functions in the Sobolev spacesW ₂ ^k (0,1) fork=0,1,...,n. To this end we associate a pencil – of operators acting fromL ₂(0,1) to the larger spaceL ₂x(0,1) ⁿ with the given problem. We establish completeness results for normal problems in certain finite codimensional subspaces ofW ₂ ^k (0,1) which are characterized by means of Jordan chains in 0 of the adjoint of the compact operator = ^–1.Dedicated to Professor Heinz Langer on the occasion of his 60th birthday     

Complete separability of time-dependent second-order ordinary differential equations

Extending previous work on the geometric characterization of separability in the autonomous case, necessary and sufficient conditions are established for the complete separability of a system of time-dependent second-order ordinary differential equations. In deriving this result, extensive use is made of the theory of derivations of scalar and vector-valued forms along the projection :J ¹ EE of the first jet bundle of a fibre bundleE . Two illustrative examples are discussed, which fully demonstrate all aspects of the constructive nature of the theory.