Convergence of mixed finite element approximations for the shallow arch problem

Summary The stability and convergence of mixed finite element methods are investigated, for an equilibrium problem for thin shallow elastic arches. The problem in its standard form contains two terms, corresponding to the contributions from the shear and axial strains, with a small parameter. Lagrange multipliers are introduced, to formulate the problem in an alternative mixed form. Questions of existence and uniqueness of solutions to the standard and mixed problems are addressed. It is shown that finite element approximations of the mixed problem are stable and convergent. Reduced integration formulations are equivalent to a mixed formulation which in general is distinct from the formulation shown to be stable and convergent, except when the order of polynomial interpolationt of the arch shape satisfies 1tmin (2,r) wherer is the order of polynomial approximation of the unknown variables.     

On the solution of singular linear systems of algebraic equations by semiiterative methods

Summary For a square matrixT ^n,n , where (I–T) is possibly singular, we investigate the solution of the linear fixed point problemx=T x+c by applying semiiterative methods (SIM's) to the basic iterationx ₀ ⁿ ,x _k T c _k–1+c(k1). Such problems arise if one splits the coefficient matrix of a linear systemA x=b of algebraic equations according toA=M–N (M nonsingular) which leads tox=M ^–1 N x+M ^–1 bT x+c. Even ifx=T x+c is consistent there are cases where the basic iteration fails to converge, namely ifT possesses eigenvalues 1 with ||1, or if =1 is an eigenvalue ofT with nonlinear elementary divisors. In these cases — and also ifx=T x+c is incompatible — we derive necessary and sufficient conditions implying that a SIM tends to a vector which can be described in terms of the Drazin inverse of (I–T). We further give conditions under which is a solution or a least squares solution of (I–T)x=c.Research supported in part by the Alexander von Humboldt-Stiftung     

The many limits of mixed means

The sequences introduced by Carlson (1971) are variants of the Gauss arithmetic geometric sequences (which have been elegantly discussed by D. A. Cox (1984, 1985)). Given (complex)a ₀,b ₀ we define

What do multistep methods approximate?

Summary Standard analysis of multistep methods for ODE's assumes the application of an initialization routine that generates the starting points. Here ak-step method is considered directly as a mappingR ^kn R ⁿ . It is shown to approximate a mapping which is expressible directly in terms of the flow of the vector field. Some useful properties of that mapping are shown and for strictly stable methods these are applied to the question of invariant circles near a hyperbolic periodic solution.     

Convolution quadrature and discretized operational calculus. I

Numerical methods are derived for problems in integral equations (Volterra, Wiener-Hopf equations) and numerical integration (singular integrands, multiple time-scale convolution). The basic tool of this theory is the numerical approximation of convolution integrals

Strukturelle Charakterisierung der Dicyanamid-Komplexe von Kupfer(II), Nickel(II) bzw. Kobalt(II) mit Aminopyridinen

Summary New dicyanamide complexes of the typeM[N(CN)₂]₂ L ₂ (M=Cu or Ni;L=2-, 3-, 4-aminopyridine, 2-amino-5-nitropyridine) and Co[N(CN)₂]₂ (2-amino-5-nitropyridine)₂ were prepared and studied by spectroscopic methods as well as by room-temperature magnetic moments. The results show that the Cu(II) complexes have elongated pseudooctahedral structures while the Ni(II) and Co(II) complexes are octahedral. In most cases the N(CN)₂ groups are in bridging function and through their cyanide nitrogens, or-more rarely-amide and cyanide nitrogens connect the basic structure units into polymeric conglomerates. In the Cu(II) systems exchange coupling is seen from the _eff value or ESR spectrum.

Professor Viktor Gutmann zum 70. Geburtstag gewidmet     

Potentiometric studies on the complexation equilibria between some trivalent lanthanide metal ions and biologically active 2-hydroxy-1-naphthaldehyde thiosemicarbazone (HNATS)

Summary The chelation behaviour of some trivalent lanthanide and yttrium metal ion with biologically active 2-hydroxy-1-naphthaldehyde thiosemicarbazone (HNATS) has been investigated by potentiomotric measurements at 20±0.5°C in 75% (v/v) dioxane-water medium at various ionic strengths of sodium perchlorate. The method of Bjerrum and Calvin, as modified by Irving and Rossotti has been used to find out the values of (average number of ligand bound per metal ion) andpL (free ligand exponent). The formation constants of metal chelates have been computed on a PC-XT computer, using a program patterned after that of Sullivan et al. to give _n values using weighted least squares method. TheS _min values (S _min =²) have been calculated. The order of formation constants of chelates was found to be: La³⁺3+3+3+3+3+3+3+3+3+. The formation constants of the chelates formed have been correlated to size and ionization potentials of the metal ions.

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Potentiometrische Untersuchungen der Komplexierungsgleichgewichte zwischen einigen trivalenten Metallionen und biologisch aktivem 2-Hydroxy-1-naphthaldehyd-thiosemicarbazon (HNATS)

Zusammenfassung Es wurde das Chelierungsverhalten einiger trivalenter Lanthanidenionen mit biologisch aktivem 2-Hydroxy-1-naphthaldehyd-thiosemicarbazon (HNATS) mittels potentiometrischer Messungen bei 20±0.5°C in 75% (v/v) Dioxan-Wasser bei verschiedener Ionenstärke an Natriumperchlorat untersucht. Die Methode nach Bjerrum und Calvin in der Modifikation nach Irving und Rossotti wurde zur Ermittlung der Werte (mittlere Anzahl an Liganden pro Metallion) undpL (Exponent an freiem Liganden) verwendet. Die Komplexbildungskonstanten wurden in Anlehnung an Sullivan et al. an einem PC-XT Computer errechnet. DieS _min-Werte (S _min=²) wurden ebenfalls bestimmt. Die Reihung der Chelatbildungskonstanten war: La³⁺3+3+3+3+3+3+3+3+3+. Die Bildungskonstanten sind mit der Größe und dem Ionisierungspotential der Metallionen zu korrelieren.

     

ZnCl2/粘土-SA01催化剂上二苯甲烷的合成

在环境友好ZnCl2/粘土-SA01催化剂上合成了二苯甲烷,较系统地考察了负载量、苯/苄基氯摩尔比、催化剂用量、反应温度、反应时间对该傅克反应的影响,并与催化剂的表面性质关联.实验结果表明,该催化剂具有良好的催化活性和稳定性并易于回收重复使用.     

Rh(Ⅰ),Co(Ⅰ)和Ru(Ⅱ)双齿磷氢化物的合成.结构表征和催化加氢活性

膦配位的过渡金属氢化物被看作是烯烃及其他一些不饱含有机化合物催化加氢反应及氢甲酰化反应的催化活性物种,关于它们的结构与催化活性关系的研究,有着重要的理论意义和实际意义,通常单齿膦配位表现出较高的催化活性,而不同的金属中心在催化活性和选择性上也表现出明显的差别,反映了催化功能与催化活性物种的电子结构和空间结构之间存在着依存关系.膦配体过渡金属氢化物,通常是以它们的相应卤化物经氢化锂铝或硼氢化钠或肼还原得     

钢中Si、Mn的电子探针定量分析与标样

采用特制的Fe-Si、Fe-Mn合金系列标样，用电子探针测定了钢或铁基合金中低含量的Si和Mn元素、与用纯元素作标样、经ZAF修正的结果相比较，提高了分析准确度．