Cochran's statistical theorem for outer inverses of matrices and matrix quadratic forms

We extend the matrix version of Cochran's statistical theorem to outer inverses of a matrix. As applications, we investigate the Wishartness and independence of matrix quadratic forms for Kronecker product covariance structures.     

On perfectly normal dense subspaces of products

Let M be a separable metric space consisting of more than one point. We construct perfectly normal dense subspaces Z⊂Mc² and (under additional set-theoretic assumption) Y⊂Mc which are not collectionwise Hausdorff.     

Tchebychev acceleration technique for large scale nonsymmetric matrices

Summary The acceleration by Tchebychev iteration for solving nonsymmetric eigenvalue problems is dicussed. A simple algorithm is derived to obtain the optimal ellipse which passes through two eigenvalues in a complex plane relative to a reference complex eigenvalue. New criteria are established to identify the optimal ellipse of the eigenspectrum. The algorithm is fast, reliable and does not require a search for all possible ellipses which enclose the spectrum. The procedure is applicable to nonsymmetric linear systems as well.     

Symmetries and conservation laws of Navier-Stokes equations

All the symmetries and conservation laws of Navier-Stokes equations are calculated.     

A characterization of the \Sigma_1-definable functions of KP\omega + (uniform\; AC)

The subject of this paper is a characterization of the -definable set functions of Kripke-Platek set theory with infinity and a uniform version of axiom of choice: . This class of functions is shown to coincide with the collection of set functionals of type 1 primitive recursive in a given choice functional and . This goal is achieved by a G?del Dialectica-style functional interpretation of and a computability proof for the involved functionals. Received October 9, 1996     

On the geometries of the rational unfoldings of X k

With a view to applications to self-regulating dynamical processes in biology, we determine the geometric structure of what we call isotangent curves, i.e. curves parametrized by the slopes of their points. They come up naturally as bifurcation curves of rational unfoldings of X ^k, and we classify them according to degree and number of cusps. They, as well as their isotangent involute curves, turn up in simulations of these processes.     

Some inequalities for partial orders

We establish some inequalities connecting natural parameters of a partial order P. For example, if every interval [a,b] contains at most maximal chains, if some antichain has cardinality v, and if there are ₁ chains whose union is cofinal and coinitial in P, then the chain decomposition number for P is ₁v (Theorem 2.2), and the inequality is sharp in a certain sense (Section 3).This paper was written while the authors were visitors at the Laboratoire d'algèbre ordinale, Département de Mathématiques, Université Claude Bernard, Lyon 1, France.Research supported by NSERC grant # A5198.     

锰（Ⅱ）—邻菲口罗啉配合物极谱吸附波及其应用

在ｐＨ９．５ＮＨ３ＮＨ４Ｃｌ缓冲溶液中，Ｍｎ（Ⅱ）与邻菲口罗啉形成的配合物在－１．３６Ｖ（ｖｓ．ＳＣＥ）处产生一灵敏的吸附波，一阶导数峰电流与Ｍｎ（Ⅱ）浓度在５×１０－８５×１０－６ｍｏｌ／Ｌ范围内呈线性关系，检出限为２×１０－８ｍｏｌ／Ｌ对极谱性质及反应机理进行了研究，用该法测定了大豆和茶叶中的微量锰，结果满意     

Synthesis ofS-(+)-hydroprene

A novel path toS-(+)-hydroprene (1) starting from the technical gradeS-(+)-dihydromyrcene (2, e.e. 50%) is proposed. The latter was selectively transformed intoS-3,7-dimethyloctanal (5) in three steps including hydroalumination. The reactions of5 with allyl- or methallylmagnesium chloride followed, respectively, either by oxygenation in the presence of PdCl₂/CuCl or by ozonolysis, affordS,E-6,10-dimethyl-3-undecen-2-one (7) which was treated with ethoxyethynylmagnesium bromide to give the title juvenile hormone analogue in 23% overall yield.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No 1, pp. 110–112, January, 1993.     

Synthesis of New Difurocoumarins

5,7-Dihydroxy-4-methyl- and 5,7-dihydroxy-4-trifluoromethylcoumarins are starting compounds in the synthesis of new 10-methyl-8H-difuro[2,3-f;2,3-h]-8-ones and 10-trifluoromethyl-8H-difuro-[2,3-f;2,3-h]chromen-8-ones with high yields.