On first order congruences of lines of ℙ4 with a fundamental curve

We discuss projective families of lines of ℙ ⁿ , and in particular congruences of order one. After giving general results, we obtain a complete classification of the case of ℙ⁴ in which there is a fundamental curve. Received: 2 August 2000 / Revised version: 11 July 2001     

不锈钢管道低温溅射镀TiN薄膜技术

 设计了一套适用于加速器细长管道真空室的低温溅射镀TiN薄膜装置。利用该装置，对86 mm×2 000 mm的不锈钢管道真空室进行溅射镀TiN膜实验，并对镀膜实验结果进行分析，得到了适用于加速器管道真空室内壁溅射镀TiN膜的表面处理参数。样品测试结果表明：在压强为80～90 Pa、基体温度为160~180 ℃的镀膜参数下，不锈钢管道内壁获得的TiN薄膜最佳，薄膜沉积速率为0.145 nm/s。镀膜后真空室的二次电子产额明显降低。     

Characteristic polynomials of symmetric matrices III: some counterexamples

When is a monic polynomial the characteristic polynomial of a symmetric matrix over an integral domain D? Known necessary conditions are shown to be insufficient when D is the field of 2-adic numbers and when D is the rational integers. The latter counterexamples lead to totally real cubic extensions of the rationals whose difierents are not narrowly equivalent to squares. Furthermorex³-4x+1 is the characteristic polynomial of a rational symmetric matrix and is the characteristic polynomial of an integral symmetric p-adic matrix for every prime p, but is not the characteristic polynomial of a rational integral symmetric matrix.     

A note on realizing homomorphisms of category algebras

The complete Boolean homomorphisms from the category algebra $\text{C}$(X) of a complete matrix space X to the category algebra $\text{C}$(Y) of a Baire topological space Y are characterized as those σ-homomorphisms which are induced by continuous maps from dense G₈-subsets of Y into X. This result is used to deduce a series of related results in topology and measure theory (some of which are well-known). Finally a similar result for the complete Boolean homomorphisms from the category algebra $\text{C}$(X) of a compact Hausdorff space X tothe category algebra $\text{C}$(Y) of a Baire topological space Y is proved.     

On Bröcker'st-invariant and separating families for constructible sets

Summary The paper looks at certain open problems in the theory of minimal generation of semi-algebraic sets and constructible sets in the real spectrum: problems about thet-invariant and the associatedp-invariant for separating families, and about the extension of the theory to arbitrary commutative rings.     

Codimension one spheres in Rn with double tangent balls

In contrast to the situation in $\text{R}$³, where a 2-sphere with double tangent balls at each point must be tamely embedded in $\text{R}$³, there exist wild (n?1)-spheres in $\text{R}$ⁿ for n>3 with this same geometric property. However, if the sphere Σ is tame moduio a subset X that lies in a polyhedron P that is tame in Σ, the dimension of P is less than n?2, n>4, and Σ has double tangent balls over X, then Σ must be tame in $\text{R}$ⁿ. Also if the tangent balls extend over P and are pairwise congruent, the dimensional restriction on P can be dropped. Examples are given to support the necessity of the hypotheses of the included theorems.     

An approximation theorem in shape theory

In this paper it is shown that if X is a compactum in the interior of a PL manifold M and if U is a neighborhood of X in M, then there is a compactum X′ in U such that X and X′ have the same relative shape in U and the embedding dimension of X′ equals the fundamental dimension of X. Whenever the dimension of M is not equal to three, the relative shape equivalence from X′ to X can be realized by an infinite isotopy of M.