Congruences of small degree in G(1,4)

We give the list of all possible congruences in G(1,4) of degree d ≤10 and we explicitely construct most of them.     

Smooth Kummer surfaces in projective three-space

In this note we prove the existence of smooth Kummer surfaces in projective three-space containing sixteen mutually disjoint smooth rational curves of any given degree.

     

Smooth approximation of polyhedral surfaces regarding curvatures

In this paper we prove that every closed polyhedral surface in Euclidean three-space can be approximated (uniformly with respect to the Hausdorff metric) by smooth surfaces of the same topological type such that not only the (Gaussian) curvature but also the absolute curvature and the absolute mean curvature converge in the measure sense. This gives a direct connection between the concepts of total absolute curvature for both smooth and polyhedral surfaces which have been worked out by several authors, particularly N. H. Kuiper and T. F. Banchoff.The present paper is a detailed version of the short announcement [3].     

Superintegrable models on Riemannian surfaces of revolution with integrals of any integer degree (I)

We present a family of superintegrable (SI) systems which live on a Riemannian surface of revolution and which exhibit one linear integral and two integrals of any integer degree larger or equal to 2 in the momenta. When this degree is 2, one recovers a metric due to Koenigs.The local structure of these systems is under control of a linear ordinary differential equation of order n which is homogeneous for even integrals and weakly inhomogeneous for odd integrals. The form of the integrals is explicitly given in the so-called “simple” case (see Definition 2). Some globally defined examples are worked out which live either in H² or in R².     

Smooth functions onC(K)

We show that every Fréchet differentiable real function onC(K), K scattered with locally uniformly continuous derivative has locally compact derivative. Using this and similar results, we investigate the existence ofC ²-Fréchet smooth surjections between various Banach spaces.     

Irregular elliptic surfaces of degree 12 in projective fourspace

So far a few families of smooth irregular surfaces are known to exist in ?⁴ up to pullbacks by suitable finite morphisms from ?⁴ onto ?⁴ itself. In this paper we present two different constructions of irregular smooth minimal elliptic surfaces of degree 12 in ?⁴. The first is a monad construction while the other uses liaison. The family constructed via liaison includes the surfaces of the first family as a special case. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Smooth surfaces in smooth fourfolds with vanishing first Chern class

According to a conjecture attributed to Hartshorne and Lichtenbaum and proven by Ellingsrud and Peskine [18], the smooth rational surfaces in ${\mathbb{P}}^4$ belong to only finitely many families. We formulate and study a collection of analogous problems in which ${\mathbb{P}}^4$ is replaced by a smooth fourfold X with vanishing first integral Chern class. We embed such X into a smooth ambient variety and count families of smooth surfaces which arise in X from the ambient variety. We obtain various finiteness results in such settings. The central technique is the introduction of a new numerical invariant for smooth surfaces in smooth fourfolds with vanishing first Chern class.     

Smooth convex limit surfaces in the space of symmetric second-rank tensors

Equations are proposed to describe smooth (regular) convex hexagonal and triangular curves in the deviatoric plane. The equations are used to construct smooth convex limit surfaces for media whose properties are arbitrarily anisotropic. The results supplement the findings in [A. Lagzdin' and A. Zilauts, Mekh. Kompozitn. Mater.,32, No. 3, 339–349 (1996)], where the third invariant of a tensor was introduced into the limit-surface equation by means of singular deviatoric curves.Institute of Polymer Mechanics of the Latvian Academy of Sciences, Riga, LV-1006 Latvia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 2, pp. 171–181, March–April, 1997.     

L^∞（G）中的一个闭凸不变集

设G是局部紧群,f是G上的右一致连续函数.本文讨论L(G)中一个闭凸不变集的关系式Co{Lxfx∈G}11@11={φ*fφ∈P＇(G)}11@11(f∈R∪C(G)).由此式易得出RUC(G)上的左不变平均与拓扑左不变平均的等价关系.     

Del Pezzo surfaces of degree 1 and Jacobians

We construct absolutely simple jacobians of nonhyperelliptic genus 4 curves, using Del Pezzo surfaces of degree 1.     

Non-normal surfaces of degree 5 and 6 in P n

The purpose of this paper is to describe the non-normal surfaces of degree 5 and 6 embedded in the complex projective space P ⁿ , with n4. The idea is to study the normalization of such a surface, and then to find how a non-normal surface can be obtained from its normalization.     

C(Ω)空间上的光滑点刻画

该文主要研究了C(Ω)型空间上的光滑点(即峰值函数)的存在性和稠密性,其中Ω为紧Hausdorff空间.当Ω不可度量化时,给出了例子说明存在紧Hausdorff空间Ω_1使得C(Ω_1)空间上的光滑点在全空间稠密,并且给出了反方面的例子说明存在紧Hausdorff空间Ω_2使得C(Ω_2)空间上的光滑点为空集.最后给出了C(Ω)型空间上的光滑点稠密的充要条件.     

On certain surfaces of revolution of the second degree

An improvement in the generation of some second-order surfaces of rotation and their construction is presented. In this case, a cube is rotated about one its diagonals to obtain a hyperboloid of one sheet with two duplicate cones on each side.     

The polynomial degree of the Grassmannian G(1,n,q) of lines in finite projective space PG(n, q)

Let G: = G(1,n,q) denote the Grassmannian of lines in PG(n,q), embedded as a point-set in PG(N, q) with For n = 2 or 3 the characteristic function of the complement of G is contained in the linear code generated by characteristic functions of complements of n-flats in PG(N, q). In this paper we prove this to be true for all cases (n, q) with q = 2 and we conjecture this to be true for all remaining cases (n, q). We show that the exact polynomial degree of is for δ: = δ(n, q) = 0 or 1, and that the possibility δ = 1 is ruled out if the above conjecture is true. The result deg( for the binary cases (n,2) can be used to construct quantum codes by intersecting G with subspaces of dimension at least