A connectedness result in positive characteristic

Let be a complete local ring of dimension at least two, which contains a separably closed coefficient field of positive characteristic. Using a vanishing theorem of Peskine-Szpiro, Lyubeznik proved that the local cohomology module is Frobenius-torsion if and only if the punctured spectrum of is connected in the Zariski topology. We give a simple proof of this theorem and, more generally, a formula for the number of connected components in terms of the Frobenius action on .

     

On a result of Avramov

We obtain some consequences in Commutative Algebra of a result of L.L. Avramov concerning deviations of local rings.     

On a result of Riemenschneider

O. Riemenschneider has recently exhibited a class of normal 2-dimensional analytic singularities for which some deformations of the minimal resolution cannot be blown down to deformations of the singularity. In this note we identify the obstructions to doing so, using algebraic techniques introduced by Schlessinger and the author.Partially supported by National Science Foundation under grant GP 32843 to Columbia University.     

On a result of Cartlidge

We give a simple proof of Cartlidge's result on the lp operator norms of weighted mean matrices.     

On a result of Birkhoff

The research of the first two authors was supported by the NSERC of Canada.     

On a result of Miyanishi-Masuda

Let X be an affine surface admitting a unique affine ruling and a -action. Assume that the ruling has a unique degenerate fibre and that this fibre is irreducible. In this paper we give a short proof of the following result of Miyanishi and Masuda: the universal covering of X is a hypersurface in the affine 3-space given by the equation x^my = z^d − 1, where m > 1. Received: 13 June 2005     

On a result by geronimus

In 1935, Ya.L. Geronimus found the best integral approximation on the period [?π,π) of the function sin(n + 1)t ? 2q sin nt, q ∈ ?, by the subspace of trigonometric polynomials of degree at most n ? 1. This result is an integral analog of the known theorem by E.I. Zolotarev (1868). At present, there are several methods of proving this fact. We propose one more variant of the proof. In the case |q| ≥ 1, we apply the (2π/n)-periodization and the fact that the function | sin nt| is orthogonal to the harmonic cos t on the period. In the case |q| < 1, we use the duality relations for Chebyshev’s theorem (1859) on a rational function least deviating from zero on a closed interval with respect to the uniform metric.     

On a strong Tauberian result

Summary We consider the determination of the behavior of a distribution function F at its endpoints in terms of the behavior of its Laplace-Stieltjes transform at the limits of its interval of convergence. The results extend various known strong and weak results to a larger class of distributions via a relatively straightforward technique based on the weak convergence of suitably normalized associated distributions. An application and examples are considered briefly.Research supported by Technion VPR Fund-Lawrence Deutsch Research Fund     

On a family of 2-automatic sequences generating algebraic continued fractions in characteristic 2

We present family of automatic sequences that define algebraic continued fractions in characteristic 2. This family is constructed from ultimately period words and contains the period-doubling sequence.     

On a rigidity result of singularities

The aim of this note is to prove, in the spirit of a rigidity result for isolated singularities of Schlessinger see Schlessinger (Invent Math 14:17–26, 1971) or also Kleiman and Landolfi (Compositio Math 23:407–434, 1971), a variant of a rigidity criterion for arbitrary singularities (Theorem 2.1 below). The proof of this result does not use Schlessinger’s Deformation Theory [Schlessinger (Trans Am Math Soc 130:208–222, 1968) and Schlessinger (Invent Math 14:17–26, 1971)]. Instead it makes use of Local Grothendieck-Lefschetz Theory, see (Grothendieck 1968, Éxposé 9, Proposition 1.4, page 106) and a Lemma of Zariski, see (Zariski, Am J Math 87:507–536, 1965, Lemma 4, page 526). I hope that this proof, although works only in characteristic zero, might also have some interest in its own.     

On multiquadratic extensions of n-hilbert fields in characteristic 2

We give a quasihomogeneity criterion for Gorenstein curves. For complete intersections, it is related to the first step of Vasconcelos’ normalization algorithm. In the process, we give a simplified proof of the Kunz–Ruppert criterion.     

On a result of M. Kanda

Probability Theory and Related Fields -     

On a characteristic Cauchy problem

Sunto Si studia un problema di Cauchy caratteristico (per un operatore di cui quello di Klein-Gordon, in coordinate cono luce, è un modello). Si stabiliscono teoremi di esistenza ed unicità. Si prova che la velocità di propagazione è infinita.     

关于杨乐及Schwick的一结果

设ψ■0为复平面区域D内的只有单零点的全纯函数,k为正整数,F为区域D内的亚纯函数族.如果每个f∈F满足f≠0且只有重极点;对F内任一组函数f与g,f(k)与g(k)在D内分担ψ(z),则F在D内正规.