Zum Andenken an Karl VonderMühll (1841–1912)

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Two Necessary Conditions for λ 2 (G) = d 2 ( G )

In this article, two necessary conditions for a graph to have an equality of the second largest Laplacian eigenvalue λ 2 ( G ) and its lower bound d 2 ( G ) are presented. Some of the graphs who satisfy λ 2 ( G )= d 2 ( G ) are also described.     

On Barycentric Interpolation. II (Grünwald–Marcinkiewicz type Theorems)

Grünwald–Marcinkiewicz type theorems with respect to barycentric Lagrange interpolation based on equidistant and Chebyshev node-sytems in [–1, 1] are proved. It turns out that the results are very similar to the ones known for the classical Lagrange interpolation.     

Asymptotic enumeration by Khintchine–Meinardus probabilistic method: necessary and sufficient conditions for sub-exponential growth

In this paper, we prove the necessity of the main sufficient condition of Meinardus for sub-exponential rate of growth of the number of structures, having multiplicative generating functions of a general form and establish a new necessary and sufficient condition for normal local limit theorem for aforementioned structures. The latter result allows to encompass in our study structures with sequences of weights having gaps in their support.     

Nachtrag zu der Abhandlung: Über neue Gültigkeitsbedingungen für die Fouriersche Integralformel (Math. Ann. 68, S. 367–408)

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Über einen geometrischen Calcül (Verknüpfungs-Calcül)

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不存在秩为r(G)+2c(G)-1或r(G)-2c(G)+1的符号图

设Γ=(G,σ)是一个符号图,其中G是Γ的基图.设r(G,σ)是Γ的秩.[Linear Algebra Appl.,2018,538:166-186]和[Linear Multilinear Algebra,2019,67:2520-2539]分别证明了r(G)-2c(G)≤r(G,σ)≤r(G)+2c(G),其中,r(G)和c(G)分别是G的秩和圈空间维数.本文主要证明没有符号图的秩能够达到r(G)+2c(G)-1和r(G)-2c(G)+1,并且证明了存在无穷多个符号图的秩r(G,σ)=r(G)+2c(G)-s,其中s∈[0,4c(G)]且s≠1及4c(G)-1.     

从L~p(G,A)到L~p(G,X)的L~1(G,A)-模同态和不变算子(1

于树模 《数学年刊A辑(中文版)》1990,(6)