104 research outputs found
Determining Finite Connected Graphs Along the Quadratic Embedding Constants of Paths
The QE constant of a finite connected graph , denoted by
, is by definition the maximum of the quadratic function
associated to the distance matrix on a certain sphere of codimension two. We
prove that the QE constants of paths form a strictly increasing sequence
converging to . Then we formulate the problem of determining all the
graphs satisfying
. The answer is
given for and by exploiting forbidden subgraphs for
and the explicit QE constants of star products of the
complete graphs.Comment: 24 pages, 6 figure
Primary Non-QE Graphs on Six Vertices
A connected graph is called of non-QE class if it does not admit a quadratic
embedding in a Euclidean space. A non-QE graph is called primary if it does not
contain a non-QE graph as an isometrically embedded proper subgraph. The graphs
on six vertices are completely classified into the classes of QE graphs, of
non-QE graphs, and of primary non-QE graphs.Comment: arXiv admin note: text overlap with arXiv:2206.0584
Initial Value Problem For White Noise Operators And Quantum Stochastic Processes
This is the proceedings of the 2nd Japanese-German Symposium on Infinite Dimensional Harmonic Analysis held from September 20th to September 24th 1999 at the Department of Mathematics of Kyoto University.この論文集は, 1999年9月20日から9月24日の日程で京都大学理学研究科数学教室において開催された第2回日独セミナー「無限次元調和解祈」の成果をもとに編集されたものである.編集 : ハーバート・ハイヤー, 平井 武, 尾畑 信明Editors: Herbert Heyer, Takeshi Hirai, Nobuaki Obata #e
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