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α-times integrated semigroups: local and global

100%
Li M., Zheng Q.
Studia Mathematica
|
2003
|
tom 154
|
nr 3
243-252
EN
We investigate the relations between local α-times integrated semigroups and (α + 1)-times integrated Cauchy problems, and then the relations between global α-times integrated semigroups and regularized semigroups.
2
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Generalized matrix graphs and completely independent critical cliques in any dimension

100%
Lattanzio J., Zheng Q.
Discussiones Mathematicae Graph Theory
|
2012
|
tom 32
|
nr 3
583-602
EN
For natural numbers k and n, where 2 ≤ k ≤ n, the vertices of a graph are labeled using the elements of the k-fold Cartesian product Iₙ × Iₙ × ... × Iₙ. Two particular graph constructions will be given and the graphs so constructed are called generalized matrix graphs. Properties of generalized matrix graphs are determined and their application to completely independent critical cliques is investigated. It is shown that there exists a vertex critical graph which admits a family of k completely independent critical cliques for any k, where k ≥ 2. Some attention is given to this application and its relationship with the double-critical conjecture that the only vertex double-critical graph is the complete graph.
3
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Local integrated C-semigroups

81%
Li M., Huang F.-l., Zheng Q.
Studia Mathematica
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2001
|
tom 145
|
nr 3
265-280
EN
We introduce the notion of a local n-times integrated C-semigroup, which unifies the classes of local C-semigroups, local integrated semigroups and local C-cosine functions. We then study its relations to the C-wellposedness of the (n + 1)-times integrated Cauchy problem and second order abstract Cauchy problem. Finally, a generation theorem for local n-times integrated C-semigroups is given.
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