The unifiedΩ-series of the Gauss and Bailey2F1(1/2)-sums will be investigated by utilizing asymptotic methods and the modified Abel lemma on summation by parts.Several remarkable transformation theorems for theΩ-ser...The unifiedΩ-series of the Gauss and Bailey2F1(1/2)-sums will be investigated by utilizing asymptotic methods and the modified Abel lemma on summation by parts.Several remarkable transformation theorems for theΩ-series will be proved whose particular cases turn out to be strange evaluations of nonterminating hypergeometric series and infinite series identities of Ramanujan-type,including a couple of beautiful expressions forπand the Catalan constant discovered by Guillera(2008).展开更多
The 2-sum of two digraphs and , denoted , is the digraph obtained from the disjoint union of and by identifying an arc in with an arc in . A digraph D is supereulerian if D contains a spanning eulerian subdigraph. It ...The 2-sum of two digraphs and , denoted , is the digraph obtained from the disjoint union of and by identifying an arc in with an arc in . A digraph D is supereulerian if D contains a spanning eulerian subdigraph. It has been noted that the 2-sum of two supereulerian (or even hamiltonian) digraphs may not be supereulerian. We obtain several sufficient conditions on and for to be supereulerian. In particular, we show that if and are symmetrically connected or partially symmetric, then is supereulerian.展开更多
A ring is said to satisfy the strong 2-sum property if every element is a sum of two commuting units.In this note,we present some sufficient or necessary conditions for the matrix ring over a commutative local ring to...A ring is said to satisfy the strong 2-sum property if every element is a sum of two commuting units.In this note,we present some sufficient or necessary conditions for the matrix ring over a commutative local ring to have the strong 2-sum property.展开更多
文摘The unifiedΩ-series of the Gauss and Bailey2F1(1/2)-sums will be investigated by utilizing asymptotic methods and the modified Abel lemma on summation by parts.Several remarkable transformation theorems for theΩ-series will be proved whose particular cases turn out to be strange evaluations of nonterminating hypergeometric series and infinite series identities of Ramanujan-type,including a couple of beautiful expressions forπand the Catalan constant discovered by Guillera(2008).
文摘The 2-sum of two digraphs and , denoted , is the digraph obtained from the disjoint union of and by identifying an arc in with an arc in . A digraph D is supereulerian if D contains a spanning eulerian subdigraph. It has been noted that the 2-sum of two supereulerian (or even hamiltonian) digraphs may not be supereulerian. We obtain several sufficient conditions on and for to be supereulerian. In particular, we show that if and are symmetrically connected or partially symmetric, then is supereulerian.
基金This research was supported by the Natural Science Foundation of China(grants 11661014,11661013,11961050)the Guangxi Natural Science Foundation(grant no.2016GXNSFDA380017)a Discovery Grant from NSERC of Canada(grant no.RGPIN-2016-04706).
文摘A ring is said to satisfy the strong 2-sum property if every element is a sum of two commuting units.In this note,we present some sufficient or necessary conditions for the matrix ring over a commutative local ring to have the strong 2-sum property.
