If a class of nitely generated groups G is closed under isometric amalgamations along free subgroups, then every G 2 G can be quasi-isometrically embedded in a group Ĝ 2 G that has no proper subgroups of nite index. Every compact, connected, non-positively curved space X admits an isometric embedding into a compact, connected, non-positively curved space X such that X has no non-trivial nite-sh...

Let L be a local system on a smooth quasi projective variety over C . We see that L is semisimple if and only if there exists a tame pure imaginary pluri-harmonic metric on L. Although it is a rather minor refinement of a result of Jost and Zuo, it is significant for the study of harmonic bundles and pure twistor D-modules. As one of the application, we show that the semisimplicity of local sys...

A connected graphG = (V ,E) is called a quasi-tree, if there exists u0 ∈ V (G) such thatG− u0 is a tree. Denote Q(n, d0) = {G : G is a quasi tree graph of order n with G− u0 being a tree and dG(u0) = d0}. In this paper, we determined the maximal and the second maximal spectral radii of all quasi-tree graphs in the set Q(n, d0). © 2008 Elsevier Inc. All rights reserved. AMS classification: 05C50...

It is shown that Morita equivalence preserves quasi-Koszulity, and a finite-dimensional K-algebra A is quasi-Koszul if and only if the skew group algebra A * G is, where G is a finite group satisfying charK ∤ |G|. It follows from these results that a finite-dimensional K-algebra A is quasi-Koszul if and only if the smash product A#G * is, where G is a finite group satisfying charK ∤ |G|. Furthe...

Let C, C be curves over a base scheme S with g(C) ≥ 2. Then the functor T 7→ {generically smooth T -morphisms T ×S C ′ → T ×S C} from ((Sschemes)) to ((sets)) is represented by a quasi-finite unramified S-scheme. From this one can deduce that for any two integers g ≥ 2 and g, there is an integer M(g, g) such that for any two curves C,C over any field k with g(C) = g, g(C) = g, there are at most...

Different concepts and decomposition theorems have been done for QTAGmodules by number of authors. We introduce quasi h-pure submodules for QTAG-modules andwe obtain several characterizations for quasih-pure submodules and as a consequence we deduce a result done by Fuchs 1973.

According to Shapley’s game-theoretical result, there exists a unique game value of finite cooperative games that satisfies axioms on additivity, efficiency, null-player property and symmetry. The original setting requires symmetry with respect to arbitrary permutations of players. We analyze the consequences of weakening the symmetry axioms and study quasi-values that are symmetric with respec...

We investigate a novel symmetry in dualities of Wu’s equation: wg(1+w)1−g = eβ( −μ) for a degenerate g-on gas with fractional exclusion statistics of g, where β = 1/kBT , the energy, and μ the chemical potential of the system. We find that the particle–hole duality between g and 1/g and the supersymmetric duality between g and 1 − g form a novel quasi-modular group of order six for Wu’s equatio...

Let X be a K3 surface and C be a holomorphic curve in X representing a primitive homology class. We count the number of curves of geometric genus g with n nodes passing through g generic points in X in the linear system |C| for any g and n satisfying C · C = 2g + 2n − 2. When g = 0, this coincides with the enumerative problem studied by Yau and Zaslow who obtained a conjectural generating funct...