In this paper, a series of sharp criterions of global existence and collapse for coupled nonlinear Schr6dinger equations are derived out in terms of the characteristics of the ground state and the local theories. And ...In this paper, a series of sharp criterions of global existence and collapse for coupled nonlinear Schr6dinger equations are derived out in terms of the characteristics of the ground state and the local theories. And the conclusion that how small the initial data are, the global solutions exist is proved.展开更多
In this paper, for an arbitrary regular biordered set E, by usingbiorder-isomorphisms between the ω-ideals of E, we construct a fundamental regular semigroup W_Ecalled NH-semigroup of E, whose idempotent biordered se...In this paper, for an arbitrary regular biordered set E, by usingbiorder-isomorphisms between the ω-ideals of E, we construct a fundamental regular semigroup W_Ecalled NH-semigroup of E, whose idempotent biordered set is isomorphic to E. We prove further thatW_E can be used to give a new representation of general regular semigroups in the sense that, forany regular semigroup S with the idempotent biordered set isomorphic to E, there exists ahomomorphism from S to W_E whose kernel is the greatest idempotent-separating congruence on S andthe image is a full symmetric subsemigroup of W_E. Moreover, when E is a biordered set of asemilattice E_0, W_E is isomorphic to the Munn-semigroup T_(E_0); and when E is the biordered set ofa band B, W_E is isomorphic to the Hall-semigroup W_B.展开更多
文摘In this paper, a series of sharp criterions of global existence and collapse for coupled nonlinear Schr6dinger equations are derived out in terms of the characteristics of the ground state and the local theories. And the conclusion that how small the initial data are, the global solutions exist is proved.
文摘In this paper, for an arbitrary regular biordered set E, by usingbiorder-isomorphisms between the ω-ideals of E, we construct a fundamental regular semigroup W_Ecalled NH-semigroup of E, whose idempotent biordered set is isomorphic to E. We prove further thatW_E can be used to give a new representation of general regular semigroups in the sense that, forany regular semigroup S with the idempotent biordered set isomorphic to E, there exists ahomomorphism from S to W_E whose kernel is the greatest idempotent-separating congruence on S andthe image is a full symmetric subsemigroup of W_E. Moreover, when E is a biordered set of asemilattice E_0, W_E is isomorphic to the Munn-semigroup T_(E_0); and when E is the biordered set ofa band B, W_E is isomorphic to the Hall-semigroup W_B.
