We describe properties of the nonstandard q-deformation U ′ q (son) of the universal enveloping algebra U (son) of the Lie algebra son which does not coincide with the Drinfeld–Jimbo quantum algebra Uq(son). In particular, it is shown that there exists an isomorphism from U ′ q (son) to Uq(sln) and that finite dimensional ir-reducible representations of U ′ q (son) separate elements of this alg...

Let CD be the category of all continuous domains and all mappings which preserve directed sups and the way-below relation. That is, a mapping f : P → Q is a morphism of CD if and only if f(sup D) = sup f(D) for any directed set D ⊂ P and f(x) œ f(y) if x œ y for any x, y ∈ P . We shall prove that the category CD is cartesian closed. 1991 Mathematics Subject Classification 06B35.

The various relations between q-deformed oscillators algebras and the q-deformed su(2) algebras are discussed. In particular, we exhibit the similarity of the q-deformed su(2) algebra obtained from q-oscillators via Schwinger construction and those obtained from q-Holstein-Primakoff transformation and show how the relation between su √ q (2) and Hong Yan q-oscillator can be regarded as an speci...

为了改善生态调度效果,提高生态调度实践成功率,采用医学领域适用性广、准确性高、直观性强的受试者工作特征曲线法(receiver operating characteristic, ROC),以三峡水库为例,提出了一套基于生物水文响应模型的刺激四大家鱼繁殖生态调度目标量化方法,包括涨水事件界定及生态水文指标选择、鱼类自然繁殖事件及有效繁殖响应界定、生物-水文响应模型构建与多指标判别优选等多个环节。运用三峡水库运行后2013—2019年(除2016年)6年47场次宜昌江段的涨水事件和24次四大家鱼有效繁殖响应的实际观测数据构建模型并量化三峡水库生态调度目标。结果表明:(1)依据初始流量Q0、洪峰流量Qpeak、流量总增长量Qsum和流量日增长率dQ这4个指标所建立的单指标生物-水文响应模型具有较好判别四大家鱼自然繁殖对水文...

A deformation of the harmonic oscillator algebra associated with the Morse potential and the SU (2) algebra is derived using the quantum analogue of the anharmonic oscillator. We use the quantum os-cillator algebra or q-boson algebra which is a generalisation of the Heisenberg-Weyl algebra obtained by introducing a deformation parameter q. Further, we present a new algebraic realization of the ...