Breather molecules and localized interaction solutions in the (2+1)-dimensional BLMP equation

The (2+1)-dimensional Boiti–Leon–Manna–Pempinelli (BLMP) equation is an important integrable model. In this paper, we obtain the breather molecule, the breather-soliton molecule and some localized interaction solutions to the BLMP equation. In particular, by employing a compound method consisting of the velocity resonance, partial module resonance and degeneration of the breather techniques, we derive some interesting hybrid solutions mixed by a breather-soliton molecule/breather molecule and a lump, as well as a bell-shaped soliton and lump. Due to the lack of the long wave limit, it is the first time using the compound degeneration method to construct the hybrid solutions involving a lump. The dynamical behaviors and mathematical features of the solutions are analyzed theoretically and graphically. The method introduced can be effectively used to study the wave solutions of other nonlinear partial differential equations.     

Cartan Invariants in the Category of Restricted Representation for gl(m|n)

Let k be an algebraically closed field of characteristic p 2, and gl(m|n) be the general linear Lie superalgebra over k. The Cartan invariants for the restricted supermodule category for gl(m|n) are presented.     

Corrigendum to: on the inheritance of the strongly π-extending property

In this corrigendum, we provide correct versions of Theorem 2.8 and Corollary 3.2, retract two consequences of the previous form of the Theorem 2.8. To this end, the main results of the article remain after the aforementioned changes.     

Gorenstein平坦模与Frobenius扩张

设R■A是环的Frobenius扩张,其中A是右凝聚环,M是任意左A-模.首先证明了_AM是Gorenstein平坦模当且仅当M作为左R-模也是Gorenstein平坦模.其次,证明了Nakayama和Tsuzuku关于平坦维数沿着Frobenius扩张的传递性定理的"Gorenstein版本":若_AM具有有限Gorenstein平坦维数,则Gfd_A(M)=Gfd_R(M).此外,证明了若R■S是可分Frobenius扩张,则任意A-模(不一定具有有限Gorenstein平坦维数),其Gorenstein平坦维数沿着该环扩张是不变的.     

完备化Witt代数中自然出现的一些非有限阶化李代数的表示

讨论了完备化Witt代数的三类非有限阶化子代数的不可约非权模的实现,并利用它们的表示得到一些有趣的组合恒等式.     

Interconnections and Initial Conditions of Linear Systems With First-Order Representations

This paper considers the initial value problem of an interconnection composed of linear systems described by the first-order differential/algebraic equations (DAEs). An initial condition of the system variable for which the DAE has a solution is called admissible. For the interconnected system, we formulate the invariance of the admissible initial condition sets (AICSs) of the sub-systems under interconnection. Namely, the AICSs are said to be invariant if they remain unchanged even when additional constraints due to interconnection are imposed on the system variables. It is shown that the feedback and regular feedback structures of the interconnection guarantee the invariance of the AICSs in the senses of impulsive-smooth distributions and smooth distributions, respectively. The results in this paper justify the use of a feedback controller in the control system design.     

On the Pure-injectivity Profile of a Ring

An analog of the injective profile of a ring, with relative injectivity replaced by relative pure-injectivity, is investigated. Emphasis is placed on comparing and contrasting the properties of both profiles. In particular, the analog in this context of the notion of poor modules is considered and properties of pure-injectively poor modules are determined. While we do not know of any ring that does not have pure-injectively poor modules, their existence has not been determined in general. Rings having pure-injectively poor modules of various types are characterized.     

On the Indecomposable Modules of Uq（sl（2）） Constructed via Ore-extension

Let A be a subalgebra of Uq (sl(2)) generated by K, K-1 and F and Aδ be a subalgebra of Uq (sl(2)) generated by K, K-1 (and also Fd if q is a primitive d-th root of unity with d an odd number). Given an Aδ -module M, a Uq (sl(2))-module AAδ M is constructed via the iterated Ore extension of Uq (sl(2)) in a unified framework for any q. Then all the submodules of AAδ M are determined for a fixed finite-dimensional indecomposable Aδ -module M . It turns out that for some indecomposable Aδ -module M , the Uq (sl(2))-module AAδ M is indecomposable, which is not in the BGG-categories Oq associated with quantum groups in general.