McCoy modules and related modules over commutative rings

Let M be a left R-module. Then M is a McCoy (resp., dual McCoy) module if for nonzero f(X)∈R[X] and m(X)∈M[X], f(X)m(X) = 0 implies there exists a nonzero r∈R (resp., m∈M) with rm(X) = 0 (resp., f(X)m = 0). We show that for R commutative every R-module is dual McCoy, but give an example of a non-McCoy module. A number of other results concerning (dual) McCoy modules as well as arithmetical, Gaussian, and Armendariz modules are given.     

Representability of actions in the category of (Pre)crossed modules in Leibniz algebras

We investigate the representability of actions in the category of (pre)crossed modules in Leibniz algebras. For this, we construct an actor of a (pre)cat¹-Leibniz algebra and then by using the natural equivalence of the categories of (pre)cat¹-Leibniz algebras and that of (pre)crossed modules, we construct the split extension classifier of the corresponding (pre)crossed module.     

On the inheritance of the strongly π-extending property

In this article, we focus on modules with the property that every projection invariant submodule is essential in a fully invariant direct summand. In contrast to π-extending condition, it is shown that the former property is inherited by direct summands and Morita invariant. An application of our results yields that the endomorphism ring of a free module enjoys the property. Moreover, we characterize generalized triangular matrix rings with the aforementioned property and apply to somewhat special cases.     

Torsion simple modules over the quantum spatial ageing algebra

Various classes of simple torsion modules are classified over the quantum spatial ageing algebra (this is a Noetherian algebra of Gelfand-Kirillov dimension 4). Explicit constructions of these modules are given and for each module its annihilator is found.     

Constacyclic codes over finite local Frobenius non-chain rings with nilpotency index 3

The main results of this paper are in two directions. First, the family of finite local Frobenius non-chain rings of length 4 (hence of nilpotency index 3) is determined. As a by-product all finite local Frobenius non-chain rings with $p^4$ elements, (p a prime) are given. Second, the number and structure of γ-constacyclic codes over finite local Frobenius non-chain rings with nilpotency index 3, of length relatively prime to the characteristic of the residue field of the ring, are determined.     

Generalized local duality,canonical modules,and prescribed bound on projective dimension

We present various approaches to J. Herzog's theory of generalized local cohomology and explore its main aspects, e.g., (non-)vanishing results as well as a general local duality theorem which extends, to a much broader class of rings, previous results by Herzog-Zamani and Suzuki. As an application, we establish a prescribed upper bound for the projective dimension of a module satisfying suitable cohomological conditions, and we derive some freeness criteria and questions of Auslander-Reiten type. Along the way, we prove a new characterization of Cohen-Macaulay modules which truly relies on generalized local cohomology, and in addition we introduce and study a generalization of the notion of canonical module.     

From Lie algebra crossed modules to tensor hierarchies

The present paper, though inspired by the use of tensor hierarchies in theoretical physics, establishes their mathematical credentials, especially as genetically related to Lie algebra crossed modules. Gauging procedures in supergravity rely on a pairing – the embedding tensor – between a Leibniz algebra and a Lie algebra. Two such algebras, together with their embedding tensor, form a triple called a Lie-Leibniz triple, of which Lie algebra crossed modules are particular cases. This paper is devoted to showing that any Lie-Leibniz triple induces a differential graded Lie algebra – its associated tensor hierarchy – whose restriction to the category of Lie algebra crossed modules is the canonical assignment associating to any Lie algebra crossed module its corresponding unique 2-term differential graded Lie algebra. This shows that Lie-Leibniz triples form natural generalizations of Lie algebra crossed modules and that their associated tensor hierarchies can be considered as some kind of ‘lie-ization’ of the former. We deem the present construction of such tensor hierarchies clearer and more straightforward than previous derivations. We stress that such a construction suggests the existence of further well-defined Leibniz gauge theories.     

改进的Faster-RCNN算法在聚乙烯管接头内部缺陷检测中的应用

超声相控阵技术是目前聚乙烯管道热熔接头内部缺陷检测的一种主流方法。提出了基于注意力机制的改进Faster-RCNN目标检测网络用于超声相控阵D扫图聚乙烯管接头内部缺陷检测。针对聚乙烯管道热熔接头内部超声相控阵D扫图小缺陷较多、特征信息容易丢失的问题,将残差网络(ResNet50)与特征金字塔网络(FPN)相结合作为骨干网络,并引入卷积注意力模块(CBAM)自适应细化特征。将SSD网络框架和Faster-RCNN网络框架用于模型训练和测试,使用VGG16、ResNet50、ResNet50+FPN、ACBM+ResNet50+FPN作为骨干网络依次对超声相控阵聚乙烯管道热熔对接接头内部缺陷样本进行训练对比。结果表明,改进的Faster-RCNN网络模型在聚乙烯管接头内部缺陷检测和分类方面有明显改进,对小缺陷的检测性能有了显著的提高。     

钙钛矿太阳能电池的商业化进展与挑战

钙钛矿太阳电池是一项颠覆性的光伏技术,具有能量转化效率高、生产成本低、制备工艺简单等优势。当前,钙钛矿太阳能电池的认证效率已达25.7%,但其面临着严重的商业化瓶颈,如稳定性差、模组效率相对低、铅毒性等,且这些问题相互关联。本文简述了钙钛矿太阳能电池的工作原理和器件结构,并归纳总结了在解决钙钛矿太阳能电池稳定性、封装和模组化等商业化瓶颈问题方面的主要研究进展。最后,本文提出了钙钛矿光伏商业化进程中值得关注的解决措施。     

Identification de la relation de dispersion dans les barresIdentification of the dispersion relation in rods

Dispersion and attenuation of longitudinal waves in elastic or weakly viscoelastic rods are measured by analysing the resonant frequencies present in the strain spectrum due to an unknown loading. The method takes the finite measuring time of the test into account. It is applied to an aluminium bar, in which the dispersion relation is identified very accurately at frequencies up to 60 kHz. To cite this article: R. Othman et al., C. R. Mecanique 330 (2002) 849–855.