局部上同调模的Artin性质

In this paper,let (R,m)be a Noetherian local ring,I(?)R an ideal, M and N be two finitely generated modules.Firstly,we study the properties of H_I~t(M),t=f-depth(I,M) and discuss the relationship between the Artinianness of H_I~i(M,N) and the Artinianness of H_I~i(N).Then,we get that H_I~d(M,N)is I-cofinite,if(R,m)is a d-dimensional Gorenstein local ring.     

正则模与半单Artin环

本文用则模的术语给出了半单Artin 环的刻划。得到如下三个条件的等价性:(1)R 是一个半单Artin 环;(2)每一个R-模都是正则模;(3)每一个单纯R-模都是正则模。     

关于正则模的自同态环

本文研究正则模Ｐ的自同态环Ｓ,主要给出使Ｓ的稳定秩为１的Ｐ的几个充分条件．     

模空间的正则性指标及其应用

用模空间的一种复合指标刻画了Navier-Stokes方程在模空间的适定性情况,得到了Nayier--Stokes方程在模空间适定性和不适定的临界条件.     

基于零模正则的神经网络剪枝方法

本文提出一种有效的神经网络剪枝方法。该方法对神经网络训练模型引入零模正则项来促使模型权重稀疏,并通过删减取值为零的权重来压缩模型。对所提出的零模正则神经网络训练模型,文中通过建立其等价MPEC形式的全局精确罚得到其等价的局部Lipschitz代理,然后通过用交替方向乘子法求解该Lipschitz代理模型对网络进行训练、剪枝。最后,对MLP和LeNet-5网络模型进行测试,分别在误差2.2%和1%下,取得97.43%和99.50%的稀疏度,达到很好的剪枝效果。     

型距离正则图的关于余弦序列的不等式

给出了     

正则蕴涵算子与左连续三角模的关系再探讨

证明了正则蕴涵算子与左连续三角模生成的剩余类蕴涵等价,且正则蕴涵算子和左连续三角一一对应,并给出了一种利用部分左连续三角模生成左连续三角模的方法.     

so(5,k)主不可分解模的Loewy序列

设k是特征为素数的代数闭域,李代数g=so(5,k).当p-特征函数χ为次正则幂零且具有标准Levi型时,得到g的主不可分解模的Lowey序列.     

E_1 ~oE_d型距离正则图的关于余弦序列的不等式

给出了E1 Ed型距离正则图的关于余弦序列的不等式.     

Abel正则球与完全正则半群

本文分别讨论了关于结合环和半群的二个定理，并且由结合环的这二个定理推出了如下准则：结合环Ｒ是Ａｂｅｌ正则的，当且仅当Ｒ的每个拟理想是正则环．     

Some criteria for the Cohen-Macaulay property and local cohomology

Let a be an ideal of a commutative Noetherian ring R and M be a finitely generated R-module of dimension d. We characterize Cohen-Macaulay rings in term of a special homological dimension. Lastly, we prove that if R is a complete local ring, then the Matlis dual of top local cohomology module Ha^d（M） is a Cohen-Macaulay R-module provided that the R-module M satisfies some conditions.     

On Vanishing and Cofiniteness of Generalized Local Cohomology Modules

Pure braid groups and pure mapping class groups of a punctured sphere have many features in common. In this article, we study the graded Lie algebra of the descending central series of the pure mapping class group of a 2-sphere. A simple presentation of this Lie algebra is obtained.     

Duality for a Cohen–Macaulay Local Ring

Let (R, 𝔪) be a Cohen–Macaulay local ring. If R has a canonical module, then there are some interesting results about duality for this situation. In this article, we show that one can indeed obtain similar results in the case R does not have a canonical module. Also, we give some characterizations of complete big Cohen–Macaulay modules of finite injective dimension, and by using them, some characterizations of Gorenstein modules over the 𝔪-adic completion of R are obtained.     

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.