Relative Ding Projective Modules over Formal Triangular Matrix Rings

Let U be a (B, A)-bimodule, A and B be rings, and be a formal triangular matrix ring. In this paper, we characterize the structure of relative Ding projective modules over T under some conditions. Furthermore, using the left global relative Ding projective dimensions of A and B, we estimate the relative Ding projective dimension of a left T-module.

n-strongly Gorenstein Projective and Injective and Flat Modules

In this paper, we study some properties of n-strongly Gorenstein projective,injective and flat modules, and discuss some connections between n-strongly Gorenstein injective, projective and flat modules. Some applications are given.

Notes on Strongly n-Gorenstein Projective, Injective and Flat Modules

In this paper, we mainly investigate some properties of strongly n-Gorenstein projective, injective and flat modules under the extension of rings, which mainly including excellent extensions, morita equivalences, polynomial extensions and localizations.

Strongly Ding projective modules with respect to a semidualizing module

This paper is a study of strongly Ding projective modules with respect to a semidualizing module. The class of strongly Ding flat modules with respect to a semidualizing module is also investigated, and the relationship between strongly Ding projective modules and strongly Ding flat modules with respect to a semidualizing module is characterized.Some well-known results on strongly Ding projective modules, n-strongly Ding projective modules and strongly D_C-projective modules are generalized and unified.

STUDY OF FAILURE MODES OF MICROELECTRONIC PACKAGING MODULES BY HOLOGRAPHY QUASI PROJECTION MOIRE METHOD

In this paper, a novel interferometric method with a wide range of sensitivities, called holography quasi projection moire, is proposed. It combines the features of the variated double projection moire method and the holographic interferometry method. This technique is used to study the failure modes of microelectronic packaging modules.

Eventually homological isomorphisms and Gorenstein projective modules

We prove that a certain eventually homological isomorphism between module categories induces triangle equivalences between their singularity categories,Gorenstein defect categories and stable categories of Gorenstein projective modules.Furthermore,we show that the Auslander-Reiten conjecture and the Gorenstein symmetry conjecture can be reduced by eventually homological isomorphisms.Applying these results to arrow removal and vertex removal,we describe the Gorenstein projective modules over some non-monomial algebras and verify the Auslander-Reiten conjecture for certain algebras.

F-perfect Rings and Modules

Let R be a ring, and let （F, C） be a cotorsion theory. In this article, the notion of F-perfect rings is introduced as a nontrial generalization of perfect rings and A-perfect rings. A ring R is said to be right dr-perfect if F is projective relative to R for any F ∈ F. We give some characterizations of F-perfect rings. For example, we show that a ring R is right F-perfect if and only if F-covers of finitely generated modules are projective. Moreover, we define F-perfect modules and investigate some properties of them.

Some Equivalences and Dualities via Static Modules

For a ring A, an extension ring B, a fixed right A-module M, the endomorphism ring D formed by M, the endomorphism ring E formed by , and the endomorphism ring F formed by HomA (B,M), we present equivalences and dualities between subcategories of B-modules which are finitely cogenerated injective as A-modules and E-modules and F-modules which are finitely generated projective as D-modules.

关于n-纯同调维数的注记

为了研究环与模的n-纯同调维数,通过同调的方法,分别给出了n-纯投射模与n-纯内射模的一些新刻画.作为应用,证明了环R的n-纯投射整体维数不超过1的充分必要条件是R的n-纯内射整体维数不超过1,得到了一个环R的n-纯投射整体维数与R的n-纯内射整体维数的对应关系.

专业群“模块递进、项目贯穿”工作过程导向的实践教学体系改革与实践——以电气自动化技术专业群为例

高职院校专业群建设的实质,就是依据产业和人才培养逻辑对群内专业进行有效整合,实现资源共享,凸显群效应,服务产业对人才的需求。明确专业群服务产业的人才培养定位,理清专业群内各专业能力培养的自身特色以及服务产业的逻辑关联。以课程为本搭建实践能力递进模块,以工作过程为导向开发课程,项目贯穿设计专业群实践教学体系。建设工程化的实践环境,利用信息化管理手段,推动过程评价和增值评价,持续改进培养质量,融“三教”改革于项目化教学,实现专业群高水平服务学生成长成才,高质量服务区域经济发展,适应产业发展新形势和新业态的要求。

基于项目+模块的模拟电子技术研究性教学建构

模拟电子技术是电类专业一门重要的专业基础必修课,具有工程性、实践性强等特点。在课时少、内容多且知识难的教学现状下,课程组以项目为依托、以模块为载体,深入剖析当前教学中的痛点,立足于“OBE”理念和“新工科”建设标准,以产教融合、科教融合和立德树人为纲转变教学中心,以“两性一度”为领重构课程教学内容、创新教学方法和教学组织形式,以工程专业认证为导向建构多元化教学体系和课程考核形式,注重课程目标达成情况和持续改进。深挖课程典型思政案例,无缝嵌入,隐形育人。通过上述举措,将抽象的知识形象化、复杂理论简单化、虚拟仿真实践化,实现“知识+能力+思政”的全面育人。

基于Java的高职实训项目管理系统设计

本研究旨在设计一个基于Java的高职实训项目管理系统,以解决传统管理方式存在的问题,提高效率和质量。通过需求分析,确定了用户管理、项目管理、任务管理和日志记录等功能模块。数据库设计包括用户、项目、任务和日志数据表。安全性设计考虑了访问控制、数据加密、安全审计和异常处理与日志记录,该系统将为高职实训项目管理提供全面的支持。

基于极化-相位调制的雷达通信一体化波束方向图设计

为进一步实现雷达与通信系统的高效协同,提出一种基于极化相位联合调制的雷达通信一体化发射波束方向图设计方法。首先,通过正交子空间投影方法将权矢量投影至指定流形空间的零空间;然后,针对通信与探测权矢量的不同指标设计目标函数并通过优化算法求解,以实现通信信息的嵌入与极化控制;最后,添加人工噪声干扰以降低非通信方向对通信信息的截获概率。仿真结果表明所提方法可以实现极化调控和旁瓣约束,通信信号相比于已有方法具有更高的传输速率和抗截获概率。

Gorenstein稳定范畴的粘合和等价不变量

引入了Gorenstein投射刚性维数,以Gorenstein投射模的稳定范畴的粘合为主要工具,证明了Gorenstein投射刚性维数是Morita等价、Gorenstein稳定等价和导出等价的不变量,刻画了某些代数类的Gorenstein投射刚性维数.

一种新型骶神经孔穿刺定位方法的初步确立

目的通过分析骶神经孔特征,确立一种新型的骶神经穿刺定位方法,帮助临床提高穿刺成功率。方法回顾性分析2019年1月—2022年8月山东大学齐鲁医院158例接受骶神经调控术(SNM)患者的临床资料和骶尾骨计算机断层扫描(CT)三维重建影像,在第3骶孔水平线测量一侧骶髂关节下缘至同侧第3骶孔内上缘距离(D1)、同侧第3骶孔内上缘至骶中线的水平距离(D2),计算二者比值(D1/D2),用于术中精确定位骶神经孔。分析本组患者的测量数据特点和穿刺结果。结果共纳入患者158例,其中男性89例,女性69例,平均年龄(49.0±16.9)岁,平均D1、D2、D1/D2分别为(29.6±4.9)mm、(13.8±3.2)mm、(2.2±0.6)。相较于男性患者,女性患者的D1[(28.7±4.2)mm vs.(30.7±5.5)mm,P=0.010]及D1/D2均较大[(2.1±0.5)vs.(2.4±0.7),P=0.001]。少年组D1小于成年组[(25.7±5.4)mm vs.(29.8±4.7)mm,P=0.006]。采用本定位方法在术中精确定位后,158例患者均穿刺成功,152例(96.20%)患者术中神经反应应答非常好,2例(1.27%)患者应答良好,4例(2.53%)患者应答一般。结论骶3神经定位点的位置大约位于骶髂关节下缘至骶中线连线中内1/3处。通过X线测量骶髂关节下缘至骶中线的水平距离,并在体表进行骶神经孔定位,有望成为辅助SNM中定位电极置入点的可靠方法。

平凡环扩张上的强Ding投射模

设R■M是平凡环扩张,其中R是环,M是(R,R)-双模.在特定条件下,证明(X,α)是强Ding投射左R■M-模当且仅当序列■正合,并且coker(α)是强Ding投射左R-模.

弱Gorenstein分次模

设R是分次环,引入弱Gorenstein gr-投射,gr-内射和gr-平坦模,给出了弱Gorenstein gr-投射模的等价刻画.证明了在分次n-Gorenstein环上,弱Gorenstein gr-投射R-模是Gorenstein gr-投射的.同时,证明了如果任意分次内射R-模具有有限的分次平坦维数,那么M是弱Gorenstein gr-平坦R-模当且仅当M是Gorenstein gr-平坦模.

The Report of Homological Algebra

The current article intends to introduce the reader to the concept of injective and projective modules and to describe the CFT. We present a clear view to show the homological algebra and injective and projective modules.

Frobenius扩张下的PGF■n-模与Gorenstein■n-平坦模

设R■S是环的Frobenius扩张,M是一个S-模.证明如果R■S是可分Frobenius扩张,则SM是投射余可解的Gorenstein■n-平坦模(Gorenstein■n-平坦模)当且仅当RM是投射余可解的Gorenstein■n-平坦模(Gorenstein■n-平坦模).

Frobenius双模和相对n-Gorenstein投射模

设R和S均是环,SMR是一Frobenius双模,MR是生成子.χ是一左R-模类,y是一左S-模类.在一定条件下,证明左R-模X是n-X-Gorenstein投射模当且仅当M■RX是n-y-Gorenstein投射左S-模.进而证明当F:RM→SM是忠实的Frobenius函子时,n-GX-pdR(X)=n-Gy-pdS(F(X)).