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.

On minimal quasi-injective modules and strong Kasch modules

设R为一个环，M为一个右R-模．若每个从M的单子模到M的同态都可以开拓为M的自同态，则称M为一个极小拟内射模．若每个单的右R-模都可以嵌入M，则称M为一个强Kasch模．本文研究了这两类模的一些刻画和性质．

On Strongly Regular Rings

In this paper we investigate strongly regular rings. In terms of W-ideals of rings some characterizations of strongly regular rings are given.

On Co-Primarily Packed Modules

Let R be a commutative ring with 1, and M is a (left) R-module. We introduce the concept of coprimarily packed submodules as a proper submodule N of an R-module M which is said to be Coprimarily Packed Submodule. If where Na is a primary submodule of M for each , then for some . When there exists such that;N is called Strongly Coprimarily Packed submodule. In this paper, we list some basic properties of this concept. We end this paper by explaining the relations between p-compactly packed and coprimarily packed submodules, and also the relations between strongly p-compactly packed and strongly coprimarily packed submodules.

强信号全覆盖环境高精密传感器微弱信号调制设计

在强信号的存在下,传感器微弱信号会被干扰、淹没或认为噪声,导致信号无法准确读取影响传感器的性能。为了解决这个问题,提出了一种强信号全覆盖环境高精密传感器微弱信号调制设计方法。该方法利用压缩感知技术重构完整的高精密传感器微弱信号集,通过自适应滤波器进行滤波以降低噪声,提高微弱信号的信噪比。利用基于正弦载波的扩频调制技术对微弱信号展开调制,将微弱信号扩展到宽频带中,以提高微弱信号的抗干扰能力和传输效率。实验结果表明,所提方法的信号重构精度高,能够有效滤除信号中的噪声,提高信号的抗噪声能力。并且信号调制性能好、抗干扰能力强。

Strongly Gorenstein Flat Modules and Dimensions

There is a variety of nice results about strongly Gorenstein flat modules over coherent rings. These results are done by Ding, Lie and Mao. The aim of this paper is to generalize some of these results, and to give homological descriptions of the strongly Gorenstein flat dimension (of modules and rings) over arbitrary associative rings.

Strongly Gorenstein graded modules

Let R be a graded ring. We define and study strongly Gorenstein gr-projective, gr-injective, and gr-flat modules. Some connections among these modules are discussed. We also explore the relations between the graded and the ungraded strongly Gorenstein modules.

Gorenstein-Projective Modules over Morita Rings

Let△(φ,ψ)=(ABMA ANBB)be a Morita ring which is an Artin algebra.In this paper we investigate the relations between the Gorenstein-projective modules over a Morita ring△(φ,ψ)and the algebras A and B.We prove that if△(φ,ψ)is a Gorenstein algebra and both Ma and aN(resp.,both NB and BM)have finite projective dimension,then A(resp.,B)is a Gorenstein algebra.We also discuss when the CM-freeness and the CM-finiteness of a Morita ring△(φ,ψ)is inherited by the algebras A and B.

Strong optical feedback in birefringent dual frequency laser

Strong optical feedback in a birefringent dual frequency He-Ne laser with a high reflectivity feedback mirror has been investigated for the first time. The output characteristics of two orthogonally polarized modes are demonstrated in two different optical feedback cases： one is for both modes being fed back and the other is for only one of the modes being fed back. Strong mode competition can be observed between the two modes with strong optical feedback, And when one mode＇s intensity is near its maximum, the other mode is nearly extinguished. When both modes are fed back into the laser cavity, the mode competition is stronger than when only one mode is fed back, The difference in initial intensity between the two orthogonally polarized modes plays an important role in the mode competition, which has been experimentally and theoretically demonstrated.

Strongly Irreducible Submodules of Modules

Strongly irreducible submodules of modules are defined as follows： A submodule N of an Rmodule M is said to be strongly irreducible if for submodules L and K of M, the inclusion L ∩ K ∈ N implies that either L ∈ N or K ∈ N. The relationship among the families of irreducible, strongly irreducible, prime and primary submodules of an R-module M is considered, and a characterization of Noetherian modules which contain a non-prime strongly irreducible submodule is given.

Gorenstein-Projective Modules over T_(m,n)(A)

A new class of Gorenstein algebras Tm,n(A) is introduced,their module categories are described,and all the Gorenstein-projective Tm,n(A)-modules are explicitly determined.

WHITEHEAD GROUPS OF MODULE EXTENSIONS

When R satisfies (strong unit) 1-stable range and M is a R-R-bimodule, the authors calculate that K_1(R(?) M)≌U(R(?) M)/L(R(?) M). As applications, the authors also calculate some Whitehead groups for exchange rings with artinian primitive factors.

Strongly lifting modules and strongly dual Rickart modules

The concepts of strongly lifting modules and strongly dual Rickart modules are introduced and their properties are studied and relations between them are given in this paper. It is shown that a strongly lifting module has the strongly summand sum property and the generalized Hopfian property, and a ring R is a strongly regular ring if and only if RR is a strongly dual Rickart module, if and only if aR is a fully invariant direct summand of RR for every a∈R.

Morphism Categories of Gorenstein-projective Modules

Let A be an algebra of finite Cohen-Macaulay type and F its Cohen-Macaulay Auslander algebra. We are going to characterize the morphism category Mor（∧-Gproj） of Gorenstein-projective ∧-modules in terms of the module category F-mod by a categorical equivalence. Based on this, we obtain that some factor category of the epimorphism category Epi（∧-Gproj） is a Frobenius category, and also, we clarify the relations among Mor（∧-Gproj）, Mor（T2（∧）-Gproj） and Mor（△-Gproj）, where T2（∧） and △ are respectively the lower triangular matrix algebra and the Morita ring closely related to ∧.

井水位潮汐响应与小地震调制作用的关系

地下流体在地震孕育和发生过程中发挥着至关重要的作用。文中从黑龙江地区18个水位观测井中,筛选出2016年以来符合一定条件的延寿台、通河台、肇东台、甘南台和绥化北林台的井水位数据,应用维尼迪柯夫调和分析方法进行潮汐分析,得到井水位潮汐响应全日波群中的周日波潮汐因子,分析了吉林松原宁江M_(S)5.0、M_(S)5.7、M_(S)5.1地震前后周日波的高值异常变化特征,并结合震源区M_(L)≥3.0小地震调制比异常,进一步探讨了周日波异常与小地震调制作用的关系。结果显示:1)周日波潮汐因子背景变化相对稳定,异常更容易被识别,具有较高的信噪比。2)吉林松原宁江地震前,井水位潮汐响应的周日波异常具有准同步性和形态一致性,主要表现为3个及以上台站的配套性异常。3)吉林松原宁江地震发生在周日波高值配套性异常结束后的2.6个月内,最短仅为7d,具有明显的短临特征,且异常持续时间、异常幅度与震级大小相关。4)吉林松原宁江地震前震源区M_L≥3.0小地震调制比存在低值异常,主要表现为短临特征,井水位潮汐响应的周日波异常反映构造内部应力状态的改变,小地震调制比则能更好地揭示震源区构造应力达到或接近临界状态,对二者进行联合分析有助于识别和捕捉地震前兆短临异常。

强杂波背景下FMCW雷达低小慢目标探测研究

强杂波背景下的雷达回波处理一直是雷达信号处理的难点和重要工作。对调频连续波雷达信号处理进行了详细分析,完成了中频采样、数字下变频、FFT处理、MTI/AMTI处理、反异步处理、CFAR和杂波图处理原理框图设计。通过对强杂波背景下FMCW雷达低小慢目标的探测能力分析,提升了强杂波背景下对近距离小木船及海面漂浮的浮筒等低小慢目标的探测能力。为复杂海洋环境下FMCW雷达低小慢目标探测提供了一种新方法。

The Short Local Algebras of Dimension 6 with Non-projective Reflexive Modules

Let A be a finite-dimensional local algebra over an algebraically closed field,let J be the radical of A.The modules we are interested in are the finitely generated left A-modules.Projectivemodules are always reflexive,and an algebra is self-injective iff allmodules are reflexive.We discuss the existence of non-projective reflexive modules in case A is not self-injective.We assume that A is short(this means that J^(3)=0).In a joint paper with Zhang Pu,it has been shown that 6 is the smallest possible dimension of A that can occur and that in this case the following conditions have to be satisfied:J^(2)is both the left socle and the right socle of A and there is no uniform ideal of length 3.The present paper is devoted to showing the converse.

On w_(∞)-Warfield Cotorsion Modules and Krull Domains

Let R be a commutative domain with 1 and Q(≠R)its field of quotients.In this note an R-module M is called w_(∞)-Warfield cotorsion if M∈WC∩P^(⊥)_(w_(∞)),where WC denotes the class of all Warfield cotorsion R-modules and P_(w_(∞))the class of all w_(∞)-projective R-modules.It is shown that R is a PVMD if and only if all w-cotorsion R-modules are w_(∞)-Warfield cotorsion,and that R is a Krull domain if and only if every w-Matlis cotorsion strong w-module over R is a w_(∞)-Warfield cotorsion w-module.

强Ω-Gorenstein投射模

引入强Ω-Gorenstein投射模的概念,给出强Ω-Gorenstein投射模的一些等价刻画.并利用强Ω-Gorenstein投射模给出Ω-Gorenstein投射模的一个简单刻画.