Gorenstein Flat Covers and Gorenstein Cotorsion Modules Over Integral Group Rings

Every module over an Iwanaga–Gorenstein ring has a Gorenstein flat cover [13] (however, only a few nontrivial examples are known). Integral group rings over polycyclic-by-finite groups are Iwanaga–Gorenstein [10] and so their modules have such covers. In particular, modules over integral group rings of finite groups have these covers. In this article we initiate a study of these covers over these group rings. To do so we study the so-called Gorenstein cotorsion modules, i.e. the modules that split under Gorenstein flat modules. When the ring is ℤ, these are just the usual cotorsion modules. Harrison [16] gave a complete characterization of torsion free cotorsion ℤ-modules. We show that with appropriate modifications Harrison's results carry over to integral group rings ℤG when G is finite. So we classify the Gorenstein cotorsion modules which are also Gorenstein flat over these ℤG. Using these results we classify modules that can be the kernels of Gorenstein flat covers of integral group rings of finite groups. In so doing we necessarily give examples of such covers. We use the tools we develop to associate an integer invariant n with every finite group G and prime p. We show 1≤n≤|G : P| where P is a Sylow p-subgroup of G and gives some indication of the significance of this invariant. We also use the results of the paper to describe the co-Galois groups associated to the Gorenstein flat cover of a ℤG-module. Presented by A. Verschoren Mathematics Subject Classifications (2000) 20C05, 16E65.     

Ordered group invariants for nonorientable one-dimensional generalized solenoids

Let be an edge-wrapping rule which presents a one-dimensional generalized solenoid , and let be the adjacency matrix of . When is a wedge of circles and leaves the unique branch point fixed, we show that the stationary dimension group of is an invariant of homeomorphism of even if is not orientable.

     

On the rings whose injective hulls are flat

Let be a commutative Noetherian ring with nonzero identity and let the injective envelope of be flat. We characterize these kinds of rings and obtain some results about modules with nonzero injective cover over these rings.

     

Nodal degenerations of plane curves and galois covers

Globally irreducible nodes (i.e. nodes whose branches belong to the same irreducible component) have mild effects on the most common topological invariants of an algebraic curve. In other words, adding a globally irreducible node (simple nodal degeneration) to a curve should not change them a lot. In this paper we study the effect of nodal degeneration of curves on fundamental groups and show examples where simple nodal degenerations produce non-isomorphic fundamental groups and this can be detected in an algebraic way by means of Galois covers.      

基于改进Hough变换的井盖目标检测与定位

市政井盖的实时告失对城市管理具有重大意义。针对图像的复杂背景,提出了改进的Hough变换算法。在经边缘提取的二值图上,利用轮廓跟踪找到所有的轮廓,接下来设计轮廓过滤器排除虚假目标,进而在轮廓链表上进行Hough变换从而确定目标可能出现的区域,最终获得准确的井盖区域定位。该方案有效地提高了传统Hough变换的处理速度,减少了无效采样和累积。实验结果表明,该算法在多种复杂背景、不同视角、不同拍摄时间和条件、目标被部分遮挡等情况下都有很好的定位效果。     

亚纯函数的正规定理

亚纯函数族在区域Ｄ内正规的充分必要条件是任取ｚ０∈Ｄ及δ＞０，存在ε＞０，对任意及任意三个单连通闭区域Ａ，Ｂ，Ｃ，只要它们两两间的球距大于δ，则ｆ在｛｜ｚ－ｚ０｜＜ε｝内单纯覆盖Ａ，Ｂ，Ｃ的总次数小于２．     

近三角剖分图的均衡二重少圈覆盖

近三角剖分图是一连通平面图，其内面均为三角形而其外面可能不是．令Ｇ为一具有ｎ个节点的近三角剖分图，Ｃ为 Ｇ的一个小圈二重覆盖（ＳＣＤＣ）^［２］．令(?)则Ｃ₀。称为Ｇ的均衡小圈二重覆盖．本文将证明：若Ｇ为外平面图，则 δ（Ｃ₀）≤ ２；否则δ（Ｃ₀）≤４。     

一种高分辨率CCD阵列扫描光学系统

系统采用了一种象元尺寸为7μm的高分辨率线阵CCD做为图象传感器。为了获得大面积成象效果,将两块CCD光学拼接从而得到2×5000元的大视场,对光学系统而言必须满足高分辨率和大视场优质成象。着重介绍了实施方案,讨论了光学设计的难点并用数学建模方法分析和平衡高级象差,得到了对象差平衡方案有指导意义的合成规律,最后,给出了MTF评价象质的计算结果,并与测试值进行比较,结果相符合,研制出了一个实用的光学系统。     

电热法测定冰的熔化热实验仪的研制

为了解决混合法测量冰的熔化热实验中热量损失的问题,设计了电热法测定冰的熔化热实验仪.真空保温杯和冰水混合物双重隔离实验对象,降低了冰与环境的热交换,通过移液管测量冰熔化成水的体积变化,进而测定冰的熔化热.