Notes on a theorem of Naji

We present a new proof of an algebraic characterization of circle graphs due to W. Naji.For bipartite graphs, Naji’s theorem is equivalent to an algebraic characterization of planar matroids due to J. Geelen and B. Gerards. Naji’s theorem also yields an algebraic characterization of permutation graphs.     

Simultaneous Subgradient Algorithms for the Generalized Split Variational Inclusion Problem in Hilbert Spaces

In this article, we study the generalized split variational inclusion problem. For this purpose, motivated by the projected Landweber algorithm for the split equality problem, we first present a simultaneous subgradient extragradient algorithm and give related convergence theorems for the proposed algorithm. Next, motivated by the alternating CQ-algorithm for the split equality problem, we propose another simultaneous subgradient extragradient algorithm to study the general split variational inclusion problem. As applications, we consider the split equality problem, split feasibility problem, split variational inclusion problem, and variational inclusion problem in Hilbert spaces.     

高应变率下硅橡胶的本构行为研究

 硅橡胶是一种高分子聚合物,可以承受大变形,用途广泛。利用改进的分离式霍普金森压杆（SHPB）实验技术,对硅橡胶试样进行了不同应变率下的冲击压缩实验,基于实验数据,利用应变能函数构建了考虑应变率效应的材料本构形式。同时,实验过程中发现,在高应变率加载条件下,材料在压缩变形后出现了损伤线区,线区直径与加载应变率及试样尺寸之间存在一定的定量关系。     

Full Field Strain Measurement in Compression and Tensile Split Hopkinson Bar Experiments

The 3D image correlation technique is used for full field measurement of strain (and strain rate) in compression and tensile split Hopkinson bar experiments using commercial image correlation software and two digital high-speed cameras that provide a synchronized stereo view of the specimen. Using an array of 128 × 80 (compression tests) and 258 × 48 (tensile tests) pixels, the cameras record about 110,000 frames per second. A random dot pattern is applied to the surface of the specimens. The image correlation algorithm uses the dot pattern to define a field of overlapping virtual gage boxes, and the 3-D coordinates of the center of each gage box are determined at each frame. The coordinates are then used for calculating the strains throughout the surface of the specimen. The strains determined with the image correlation method are compared with those determined from analyzing the elastic waves in the bars, and with strains measured with strain gages placed on the specimens. The system is used to study the response of OFE C10100 copper. In compression tests, the image correlation shows a nearly uniform deformation which agrees with the average strain that is determined from the waves in the bars and the strains measured with strain gages that are placed directly on the specimen. In tensile tests, the specimen geometry and properties affect the outcome from the experiment. The full field strain measurement provides means for examining the validity and accuracy of the tests. In tests where the deforming section of the specimen is well defined and the deformation is uniform, the strains measured with the image correlation technique agree with the average strain that is determined from the split Hopkinson bar wave records. If significant deformation is taking place outside the gage section, and when necking develops, the strains determined from the waves are not valid, but the image correlation method provides the accurate full field strain history.     

应用高速摄影机对泡沫铝在SHPB实验过程的变形跟踪与分析

SHPB技术虽然能方便地得出材料的动态应力应变关系,但却不能直观地揭示材料在经受冲击荷载时的变形特征,而这恰恰是泡沫金属力学性能研究的重要方面.为此,本文设计了一套SHPB-高速摄影机系统,借此系统对SHPB实验中的泡沫铝试件进行了实时的变形跟踪拍摄,然后应用图像处理软件对泡沫铝试件的动态变形进行分析并提取了位移信息,...     

低阻抗多孔介质材料的SHPB实验技术

低阻抗多孔介质材料具有较低的密度和弹性波速，对其实施动态压缩实验具有一定的难度。本文在充分分析聚氨酯泡沫试件由于低阻抗所带来的各种影响因素后，提出了在ＳＨＰＢ装置上对低阻抗多孔介质材料进行动态测试时所应采取的半导体应变片技术及新的ＳＨＰＢ数据计算模式，初步解决了ＳＨＰＢ装置上对低阻抗多孔介质测试的难点。     

Actions in the Category of Precrossed Modules in Lie Algebras

For any object L in the category of precrossed modules in Lie algebras PXLie, we construct the object Act(L), which we call the actor of this object. From this construction, we derive the notions of action, center, semidirect product, derivation, commutator, and abelian precrossed module in PXLie. We show that the notion of action is equivalent to the one given in semi-abelian categories, and Act(L) is the split extension classifier for L. In the case of a crossed module in Lie algebras we show how to recover its actor in the category of crossed modules from its actor in the category of precrossed modules.     

The split common fixed point problem for generalized demimetric mappings in two Banach spaces

ABSTRACT

In this paper, we consider the split common fixed point problem for new demimetric mappings in two Banach spaces. Using the hybrid method, we prove a strong convergence theorem for finding a solution of the split common fixed point problem in two Banach spaces. Furthermore, using the shrinking projection method, we obtain another strong convergence theorem for finding a solution of the problem in two Banach spaces. Using these results, we obtain well-known and new strong convergence theorems in Hilbert spaces and Banach spaces.