Schrödinger方程的连续时空有限元方法

本文讨论Schr?dinger方程的连续时空有限元方法,通过引入相应的时空投影算子,利用实部虚部分离技巧,得到了变量u在时间节点处的L²范数,以及u和u_t的全局L²(H¹)和L²(L²)范数意义下的最优误差估计结果.该文的结论对进一步探索和设计Schr?dinger方程的数值算法是有益的.     

农业供应链金融能有效缓解企业的融资约束？——涉农企业参与精准扶贫的实证研究

农业供应链金融为涉农企业融资难问题提供了新思路。本文以上市涉农上市企业2016~2018年的财务数据为样本,探讨了农业供应链金融对缓解企业融资约束的影响,以及涉农企业参与精准扶贫对缓解融资约束的调节作用。研究发现:涉农企业普遍面临融资约束问题,而农业供应链金融显著缓解了涉农企业的融资约束,且对参与精准扶贫企业的融资约束缓解更为显著。本文揭示了:农业供应链金融能有效缓解涉农企业的融资约束问题,再次证明了农业供应链金融缓解涉农企业融资约束的重要性和必要性,拓展了供应链金融研究的领域,同时对企业参与精准扶贫,响应新时期涉农企业社会责任的具体要求,形成政府、企业等共同承担社会责任的多元化减贫治理机制,助力乡村振兴提供相应借鉴。     

Convergence of an augmented Lagrange algorithm for nonlinear optimizations with second-order cone constraints

An augmented Lagrange algorithm for nonlinear optimizations with second-order cone constraints is proposed based on a Löwner operator associated with a potential function for the optimization problems with inequality constraints. The favorable properties of both the Löwner operator and the corresponding augmented Lagrangian are discussed. And under some mild assumptions, the rate of convergence of the augmented Lagrange algorithm is studied in detail.     

Some Properties of Solutions to the Novikov Equation with Weak Dissipation Terms

In this paper, we investigate the Novikov equation with weak dissipation terms. First, we give the local well-posedness and the blow-up scenario. Then, we discuss the global existence of the solutions under certain conditions. After that, on condition that the compactly supported initial data keeps its sign, we prove the infinite propagation speed of our solutions, and establish the large time behavior. Finally, we also elaborate the persistence property of our solutions in weighted Sobolev space.     

分裂的正则Hom-Leibniz-Rinehart代数

作为Hom-Leibniz代数胚的代数类比, 本文引入Hom-Leibniz-Rinehart代数的概念. 证明了分裂的正则Hom-Leibniz-Rinehart代数$L$写成$L=U+\sum_{\gamma}I_\gamma$, 其中$U$为极大交换子代数$H$的子空间和$I_\gamma$为$L$的理想, 若$[\gamma]\neq[d]$, 满足$[I_\gamma, I_d]=0$. 随后分别发展了分裂Hom-Leibniz-Rinehart代数的根和权的连通技术.最后研究了紧致的正则Hom-Leibniz-Rinehart代数的结构.     

Artificial convolution neural network techniques and applications for lung nodule detection

We have developed a double-matching method and an artificial visual neural network technique for lung nodule detection. This neural network technique is generally applicable to the recognition of medical image pattern in gray scale imaging. The structure of the artificial neural net is a simplified network structure of human vision. The fundamental operation of the artificial neural network is local two-dimensional convolution rather than full connection with weighted multiplication. Weighting coefficients of the convolution kernels are formed by the neural network through backpropagated training. In addition, we modeled radiologists' reading procedures in order to instruct the artificial neural network to recognize the image patterns predefined and those of interest to experts in radiology. We have tested this method for lung nodule detection. The performance studies have shown the potential use of this technique in a clinical setting. This program first performed an initial nodule search with high sensitivity in detecting round objects using a sphere template double-matching technique. The artificial convolution neural network acted as a final classifier to determine whether the suspected image block contains a lung nodule. The total processing time for the automatic detection of lung nodules using both prescan and convolution neural network evaluation was about 15 seconds in a DEC Alpha workstation.     

An identification of the connections of Quillen and Beilinson-Schechtman

Given a family of Riemann surfaces and a holomorphic vector bundle Beilinson and Schechtman construct a canonical connection on the associated determinant bundle. We prove the conjecture which states that their connection coincides with the Quillen connection. This is done by reducing to the case where along fibers are invertible. Both connection forms become more accessible in this case.Supported in part by N.S.F. Grant No. DMS-9201022Supported in part by National Science Council of Republic of China Grant No. NSC 82-0208-M-002-125-T, and NSERC of Canada Grant No. OGP 0121883