局部凸Hausdorff线性拓扑空间上Kannan映射的不动点

本文在局部凸空间上考虑了一类比Kannan自映射更广的带边界条件Kannan映射的不动点问题。证明了当空间具有亚正规结构或映射满足一定的连续性时,这类映射有不动点。推广了文献[1][2][3]中的一些相应结论。     

运用多维画法几何理论解决非线性规划问题

本文运用多维空间投影的理论和方法，给出了非线性规划的一个通用解法。     

关于CATT齿轮径向变位原理的研究

本文通过对ＣＡＴＴ齿轮径向变位原理的分析，论述了ＣＡＴＴ齿轮在啮合过程中不发生曲率干涉的条件，从而得出了刀盘半径的调整公式。     

多目标规划的共轭对偶

Tanino.T与Swaragi.Y[1]在R~n空间中讨论了多目标规划的共轭对偶,本文在实赋范线性空间中,利用凸锥的性质(π)[4],保证了紧性,讨论了多目标规划问题的共轭对偶,文[1]中的结论是本文的特例。     

无穷维线性规划的对偶问题

本文对定义在局部凸线性拓扑空间上的线性规划问题,引入了双函数的概念,从而研究了原问题和对偶问题解的存在性,得出原问题与对偶问题的相互关系.     

矢值序列空间BMC（X）中的序列紧集

利用局部凸空间理论，讨论了矢值序列空间ＢＭＣ（Ｘ）中的相对序列紧集的性质，给出了其特征刻划，即ＢＭＣ（Ｘ）中的子集是相对序列紧集，当且仅当它是一致收敛集及其每个坐标射影集是相对序列紧集。同时，在局部凸空间Ｘ不包含ｃ０的情况下，给出了ＢＭＣ（Ｘ）中的相对序列紧集的另一种特征刻划。     

r凸函数的运算性质

广义凸函数是凸函数的推广,它包括伪凸函数,拟凸函数和r凸函数等.广义凸函数的性质和运算性质在广义凸规划中有很重要的作用.薛家声对伪凸函数的构造方法进行了讨论;J.P.Crouzeix~[6]讨论了拟凸函数的性质.本文旨在对广义凸函数中的一类即r凸函数进行讨论.     

局部凸线性Hausdorff拓扑空间上非膨胀型映射的不动点

本文考虑了一类带边界条件的非膨胀型映射的不动点问题,在空间具有正规结构性质的假设下,证明了这类映射有不动点存在,推广了某些非膨胀自映射的不动点定理.     

Subgradient-based feedback neural networks for non-differentiable convex optimization problems

1 Introduction Optimization problems arise in a broad variety of scientific and engineering applica- tions. For many practice engineering applications problems, the real-time solutions of optimization problems are mostly required. One possible and very pr…     

A New Active Convex Hull Model for Image Regions

This paper presents a new active convex hull model with the following advantages: invariant with respect to the number of pixels to be enveloped; the number of time iterations is invariant, with respect to the image size; time-cheap for large image regions. The model is based on the geometric heat differential equations, derived from parabolic equation, and parameterized by arc length. To prevent the active contour from intruding into concavities and evolve it to the proper convex hull we use a vector field given as a difference between normal and tangent forces. The vector field is also used to segment an image to shells, such that a single region is present in each shell. A penalty function is developed to stop evolvement of those arc segments, whose vectors encountered boundary points of an image region. Based on the model a discrete algorithm is designed and coded by Mathematica 5.2. A condition is developed, with respect to the image size, to guarantee stable convergence of the active contour to the convex hull of the desired region. To validate the advantages and contributions a set of experiments is performed using synthetic, groundwater and medical images of different size and modalities. The paper concludes with a discussion and comparison of the active convex hull model with set of existing convex hull algorithms. Nikolay M. Sirakov received B.S. degree from School of Mathematics and Informatics-Sofia University in 1982, M.S. degree from the same University in the field of Coding Theory in 1983, and Ph.D. degree from Institute of Mechanics-Bulgarian Academy of Sciences in the field of 3D modeling and recognition in 1991. He had research and teaching positions at the Institute of Mechanics (1984–2000—Associate Professor since 1999), International Lab of Artificial Intelligence-Slovak Academy of Sciences (1990), Instituto Superior Technico–CVRM-Portugal (1993, 1998–2000), and Northern Arizona University (2001–2004). Currently Dr. Sirakov is an Assistant Professor of Mathematics and Computer Science at Texas A&M University Commerce. His research interests fall in Active Contours/Surfaces Models to image segmentation and features extraction, 3D reconstruction and visualization, 2D/3D objects matching and classification, Image Processing and Analysis, and Content Based Image Retrieval. He published over seventy papers and was a co-author of two books in the above listed fields.