基于随机数三角阵映射的高维大数据二分聚类初始中心高效鲁棒生成算法

Bisecting K-means算法通过使用一组初始中心对分割簇,得到多个二分聚类结果,然后从中选优以减轻局部最优收敛问题对算法性能的不良影响。然而,现有的随机采样初始中心对生成方法存在效率低、稳定性差、缺失值等不同问题,难以胜任大数据聚类场景。针对这些问题,该文首先创建出了初始中心对组合三角阵和初始中心对编号三角阵,然后通过建立两矩阵中元素及元素位置间的若干映射,从而实现了一种从随机整数集合中生成二分聚类初始中心对的线性复杂度算法。理论分析与实验结果均表明,该方法的时间效率及效率稳定性均明显优于常用的随机采样方法,特别适用于高维大数据聚类场景。     

一种求二元有理插值函数的方法

给出一种方法可直接计算基于矩形节点的二元有理插值函数的分母在节点处的值 ,进而判断相应的二元有理插值函数是否存在 .此方法运用灵活 ,适用范围广 ,在相应的有理插值函数存在时 ,能给出它的具体表达式 .此外 ,我们还针对文中两个主要逆矩阵 ,给出了相应的递推公式 ,避免了求逆计算 .     

三角形二次插值系数有限元法解半线性椭圆问题的超收敛性

基于均匀三角形的剖分求解一类二阶半线性椭圆问题,用插值系数有限元方法比经典有限元法更容易实现,与经典二次有限元一样,二次插值系数有限元方法在对称点处也有四阶超收敛精度,数值计算表明这些结论是正确的.     

Triangular pattern formation on silicon through self-organization of GaN nanoparticles

Nanoparticles of gallium nitride, synthesized by a low-temperature reaction between triethyl gallium and ammonia, were introduced onto silicon wafers containing a thin layer of chemically prepared silicon dioxide. At room temperature, the nanoparticles form unstructured agglomerates on the surface. However, upon annealing the samples beyond the decomposition temperature of the silicon dioxide layer, the gallium nitride particles self-organize to form triangular structures. The pattern formation is attributed to the domain separation associated with the (1 × 1)-(7 × 7) surface phase transformation followed by selective incorporation of the nanoparticles.     

Extreme points in triangular UHF algebras

We examine the strongly extreme point structure of the unit balls of triangular UHF algebras. The semisimple triangular UHF algebras are characterized as those for which this structure is minimal in the sense that every strongly extreme point belongs to the diagonal. In contrast to this, for the class of full nest algebras we prove a Krein-Milman type theorem which asserts that every operator in the open unit ball of the algebra is a convex combination of strongly extreme points.

     

C r -finite elements of Powell-Sabin type on the three direction mesh

Let be the triangulation generated by a uniform three direction mesh of the plane. Let ₆ be the Powell-Sabin subtriangulation obtained by subdividing each triangleT by connecting each vertex to the midpoint of the opposite side.Given a smooth functionu, we construct a piecewise polynomial function C ^r (²) of degreen=2r (resp. 2r+1) forr odd (resp. even) in each triangle of ₆, interpolating derivatives ofu up to orderr at the vertices of.     

A new method for solving differential equations with vague parameters

In the literature, it is pointed out that it is better to use vague sets instead of fuzzy sets. Several authors have proposed different methods for solving such differential equations in which all the parameters are represented by fuzzy numbers but to the best of our knowledge till now no one have represented the same as vague sets. In this paper, a new representation of (α, β)-cut, named as JMD (α, β)-cut, is proposed and with the help of JMD (α, β)-cut a new method is proposed to find the analytical solution of vague differential equations. To show the application of proposed method in real life problems the vague Kolmogorov’s differential equations, obtained by using vague Markov model of piston manufacturing system, are solved by proposed method. Also, to show the advantage of JMD (α, β)-cut over existing (α, β)-cut the same vague Kolmogorov’s differential equations are solved by using the proposed method with the help of existing (α, β)-cut and it is shown that the obtained results are not necessarily vague sets while the results, obtained by using JMD (α, β)-cut, are always vague sets.     

Arrangement effects of triangular defects on magnetization reversal process in a permalloy dot

The arrangement effects of triangular defects on the magnetization configurations and switching process of a permalloy disk are investigated by micromagnetic simulations. For the case of one defect, the vortex is nucleated via the S state (W state) as the direction of the triangular defect is parallel (perpendicular) to the orientation of the external field. For the case of two defects, two types of switching processes are found dependent on their arrangement. For the two triangular defects with the same direction, the reversal occurs via formation, pinning, depinning and annihilation of the vortex state, however, for the two triangular defects with the opposite directions, the reversal is realized by formation and annihilation of the double-vortex state. The nucleation field for the disk with a triangular defect is more sensitive to the defect position than the case of a circular (square) defect, and it shows different variation trends for different triangular directions. The chirality of the vortex state nucleated in the reversal process can be controlled by the triangular defect.     

A fast method to block-diagonalize a Hankel matrix

In this paper, we consider an approximate block diagonalization algorithm of an n×n real Hankel matrix in which the successive transformation matrices are upper triangular Toeplitz matrices, and propose a new fast approach to compute the factorization in O(n ²) operations. This method consists on using the revised Bini method (Lin et al., Theor Comp Sci 315: 511–523, 2004). To motivate our approach, we also propose an approximate factorization variant of the customary fast method based on Schur complementation adapted to the n×n real Hankel matrix. All algorithms have been implemented in Matlab and numerical results are included to illustrate the effectiveness of our approach.