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21.
Usha N. Bhosle 《Proceedings Mathematical Sciences》2005,115(4):445-451
LetM be the moduli space of generalized parabolic bundles (GPBs) of rankr and degree dona smooth curveX. LetM
−L
be the closure of its subset consisting of GPBs with fixed determinant− L. We define a moduli functor for whichM
−L
is the coarse moduli scheme. Using the correspondence between GPBs onX and torsion-free sheaves on a nodal curveY of whichX is a desingularization, we show thatM
−L
can be regarded as the compactified moduli scheme of vector bundles onY with fixed determinant. We get a natural scheme structure on the closure of the subset consisting of torsion-free sheaves
with a fixed determinant in the moduli space of torsion-free sheaves onY. The relation to Seshadri-Nagaraj conjecture is studied. 相似文献
22.
B. M. Podlevskii 《Computational Mathematics and Mathematical Physics》2008,48(12):2140-2145
An iterative algorithm is examined for finding the eigenvalues of the two-parameter (multiparameter) algebraic eigenvalue problem. This algorithm uses Newton’s method and an efficient numerical procedure for differentiating determinants. Some numerical examples are given. 相似文献
23.
24.
The importance of variable selection and regularization procedures in multiple regression analysis cannot be overemphasized. These procedures are adversely affected by predictor space data aberrations as well as outliers in the response space. To counter the latter, robust statistical procedures such as quantile regression which generalizes the well-known least absolute deviation procedure to all quantile levels have been proposed in the literature. Quantile regression is robust to response variable outliers but very susceptible to outliers in the predictor space (high leverage points) which may alter the eigen-structure of the predictor matrix. High leverage points that alter the eigen-structure of the predictor matrix by creating or hiding collinearity are referred to as collinearity influential points. In this paper, we suggest generalizing the penalized weighted least absolute deviation to all quantile levels, i.e., to penalized weighted quantile regression using the RIDGE, LASSO, and elastic net penalties as a remedy against collinearity influential points and high leverage points in general. To maintain robustness, we make use of very robust weights based on the computationally intensive high breakdown minimum covariance determinant. Simulations and applications to well-known data sets from the literature show an improvement in variable selection and regularization due to the robust weighting formulation. 相似文献
25.
利用多项式因式分解的逆变换,结合循环矩阵和切比雪夫多项式的特殊结构,首先研究第三类和第四类切比雪夫多项式的通项公式,并给出第三类、第四类切比雪夫多项式的关于行首加r尾r右循环矩阵和行尾加r首r左循环矩阵的行列式的显式表达式,最后给出算法实施步骤. 相似文献
26.
We consider the 1D Dirac operator on the half-line with compactly supported potentials. We study resonances as the poles of scattering matrix or equivalently as the zeros of modified Fredholm determinant. We obtain the following properties of the resonances: (1) asymptotics of counting function, (2) estimates on the resonances and the forbidden domain. 相似文献
27.
文献[1,2]中对一道美国大学生数学竞赛题通过设定函数利用插值的方法进行了证明,本文根据问题的特点,给出另外的证明,用同一方法还对另一行列式问题给出一般求解公式. 相似文献
28.
构造了一个对称正定矩阵,矩阵元素与组合数有关,讨论了该矩阵的一些性质.根据MATLAB数值计算的结果,提出了该矩阵有关特征值性质的一些猜想. 相似文献
29.
30.
Guo-Dong LinYi-Tian Gao Zhi-Yuan SunXin Yu De-Xin Meng 《Applied mathematics and computation》2011,217(9):4805-4811
Under investigation in this paper is a variable-coefficient variant Boussinesq (vcvB) model for the nonlinear and dispersive long gravity waves in shallow water traveling in two horizontal directions with varying depth. Connection between the vcvB model and a variable-coefficient Ablowitz-Kaup-Newell-Segur system is revealed under certain constraints with the help of the symbolic computation. Multi-solitonic solutions in terms of the double Wronskian determinant for the vcvB model are derived. Interactions among the vcvB-solitons are discussed. A novel dynamic property is observed, i.e., the coexistence of elastic-inelastic-interactions. 相似文献