共查询到18条相似文献,搜索用时 461 毫秒
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对于一类Hamilton算子,考虑其特征值的重数,以及特征向量组和根向量组的完备性.首先给出了特征值的几何重数、代数指标和代数重数,再结合特征向量和根向量的辛正交性得到了特征向量组和根向量组完备的充分必要条件,最后将上述结果应用于板弯曲方程、平面弹性问题和Stokes流等问题中. 相似文献
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无穷维Hamilton算子特征函数系是否完备与其代数指标有关,研究了上三角无穷维Hamilton算子特征值的代数指标问题,基于主对角元的特征值和特征向量的某些性质,得到上三角无穷维Hamilton算子的几何重数和代数重数. 相似文献
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利用扰动理论和算子矩阵的因式分解,研究了辛对称Hamilton算子值域的闭性.针对对角占优、上行占优等情形,在一定条件下给出了值域闭性的若干描述,并得到了一般情形的结果. 相似文献
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《数学的实践与认识》2019,(20)
讨论了希尔伯特空间上有界上三角算子矩阵的亏谱扰动性质,当对角元算子给定时,得到上三角算子矩阵的亏谱恰等于对角元算子的亏谱之并集的充要条件,特别地,给出有界上三角Hamilton型算子矩阵相应问题成立的条件,并辅以实例佐证. 相似文献
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研究了一类四阶Hamilton算子H_A特征值的代数指标问题.根据算子A与Hamilton算子H_A的关系,讨论了Hamilton算子H_A特征值的几何重数,代数指标及代数重数.最后结合例子说明其结果的有效性. 相似文献
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The authors investigate the completeness of the system of eigen or root vectors of the 2 × 2 upper triangular infinite-dimensional
Hamiltonian operator H
0. First, the geometrical multiplicity and the algebraic index of the eigenvalue of H
0 are considered. Next, some necessary and sufficient conditions for the completeness of the system of eigen or root vectors
of H
0 are obtained. Finally, the obtained results are tested in several examples. 相似文献
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Cameron, Goethals, Seidel, and Shult classified the graphs with eigenvalues at least – 2 by viewing their vertices as elements of a root system of type An, Dn, E6, E7, or E8. In this paper we characterize graphs satisfying more general algebraic conditions by viewing edges as elements in a root system. Specifically, vertices are viewed as equal length vectors spanning some Euclidean space that is also spanned by a root system Φ, such that vertices are adjacent if and only if their differences is in Φ. We conclude with some open problems. 相似文献
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本文主要讨论广义Jacobi阵及多个特征对的广义Jacobi阵逆特征问题.通过相似变换将广义Jacobi阵变换为三对角对称矩阵,其特征不变、特征向量只作线性变换,再应用前人理论求得广义Jacobi阵元素ai,|bi|,|ci|有唯一解的充要条件及其具体表达式. 相似文献
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《European Journal of Operational Research》1987,29(3):360-369
In addition to Saaty's eigenvector, there are infinitely many eigen weight vectors which can be constructed for any given data of estimated weight ratios. As the judgment of the ratios are dependent on personal experience, learning, situations and state of mind, inconsistencies and degree of easiness or judgment on these individual ratios can be different, we study the properties of the different eigen weight vectors, including that of Saaty and that recently proposed by Cogger and Yu. A general framework for the construction of eigen weight vectors incorporating that confidence in obtaining the individual ratios can be different will be proposed and discussed. 相似文献
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Using the framework provided by Clifford algebras, we consider a non‐commutative quotient‐difference algorithm for obtaining
the elements of a continued fraction corresponding to a given vector‐valued power series. We demonstrate that these elements
are ratios of vectors, which may be calculated with the aid of a cross rule using only vector operations. For vector‐valued
meromorphic functions we derive the asymptotic behaviour of these vectors, and hence of the continued fraction elements themselves.
The behaviour of these elements is similar to that in the scalar case, while the vectors are linked with the residues of the
given function. In the particular case of vector power series arising from matrix iteration the new algorithm amounts to a
generalisation of the power method to sub‐dominant eigenvalues, and their eigenvectors.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
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In this paper we investigate the deficiency indices theory and the selfad-joint and nonselfadjoint (dissipative, accumulative) extensions of the minimal symmetric direct sum Hamiltonian operators. In particular using the equivalence of the Lax-Phillips scattering matrix and the Sz.-Nagy-Foia¸s characteristic function, we prove that all root (eigen and associated) vectors of the maximal dissipative extensions of the minimal symmetric direct sum Hamiltonian operators are complete in the Hilbert spaces. 相似文献
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According to the Feigin–Frenkel–Reshetikhin theorem, the eigenvalues of higher Gaudin Hamiltonians on Bethe vectors can be found using the center of an affine vertex algebra at the critical level. We recently calculated explicit Harish-Chandra images of the generators of the center in all classical types. Combining these results leads to explicit formulas for the eigenvalues of higher Gaudin Hamiltonians on Bethe vectors. The Harish-Chandra images can be interpreted as elements of classical W-algebras. By calculating classical limits of the corresponding screening operators, we elucidate a direct connection between the rings of q-characters and classical W-algebras. 相似文献
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Sufficient Dimension Reduction (SDR) in regression comprises the estimation of the dimension of the smallest (central) dimension reduction subspace and its basis elements. For SDR methods based on a kernel matrix, such as SIR and SAVE, the dimension estimation is equivalent to the estimation of the rank of a random matrix which is the sample based estimate of the kernel. A test for the rank of a random matrix amounts to testing how many of its eigen or singular values are equal to zero. We propose two tests based on the smallest eigen or singular values of the estimated matrix: an asymptotic weighted chi-square test and a Wald-type asymptotic chi-square test. We also provide an asymptotic chi-square test for assessing whether elements of the left singular vectors of the random matrix are zero. These methods together constitute a unified approach for all SDR methods based on a kernel matrix that covers estimation of the central subspace and its dimension, as well as assessment of variable contribution to the lower-dimensional predictor projections with variable selection, a special case. A small power simulation study shows that the proposed and existing tests, specific to each SDR method, perform similarly with respect to power and achievement of the nominal level. Also, the importance of the choice of the number of slices as a tuning parameter is further exhibited. 相似文献