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次Hermite矩阵的对角化及次Hermite矩阵的应用 总被引:1,自引:0,他引:1
循环矩阵在理论及实际问题上都得到了广泛的应用,而循环矩阵是一类典型的次对称矩阵,此外Hadamare 矩阵中也涉及到了次对称矩阵,本文将对次对称矩阵进一步的推广,定义了次Hermite 矩阵及次正定的次Hermite 矩阵.并且讨论它们的对角化方法,得出了类以于Hermite 矩阵的一些结论,最后作为应用,讨论了次Hermite 矩阵的算子范数及F—范数的理论值。关键词次Hermite 矩阵次特征值及次特征向量次正定的次Hermite 矩阵. 相似文献
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郑建青 《纯粹数学与应用数学》2014,(1):45-52
利用复矩阵的Schur补和次正定性,研究了次正定复矩阵的次Schur补的一些性质,得到了次正定复矩阵次Schur补的几个行列式不等式,将相关文献的相应结果由次正定次Hermite矩阵推广到次正定复矩阵. 相似文献
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本文研究了次亚正定矩阵子阵的次L(o)wner偏序,利用次Lwner偏序,获得了几个用低阶矩阵的次亚正定性判别高阶矩阵次亚正定性的充要条件. 相似文献
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提出了血样的二次分组检验方法,建立了二次分组验血法预期人均检验次数最小的模型,给出了二次分组法的最佳小组人数和最佳小组数的范围,得到了求二次分组最佳方案的方法.计算结果表明模型和方法是可信的,在单个人血样呈阴性概率较大时,采用二次分组验血法能比一次分组验血法更进一步地减少检验次数,有较大的实用价值. 相似文献
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本文讨论了区间值映射的次可微性问题,给出了次可微的概念及其基本性质,证明了区间值映射的次微分是空集或闭凸集;作为次微分的一种应用,讨论了区间值映射的次可微与其凸化区间值映射的次可微之间的关系,给出了一类区间值映射存在凸扩张区间值映射的充分条件。 相似文献
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We obtain integral representations for solutions of some types of the Beltrami equations. These representations allow us to prove analogs of some classical complex analysis for these solutions. 相似文献
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In this paper, by using the method of partial fraction decomposition and integral representations of series, we establish some expressions of series involving harmonic numbers and binomial coefficients in terms of zeta values and harmonic numbers. Furthermore, we can obtain some closed form representations of sums of products of quadratic (or cubic) harmonic numbers and reciprocal binomial coefficients, and some explicit evaluations are given as applications. The given representations are new. 相似文献
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We investigate representations of *-algebras associated with posets. Unitarizable representations of the corresponding (bound) quivers (which are polystable representations for some appropriately chosen slope function) give rise to representations of these algebras. Considering posets which correspond to unbound quivers this leads to an ADE-classification which describes the unitarization behaviour of their representations. Considering posets which correspond to bound quivers, it is possible to construct unitarizable representations starting with polystable representations of related unbound quivers which can be glued together with a suitable direct sum of simple representations. Finally, we estimate the number of complex parameters parametrizing irreducible unitary non-equivalent representations of the corresponding algebras. 相似文献
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S. A. Kruglyak L. A. Nazarova A. V. Roiter 《Functional Analysis and Its Applications》2010,44(2):125-138
It is known that finitely representable quivers correspond to Dynkin graphs and tame quivers correspond to extended Dynkin
graphs. In an earlier paper, the authors generalized some of these results to locally scalar (later renamed to orthoscalar)
quiver representations in Hilbert spaces; in particular, an analog of the Gabriel theorem was proved. In this paper, we study
the relationships between indecomposable representations in the category of orthoscalar representations and indecomposable
representations in the category of all quiver representations. For the quivers corresponding to extended Dynkin graphs, the
indecomposable orthoscalar representations are classified up to unitary equivalence. 相似文献
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Kaiming Zhao 《代数通讯》2013,41(14):4373-4383
In this paper, the weight sets of some irreducible and integrable representations, which are not highest or lowest weight representations, of rank two Kac-Moody algebras of indefinite type are completely determined. 相似文献
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讨论了四对谱问题、相应的保谱方程族以及它们Lax表示的等价住,并利用这种等价关系可导出一些方程的Lax表示. 相似文献
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We remove a parity condition from the construction of automorphic Galois representations carried out in the Paris Book Project. We subsequently generalize this construction to the case of ‘mixed-parity’ (but still regular essentially self-dual) automorphic representations over totally real fields, finding associated geometric projective representations. Finally, we optimize some of our previous results on finding geometric lifts, through central torus quotients, of geometric Galois representations, and apply them to the previous mixed-parity setting. 相似文献
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Toby Gee 《Mathematische Annalen》2011,350(1):107-144
We prove a variety of results on the existence of automorphic Galois representations lifting a residual automorphic Galois
representation. We prove a result on the structure of deformation rings of local Galois representations, and deduce from this
and the method of Khare and Wintenberger a result on the existence of modular lifts of specified type for Galois representations
corresponding to Hilbert modular forms of parallel weight 2. We discuss some conjectures on the weights of n-dimensional mod p Galois representations. Finally, we use recent work of Taylor to prove level raising and lowering results for n-dimensional automorphic Galois representations. 相似文献
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Chris Bills 《Research in Mathematics Education》2013,15(1):45-60
Teachers use a variety of external representations to communicate mathematical ideas to their pupils. This paper reports a preliminary study of the internal mental representations that 6- and 7- year-old pupils form as a result of their interactions with the teacher's verbal, written, pictorial and concrete material representations, involving two-digit numbers and operations on them. The results presented here concern the picture-like mental representations that pupils use in performing two-digit calculations mentally. The evidence suggests that pupils seldom spontaneously visualise teachers’ representations or attempt mental manipulation of visual images to help with calculation. Pupils can, however, have mental representations which reproduce some aspects of the teachers’ representations. 相似文献