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61.
We describe the multilinear components of the prime subvarieties of the variety Var(M 2(F)) generated by the matrix algebra of order 2 over a field of characteristic p>0.  相似文献   
62.
Some recent methods of Computer Aided Geometric Design are related to the apolar bilinear form, an inner product on the space of homogeneous multivariate polynomials of a fixed degree, already known in 19th century invariant theory. Using a generalized version of this inner product, we derive in a straightforward way some of the recent results in CAGD, like Marsden's identity, the expression for the de Boor-Fix functionals, and recursion schemes for the computation of B-patches and their derivatives.

  相似文献   

63.
Partition identities and the coin exchange problem   总被引:1,自引:1,他引:0  
The number of partitions of n into parts divisible by a or b equals the number of partitions of n in which each part and each difference of two parts is expressible as a non-negative integer combination of a and b. This generalizes identities of MacMahon and Andrews. The analogous identities for three or more integers (in place of a,b) hold in certain cases.  相似文献   
64.
65.
We continue our study of operator algebras with contractive approximate identities (cais) by presenting a couple of interesting examples of operator algebras with cais, which in particular answer questions raised in previous papers in this series, for example about whether, roughly speaking, ‘weak compactness’ of an operator algebra, or the lack of it, can be seen in the spectra of its elements.  相似文献   
66.
By means of Jacobi?s triple product identity and the t  -coefficient method, we establish a general series expansion formula with five free parameters for the product of arbitrary two Jacobi theta functions. It embodies the triple, quintuple, sextuple and septuple theta function product identities and the generalized Schröter formula. As further applications, we also set up a series expansion formula for the product of three theta functions. It not only generalizes Ewell?s and Chen–Chen–Huang?s octuple product identities, but also contains three cubic theta function identities due to Farkas–Kra and Ramanujan respectively and the Macdonald identity for the root system A2A2 as special cases. In the meantime, many other new identities including a new short expression of the triple theta series of Andrews are also presented.  相似文献   
67.
In this paper we prove the S‐inequality for certain product probability measures and ideals in . As a result, for the Weibull and Gamma product distributions we derive concentration of measure type estimates as well as optimal comparison of moments.  相似文献   
68.
We study existence of unbiased estimators of risk for estimators of the location parameter of a spherically symmetric distribution, when a residual vector is available to estimate scale, under invariant quadratic loss. We show such existence often characterizes normality.  相似文献   
69.
Based on a general isospectral problem of fractional order and the fractional quadratic-form identity by Yue and Xia, the new integrable coupling of fractional coupled Burgers hierarchy and its fractional bi-Hamiltonian structures are obtained.  相似文献   
70.
In this paper, we introduce new Triebel–Lizorkin and Besov Spaces associated with the different homogeneities of two singular integral operators. We then establish the boundedness of composition of two Calder′on–Zygmund singular integral operators with different homogeneities on these Triebel–Lizorkin and Besov spaces.  相似文献   
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