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881.
In this paper we present systematic differential representations
for the dynamical group SO(4). These representations include the
left and the right differential representations and the left and
the right adjoint differential representations in both the group
parameter space and its coset spaces. They are the generalization
of the differential representations of the SO(3) rotation group in
the Euler angles. These representations may find their applications in
the study of the physical systems with SO(4) dynamical symmetry. 相似文献
882.
A rotational parameter
Rθ has been introduced
to complex wavelet transform (CWT). The rotational CWT (RCWT) corresponds
to a matrix element 〈ψ|U2 (θ;μ;k)|F〉in the context of quantum mechanics, where
U2(θ;μ;k) is a two-mode rotational displacing-squeezing
operator in the 〈η| representation. Based on this, the Parseval theorem and the inversion formula of RCWT have been
proved. The concise proof not only manifestly shows the merit of Dirac's
representation theory but also leads to a new orthogonal property of complex
mother wavelets in parameter space. 相似文献
883.
基于本体的个性化教学系统的设计 总被引:1,自引:0,他引:1
程南清 《宁波大学学报(理工版)》2008,21(2):211-215
基于本体构建了一种个性化网络教学系统,重点阐述了利用本体构建课程知识体系,详细说明了系统可根据学生历史学习行为信息、利用课程知识语义网络和本体推理函数实现动态地向远程师生提供高效、准确的个性化教学信息服务. 相似文献
884.
Let
be a triangulated category with coproducts,
the full subcategory of compact objects in
. If
is the homotopy category of spectra, Adams (Topology 10 (1971) 185–198), proved the following: All homological functors
are the restrictions of representable functors on
, and all natural transformations are the restrictions of morphisms in
. It has been something of a mystery, to what extent this generalises to other triangulated categories. In Neeman (Topology 36 (1997) 619–645), it was proved that Adams’ theorem remains true as long as
is countable, but can fail in general. The failure exhibited was that there can be natural transformations not arising from maps in
. A puzzling open problem remained: Is every homological functor the restriction of a representable functor on
? In a recent paper, Beligiannis (Relative homological and purity in triangulated categories, 1999, preprint) made some progress. But in this article, we settle the problem. The answer is no. There are examples of derived categories
of rings, and homological functors
which are not restrictions of representables. 相似文献
885.
Mircea Geanău 《Southeast Asian Bulletin of Mathematics》2001,25(1):105-110
One consider the variety of the unitary binary group in n variables and it is shown that this algebraic variety is rational and it has n2 parameters. Then it is given a parametrical rational representation of this variety.AMS Subject Classification (1991) 20G20 相似文献
886.
在文献 [1]中,从 Z2n上的某些线性递归序列到它的最高位坐标序列的映射的单一性已被证明;本文利用序列的迹表示将此结论推广到任意特征的 Galois环上,并且给出一个算法,在已知特征多项式和最高位坐标序列的条件下,还原出本来的环上序列. 相似文献
887.
定义了子空间格代数的(弱闭双边)模,对有限维Hilbert空间的强自反子空间格代数的模及原子Boolean格代数的模中的有限秩算子进行了讨论,得到了有限秩算子一定可以表示为秩1算子的和。 相似文献
888.
Peng‐Dong Fan 《International journal of quantum chemistry》2001,83(5):259-270
Using the right‐induced technique and the eigenfunction method, concise algebraic expressions of the projection operators for both single‐valued and double‐valued representations are found for the group chain O?T?C3 in terms of the projection operators of T?C3. Extremely simple relations are discovered between the symmetry adapted functions (SAFs) of the groups T and O; namely the SAFs of the subgroup T which have proper symmetry are the SAFs of the group O. The projection operators and SAFs are functions of only the quantum numbers of the group chain [the analogy of ( j,m) for the group chain SO3?SO2], without involving any irreducible matrix elements. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 83: 259–270, 2001 相似文献
889.
Physical models of various phenomena are often represented by a mathematical model where the output(s) of interest have a multivariate dependence on the inputs. Frequently, the underlying laws governing this dependence are not known and one has to interpolate the mathematical model from a finite number of output samples. Multivariate approximation is normally viewed as suffering from the curse of dimensionality as the number of sample points needed to learn the function to a sufficient accuracy increases exponentially with the dimensionality of the function. However, the outputs of most physical systems are mathematically well behaved and the scarcity of the data is usually compensated for by additional assumptions on the function (i.e., imposition of smoothness conditions or confinement to a specific function space). High dimensional model representations (HDMR) are a particular family of representations where each term in the representation reflects the individual or cooperative contributions of the inputs upon the output. The main assumption of this paper is that for most well defined physical systems the output can be approximated by the sum of these hierarchical functions whose dimensionality is much smaller than the dimensionality of the output. This ansatz can dramatically reduce the sampling effort in representing the multivariate function. HDMR has a variety of applications where an efficient representation of multivariate functions arise with scarce data. The formulation of HDMR in this paper assumes that the data is randomly scattered throughout the domain of the output. Under these conditions and the assumptions underlying the HDMR it is argued that the number of samples needed for representation to a given tolerance is invariant to the dimensionality of the function, thereby providing for a very efficient means to perform high dimensional interpolation. Selected applications of HDMR's are presented from sensitivity analysis and time-series analysis. 相似文献
890.
E. Yu. Emel'yanov U. Kohler F. Rä biger M. P. H. Wolff 《Proceedings of the American Mathematical Society》2001,129(9):2633-2642
We discuss conditions such that strong stability and strong asymptotic compactness of a (discrete or continuous) semiflow defined on a subset in the positive cone of an ordered Banach space is preserved under asymptotic domination. This is used to show that on a Banach lattice with order continuous norm strong stability and almost periodicity of a (discrete or strongly continuous) semigroup of positive operators is preserved under asymptotic domination.