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设X是维数大于2的Banach空间,映射δ:B(X)→B(X)是2-局部Lie三重导子,则对所有A∈B(X)有δ(A)=[A,T]+φ(A),这里T∈B(X),φ是从B(X)到FI的齐次映射且满足对所有A,B∈B(X)有φ(A+B)=φ(A),其中B是交换子的和. 相似文献
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ABSTRACTThe Coupled-Cluster (CC) theory is one of the most successful high precision methods used to solve the stationary Schrödinger equation. In this article, we address the mathematical foundation of this theory with focus on the advances made in the past decade. Rather than solely relying on spectral gap assumptions (non-degeneracy of the ground state), we highlight the importance of coercivity assumptions – Gårding type inequalities – for the local uniqueness of the CC solution. Based on local strong monotonicity, different sufficient conditions for a local unique solution are suggested. One of the criteria assumes the relative smallness of the total cluster amplitudes (after possibly removing the single amplitudes) compared to the Gårding constants. In the extended CC theory the Lagrange multipliers are wave function parameters and, by means of the bivariational principle, we here derive a connection between the exact cluster amplitudes and the Lagrange multipliers. This relation might prove useful when determining the quality of a CC solution. Furthermore, the use of an Aubin–Nitsche duality type method in different CC approaches is discussed and contrasted with the bivariational principle. 相似文献
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In this paper, the deformation of the Heisenberg algebra, consistent with both the generalized uncertainty principle and doubly special relativity, has been analyzed. It has been observed that, though this algebra can give rise to fractional derivative terms in the corresponding quantum mechanical Hamiltonian, a formal meaning can be given to them by using the theory of harmonic extensions of function. Depending on this argument, the expression of the propagator of the path integral corresponding to the deformed Heisenberg algebra, has been obtained. In particular, the consistent expression of the one dimensional free particle propagator has been evaluated explicitly. With this propagator in hand, it has been shown that, even in free particle case, normal generalized uncertainty principle and doubly special relativity show very much different result. 相似文献
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Summary This paper is concerned with the problem of developing numerical integration algorithms for differential equations that, when
viewed as equations in some Euclidean space, naturally evolve on some embedded submanifold. It is desired to construct algorithms
whose iterates also evolve on the same manifold. These algorithms can therefore be viewed as integrating ordinary differential
equations on manifolds. The basic method “decouples” the computation of flows on the submanifold from the numerical integration
process. It is shown that two classes of single-step and multistep algorithms can be posed and analyzed theoretically, using
the concept of “freezing” the coefficients of differential operators obtained from the defining vector field. Explicit third-order
algorithms are derived, with additional equations augmenting those of their classical counterparts, obtained from “obstructions”
defined by nonvanishing Lie brackets. 相似文献
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Algebra matrix and similarity classification of operators 总被引:1,自引:0,他引:1
ZHANG Zilong & LI Yucheng Department of Mathematics Hebei Normal University Shijiazhuang China 《中国科学A辑(英文版)》2006,49(3):398-409
In this paper, by the Gelfand representation theory and the Silov idempotents theorem, we first obtain a central decomposition theorem related to a unital semi-simple n-homogeneous Banach algebra, and then give a similarity classification of two strongly irreducible Cowen-Douglas operators using this theorem. 相似文献
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We give a coring version for the duality theorem for actions and coactions of a finitely generated projective Hopf algebra.
We also provide a coring analogue for a theorem of H.-J. Schneider, which generalizes and unifies the duality theorem for
finite Hopf algebras and its refinements.
This paper was written while the first author visited the Mathematics Departments of Syracuse University and California State
University Dominguez Hills. He would like to thank both departments for their hospitality. 相似文献