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1.
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
2.
V. V. Sagaradze N. V. Kataeva V. A. Zavalishin K. A. Kozlov V. V. Makarov A. R. Kuznetsov 《哲学杂志》2020,100(14):1868-1879
ABSTRACT The authors present the results of an investigation in Fe–Ni-Cr austenitic alloys of the low-temperature deformation-induced segregations of nickel that form in the micro regions being (i) located close to grain- and subgrain boundaries and (ii) characteristic of the concentration and magnetic inhomogeneities indicated by the appearance of a dark diffraction contrast at the electron diffraction patterns taken from these regions typical (at the same time) of an enhanced value of Curie temperature. The observed effects were connected with the micro distortions caused by the local change of lattice parameter because of an increase in nickel concentration, as well as in the result of a magnetostriction dilatation. Using methods of the X-ray energy dispersive spectroscopy (XEDS) and atomic-probe body-section radiography (tomography – APT) has made it possible to determine the borders of those regions of austenite that were characteristic of an enhanced concentration of nickel in the fields of the localisation of a deformation-induced segregation of nickel in the vicinity of grain (subgrain) boundaries of austenitic alloys of the types Fe–13Cr–30Ni and Fe–37Ni–3Ti. 相似文献
3.
In this paper, we propose a sufficient and necessary condition for the boundedness of all the solutions for the equation with the critical situation that on g and p, where , is periodic and is bounded. 相似文献
4.
M.A. Tawhid 《Journal of Optimization Theory and Applications》2002,113(1):149-164
In this paper, we give some sufficient conditions for the local uniqueness of solutions to nonsmooth variational inequalities where the underlying functions are H-differentiable and the underlying set is a closed convex set/polyhedral set/box/polyhedral cone. We show how the solution of a linearized variational inequality is related to the solution of the variational inequality. These results extend/unify various similar results proved for C
1 and locally Lipschitzian variational inequality problems. When specialized to the nonlinear complementarity problem, our results extend/unify those of C
2 and C
1 nonlinear complementarity problems. 相似文献
5.
Jinchao Xu 《应用数学学报(英文版)》2002,18(2):185-200
Abstract Some new local and parallel finite element algorithms are proposed and analyzed in this paper foreigenvalue problems.With these algorithms, the solution of an eigenvalue problem on a fine grid is reduced tothe solution of an eigenvalue problem on a relatively coarse grid together with solutions of some linear algebraicsystems on fine grid by using some local and parallel procedure.A theoretical tool for analyzing these algorithmsis some local error estimate that is also obtained in this paper for finite element approximations of eigenvectorson general shape-regular grids. 相似文献
6.
7.
Mathematical Notes - 相似文献
8.
Michael R. Caputo 《Natural Resource Modeling》1989,3(2):241-259
This paper analyzes the extent to which standard dynamic renewable resource models possess refutable implications. Both the steady state comparative static and local comparative dynamic properties of the standard model are studied. A unified framework is developed which enables one to analyze the qualitative properties of any standard renewable resource model. This is achieved by explicitly linking the local stability, steady state comparative static, and local comparative dynamic properties of the model. 相似文献
9.
10.
Kasper K. Berthelsen Jesper Møller 《Bulletin of the Brazilian Mathematical Society》2002,33(3):351-367
This primer provides a self-contained exposition of the case where spatial birth-and-death processes are used for perfect
simulation of locally stable point processes. Particularly, a simple dominating coupling from the past (CFTP) algorithm and
the CFTP algorithms introduced in [13], [14], and [5] are studied. Some empirical results for the algorithms are discussed.
Received: 30 June 2002 相似文献