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101.
In this paper using finite difference method the lower bound buckling load for simply supported (a) stepped and stiffened rectangular thin plate (b) linear and non-linear variation of thickness (c) uniformly distributed compressive forces in both directions (d) uniformly distributed compressive force in y direction and non-uniform distribution of compressive force in x-direction is discussed. The thin plate is divided into 900 rectangular meshes. The partial derivatives are approximated using central difference formula. Eight hundred and forty one equations are formed and using the program developed and the least eigenvalue is obtained. The buckling coefficients are calculated for different types of stepped and non prismatic plates and the results are presented in tables and graphs for ready use by designers. Buckling factors for some cases are presented in the form of three separate tables and compared with the values obtained by Xiang, Wei and Wang. The results are in close agreement. 相似文献
102.
Yuanji Cheng 《Czechoslovak Mathematical Journal》1997,47(4):681-687
In this paper, we consider the existence and nonexistence of positive solutions of degenerate elliptic systems
where –p is the p-Laplace operator, p > 1 and is a C
1,-domain in
. We prove an analogue of [7, 16] for the eigenvalue problem with
and obtain a non-existence result of positive solutions for the general systems. 相似文献
103.
Andrew V. Knyazev. 《Mathematics of Computation》1997,66(219):985-995
The following estimate for the Rayleigh-Ritz method is proved:
Here is a bounded self-adjoint operator in a real Hilbert/euclidian space, one of its eigenpairs, a trial subspace for the Rayleigh-Ritz method, and a Ritz pair. This inequality makes it possible to analyze the fine structure of the error of the Rayleigh-Ritz method, in particular, it shows that if an eigenvector is close to the trial subspace with accuracy and a Ritz vector is an approximation to another eigenvector, with a different eigenvalue. Generalizations of the estimate to the cases of eigenspaces and invariant subspaces are suggested, and estimates of approximation of eigenspaces and invariant subspaces are proved.
104.
Roman F. Nalewajski 《Journal of mathematical chemistry》2008,44(3):802-815
Within the fragment resolution of molecular systems the conceptual and interpretative advantages of using the separate eigenvalue
problems for the internal and external part of the Hermitian matrix representing a physical quantity in quantum mechanics are examined. By definition, these two
parts accordingly combine only the diagonal and off-diagonal subsystem-resolved blocks of matrix elements. These two partial eigenvalue problems bring about the matrix internal or external
decouplings, respectively, which have recently been used in several interpretations of the molecular electronic structure.
A character and structure of the external eigensolutions is examined in some detail and their recent applications in the Charge
Sensitivity Analysis—to extract the most important electron-transfer effects between constituent atoms of model chemisorption
systems, and in the Molecular-Orbital theory—to precisely identify the inter-orbital flows of electrons, are summarized and
commented upon. The grouping relation, for combining the external/internal eigensolutions into those for the whole matrix,
is derived in the context of the complementary “rotations” of the basis set vectors. 相似文献
105.
In this article, we consider the following eigenvalue problems('∗ where λ>0, N2 and is the upper semi-strip domain with a hole in . Under some suitable conditions on f and h, we show that there exists a positive constant λ* such that Eq. (*)λ has at least two solutions if λ(0,λ*), a unique positive solution if λ=λ*, and no positive solution if λ>λ*. We also obtain some further properties of the positive solutions of (*)λ. 相似文献
λ' render=n">
106.
We study the complexity of approximating the smallest eigenvalue of -Δ+q with Dirichlet boundary conditions on the d-dimensional unit cube. Here Δ is the Laplacian, and the function q is non-negative and has continuous first order partial derivatives. We consider deterministic and randomized classical algorithms, as well as quantum algorithms using quantum queries of two types: bit queries and power queries. We seek algorithms that solve the problem with accuracy . We exhibit lower and upper bounds for the problem complexity. The upper bounds follow from the cost of particular algorithms. The classical deterministic algorithm is optimal. Optimality is understood modulo constant factors that depend on d. The randomized algorithm uses an optimal number of function evaluations of q when d≤2. The classical algorithms have cost exponential in d since they need to solve an eigenvalue problem involving a matrix with size exponential in d. We show that the cost of quantum algorithms is not exponential in d, regardless of the type of queries they use. Power queries enjoy a clear advantage over bit queries and lead to an optimal complexity algorithm. 相似文献
107.
Xin-guo Liu 《计算数学(英文版)》1999,17(6):629-638
108.
一个Jordan块的平方根矩阵 总被引:7,自引:1,他引:6
朱德高 《数学物理学报(A辑)》1999,19(3):318-321
设J=Jm(λ)是一个特征值为λ的m阶Jordan块矩阵,则J能开平方的充要条件是m=1,或者m≥2时,λ≠0.且当m≥2,λ≠0,J的平方根矩阵恰有两个:±A,这里 相似文献
109.
In this paper, a two-scale higher-order finite element discretization scheme is proposed and analyzed for a Schroedinger equation on tensor product domains. With the scheme, the solution of the eigenvalue problem on a fine grid can be reduced to an eigenvalue problem on a much coarser grid together with some eigenvalue problems on partially fine grids. It is shown theoretically and numerically that the proposed two-scale higher-order scheme not only significantly reduces the number of degrees of freedom but also produces very accurate approximations. 相似文献
110.
The energy of a graph is the sum of the absolute values of the eigenvalues of the graph. In a paper [G. Caporossi, D. Cvetkovi, I. Gutman, P. Hansen, Variable neighborhood search for extremal graphs. 2. Finding graphs with external energy, J. Chem. Inf. Comput. Sci. 39 (1999) 984-996] Caporossi et al. conjectured that among all connected graphs G with n≥6 vertices and n−1≤m≤2(n−2) edges, the graphs with minimum energy are the star Sn with m−n+1 additional edges all connected to the same vertices for m≤n+⌊(n−7)/2⌋, and the bipartite graph with two vertices on one side, one of which is connected to all vertices on the other side, otherwise. The conjecture is proved to be true for m=n−1,2(n−2) in the same paper by Caporossi et al. themselves, and for m=n by Hou in [Y. Hou, Unicyclic graphs with minimal energy, J. Math. Chem. 29 (2001) 163-168]. In this paper, we give a complete solution for the second part of the conjecture on bipartite graphs. Moreover, we determine the graph with the second-minimal energy in all connected bipartite graphs with n vertices and edges. 相似文献