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71.
72.
A consistent set of fitted electronic density functions was generated for the elements from hydrogen to radon using an algorithm based on the elementary Jacobi rotations (EJR) technique. The main distinguishing attribute of this fitting procedure is the production of approximated electronic density functions with positive definite expansion coefficients; in this way, the statistical meaning of the probability distribution is preserved. The methodology, which was fully described previously, was modified in this work to improve and accelerate the fitting procedure. This variation concerns the optimization method employed to obtain the optimal angle of the EJR, implementing an algorithm based on a Taylor series expansion. Additionally, a new 1S-Type Gaussian basis set for atoms H to Rn is presented, that was fitted from a primitive basis set of Huzinaga. Fitted density functions facilitate theoretical calculations over large molecules and may be employed in many areas of computational chemistry, for example, in quantum similarity measures (QSM). To verify the basis set, a sound example related to QSM applications is given. This corresponds to the comparison of experimental structures obtained from X-ray determination for cis-diamminedichloroplatinum(II) complex with optimized molecular geometries using several theoretical methods to quantify the differences between the analyzed levels of theory. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 911–920, 1999 相似文献
73.
74.
Patrick Bonckaert 《Journal of Differential Equations》2005,214(1):128-155
We consider one parameter families of vector fields depending on a parameter ? such that for ?=0 the system becomes a rotation of R2×Rn around {0}×Rn and such that for ?>0 the origin is a hyperbolic singular point of saddle type with, say, attraction in the rotation plane and expansion in the complementary space. We look for a local subcenter invariant manifold extending the stable manifolds to ?=0. Afterwards the analogous case for maps is considered. In contrast with the previous case the arithmetic properties of the angle of rotation play an important role. 相似文献
75.
Patrick Bonckaert 《Journal of Differential Equations》2003,191(2):490-517
We consider families of maps depending on a parameter ε such that for ε=0 the map becomes a product of linear rotations in and for ε≠0 the map is weakly attracting in the product of the rotation planes and weakly repelling in some complementary subspace. We prove that the unstable manifold converges to the complementary subspace in the Cr topology, the case r=∞ included. We consider both the local and the global manifolds. For that we prove some results on families of maps near a norm one linear map, which are of independent interest. 相似文献
76.
Reinhard Winkler 《Monatshefte für Mathematik》2002,135(4):333-343
Let be a homomorphism with dense image in the compact group C. If is a continuity set, i.e. its topological boundary has Haar measure 0, then is called a Hartman set. If M is aperiodic then S contains the essential information about (C, ι) or, equivalently, about the dynamical system (C, T) where T is the ergodic group rotation . Using Pontryagin’s duality the paper presents a new method to get this information from S: The set S induces a filter on which is an isomorphism invariant for (C, T) and turns out to be a complete invariant for ergodic group rotations. If one takes , , , , one gets the interesting special case of Kronecker sequences (nα) which are classical objects in number theory and diophantine analysis.
Received 3 November 2000; in final form 25 January 2002 相似文献
77.
The paper deals with the geometrically non-linear analysis of laminated composite beams, plates and shells in the framework of the first-order transverse shear deformation (FOSD) theory. A central point of the present paper is the discussion of the relevance of five- and six-parameter variants, respectively, of the FOSD hypothesis for large rotation plate and shell problems. In particular, it is shown that the assumption of constant through-thickness distribution of the transverse normal displacements is acceptable only for small and moderate rotation problems. Implications inherent in this assumption that are incompatible with large rotations are discussed from the point of view of the transverse normal strain-displacement relations as well as in the light of an enhanced, accurate large rotation formulation based on the use of Euler angles. The latter one is implemented as an updating process within a Total Lagrangian formulation of the six-parameter FOSD large rotation plate and shell theory. Numerical solutions are obtained by using isoparametric eight-node Serendipity-type shell finite elements with reduced integration. The Riks-Wempner-Ramm arc-length control method is used to trace primary and secondary equilibrium paths in the pre- and post-buckling range of deformation. A number of sample problems of non-linear, large rotation response of composite laminated plate and shell structures are presented including symmetric and asymmetric snap-through and snap-back problems. 相似文献
78.
Fumio Tanaka 《Journal of fluorescence》2000,10(1):13-20
Effects of internal rotations of chromophores under the energy transfer interaction in proteins on the time-resolved fluorescence were examined by numerical calculations. Expressions used for the calculations are based on the approximations that the energy transfer takes place according to Foöurster's mechanism and the rotational motions of the energy donor and acceptor along the surfaces of cones are described by a set of rotational diffusion equations. The intensity decay of the donor depended a little on the rotational diffusion coefficient of the donor in some cases, while that of the acceptor did very little. Anisotropy of the donor decayed faster as the diffusion coefficient of the donor increased. Anisotropy decay of the acceptor markedly depended not only on the mutual configuration of the pair in the protein, but also on the diffusion coefficient of the donor. The dependence of the time-resolved fluorescence on the diffusion coefficient of the acceptor was not as great as that of the donor. 相似文献
79.
80.
Joerg Schmeling 《Mathematische Nachrichten》1997,183(1):211-227
In this paper we introduce the notion of pseudo -ergodicity to generalize Pustyl'nikov's estimates of Weyl sums to Weyl sums over subsequence of the natural numbers. 相似文献