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961.
M. Goldstern 《Algebra Universalis》1997,38(2):97-114
We show that for "almost all" algebras on a given set A, every function on A can be interpolated by a polynomial on any set of cardinality (for reasonable ).
Received August 27, 1996; accepted in final form July 3, 1997. 相似文献
962.
A. Leizarowitz 《Journal of Optimization Theory and Applications》1997,94(3):533-560
We study polynomial ordinary differential systems
whereQ0 is an n×n matrix and M(t) is an n×k matrix. It is proven that, as t grows to infinity, the solution M(t) tends to a limit BU, where U is a k×k orthogonal matrix and B is an n×k matrix whose columns are k pairwise orthogonal, normalized eigenvectors of Q. Moreover, for almost every M
0, these eigenvectors correspond to the k maximal eigenvalues of Q; for an arbitrary Q with independent columns, we provide a procedure of computing B by employing elementary matrix operations on M
0. This result is significant for the study of certain neural network systems, and in this context it shows that M() provides a principal component analyzer. 相似文献
963.
Pierre Gaillard 《Journal of Nonlinear Modeling and Analysis》2022,4(4):615-627
Here, we construct rational solutions to the KdV equation by particular polynomials. We get the solutions in terms of determinants of the order $n$ for any positive integer $n$, and we call these solutions, solutions of the order $n$. Therefore, we obtain a very efficient method to get rational solutions to the KdV equation, and we can construct explicit solutions very easily. In the following, we present some solutions until order $10$. 相似文献
964.
The static dipole polarizability α
d,
i
for an arbitrary bound state i of the non-relativistic hydrogen-like atom has been known for a long time from, e.g; the second-order perturbation theory
treatment of the Stark effect. A reliable result for the ground state requires both summation over the discrete spectrum and
inclusion of the continuum contribution. This continuum contribution is known to decrease for excited states, but a systematic
study of this decrease has not been available so far. We present here representative results from a systematic study of α
d,
i
, which was performed as a first test of a new algorithm for the radial integrals involved. Partial sum approximations of
the discrete contribution yield the total α
d,
i
with a relative error of less than 1% for all states i with principal quantum number n≥5. Corresponding results for the relativistic case, for which the radial integral algorithm was developed, will be presented
elsewhere.
Dedicated to Professor Hermann Stoll on the occasion of his 60th birthday
An erratum to this article is available at . 相似文献
965.
Igor V. Tokmakov Albert F. Wagner Michael Minkoff Donald L. Thompson 《Theoretical chemistry accounts》2007,118(4):755-767
We present several approaches to use gradients in higher degree interpolating moving least squares (IMLS) methods for representing
a potential energy surface (PES). General procedures are developed to obtain smooth approximations of the PES and its derivatives
from quasi-uniform sets of energy and gradient data points. These methods are illustrated and analyzed for the Morse oscillator
and a 1-D slice of the ground-state PES for the HCO radical computed using density functional theory. Variations in the IMLS
fits with the number and distribution of points and the degree of the polynomial fitting basis set are examined. We determine
the effects of gradient inclusion on the accuracy of the IMLS values of the energy, first and second derivatives for two 1-D
test cases. Gradient inclusion reduces the number of data points required by up to 40%. 相似文献
966.
The vertex packing problem for a given graph is to find a maximum number of vertices no two of which are joined by an edge. The weighted version of this problem is to find a vertex packingP such that the sum of the individual vertex weights is maximum. LetG be the family of graphs whose longest odd cycle is of length not greater than 2K + 1, whereK is any non-negative integer independent of the number (denoted byn) of vertices in the graph. We present an O(n
2K+1) algorithm for the maximum weighted vertex packing problem for graphs inG 1. A by-product of this algorithm is an algorithm for piecing together maximum weighted packings on blocks to find maximum weighted packings on graphs that contain more than one block. We also give an O(n
2K+3) algorithm for testing membership inG
This work was supported by NSF grant ENG75-00568 to Cornell University. Some of the results of this paper have appeared in Hsu's unpublished Ph.D. dissertation [9]. 相似文献
967.
H. Bavinck 《Proceedings of the American Mathematical Society》1997,125(12):3561-3567
We consider the polynomials orthogonal with respect to the Sobolev type inner product
where and is a nonnegative integer. It is the purpose of this paper to show that these polynomials are eigenfunctions of a class of linear differential operators containing one that is of finite order if is a nonnegative integer and
968.
James J. Zhang 《Proceedings of the American Mathematical Society》1997,125(2):363-373
Let be a finitely generated commutative domain over an algebraically closed field , an algebra endomorphism of , and a -derivation of . Then if and only if is locally algebraic in the sense that every finite dimensional subspace of is contained in a finite dimensional -stable subspace.
Similarly, if is a finitely generated field over , a -endomorphism of , and a -derivation of , then if and only if is an automorphism of finite order.
969.
Mara D. Neusel 《Proceedings of the American Mathematical Society》1997,125(7):1921-1931
970.
Stergios B. Fotopoulos Lijian He 《Annals of the Institute of Statistical Mathematics》1999,51(4):731-747
Let X= A
1/2
G be a scale mixture of a multivariate normal distribution with X, G
n
, Gis a multivariate normal vector, and A is a positive random variable independent of the multivariate random vector G. This study presents asymptotic results of the conditional variance-covariance, Cov(X
2|X
1), X
1
m
, m < n, under some moment expressions. A new representation form is also presented for conditional expectation of the scale variable on the random vector X
1
m
, m < n. Both the asymptotic expression and the representation are manageable and in computable form. Finally, an example is presented to illustrate how the computations are carried out. 相似文献