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61.
Zsolt Katona 《Graphs and Combinatorics》2005,21(1):71-76
Let f(l, t, n) be the maximal size of a family such that any l2 sets of have an exactly t1-element intersection. If l3, it trivially comes from [8] that the optimal families are trivially intersecting (there is a t-element core contained by all the members of the family). Hence it is easy to determine Let g(l,t,n) be the maximal size of an l-wise exaclty t-intersecting family that is not trivially t-intersecting. We give upper and lower bounds which only meet in the following case: g(3, 1, n) = n2/3(1 + o(1)). 相似文献
62.
William M. Kantor Michael E. Williams 《Transactions of the American Mathematical Society》2004,356(3):895-938
There are lovely connections between certain characteristic 2 semifields and their associated translation planes and orthogonal spreads on the one hand, and -linear Kerdock and Preparata codes on the other. These inter-relationships lead to the construction of large numbers of objects of each type. In the geometric context we construct and study large numbers of nonisomorphic affine planes coordinatized by semifields; or, equivalently, large numbers of non-isotopic semifields: their numbers are not bounded above by any polynomial in the order of the plane. In the coding theory context we construct and study large numbers of -linear Kerdock and Preparata codes. All of these are obtained using large numbers of orthogonal spreads of orthogonal spaces of maximal Witt index over finite fields of characteristic 2.
We also obtain large numbers of ``boring' affine planes in the sense that the full collineation group fixes the line at infinity pointwise, as well as large numbers of Kerdock codes ``boring' in the sense that each has as small an automorphism group as possible.
The connection with affine planes is a crucial tool used to prove inequivalence theorems concerning the orthogonal spreads and associated codes, and also to determine their full automorphism groups.
63.
Anne‐Sophie Bonnet‐Bendhia Axel Tillequin 《Mathematical Methods in the Applied Sciences》2001,24(14):1089-1111
A generalized mode matching method that applies to a wide class of scattering problems is developed in the time harmonic two‐dimensional Helmholtz case. This method leads by variational means to an integro‐differential formulation whose unknown is the trace of the field on an unbounded one‐dimensional interface. The well‐posedness is proved after a careful study of the rather original functional framework. Owing to a fundamental density result—based upon some properties of a singular integral operator similar to the Hilbert transform—the limiting absorption principle related to this original formulation is established. Finally, two other situations are emphasized. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
64.
The effect of the inclusion of the exact exchange into self-interaction corrected generalized gradient approximation density
functional theory (GGA-DFT) for the simplest hydrogen abstraction reaction, H + H2 → H3 → H2 + H, is presented using a triple-zeta augmented 6-311++G(d,3pd) basis set. The introduction of the self-interaction correction has a considerably larger effect on molecular geometry and
vibrational frequencies than the inclusion of the exact exchange. We investigate the influence of the self-interaction error
on the shape of the potential energy surface around the transition state of the hydrogen abstraction reaction. The decomposition
of the self-interaction error into correlation and exchange parts shows that the exchange self-interaction error is the main
component of the energy barrier error. The best agreements with the experimental barrier height were achieved by self-interaction
corrected B3LYP, B-LYP and B3PW functionals with errors of 1.5, 2.9 and 3.0 kcal/mol, respectively.
Received: 13 August 1997 / Accepted: 14 November 1997 相似文献
65.
本文使用分子轨道从头算方法,在HF/6—31G和MP2/6—31G“水平下,计算了小硅化物SiXm的平衡几何和谐振子振动频率。理论值和实验值的比较表明,对于SiHm分子,实验的键长位于HF键长和MP2键长之间,而MP2振动频率更接近于实验的振动;率。对于SiClm分子,无论是键长还是振动频率HF值和MP2值都比较接近。对于SiFm分子,处于这两类的中间情况。关联作用随着X原子的原子序数的增加而减弱。 相似文献
66.
The equilibrium geometries and electronic properties of AunAl,
up to n=13, have been systematically investigated using the density
functional theory. The results show that, for the AunAl
clusters, two patterns are identified. Pattern one (n=2, 3, 8),
the lowest-energy geometries prefer two-dimensional structures.
Pattern two (n=4-7, 9--13), the lowest-energy geometries prefer
three-dimensional structures. According to the analysis of the
binding energy and the fragmentation energy, AunAl clusters
with odd n are found to be more stable than those with even n.
The same trend of alternation can be illuminated according to the
computational results in the HOMO--LUMO gap, the ionization
potential, and the electron affinities. The Al atom not only changes
the structures of pure gold clusters, but also enhances their
stabilities. NBO analysis indicates 6s orbital of Au atom hybridizes
with 3p orbital of Al atom. 相似文献
67.
68.
Paul W. Vos 《Annals of the Institute of Statistical Mathematics》1989,41(3):429-450
Many applications of Amari's dual geometries involve one or more submanifolds imbedded in a supermanifold. In the differential geometry literature, there is a set of equations that describe relationships between invariant quantities on the submanifold and supermanifold when the Riemannian connection is used. We extend these equations to statistical manifolds, manifolds on which a pair of dual connections is defined. The invariant quantities found in these equations include the mean curvature and the statistical curvature which are used in statistical calculations involving such topics as information loss and efficiency. As an application of one of these equations, the Bartlett correction is interpreted in terms of curvatures and other invariant quantities. 相似文献
69.
H.-H. v. Borzeszkowski B. K. Datta V. de Sabbata L. Ronchetti H.-J. Treder 《Foundations of Physics》2002,32(11):1701-1716
The analysis of the measurement of gravitational fields leads to the Rosenfeld inequalities. They say that, as an implication of the equivalence of the inertial and passive gravitational masses of the test body, the metric cannot be attributed to an operator that is defined in the frame of a local canonical quantum field theory. This is true for any theory containing a metric, independently of the geometric framework under consideration and the way one introduces the metric in it. Thus, to establish a local quantum field theory of gravity one has to transit to non-Riemann geometry that contains (beside or instead of the metric) other geometric quantities. From this view, we discuss a Riemann–Cartan and an affine model of gravity and show them to be promising candidates of a theory of canonical quantum gravity. 相似文献
70.
K. Menger and G. Birkhoff recognized 70 years ago that lattice theory provides a framework for the development of incidence
geometry (affine and projective geometry). We show in this article that lattice theory also provides a framework for the development
of metric geometry (including the euclidean and classical non-euclidean geometries which were first discovered by A. Cayley
and F. Klein). To this end we introduce and study the concept of a Cayley–Klein lattice. A detailed investigation of the groups
of automorphisms and an algebraic characterization of Cayley–Klein lattices are included.
The authors would like to thank an unknown referee for his helpful suggestions. 相似文献