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81.
Pavol Ševera 《Letters in Mathematical Physics》2006,75(3):273-277
We introduce an affine-invariant version of generating functions of symplectic transformations of affine symplectic spaces,
together with a generalization for other symmetric symplectic spaces. The composition of these functions has a nice connection
with the Moyal product. 相似文献
82.
Andrew V. Sills 《Journal of Combinatorial Theory, Series A》2006,113(7):1368-1380
Dyson's celebrated constant term conjecture [F.J. Dyson, Statistical theory of the energy levels of complex systems I, J. Math. Phys. 3 (1962) 140-156] states that the constant term in the expansion of ∏1≦i≠j≦naj(1−xi/xj) is the multinomial coefficient (a1+a2+?+an)!/(a1!a2!?an!). The definitive proof was given by I.J. Good [I.J. Good, Short proof of a conjecture of Dyson, J. Math. Phys. 11 (1970) 1884]. Later, Andrews extended Dyson's conjecture to a q-analog [G.E. Andrews, Problems and prospects for basic hypergeometric functions, in: R. Askey (Ed.), The Theory and Application of Special Functions, Academic Press, New York, 1975, pp. 191-224]. In this paper, closed form expressions are given for the coefficients of several other terms in the Dyson product, and are proved using an extension of Good's idea. Also, conjectures for the corresponding q-analogs are supplied. Finally, perturbed versions of the q-Dixon summation formula are presented. 相似文献
83.
We have carried out some photon interaction measurements using 59.54 keV γ-rays from a 241Am source. These include γ attenuation studies as well as photoelectric absorption studies in various samples. The attenuation
studies have been made using leaf and wood samples, samples like sand, sugar etc., which contain particles of varying sizes
as well as pellets and aqueous solutions of rare earth compounds. In the case of the leaf and wood samples, we have used the
γ-ray attenuation technique for the determination of the water content in fresh and dried samples. The variation of the attenuation
coefficient with particle size has been investigated for sand and sugar samples. The attenuation studies as well as the photoelectric
studies in the case of rare earth elements have been carried out on samples containing such elements whose K-absorption edge
energies lie below and close to the γ-energy used. Suitable compounds of the rare earth elements have been chosen as mixture
absorbers in these investigations. A narrow beam good geometry set-up was used for the attenuation measurements. A well-shielded
scattering geometry was used for the photoelectric measurements. The mixture rule was invoked to extract the values of the
mass attenuation coefficients for the elements from those of the corresponding compounds. The results are consistent with
theoretical values derived from the XCOM package. 相似文献
84.
85.
Klaus Ziegler 《Journal of multivariate analysis》1997,62(2):233-272
Functional central limit theorems for triangular arrays of rowwise independent stochastic processes are established by a method replacing tail probabilities by expectations throughout. The main tool is a maximal inequality based on a preliminary version proved by P. Gaenssler and Th. Schlumprecht. Its essential refinement used here is achieved by an additional inequality due to M. Ledoux and M. Talagrand. The entropy condition emerging in our theorems was introduced by K. S. Alexander, whose functional central limit theorem for so-calledmeasure-like processeswill be also regained. Applications concern, in particular, so-calledrandom measure processeswhich include function-indexed empirical processes and partial-sum processes (with random or fixed locations). In this context, we obtain generalizations of results due to K. S. Alexander, M. A. Arcones, P. Gaenssler, and K. Ziegler. Further examples include nonparametric regression and intensity estimation for spatial Poisson processes. 相似文献
86.
Hirotaka Okamoto Tadashi Inoue Kunihiro Osaki 《Journal of Polymer Science.Polymer Physics》1995,33(3):417-424
The complex Young's modulus, E*(ω), and the complex strain-optical coefficient, O*(ω), which is the ratio of the birefringence to the strain, were measured for polyisoprene (PIP) over a frequency range of 1 ~ 130 Hz and a temperature range of 22 ~ ?100°C. The imaginary part of O*, O″, was positive at low frequencies and negative at high frequencies. The real part, O′, was always positive and showed a maximum. The complicated behavior of O* could be understood by the assumption that E* = ER* + EG* and O* = CRER* + CGEG*, where ER* and EG* were complex quantities and CR and CG were constants. The CR value, equal to the ordinary stress-optical coefficient measured in the rubbery plateau zone, was 2.0 × 10?9 Pa?1. The CG value, defined as the ratio O″/E″ in the glassy zone, was ?1.1 × 10?11 Pa?1. The EG*, which was the major component of E* in the glassy zone, showed almost the same frequency dependence as that of polystyrene and polycarbonate. The ER*, which was dominant in the rubbery zone, was described well by the bead-spring theory. The temperature dependence of the EG* was stronger than that of the ER*. This difference caused the breakdown of the thermorheological simplicity for E* and O* around the glass-to-rubber transition zone. © 1995 John Wiley & Sons, Inc. 相似文献
87.
One of the central problems in the theory of ordered sets is to describe the orientations of the covering graph of an ordered set. We show that the particular operation called inversion, together with the classical constructions of retraction and product, provide a context for the classification of all such orientations.
AMS subject classifications (1980). 06A10, 05C75, 05C20. 相似文献
88.
89.
90.
For an arbitrary poset P, subposets {P
i
: 1ik} form a transitive basis of P if P is the transitive closure of their union. Let u be the minimum size of a covering of P by chains within posets of the basis, s the maximum size of a family of elements with no pair comparable in any basis poset, and a the maximum size of an antichain in P. Define a dense covering to be a collection D of chains within basis posets such that each element belongs to a chain in D within each basis poset and is the top of at least k-1 chains and the bottom of at least k-1 chains in D. Dense coverings generalize ordinary chain coverings of poset. Let d=min {|D|–(k–1)|P|}. For an arbitrary poset and transitive basis, a convenient network model for dense coverings yields the following: Theorem 1: da, with equality iff P has a minimum chain decomposition in which every pair of consecutive elements on each chain are comparable in some basis poset. Theorem 2: usda. Theorem 3: s=d iff s=a. The most interesting special case is where the transitive basis expresses P as the product of two posets, in which case u and s measure the minimum and maximum sizes of unichain coverings and semiantichains. 相似文献