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1.
This paper deals mainly with generalizations of results in finitary combinatorics to infinite ordinals. It is well-known that for finite ordinals ∑bT<αβ is the number of 2-element subsets of an α-element set. It is shown here that for any well-ordered set of arbitrary infinite order type α, ∑bT<αβ is the ordinal of the set M of 2-element subsets, where M is ordered in some natural way. The result is then extended to evaluating the ordinal of the set of all n-element subsets for each natural number n ≥ 2. Moreover, series ∑β<αf(β) are investigated and evaluated, where α is a limit ordinal and the function f belongs to a certain class of functions containing polynomials with natural number coefficients. The tools developed for this result can be extended to cover all infinite α, but the case of finite α appears to be quite problematic. 相似文献
2.
Aminonaphthols are easily transformed into a variety of 1- and 2-naphthyl piperazines using a sequence of diazotization, iodide substitution and Pd(0) catalyzed coupling reactions. 相似文献
3.
The title compound (C2H7NO·C7H4N2O6) has been obtained by the reaction of etha- nolamine with 3,5-dinitrobenzoic acid in deionized water at room temperature. The crystal crystal- lizes in orthorhombic, space group P212121 with a = 6.048(2), b = 9.146(3), c = 21.955(7)(A), C9H11N3O7, Mr = 273.21, Z = 4, V = 1214.3(7)(A)3, Dc = 1.494 g/cm3, F(000) = 568, μ(MoKα) = 0.131 mm-1, R1 = 0.0338 and wR2 = 0.0497. The new organic adduct is composed of one ethanolamine and one 3,5-dinitrobenzoic acid, which are linked up by O-H…O and N-H…O types of hydrogen bonds to form a nine-membered ring and an eleven-membered ring, extending into a one-dimensional network structure. 相似文献
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5.
陈永静 朱胜江 J.H.Hamilton A.V.Ramayya J.K.Hwang Y.X.Luo J.O.Rasmussen 车兴来 丁怀博 李明亮 《中国物理 C》2006,30(8):740-744
通过测量252Cf自发裂变所产生的瞬发γ射线, 对146Ce核的高自旋结构进行了重新研究, 结果更新了以前报道的能级纲图, 把八级形变集体带扩展到更高的自旋, 并且重新构建了可能的准γ带结构. 此外, 用反射不对称壳模型(RASM)对146Ce核的八级形变带进行了计算, 低自旋处的计算结果与实验数据符合得很好. 相似文献
6.
R. Hart P. Hue D. Burton G. F. Robertshaw F. G. H. Tate L. A. Warren und P. Eisenstein 《Fresenius' Journal of Analytical Chemistry》1938,115(7-8):272-274
Ohne Zusammenfassung 相似文献
7.
Joe Warren Scott Schaefer Anil N. Hirani Mathieu Desbrun 《Advances in Computational Mathematics》2007,27(3):319-338
In this paper we provide an extension of barycentric coordinates from simplices to arbitrary convex sets. Barycentric coordinates
over convex 2D polygons have found numerous applications in various fields as they allow smooth interpolation of data located
on vertices. However, no explicit formulation valid for arbitrary convex polytopes has been proposed to extend this interpolation
in higher dimensions. Moreover, there has been no attempt to extend these functions into the continuous domain, where barycentric
coordinates are related to Green’s functions and construct functions that satisfy a boundary value problem. First, we review
the properties and construction of barycentric coordinates in the discrete domain for convex polytopes. Next, we show how
these concepts extend into the continuous domain to yield barycentric coordinates for continuous functions. We then provide
a proof that our functions satisfy all the desirable properties of barycentric coordinates in arbitrary dimensions. Finally,
we provide an example of constructing such barycentric functions over regions bounded by parametric curves and show how they
can be used to perform freeform deformations.
相似文献
8.
Mauel M.E. Warren H.H. Hasegawa A. 《IEEE transactions on plasma science. IEEE Nuclear and Plasma Sciences Society》1992,20(6):626-630
A new laboratory terrella has been constructed in order to study collisionless radial diffusion of particles trapped within a dipole magnetic field. Columbia's collisionless terrella experiment (CTX) aims to reproduce the process of wave-induced radial transport and does not try to simulate magnetospheric structure. The first experiment planned for CTX is the direct measurement of stochastic radial diffusion induced from wave-particle drift resonances. The motivation for the CTX experiment is described, and the procedures to be used to measure the intensity and spectrum of fluctuations generating chaos, the rate of radial transport, and the evolution of the density and pressure profiles are illustrated. Because of the success of similar experiments conducted earlier in a long thin magnetic mirror, these dipole experiments can be performed with a high degree of confidence. An example from these earlier experiments is presented 相似文献
9.
10.
In previous work the authors consider the dynamic assignment problem, which involves solving sequences of assignment problems over time in the presence of uncertain information about the future. The algorithm proposed by the authors provides generally high-quality but non-optimal solutions. In this work, though, the authors prove that if the optimal solution to a dynamic assignment problem in one of two problem classes is unique, then the optimal solution is a fixed point under the algorithm. 相似文献