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91.
The equilibrium C-H bond length has been determined up to now for about 40 polyatomic molecules. These data are used to demonstrate the existence of quantitative correlations betweenr
e(C-H), isolated C-H bond stretching frequency and average distancer
g. It is also shown that ab initio calculations are often reliable to calculate the absolute value ofr
e(C-H), if an empirical correction is made. Some other correlations are also discussed. Finally, accurater
e(C-H) values are predicted for simple molecules. 相似文献
92.
93.
Pb8FeIIFeF24 is triclinic: a = 20.118(3) Å, b = 5.597(1) Å, c = 9.440(2) Å, α = 89.75(2)°, β = 105.79(2)°, α = 89.38(2)°, Z = 2. The structure is solved in the unconventional space group C1 , from X-ray single crystal data using 1 641 independent reflections (R = 0.048, Rw = 0.051). It is built up from the stacking of two subnetworks along the a axis: fluorite-like [Pb8F10]n6n+ layers and infinite dimetallic [FeIIFeF14]n6n? double-chains of corner-sharing octahedra running along the b axis. 相似文献
94.
Jean Saint Raymond 《Rendiconti del Circolo Matematico di Palermo》1995,44(1):162-168
Let (T, ℐ, μ) be a σ-finite atomless measure space,p∈[1,∞),E a real Banach space andf a measurable function:E xT→ℝ. We denote byF the functionalF:
and byDom(F) its domain, it is the set {uεL
p(T,E):ū(t)=f(u),t)εL
1(T)}, and we prove that the sublevelsS(λ)={u:F(u)≤λ} are all connected in the subspaceDom(F) of the Banach spaceL
p(T, E). 相似文献
95.
We show that, when music pieces are cast in the form of time series of pitch variations, the concepts and tools of dynamical systems theory can be applied to the analysis of temporal dynamics in music. (i) Phase space portraits are constructed from the time series wherefrom the dimensionality is evaluated as a measure of the global dynamics of each piece. (ii) Spectral analysis of the time series yields power spectra ( approximately f(-nu)) close to red noise (nu approximately 2) in the low frequency range. (iii) We define an information entropy which provides a measure of the local dynamics in the musical piece; the entropy can be interpreted as an evaluation of the degree of complexity in the music, but there is no evidence of an analytical relation between local and global dynamics. These findings are based on computations performed on eighty sequences sampled in the music literature from the 18th to the 20th century. (c) 1995 American Institute of Physics. 相似文献
96.
LetG be a nilpotent Lie group. The adapted nilpotent Fourier transform was introduced by D. Arnal and J. C. Cortet,:L(G) C
(V,L(2d
)), whereL(G) is the Schwartz space ofG andV × 2k
is aG-invariant Zariski open set ing
* the dual of the Lie algebra ofG. We prove the surjectivity of this transformation, which allows us to extend it to distribution spaces. 相似文献
97.
Jean Bourgain 《Communications in Mathematical Physics》1996,176(2):421-445
Consider the2D defocusing cubic NLSiu
t+u–u|u|2=0 with Hamiltonian
. It is shown that the Gibbs measure constructed from the Wick ordered Hamiltonian, i.e. replacing ||4 by ||4 :, is an invariant measure for the appropriately modified equationiu
t
+ u‒ [u|u
2–2(|u|2
dx)u]=0. There is a well defined flow on thesupport of the measure. In fact, it is shown that for almost all data the solutionu, u(0)=, satisfiesu(t)–e
it C
Hs
(), for somes>0. First a result local in time is established and next measure invariance considerations are used to extend the local result to a global one (cf. [B2]). 相似文献
98.
Jean Calbrix 《Transactions of the American Mathematical Society》1996,348(5):2085-2090
We say that a countable, Hausdorff, topological space with one and only one accumulation point is a point-space. For such a space, we give several properties which are equivalent to the property of being a k-space. We study some free filters on the set of integers and we determine if the associated point-spaces are k-spaces or not. We show that the filters of Lutzer-van Mill-Pol are k-filters. We deduce that, for each countable ordinal , there exists a free filter of true additive class (Baire's classification) and a free filter of true multiplicative class for which the associated point-spaces are k-spaces but not , the existence being true in the additive case for . In particular, we answer negatively a question raised in J. Calbrix, C. R. Acad. Sci. Paris 305 (1987), 109--111.
99.
Jean Bénabou 《Applied Categorical Structures》1996,4(2-3):139-165
We give necessary and sufficient conditions on class S of maps of a category C so that a good calculus of fractions is possible in C[S
-1], and a geometric characterization of the communitative diagrams in the category of fractions. These conditions are also described simply in terms of Grothendiek topologies.We characterize the categories which arise in this manner by the fact that the functor C C[S
-1] is uniformly flat and give some applications of this result. 相似文献
100.
Two Fraenkel-Mostowski models are constructed in which the Boolean Prime Ideal Theorem is true. In both models, AC for countable sets is true, but AC for sets of cardinality 2 and the 2m = m principle are both false. The Principle of Dependent Choices is true in the first model, but false in the second. Mathematics Subject Classification: 03E25, 03E35, 04A25. 相似文献