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1.
Ciprian Borcea Xavier Goaoc Sylvain Lazard Sylvain Petitjean 《Discrete and Computational Geometry》2006,35(2):287-300
We prove that four spheres in ℝ3 have infinitely many real common tangents if and only if they have aligned centers and at least one real common tangent. 相似文献
2.
A Lorentz-invariant gauge theory for massive fermions on R × S
3
spacetime is built up. Using the symmetry of S
3,we obtain Dirac-type equation and derive the expression of the fermionic propagator. Finally, starting from the SU(N) gauge-invariant Lagrangian, we obtain the set of Dirac-Yang-Mills equations on R × S
3
spacetime, pointing out major differences from the Minkowskian case. 相似文献
3.
Nuclear spin-spin coupling constants (1)J(Hg-Hg) in the systems Hg(2)(2+) and Hg(3)(2+) represent the largest coupling constants so far observed in NMR experiments. We have performed a computational study on these ions, on Hg(2)(2+) complexes with 18-crown-6 and 15-crown-5, and on Hg(3)(2+) with solvent molecules and counterions. The results obtained with our recently developed program for the density functional computation of heavy nucleus spin-spin coupling constants are in good agreement with experiments. The data reveal that the bare ions Hg(2)(2+) and Hg(3)(2+) would afford much larger coupling constants than those experimentally observed, with an upper limit of approximately 0.9 MHz for Hg(2)(2+). This limit is much larger than that previously estimated by Hückel theory. It is demonstrated that in solution or due to complexation the experimentally determined values are much smaller than the free ion's coupling constants. With the help of intuitive MO arguments, it is illustrated how the environment strongly reduces the coupling constants in Hg(2)(2+) and Hg(3)(2+). The two-bond coupling constant (2)J(Hg-Hg) in Hg(3)(2+) is also examined. 相似文献
4.
Xiaomeng Zheng Bogdan Dumitrescu Jiamou Liu Ciprian Doru Giurcneanu 《Entropy (Basel, Switzerland)》2022,24(8)
The problem addressed by dictionary learning (DL) is the representation of data as a sparse linear combination of columns of a matrix called dictionary. Both the dictionary and the sparse representations are learned from the data. We show how DL can be employed in the imputation of multivariate time series. We use a structured dictionary, which is comprised of one block for each time series and a common block for all the time series. The size of each block and the sparsity level of the representation are selected by using information theoretic criteria. The objective function used in learning is designed to minimize either the sum of the squared errors or the sum of the magnitudes of the errors. We propose dimensionality reduction techniques for the case of high-dimensional time series. For demonstrating how the new algorithms can be used in practical applications, we conduct a large set of experiments on five real-life data sets. The missing data (MD) are simulated according to various scenarios where both the percentage of MD and the length of the sequences of MD are considered. This allows us to identify the situations in which the novel DL-based methods are superior to the existing methods. 相似文献
5.
6.
One-bond Pt-Pt nuclear spin-spin coupling constants J(Pt-Pt) for closely related dinuclear Pt complexes can differ by an order of magnitude without any obvious correlation with Pt-Pt distances. As representative examples, the spin-spin couplings of the dinuclear Pt(I) complexes [Pt(2)(CO)(6)](2+) (1) and [Pt(2)(CO)(2)Cl(4)](2-) (2) have been computationally studied with a recently developed relativistic density functional method. The experimental values are (1)J((195)Pt-(195)Pt) = 5250 Hz for 2 but 551 Hz for 1. Many other examples are known in the literature. The experimental trends are well reproduced by the computations and can be explained based on the nature of the ligands that are coordinated to the Pt-Pt fragment. The difference for J(Pt-Pt) of an order of magnitude is caused by a sensitive interplay between the influence of different ligands on the Pt-Pt bond, and relativistic effects on metal-metal and metal-ligand bonds as well as on "atomic orbital contributions" to the nuclear spin-spin coupling constants. The results can be intuitively rationalized with the help of a simple qualitative molecular orbital diagram. 相似文献
7.
Ciprian A. Tudor Nakahiro Yoshida 《Stochastic Processes and their Applications》2019,129(9):3499-3526
We develop the asymptotic expansion theory for vector-valued sequences of random variables in terms of the convergence of the Stein–Malliavin matrix associated with the sequence . Our approach combines the classical Fourier approach and the recent Stein–Malliavin theory. We find the second order term of the asymptotic expansion of the density of and we illustrate our results by several examples. 相似文献
8.
9.
We consider a transmission problem consisting of two semilinear parabolic equations involving fractional diffusion operators of different orders in a general non-smooth setting with emphasis on Lipschitz interfaces and transmission conditions along the interface. We give a unified framework for the existence and uniqueness of strong and mild solutions, and their global regularity properties. 相似文献
10.
We provide a general scheme for proving L p estimates for certain bilinear Fourier restrictions outside the local L 2 setting. As an application, we show how such estimates follow for the lacunary polygon. In contrast with prior approaches, our argument avoids any use of the Rubio de Francia Littlewood?CPaley inequality. 相似文献