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1.
2.
The aim of this Note is to give explicit limit expressions, for diffusion equations involving a small parameter ε, describing both nonperiodic homogenization and reduction of dimension. We consider two kinds of reduction of dimension: the case of plates and the case of thin cylinders. In particular, we give the limit diffusion equation for stratified plates. This is completely explicit and requires no special assumption, except stratification. In the case of thin cylinders, the formulae are less explicit, but we also indicate some simple applications to fibered materials. To cite this article: B. Gustafsson, J. Mossino, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 977–982. 相似文献
3.
4.
An acoustic pulse propagating on a two-mode fiber can act as a beam splitter in a scanning interferometer. When this device
is employed in white-light interferometry, the effects of distributed coupling and dispersive interferometer arms need to
be considered. A theory suitable for treating acousto-optic interaction of partially coherent light in a moving interaction
region was developed. It was found that differential optical dispersion should be negligible and the acoustic pulse length
short. Also the coherence time should be short but long compared to the intermodal group delay difference over a pulse length.
Experiments with long acoustic pulses were performed, and fairly good agreement with theory was obtained. 相似文献
5.
Given a simplicial complex δ on vertices {1, …,n} and a fieldF we consider the subvariety of projective (n−1)-space overF consisting of points whose homogeneous coordinates have support in δ. We give a simple rational expression for the zeta function
of this singular projective variety overF
q and show a close connection with the Betti numbers of the corresponding variety over ℂ. This connection is particularly simple
in the case when Δ is Cohen-Macaulay. 相似文献
6.
Let R be a local ring and let (x
1, …, x
r) be part of a system of parameters of a finitely generated R-module M, where r < dimR
M. We will show that if (y
1, …, y
r) is part of a reducing system of parameters of M with (y
1, …, y
r) M = (x
1, …, x
r) M then (x
1, …, x
r) is already reducing. Moreover, there is such a part of a reducing system of parameters of M iff for all primes P ε Supp M ∩ V
R(x
1, …, x
r) with dimR
R/P = dimR
M − r the localization M
P of M at P is an r-dimensional Cohen-Macaulay module over R
P.
Furthermore, we will show that M is a Cohen-Macaulay module iff y
d is a non zero divisor on M/(y
1, …, y
d−1) M, where (y
1, …, y
d) is a reducing system of parameters of M (d:= dimR
M). 相似文献
7.
We analyze the quantum measurement properties of dual non-degenerate parametric amplifers in the twin-beam configuration,
in the cascaded back-action-evasion configuration, and in Kerr-type photon-number quantum non-demolition measurements. It
is found that Einstein-Podolsky-Rosen correlations can be obtained between the quadrature components of an idler mode and
the sum of the readout of two signal modes. Furthermore, we discuss dual-mode quantum non-demolition measurements on the combination
of two light modes, and the generation of number-state entanglement.
Received: 12 April 1996/Revised version: 2 July 1996 相似文献
8.
9.
Björn O. Roos Valera Veryazov Per-Olof Widmark 《Theoretical chemistry accounts》2004,111(2-6):345-351
New basis sets of the atomic natural orbital (ANO) type have been developed for the atoms Li–Fr and Be–Ra. The ANOs have been obtained from the average density matrix of the ground states and the lowest excited states of the atom, the positive ion, and the dimer at its equilibirium geometry. Scalar realtivisitc effects are included through the use of a Douglas–Kroll Hamiltonian. Multiconfigurational wave functions have been used with dynamic correlation included using second-order perturbation theory (CASSCF/CASPT2). The basis sets are applied in calculations of the ground-state potentials for the dimers. Computed bond energies are accurate to within 0.05 eV for the alkaline dimers and 0.02 eV for the alkaline-earth dimers (except for Be2).Acknowledgments.ensp;B.O.R. would like to express his gratitude to Prof. Jacopo Tomasi for all the inspiration that his scientific work has given him through the years and continues to do in particular through the work on solvent effects on molecular properties. This work has been supported by a grant from the Swedish Science Research Council, VR.Contribution to the Jacopo Tomasi Honorary Issue 相似文献
10.
Large configuration interaction calculations of the proton—proton coupling constant for several geometrical configurations of the ammonia molecules are reported. The analytical expressions for the energy surface and the coupling constant as functions of two cartesian displacement coordinates are fitted to the calculated values. The potential is used for the calculation of the vibrational wavefunctions for 15NH3 and 15ND3 species and the vibrational averaging of the coupling constant is carried out using these functions. Though the value of the coupling constants shows a very strong geometry dependence, the vibrational corrections are found to be small. A possible correlation of the proton—proton coupling constant with an angular parameter in the NH2 group in RNH2 compounds is indicated. 相似文献