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91.
Jean-André Marti 《Acta Appl Math》2009,105(3):267-302
We introduce a general context involving a presheaf
and a subpresheaf ℬ of
. We show that all previously considered cases of local analysis of generalized functions (defined from duality or algebraic
techniques) can be interpretated as the ℬ-local analysis of sections of
.
But the microlocal analysis of the sections of sheaves or presheaves under consideration is dissociated into a “frequential
microlocal analysis” and into a “microlocal asymptotic analysis”. The frequential microlocal analysis based on the Fourier
transform leads to the study of propagation of singularities under only linear (including pseudodifferential) operators in
the theories described here, but has been extended to some non linear cases in classical theories involving Sobolev techniques.
The microlocal asymptotic analysis is a new spectral study of singularities. It can inherit from the algebraic structure of
ℬ some good properties with respect to nonlinear operations.
相似文献
92.
Consider an operator T:C2(R)→C(R) and isotropic maps A1,A2:C1(R)→C(R) such that the functional equation
93.
A mode-based clustering method is developed for identifying spatially dense clusters in brain maps. This type of clustering focuses on identifying clusters in brain maps independent of their shape or overall variance. This can be useful for both localization in terms of interpretation and for subsequent graphical analysis that might require more coherent or dense regions of interest as starting points. The method automatically does signal/noise sharpening through density mode seeking. We also discuss the problem of parameter selection with this method and propose a new method involving 2-parameter control surface, in which we show that the same cluster solution results from tradeoff of these 2 parameters (the local density k and the radius r of the spherical kernel). We benchmark the new dense mode clustering by using several artificially created data sets and brain imaging data sets from an event perception task by perturbing the data set with noise and measuring three kinds of deviation from the original cluster solution. We present benchmark results that demonstrate that the mode clustering method consistently outperforms the commonly used single-linkage clustering, k means method (centroid method) and Ward's method (variance method). 相似文献
94.
A minimal distortion localization procedure is devised for defining subsystems in super-molecule calculations on weakly bonded
complexes. When a set of orbitals for the isolated subsystem have been chosen, the localized supersystem orbitals are obtained
by minimizing the sum of the least-square deviations from the isolated subsystem orbitals. Test calculations are presented
for the beryllium complexes Be2, Be3 and Be4, and the neon dimer.
Received: 15 December 1996 / Accepted: 15 March 1997 相似文献
95.
Wu Zhuoqun 《东北数学》1997,(1)
SomePropertiesofSolutionsforaNonlinearDifusionSystem(I)*)WuZhuoqun(伍卓群)andYinJingxue(尹景学)(DepartmemtofMathmatics,JilinUnivers... 相似文献
96.
97.
M. M. Fogler A. Yu. Dobin B. I. Shklovskii 《Physica E: Low-dimensional Systems and Nanostructures》1998,1(1-4)
The quantum localization is known to be responsible for the deep conductivity minima of the quantum Hall effect. In this paper we calculate the localization length
as a function of magnetic field
at such minima for several models of disorder (“white-noise”, short-range, and long-range random potentials). We find that
with the exponent
between one and
, depending on the model. In particular, for the “white-noise” random potential
roughly coincides with the classical cyclotron radius. Our results are in agreement with available experimental data. 相似文献
98.
99.
100.
François Willot Yves-Patrick Pellegrini Pedro Ponte Castañeda 《Journal of the mechanics and physics of solids》2008,56(4):1245-1268
Exact solutions are derived for the problem of a two-dimensional, infinitely anisotropic, linear-elastic medium containing a periodic lattice of voids. The matrix material possesses either one infinitely soft, or one infinitely hard loading direction, which induces localized (singular) field configurations. The effective elastic moduli are computed as functions of the porosity in each case. Their dilute expansions feature half-integer powers of the porosity, which can be correlated to the localized field patterns. Statistical characterizations of the fields, such as their first moments and their histograms are provided, with particular emphasis on the singularities of the latter. The behavior of the system near the void close-packing fraction is also investigated. The results of this work shed light on corresponding results for strongly non-linear porous media, which have been obtained recently by means of the “second-order” homogenization method, and where the dilute estimates also exhibit fractional powers of the porosity. 相似文献