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31.
32.
In this paper, we study discontinuous solutions of a partial differential equation of strongly degenerate parabolic type. A notion of weak solutions of BV class is proposed, and existence and uniqueness results are obtained. 相似文献
33.
We propose a new variational model to reduce the staircase that often appears in Total variation (TV) based models in image denoising. The model uses BV-seminorm and Besov-seminorm to measure the piece-wise constant component and piecewise smooth component of the image, respectively. We discuss the nontrivial prop-erty of the proposed model and introduce an alternating iteration algorithm that combines the dual projection al-gorithm with Wavelet soft thresholding (WST) algorithm to solve the model numerically. The experimental results show that the proposed model is effective for noise removal and staircase reduction, while the contour can be preserved in the denoised images. Furthermore, compared with two classical staircase reduction models, CEP2 and TGV, the proposed model is much faster than these two models. 相似文献
34.
《Arabian Journal of Chemistry》2022,15(12):104304
Eucommia ulmoides Oliv. (EU) is an herb with variety of pharmacological activities. As the demand for EU as a medical source increases, its limited availability is becoming an urgent problem. The bark of EU—Eucommia cortex (EC)—was the main medicinal part of EU, whose yield has been too low to meet market requirements. The EU leaves—Eucommiae folium (EF)—obtained easily from the trees, traditionally considered less valuable than the EU bark. This study compared chemical components and metabolic regulations in different parts of EU using metabolomics to explore the potential for alternative medical sources of EU. The results demonstrated that the composition of EC differs slightly from the composition of EF, and there are some differences in the content of individual ingredients between EC and EF. Combined pharmacodynamic/metabolomics analysis showed that both EC and EF could improve the bone metabolism markers and trabecular microarchitecture of ovariectomized rats mainly by intervening in amino acid metabolism. Our data suggest that EF is a potential alternative medicinal option when EU resources are scarce, and this study provides a mechanistic framework for the benefits of EF in osteoporosis disease. 相似文献
35.
Zhi‐Qiang Shao 《Mathematical Methods in the Applied Sciences》2014,37(11):1700-1716
We investigate the existence of a global classical solution to the Goursat problem for linearly degenerate quasilinear hyperbolic systems. As the result in [A. Bressan, Contractive metrics for nonlinear hyperbolic systems, Indiana Univ. Math. J. 37 (1988) 409–421] suggests that one may achieve global smoothness even if the C1 norm of the initial data is large, we prove that, if the C1 norm of the boundary data is bounded but possibly large, and the BV norm of the boundary data is sufficiently small, then the solution remains C1 globally in time. Applications include the equation of time‐like extremal surfaces in Minkowski space R1 + (1 + n) and the one‐dimensional Chaplygin gas equations. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
36.
We review and extend the Alexandrov–Kontsevich–Schwarz–Zaboronsky construction of solutions of the Batalin–Vilkovisky classical master equation. In particular, we study the case of sigma models on manifolds with boundary. We show that a special case of this construction yields the Batalin–Vilkovisky action functional of the Poisson sigma model on a disk. As we have shown in a previous paper, the perturbative quantization of this model is related to Kontsevich's deformation quantization of Poisson manifolds and to his formality theorem. We also discuss the action of diffeomorphisms of the target manifolds. 相似文献
37.
We prove a uniqueness result for BV solutions of scalar conservation laws with discontinuous flux in several space dimensions. The proof is based on the notion of kinetic solution and on a careful analysis of the entropy dissipation along the discontinuities of the flux. 相似文献
38.
Debora Amadori 《偏微分方程通讯》2013,38(9):1003-1040
In this paper we analyze a set of equations proposed by Hadeler and Kuttler [20], describing the flow of granular matter in terms of the heights of a standing layer and of a moving layer. By a suitable change of variables, the system can be written as a 2 × 2 hyperbolic system of balance laws, which we study in the one-dimensional case. The system is linearly degenerate along two straight lines in the phase plane, and therefore is weakly linearly degenerate at the point of the intersection. The source term is quadratic, consisting of product of two quantities, which are transported with strictly different speeds. Assuming that the initial height of the moving layer is sufficiently small, we prove the global existence of entropy-weak solutions to the Cauchy problem, for a class of initial data with bounded but possibly large total variation. 相似文献
39.
40.
T. Akhobadze 《Acta Mathematica Hungarica》2002,97(3):223-256
Generalized Wiener classes are considered. For these classes the exact order of Fourier coefficients with respect to the trigonometric
system is established and the estimation of ‖S
n(·, f)-f(·)‖C
[0,2π] where S
n(·, f) are the Fourier partial sums, is given. In particular, a uniform convergence criterion for the Fourier trigonometric series
is obtained.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献