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71.
72.
We solve the problem of describing compatible nonlocal Poisson brackets of hydrodynamic type. We prove that for nonsingular pairs of compatible nonlocal Poisson brackets of hydrodynamic type, there exist special local coordinates such that the metrics and the Weingarten operators of both brackets are diagonal. The nonlinear evolution equations describing all nonsingular pairs of compatible nonlocal Poisson brackets of hydrodynamic type are derived in these special coordinates, and the integrability of these equations is proved using the inverse scattering transform. The Lax pairs with a spectral parameter for these equations are found. We construct various classes of integrable reductions of the derived equations. These classes of reductions are of an independent differential-geometric and applied interest. In particular, if one of the compatible Poisson brackets is local, we obtain integrable reductions of the classical Lamé equations describing all orthogonal curvilinear coordinate systems in a flat space; if one of the compatible brackets is generated by a constant-curvature metric, the corresponding equations describe integrable reductions of the equations for orthogonal curvilinear coordinate systems in a space of constant curvature. 相似文献
73.
Alexander Koldobsky 《Advances in Applied Mathematics》2004,33(4):728-732
The Busemann–Petty problem asks whether origin-symmetric convex bodies in Rn with smaller areas of all central hyperplane sections necessarily have smaller n-dimensional volume. The solution was completed in the end of the 1990s, and the answer is affirmative if n4 and negative if n5. Since the answer is negative in most dimensions, it is natural to ask what information about the volumes of central sections of two bodies does allow to compare the n-dimensional volumes of these bodies in all dimensions. In this article we give an answer to this question in terms of certain powers of the Laplace operator applied to the section function of the body. 相似文献
74.
Milan Merkle 《Journal of Mathematical Analysis and Applications》2004,293(1):210-218
We say that f is reciprocally convex if x?f(x) is concave and x?f(1/x) is convex on (0,+∞). Reciprocally convex functions generate a sequence of quasi-arithmetic means, with the first one between harmonic and arithmetic mean and others above the arithmetic mean. We present several examples related to the gamma function and we show that if f is a Stieltjes transform, then −f is reciprocally convex. An application in probability is also presented. 相似文献
75.
Yong Chan Kim 《Journal of Mathematical Analysis and Applications》2004,299(2):433-447
In this paper, nonlinear integral operators on normalized analytic functions in the unit disk are investigated in connection with the pre-Schwarzian derivative and the Hornich operation. In particular, several nontrivial relations between these operators and the class of strongly starlike functions will be deduced. 相似文献
76.
Frictionless indentation responses of transversely isotropic piezoelectric film/rigid substrate systems under circular cylindrical indenter (i.e., punch), conical indenter (i.e., cone), and spherical indenter (i.e., sphere) are investigated. Both insulating and conducting indenters are considered. The technique of Hankel transformation is employed to derive the corresponding dual integral equations for the mixed boundary value indentation problems. For the two limiting cases of infinitely thick and infinitely thin piezoelectric films, closed-form solutions are obtained. For piezoelectric films of finite thickness, a numerical method is constructed to solve the dual integral equations and semi-empirical models having only two unknown parameters are proposed for the responses of indentation force, electric charge and electric potential, and contact radius. With the two parameters inferred from the numerical results, the semi-empirical formulae are found to provide good estimates of the indentation responses for the two limiting cases of infinitely thick and thin piezoelectric films, as well as those in between. The inferred parameters in the proposed semi-empirical formulae for normalized indentation force and electric charge are checked against four different piezoelectric materials and are found to be insensitive to the selection of piezoelectric materials. It is believed that the proposed semi-empirical indentation formulae are useful in developing experimental indentation techniques to extract the material properties of piezoelectric films. 相似文献
77.
Michaël Lejeune Andrea Valsesia Martin Kormunda Pascal Colpo François Rossi 《Surface science》2005,583(1):L142
In this work, chemically and topographically nanopatterned surfaces were produced by a top-down processing approach for biosensing devices. The nanopatterning was the result of the combination of plasma polymerisation (pp) of biofunctional materials and colloidal lithography techniques. The morphological and chemical properties induced by the plasma deposition-etching treatment were characterised by optical method combining ellipsometry and Fourier Transform Infrared spectroscopy studies. This method supported by atomic force microscopy measurements, allowed the full optical characterization of each step of the top-down process. The optical characterization of the end-up nanopatterned samples demonstrated that the chosen process is able to produce well-defined nanostructured surfaces with controlled chemical and morphological properties. 相似文献
78.
In this paper, the authors obtain sharp upper and lower hounds for the heat kernel associated with Jacobi transform, and get some analogues of Hardy‘s Theorem for Jacobi transform by using the sharp estimate of the heat kernel. 相似文献
79.
Radon变换和衰减Radon变换的分析研究 总被引:1,自引:0,他引:1
衰减Radon变换出现在单光子放射型计算机层析成像中。本文首先回顾和研究了Radon变换和衰减Radon变换及其反演的有关结论,进而提出了Tretiak-Metz结果的一种新证明方法,对于一般对象,本文用变换方法非滤子背投影法导出了衰减Radon变换的反演公式。 相似文献
80.
This article concerns the existence of global smooth solution for scalar conservation laws with degenerate viscosity in 2-dimensional space. The analysis is based on successive approximation and maximum principle. 相似文献