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41.
Rupert L. Frank Ari Laptev Elliott H. Lieb Robert Seiringer 《Letters in Mathematical Physics》2006,77(3):309-316
Inequalities are derived for power sums of the real part and the modulus of the eigenvalues of a Schrödinger operator with a complex-valued potential. 相似文献
42.
Electrostriction refers to the strain induced in a dielectric by electric polarization, which is usually very small for practical application. In this paper, we present a micromechanical analysis on the effective electrostriction of a ferroelectric polyvinylidene fluoride trifluoroethylene [P(VDF-TrFE)] polymer-based composite, where the exact connections between the effective electrostrictive coefficients and effective elastic moduli are established, and numerical algorithm for the prediction of the effective electrostrictive coefficients of the composite in terms of its microstructural information is developed. From our calculations, enhanced electrostriction in the composite has been demonstrated, and optimal microstructure for electrostriction enhancement has been identified. Our analysis provides a mechanism for the electrostriction enhancement, where the electrostrictive strain several times higher than that of polymer matrix can be obtained, if the microstructure of the composites can be carefully tailored. 相似文献
43.
44.
45.
The modified wave and scattering operators are shown to be bounded between weighted L
2-spaces for two-body Schrödinger operators with long range potentials. 相似文献
46.
47.
A review of immiscibility data in binary borate and germanate systems was performed in order to compare miscibility gap consolute temperatures with ionic potentials and radii of their associated cations. The trends obtained demonstrate that a selective solution mechanism similar to the one identified for the binary silicate systems is present in the borate and germanate binaries. More importantly, the borate and germanate immiscibility data permitted the identification of a new group of cations depicting an immiscibility behaviour different from the ones identified in binary silicate systems. The new group involves highly polarizable cations possessing a lone pair of electrons. This lone pair of electrons together with oxygen bonded by strong covalent bonds to modifier cations provides efficient shielding to the cations' nuclei which considerably reduces the coulombic repulsions and produces miscibility gaps with very low consolute temperatures. A new group of cations having an homogenizing effect on melts (i.e. a capacity to make immiscible melts single phase) is thus reported. Experimental and spectroscopic data suggest that miscibility gaps associated with cations having a lone pair of electrons exist in binary silicate systems such as TlO1/2-SiO2, PbO-SiO2, SnO-SiO2 and Bi2O3-SiO2. The consolute temperature of their miscibility gaps is expected to be relatively low and metastable. 相似文献
48.
L. Stoyanov 《Mathematische Annalen》2002,324(4):743-771
In this paper we consider properties of obstacles satisfying some non-degeneracy conditions that can be recovered from the
scattering length spectrum (SLS). Clearly the latter tells us whether the obstacle K is trapping or non-trapping. If the set of trapped points is relatively small, then the SLS also determines the volume of
the obstacle, the number of its connected components, and whether its boundary is convex everywhere or it has non-trivial
concavities. Under the additional assumption that the curvature of the obstacle does not vanish of infinite order, it is proved
that from the SLS one can recover certain information about the number of reflection points of any simply reflecting ray in
the exterior of the obstacle. Finally, for some special classes of obstacles (e.g. star-shaped ones), it is shown that the
SLS completely determines the obstacle.
Received: 2 March 1999 / Revised version: 16 January 2001 / Published online: 5 September 2002 相似文献
49.
Various topological properties of projective duality between real projective varieties and their duals are obtained by making use of the microlocal theory of (subanalytically) constructible sheaves developed by Kashiwara [M. Kashiwara, Index theorem for constructible sheaves, Astérisque 130 (1985) 193-209] and Kashiwara-Schapira [M. Kashiwara, P. Schapira, Sheaves on Manifolds, Grundlehren Math. Wiss., vol. 292, Springer, Berlin-Heidelberg-New York, 1990]. In particular, we prove in the real setting some results similar to the ones proved by Ernström in the complex case [L. Ernström, Topological Radon transforms and the local Euler obstruction, Duke Math. J. 76 (1994) 1-21]. For this purpose, we describe the characteristic cycles of topological Radon transforms of constructible functions in terms of curvatures of strata in real projective spaces. 相似文献
50.
In this paper we prove the semialgebraic version of Palais' covering homotopy theorem, and use this to prove Bredon's covering mapping cylinder conjecture positively in the semialgebraic category. Bredon's conjecture was originally stated in the topological category, and a topological version of our semialgebraic proof of the conjecture answers the original topological conjecture for topological G-spaces over “simplicial” mapping cylinders. 相似文献