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91.
Gabriele Grillo Hynek Kovařík Yehuda Pinchover 《Archive for Rational Mechanics and Analysis》2014,213(1):215-243
We prove on-diagonal bounds for the heat kernel of the Dirichlet Laplacian ${-\Delta^D_\Omega}$ in locally twisted three-dimensional tubes Ω. In particular, we show that for any fixed x the heat kernel decays for large times as ${{\rm e}^{-E_1t} t^{-3/2}}$ , where E 1 is the fundamental eigenvalue of the Dirichlet Laplacian on the cross section of the tube. This shows that any, suitably regular, local twisting speeds up the decay of the heat kernel with respect to the case of straight (untwisted) tubes. Moreover, the above large time decay is valid for a wide class of subcritical operators defined on a straight tube. We also discuss some applications of this result, such as Sobolev inequalities and spectral estimates for Schrödinger operators ${-\Delta^D_\Omega-V}$ . 相似文献
92.
Let P be a second-order, linear, elliptic operator with real coefficients which is defined on a noncompact and connected Riemannian manifold M. It is well known that the equation in M admits a positive supersolution which is not a solution if and only if P admits a unique positive minimal Green function on M, and in this case, P is said to be subcritical in M. If P does not admit a positive Green function but admits a global positive (super)solution, then such a solution is called a ground state of P in M, and P is said to be critical in M.We prove for a critical operator P in M, the existence of a Green function which is dominated above by the ground state of P away from the singularity. Moreover, in a certain class of Green functions, such a Green function is unique, up to an addition of a product of the ground states of P and . Under some further assumptions, we describe the behavior at infinity of such a Green function. This result extends and sharpens the celebrated result of P. Li and L.-F. Tam concerning the existence of a symmetric Green function for the Laplace–Beltrami operator on a smooth and complete Riemannian manifold M. 相似文献
93.
94.
Yehuda Niv 《Hyperfine Interactions》1985,24(1-4):301-310
The nuclear tilted-foil experimental field has matured from the early time-integral measurements to the current multifoil
time-differential precession and polarization configurations, leading to a wide range of measurements-magnetic moments, quadrupole
moments and parity-non-conservation. The physical basis of these experiments will be discussed and experimental results will
be reviewed. 相似文献
95.
96.
An electric field is employed to convert lithium 42 D Zeeman level crossings into anti-crossings. The lithium atoms are excited by electron impact. The anti-crossings are detected by the change in polarization of the light emitted in the 42 D-22 P transition. From the corresponding values of the magnetic field, we obtain 400 (10) MHz for the zero field fine structure energy separationE(42 D 5/2)-E(42 D 3/2). 相似文献
97.
98.
99.
Ozonation of phenyl ethylenes adsorbed on untreated silica gel results in aromatic aldehydes and on dried silica gel in ozonides and aldehydes. On the other hand ozonation of alkyl ethylenes on both types of silica gel results in a mixture of ozonides or polymeric peroxides similar to that obtained in aprotic solvents. 相似文献
100.