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11.
We give manifolds whose Riemann curvature operators commute, i.e. which satisfy
for all tangent vectors xi in both the Riemannian and the higher signature settings. These manifolds have global geometric phenomena which are quite
different for higher signature manifolds than they are for Riemannian manifolds. Our focus is on global properties; questions
of geodesic completeness and the behaviour of the exponential map are investigated.
Dedicated to the memory of Jean Leray 相似文献
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Let D be an open set in Euclidean space Rm with boundary D,and let :D[0, ) be a bounded, measurable function. Let u:DDx[0,)[0, ) be the unique weak solution of the heat equation [formula] with initial condition [formula] and with inhomogeneous Dirichlet boundary condition [formula] Then u(x; t) represents the temperature at a point xD at timet if D has initial temperature 0, while the temperature at apoint xD is kept fixed at (x) for all t>0. We define thetotal heat content (or energy) in D at time t by [formula] In this paper we wish to examine the effect of imposing additionalcooling on some subset C on both u and ED. 1991 MathematicsSubject Classification 35K05, 60J65, 28A80. 相似文献
14.
Periodica Mathematica Hungarica - Let ?= 2ν &;gt; 1. Let M be an orientable manifold of odd dimension m with $\pi _1 (M) = \mathbb{Z}_\ell $ whose universal cover $\tilde M$ is... 相似文献
15.
Peter B. Gilkey John V. Leahy Jeong Hyeong Park 《Proceedings of the American Mathematical Society》1998,126(6):1845-1850
Let be a Riemannian submersion of closed manifolds. Let be an eigen -form of the Laplacian on with eigenvalue which pulls back to an eigen -form of the Laplacian on with eigenvalue . We are interested in when the eigenvalue can change. We show that , so the eigenvalue can only increase; and we give some examples where , so the eigenvalue changes. If the horizontal distribution is integrable and if is simply connected, then , so the eigenvalue does not change.
16.
We consider the short-time heat content asymptotics for oblique boundary conditions. The first few coefficients in the asymptotic expansion are calculated. 相似文献
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19.
Let P be an operator of Dirac type and let D=P
2 be the associated operator of Laplace type. We impose spectral boundary conditions and study the leading heat content coefficients for D. 相似文献
20.
B Kollmeier R H Gilkey U K Sieben 《The Journal of the Acoustical Society of America》1988,83(5):1852-1862
Data from a simple tone-in-noise simultaneous masking task were used to evaluate each of two common adaptive staircase rules (a "1 up 2 down" rule and a "1 up 3 down" rule) and the parameter estimation by sequential testing (PEST) technique in combination with each of two psychophysical procedures [a two-alternative forced-choice (2AFC) and a three-alternative forced-choice (3AFC) procedure]. These human data were compared to predictions generated by a mathematical model based on Markov theory. The model predicts that threshold estimates obtained with the adaptive techniques should be equal to those derived with equivalent "fixed signal level" techniques. However, the human data indicate that the adaptive techniques tend to yield lower thresholds. The model predicts that the standard error of a threshold estimate obtained from an adaptive technique will decrease and approach zero as the number of trials used to compute the estimate increases. The human data show greater variability than predicted and approach a nonzero value as the number of trials increases. The predictions of the model suggest that the commonly used combination of the 2AFC procedure and the 1 up 2 down rule is the least efficient method of estimating a threshold and that the 3AFC procedure in combination with the 1 up 3 down rule is the most efficient method. The human data are less consistent, but generally show the combination of the 2AFC procedure and the 1 up 2 down rule to be one of the least efficient methods. Possible explanations for the differences between the model's predictions and the human data, as well as suggestions for laboratory practice, are discussed. 相似文献