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Gary M. Lieberman 《manuscripta mathematica》2003,112(4):459-472
If u is a solution of the second order elliptic differential equation Lu=f in some Lipschitz domain in
n
, we estimate the maximum of u in terms of some oblique derivative prescribed on the boundary of the domain and in terms of the L
p
norm of f with p<n. 相似文献
44.
Davies AJ Scott JP Bishop BC Brands KM Brewer SE Dasilva JO Dormer PG Dolling UH Gibb AD Hammond DC Lieberman DR Palucki M Payack JF 《The Journal of organic chemistry》2007,72(13):4864-4871
This paper describes a remarkably efficient process for the preparation of gamma-secretase inhibitor 1. The target is synthesized in only five steps with an overall yield of 58%. The key operation is a highly selective and practical, crystallization-driven transformation for the conversion of a mixture of tertiary benzylic alcohols into the desired sulfide diastereomer with 94:6 dr. This unprecedented process is based upon a reversible carbon-sulfur bond formation under acidic conditions. 相似文献
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Hessian‐based model reduction was previously proposed as an approach in deriving reduced models for the solution of large‐scale linear inverse problems by targeting accuracy in observation outputs. A control‐theoretic view of Hessian‐based model reduction that hinges on the equality between the Hessian and the transient observability gramian of the underlying linear system is presented. The model reduction strategy is applied to a large‐scale ( degrees of freedom) three‐dimensional contaminant transport problem in an urban environment, an application that requires real‐time computation. In addition to the inversion accuracy, the ability of reduced models of varying dimension to make predictions of the contaminant evolution beyond the time horizon of observations is studied. Results indicate that the reduced models have a factor speedup in computing time for the same level of accuracy. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
47.
Gary M. Lieberman 《Mathematical Methods in the Applied Sciences》1993,16(7):457-474
We study global solutions of ut=Δu + f(u, Du) with zero boundary data. Under suitable hypotheses on f, we show that an energy, which is roughly the H1 norm of u, cannot change too rapidly. When f depends only on u, this estimate implies that all global solutions are bounded. 相似文献
48.
The functional Ito formula, in the form df() = f( + d ) f(),is formulated and proved in the context of a Lie algebra L associatedwith a quantum (non-commutative) stochastic calculus. Here fis an element of the universal enveloping algebra U of L, andf() + d() f() is given a meaning using the coproductstructure of U even though the individual terms of this expressionhave no meaning. The Ito formula is equivalent to a chaoticexpansion formula for f() which is found explicitly. 1991 MathematicsSubject Classification: primary 81S25; secondary 60H05; tertiary18B25. 相似文献
49.
We study the approach to near-equipartition in the N-dimensional Fermi-Pasta-Ulam Hamiltonian with quartic (hard spring) nonlinearity. We investigate numerically the time evolution of orbits with initial energy in some few low-frequency linear modes. Our results indicate a transition where, above a critical energy which is independent of N, one can reach equipartition if one waits for a time proportional to N(2). Below this critical energy the time to equipartition is exponentially long. We develop a theory to determine the time evolution and the excitation of the nonlinear modes based on a resonant normal form treatment of the resonances among the oscillators. Our theory predicts the critical energy for equipartition, the time scale to equipartition, and the form of the nonlinear modes below equipartition, in qualitative agreement with the numerical results. (c) 1995 American Institute of Physics. 相似文献
50.
Bushra Y Ahmed Sridhara Chakravarthy Ruben Eggers Wim TJMC Hermens Jing Ying Zhang Simone P Niclou Christiaan Levelt Fred Sablitzky Patrick N Anderson AR Lieberman Joost Verhaagen 《BMC neuroscience》2004,5(1):1-11