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11.
V. G. Bagrov D. M. Gitman V. N. Zadorozhnyi Sh. M. Shvartsman 《Russian Physics Journal》1975,18(1):34-36
Solutions of the Dirac and Klein-Gordon equations have been obtained for an electron moving in the field of two plane waves propagating in slightly different directions. The solutions were obtained as an expansion in terms of the small angle between the two waves. Terms linear in this angle were considered. 相似文献
12.
We prove that a linear bounded extension operator exists for the trace of C
1·ω (R
n
)to an arbitrary closed subset of
R
n
.The similar result is obtained for some other spaces of multivariate smooth functions. We also show that unlike the one-dimensional
case treated by Whitney, for some trace spaces of multivariate smooth functions a linear bounded extension operator does not
exist. The proofs are based on a relation between the problem under consideration and a similar problem for Lipschitz spaces
defined on hyperbolic Riemannian manifolds. 相似文献
13.
Pavel Shvartsman 《Transactions of the American Mathematical Society》2008,360(10):5529-5550
We study a variant of the Whitney extension problem (1934) for the space . We identify with a space of Lipschitz mappings from into the space of polynomial fields on equipped with a certain metric. This identification allows us to reformulate the Whitney problem for as a Lipschitz selection problem for set-valued mappings into a certain family of subsets of . We prove a Helly-type criterion for the existence of Lipschitz selections for such set-valued mappings defined on finite sets. With the help of this criterion, we improve estimates for finiteness numbers in finiteness theorems for due to C. Fefferman.
14.
Ilya Shvartsman 《Journal of Optimization Theory and Applications》2012,153(3):578-586
In this paper, we provide a simple proof of the maximum principle for a nonsmooth discrete-time optimal control problem. The
methodology is general and encompasses all generalized derivatives for which the Lagrange multiplier rule and the chain rule
hold. This includes, but is not limited to, limiting (Mordukhovich) and Michel–Penot subdifferentials. 相似文献
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17.
Xingxian Shou Jamal Derakhshan Timothy Eagan Shmaryu Shvartsman Jeffrey Duerk Robert Brown 《Applied Acoustics》2010,71(3):191-200
A study is made of certain dominant frequencies in the acoustic noise spectrum of the magnetic resonance imaging system. Motivated by both spring and string ideas, we investigate whether the contributions to the sound from certain frequencies can be canceled by the appropriate gradient pulse sequence design. From both simulations and experiments, vibrations resulting from an impulsive force associated with a ramping up of a gradient pulse are shown to be cancelled immediately upon the application of another impulsive force coming from the subsequent appropriately timed ramping down of that pulse. A general approach to suppression of multiple-frequency contributions involving a series of gradient pulses with variable timings is given for the cancellations between pairs of impulsive forces. Various examples are confirmed through string simulations, MRI experiments, and linear response theory. This also provides a foundation to explain some results in previous papers on this subject. The method suggests that a variety of pulse profiles and timing combinations can be used to attenuate important contributions to the acoustic spectrum. 相似文献
18.
The ferroelectric and dielectric properties of Pb0.99[(Zr1−x Snx)1−y Tiy]0.98Nb0.02O3 ceramic of composition (I) x=0.5, y=0.04–0.12 and (II) x=0.4, y=0.06–0.09 were studied, and the T-x and E-T diagrams were constructed. When zinc is substituted for tin, the range of coexistence of the ferroelectric and antiferroelectric phases extends. The range of the nonpolar phase shrinks when the titanium content is increased. 相似文献
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