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11.
Fritz Rohrlich 《Foundations of Physics》1998,28(7):1045-1056
It is argued that time's arrow is present in all equations of motion. But it is absent in the point particle approximations commonly made. In particular, the Lorentz-Abraham-Dirac equation is time-reversal invariant only because it approximates the charged particle by a point. But since classical electrodynamics is valid only for finite size particles, the equations of motion for particles of finite size must be considered. Those equations are indeed found to lack time-reversal invariance, thus ensuring an arrow of time. Similarly, more careful considerations of the equations of motion for gravitational interactions also show an arrow of time. The existence of arrows of time in quantum dynamics is also emphasized. 相似文献
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13.
J. Fritz 《Probability Theory and Related Fields》1989,81(2):291-318
Summary A lattice system of interacting diffusion processes is investigated. The evolution is attractive and time reversible, the spin satisfies a conservation law. It is shown that the rescaled spin field converges in probability to the corresponding solution to a nonlinear diffusion equation.Supported in part by the Hungarian National Foundation for Scientific Research, grant No. 819/1, and by the Mathematical Department of Rutgers University, N.S.F. grant DMR 8612369 相似文献
14.
Fritz Gesztesy Karl Unterkofler Rudi Weikard 《Transactions of the American Mathematical Society》2006,358(2):603-656
Combining theorems of Halphen, Floquet, and Picard and a Frobenius type analysis, we characterize rational, meromorphic simply periodic, and elliptic KdV potentials. In particular, we explicitly describe the proper extension of the Airault-McKean-Moser locus associated with these three classes of algebro-geometric solutions of the KdV hierarchy with special emphasis on the case of multiple collisions between the poles of solutions. This solves a problem left open since the mid-1970s.
15.
16.
For smooth nonlinear systems
相似文献
17.
Gregory H. Robinson Fritz Moise William T. Pennington Samuel A. Sangokoya 《Journal of chemical crystallography》1988,18(4):387-393
The crystalline condensation product [Al(CH3)2]2[C10H22N4][Al(CH3)3]2 is prepared from reaction of the multidentate open-chain amine 1,4-bis(3-aminopropyl)piperazine with trimethylaluminum in methylene chloride. The compound crystallized in the monoclinic space groupC2/c with unit cell parametersa=25.166(12),b=7.268(4),c=17.316(4) Å,=115.3(4)°, andD
c
=1.06 g cm–3 forZ=4. Least-squares refinement based on 1054 observed reflections with intensitiesI 3(I) in the range 2<2<45° led to a finalR factor of 0.053 (R
w
=0.064). The title compound resides on a crystallographic center of symmetry with independent Al-N distances of 1.889(5), 2.058(5), and 2.030(5) Å. 相似文献
18.
The properties and advantages of membrane disks for solid-phase extraction (SPE) are described. Miniaturization is a trend in SPE, as well as chemical analysis in general. A semimicro method is reviewed in which an extraction disk 4 mm in diameter is used for SPE. Even smaller scale separations are possible with a device in which a membrane 0.7 mm in diameter was incorporated into the needle of a 50-micro syringe. Aqueous samples containing 10 ppb of eight substituted benzenes were passed through the miniaturized-SPE syringe automatically using a single-syringe infusion pump. Elution volumes of 5 microl provided 500-fold concentrations and delivered average recoveries greater than 90% and an average relative standard deviation (RSD) of 4.6% for the analytes. Direct injection of the 5 microl eluate from the miniaturized-SPE syringe into a gas chromatograph also produced average recoveries greater than 90% and an average RSD of 6.2%. 相似文献
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Meerwein reactions of 1,5-anthraquinone bis(diazonium hydrogen sulfate) with sufficiently activated olefins, such as acrylonitrile, acrylic esters, methacrylonitrile and its esters, styrene and α-methylstyrene yielded derivatives of the new heterocyclic system anthra[9,1-bc:10,5-b'c']-2,3,7,8-tetrahydrodipyran. Isolation of derivatives was realized and yields enhanced by using dimethyl methylphosphonate as reaction medium. Compounds 5–18 were isolated as mixtures of diastereomers, some of which were separated by crystallization. Proof of structure and stereochemistry was obtained for some of the compounds by X-ray crystallographic analysis. The 1H- and 13C-nmr data provided further support. Surprisingly large chemical shift differences between some of the proton signals of isomers were observed although the two asymmetric centers are far apart through bonds and through space. The mechanism of formation is explained on the basis of redox modulation of a charge transfer complex in which the aliphatic radical attacks the oxygen atom of the anthraquinone. It is proposed to classify this new type of reaction as an intramolecular Meerwein reaction. 相似文献
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