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In the nineteenth century, field theory brilliantly resolveda number of questions that had taxed mathematicians for centuries;for example, The circle cannot be squared by straightedge and compass, and solving polynomial equations by radicalsis not always possible. These successes have continued to beheld up as superb examples of the power of mathematical thought,and are demonstrated at an undergraduate level. The purposeof this article is to provide another such natural example whichleads to a concrete realisation of the free group on 2 generators. 相似文献
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Serguei Foss Takis Konstantopoulos Stan Zachary 《Journal of Theoretical Probability》2007,20(3):581-612
We consider a modulated process S which, conditional on a background process X, has independent increments. Assuming that S drifts to −∞ and that its increments (jumps) are heavy-tailed (in a sense made precise in the paper), we exhibit natural
conditions under which the asymptotics of the tail distribution of the overall maximum of S can be computed. We present results in discrete and in continuous time. In particular, in the absence of modulation, the
process S in continuous time reduces to a Lévy process with heavy-tailed Lévy measure. A central point of the paper is that we make
full use of the so-called “principle of a single big jump” in order to obtain both upper and lower bounds. Thus, the proofs
are entirely probabilistic. The paper is motivated by queueing and Lévy stochastic networks. 相似文献
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Jaffe DE Straub PB Adams MR Brown CN Charpak G Cooper WE Crittenden JA Finley DA Glass HD Gray R Hemmi Y Hsiung YB Hubbard JR Jonckheere AM Jöstlein H Kaplan DM Lederman LM Luk KB Maki A Mangeot P McCarthy RL Miyake K Plaag RE Rutherfoord JP Sakai Y Santiard JC Sauli F Smith SR Yoshida T Young KK 《Physical review D: Particles and fields》1989,40(9):2777-2795
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J. T. Glass J. F. McCann D. S. F. Crothers 《Zeitschrift für Physik D Atoms, Molecules and Clusters》1996,36(2):119-124
Starting with the impulse approximation, we analyse second-order effects in relativistic electron capture. The relation of this model with relativistic distorted-wave approximations is clarified. In particular it is shown that the second-order spin-coupling terms in the RCDW theory are consistent with the correct form given by perturbation theory. In the semirelativistic limit, the RCDW results are shown to accord with the formulae of Moiseiwitsch for flip and nonflip transitions in the ultra-relativistic limit. This confirms that the continuum-distorted-wave model generalises to relativistic spinors, and highlights the defects of scalar models. We also present a new symmetric eikonal theory which gives reliable results for capture without change of spin, but leads to a divergent total cross section for spin-flip transitions in the second-order term. This effect, which is quite distinct from the spurious spin-flip amplitudes of the scalar symmetric eikonal theory, is taken as further evidence that the eikonal approximation is not valid for magnetic transitions. 相似文献
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The trans reduction of all types of alkynes to give (E)-olefins is achieved through a two-stage trans hydrosilylation and protodesilylation. Reaction of an alkyne and a silane with the ruthenium catalyst [Cp*Ru(MeCN)3]PF6 results in clean hydrosilylation to give only the (Z)-trans addition product at ambient temperature with catalyst loadings of 1-5 mol %. The crude vinylsilane products are then protodesilylated by the action of cuprous iodide and TBAF at rt-35 degrees C. The reaction is compatible with many sensitive functional groups and provides a general trans-alkyne reduction not possible by other means. 相似文献