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21.
For a simple graph of maximum degree Δ, it is always possible to color the edges with Δ + 1 colors (Vizing); furthermore, if the set of vertices of maximum degree is independent, Δ colors suffice (Fournier). In this article, we give a short constructive proof of an extension of these results to multigraphs. Instead of considering several color interchanges along alternating chains (Vizing, Gupta), using counting arguments (Ehrenfeucht, Faber, Kierstead), or improving nonvalid colorings with Fournier's Lemma, the method of proof consists of using one single easy transformation, called “sequential recoloring”, to augment a partial k-coloring of the edges.  相似文献   
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In the introduction of the Arithmetica Diophantus says that in order to solve arithmetical problems one has to “follow the way he (Diophantus) will show.” The present paper has a threefold objective. Firstly, the meaning of this sentence is discussed, the conclusion being that Diophantus had elaborated a program for handling various arithmetical problems. Secondly, it is claimed that what is analyzed in the introduction is definitions of several terms, the exhibition of their symbolism, the way one may operate with them, but, most significantly, the main stages of the program itself. And thirdly, it is argued that Diophantus' intention in the Arithmetica is to show the way the stages of his program should be practically applied in various arithmetical problems.  相似文献   
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We show a faithful restriction theorem among infinite chains which implies a reconstructibility conjecture of Halin. This incite us to study the reconstructibility in the sense of Fraïssé and to prove it for orders of cardinality infinite or ≥ 3 and for multirelations of cardinality infinite or ≥ 7, what improves the theory obtained by G. Lopez in the finite case. For this work we had to study the infinite classes of difference which have to be a linear order of type ω, ω* or ω* + ω; this complete the theory made by G. Lopez for the finite case ([13]). We show also Ulam-reconstructibility for linear orders which have a fixed point.  相似文献   
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Pancreatic cancer has an extremely poor prognosis, due, in part, to lack of methods for early diagnosis. The present study was designed to evaluate the potential of labeling low‐density lipoprotein (LDL) with a radionuclide using a lipid chelating agent, bis(stearylamide) of diethylenetriaminepentaacetic acid (L), to detect pancreatic tumors by gamma‐scintigraphy. Previous studies indicated that the difficulty of visualization of pancreatic tumors was due to their poor vascularization. This study compares the ability of two radiotracers, 111In–L–LDL and 153Gd–L–LDL to target highly vascularized rat pancreatic tumors (AR4‐2J) implanted in nude mice. Biodistribution studies showed that the tumor uptake of 111In–L–LDL and 153Gd–L–LDL tracers was twofold and fivefold higher respectively than with the controls (111In citrate and 153Gd citrate respectively). These tracers would thus be suitable for scintigraphic imaging. We show here that LDL could be employed as a delivery system for tracers such as 111In or 153Gd when these two radionuclides are complexed by a lipid‐chelating anchor, and that 111In–L–LDL and 153Gd–L–LDL enabled better visualization of the pancreatic tumor tissues, with a better result with 153Gd–L–LDL. Copyright © 2004 John Wiley & Sons, Ltd.  相似文献   
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We prove some sharp Hardy-type inequalities related to the Dirac operator by elementary, direct methods. Some of these inequalities have been obtained previously using spectral information about the Dirac-Coulomb operator. Our results are stated under optimal conditions on the asymptotics of the potentials near zero and near infinity.  相似文献   
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Nine brands of tobacco cigarettes manufactured and distributed in the Mexican market were analyzed by γ-spectrometry to certify their non-artificial radioactive contamination. Since natural occurring radioactive materials (NORM) 40K, 232Th, 235U, and 239U (and decay products from the latter three nuclides) are the main sources for human radiation exposure, the aim of this work was to determine the activity of 40K and potassium concentration. Averages of 40K and potassium concentration were of 1.29±0.18 Bq·g−1, and 4.0±0.57%. The annual dose equivalents to the whole body from ingestion and inhalation of 26 Bq 40K were 0.23 μSv and 15.8 μSv, respectively. The corresponding 50 years committed dose equivalents was 0.23 μSv. The total committed dose to the lungs due to inhalation of 40K in tobacco was 16 μSv. Potassium concentrations obtained in this work were in the same range of those obtained by INAA, so showing that the used technique is acute, reproducible, and accessible to laboratories equipped with low background scintillation detectors.  相似文献   
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