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Glass fragments dating from the seventh and eighth century AD were excavated in the Crypta Balbi in Rome. They were studied to detect agents involved in colour development and opacification. Reflectance spectra recorded on powdered samples revealed the contribution of Fe(II), Fe(III), Mn(III), Cu(II), and Co(II) ions in determining colour hues. The effect of the Mn/Fe atomic ratio on glass colour is discussed. It is apparent that medieval glassmakers in Italy could obtain a wide range of colours by exploiting the presence of iron and manganese as contaminants of sand and flux and controlling the amount of oxygen let into the furnace. X-ray diffraction and scanning electron microscopy coupled with energy-dispersive X-ray analysis were used to study opaque fragments. The presence of calcium antimonate was detected in white, blue, and blue-green fragments, and elemental copper was detected in a red glass. 相似文献
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An explicit coloring of the edges of Kn is constructed such that every copy of K4 has at least four colors on its edges. As n , the number of colors used is n1/2+o(1). This improves upon the previous bound of O(n2/3) due to Erds and Gyárfás obtained by probabilistic methods. The exponent 1/2 is optimal, since it is known that at least (n1/2) colors are required in such a coloring.The coloring is related to constructions giving lower bounds for the multicolor Ramsey number rk(C4). It is more complicated however, because of restrictions imposed on interactions between color classes.* Research supported in part by NSF Grant No. DMS–9970325. 相似文献
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Let be graphs. The multicolor Ramsey number is the minimum integer r such that in every edge‐coloring of by k colors, there is a monochromatic copy of in color i for some . In this paper, we investigate the multicolor Ramsey number , determining the asymptotic behavior up to a polylogarithmic factor for almost all ranges of t and m. Several different constructions are used for the lower bounds, including the random graph and explicit graphs built from finite fields. A technique of Alon and Rödl using the probabilistic method and spectral arguments is employed to supply tight lower bounds. A sample result is for any t and m, where c1 and c2 are absolute constants. 相似文献
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Davit Varron 《Stochastic Processes and their Applications》2011,121(2):337-356
Given an observation of the uniform empirical process αn, its functional increments αn(u+an⋅)−αn(u) can be viewed as a single random process, when u is distributed under the Lebesgue measure. We investigate the almost sure limit behaviour of the multivariate versions of these processes as n→∞ and an↓0. Under mild conditions on an, a convergence in distribution and functional limit laws are established. The proofs rely on a new extension of the usual Poissonisation tools for the local empirical process. 相似文献
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Katritzky AR Jishkariani D Sakhuja R Hall CD Steel PJ 《The Journal of organic chemistry》2011,76(10):4082-4087
Carbene-mediated transformations of N-(3-butylbenzimidazol-3-ium-1-yl)-1-arylmethanimine iodides with carbon disulfide and benzoyl isothiocyanate gave the corresponding NHC·CS(2) betaines in 68-85% and benzoyl-[1-butyl-3-[(E)-(aryl)methyleneamino]benzimidazol-1-ium-2-carbothioyl]azanides, respectively, in 74-85% yields. However, reaction with excess isopropyl isothiocyanate in NaH/THF at room temperature yielded the 1-butyl-1',3'-diisopropyl-3-[(E)-(aryl)methyleneamino]spiro[benzimidazole-2,5'-imidazolidine]-2',4'-dithiones (74-77%). 相似文献
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Davit Harutyunyan 《Comptes Rendus Mathematique》2018,356(5):575-580
We consider shells in three-dimensional Euclidean space that have bounded principal curvatures. We prove Korn's interpolation (or the so-called first and a half1) and the second inequalities on that kind of shells for vector fields, imposing no boundary or normalization conditions on u. The constants in the estimates are optimal in terms of the asymptotics in the shell thickness h, having the scalings h or . The Korn interpolation inequality reduces the problem of deriving any linear Korn type estimate for shells to simply proving a Poincaré-type estimate with the symmetrized gradient on the right-hand side. In particular, this applies to linear geometric rigidity estimates for shells, i.e. Korn's fist inequality without boundary conditions. 相似文献
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Dhruv Mubayi 《Advances in Mathematics》2010,225(5):2731-2740
Let F be a graph which contains an edge whose deletion reduces its chromatic number. We prove tight bounds on the number of copies of F in a graph with a prescribed number of vertices and edges. Our results extend those of Simonovits (1968) [8], who proved that there is one copy of F, and of Rademacher, Erd?s (1962) [1] and [2] and Lovász and Simonovits (1983) [4], who proved similar counting results when F is a complete graph.One of the simplest cases of our theorem is the following new result. There is an absolute positive constant c such that if n is sufficiently large and 1?q<cn, then every n vertex graph with ⌊n2/4⌋+q edges contains at least