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William T. Murray Anne Pautard-cooper Nita A. Eskew Slayton A. Evans Jr 《Phosphorus, sulfur, and silicon and the related elements》2013,188(1-4):101-104
Abstract The kinetics of Lewis acid-mediated decomposition and definitions of the synthetic applicability of 1,3,2λ5-dioxaphospholanes for (i) the syntheses of highly-hindered epoxides, and (ii) the stereospecific functionalizations of stereocenters in 1,2-diol arrays are described. 相似文献
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Applying calculus to the horizontal and vertical unit hyperbolas we derive the obtuse exterior and the acute angle of parallelism formulas for the arc length of a unit circle. When the analogous arc length of a hyperbola is figured, we further define metric distance with radian measure. Employing a non-conventional velocity of light formula, we explain several aspects of physics with a logical geometry. The hyperbolic geometry Lobacevskii angle of parallelism is mathematically measured to agree with the physical measure, without using the gravitational constant, but rather the electromagnetic spectrum and geodesics. Space is hereby measured with units of radians and time. Half-angle formulas for slopes and boosts pertain to spinor algebra. The new light velocity is justified when its derivative results in Einstein's mass–energy formula. Relativity is reformulated with these half-angle formulas. 相似文献
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Monroe Eskew 《Mathematical Logic Quarterly》2020,66(2):235-238
We discuss a system of strengthenings of “ is Jónsson” indexed by real numbers, and identify a strongest one. We give a proof of a theorem of Silver and show that there is a barrier to weakening its hypothesis. 相似文献
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Diethoxytriphenylphosphorane (DTPP) efficiently oxaphosphoranylates methyl α-d -glucopyranoside to afford two unstable isomeric 1,3,2λ5-dioxaphospholanes. Thermolysis (60–90°C) of these 1,3,2λ5-dioxaphospholanes affords only two of four possible isomeric anhydropyranosides. Two distinct intermediate betaines and their unique “pre-transition state” chair or twist-boat structures are used to rationalize the regiochemistry-attending cyclodehydration. The decomposition of these rapidly interconverting 1,3,2λ5-dioxaphospholanes is accelerated in the presence of lithium bromide (LiBr) to afford a single anhydropyranoside. 相似文献
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