Generation of Molecular Complexity from Cyclooctatetraene: Preparation of Optically Active Protected Aminocycloheptitols and Bicyclo[4.4.1]undecatriene

The racemic (6-cyclo-heptadienyl)Fe(CO)3+ cation ((±)-7), prepared from cyclooctatetraene, was treated with a variety of carbon and heteroatom nucleophiles. Attack took place at the less hindered C1 dienyl carbon and decomplexation of the (cycloheptadiene)Fe(CO)3 complexes gave products rich in functionality for further synthetic manipulation. In particular, a seven-step route was developed from racemic (6-styryl-2,4-cycloheptadien-1-yl)phthalimide ((±)-9 d) to afford the optically active aminocycloheptitols (−)-20 and (+)-20

Semistable reduction for overconvergent F-isocrystals, II: A valuation-theoretic approach

We introduce a valuation-theoretic approach to the problem of semistable reduction (i.e., existence of logarithmic extensions on suitable covers) of overconvergent isocrystals with Frobenius structure. The key tool is the quasicompactness of the Riemann-Zariski space associated to the function field of a variety.Comment: 20 pages; v3: refereed version; corrections to 4.2.1, 4.3.1; some results extended to the partially overconvergent case (replacing Remark 4.3.7

Year 1 phonics screening check : framework for the pilot in 2011

"For the development of the year 1 phonics screening check" -- front cover

Explicit averages of square-free supported functions: to the edge of the convolution method

We give a general statement of the convolution method so that one can provide explicit asymptotic estimations for all averages of square-free supported arithmetic functions that have a sufficiently regular order on the prime numbers and observe how the nature of this method gives error term estimations of order $X^{-\delta}$, where $\delta$ belongs to an open real positive set $I$. In order to have a better error estimation, a natural question is whether or not we can achieve an error term of critical order $X^{-\delta_0}$, where $\delta_0$, the critical exponent, is the right hand endpoint of $I$. We reply positively to that question by presenting a new method that improves qualitatively almost all instances of the convolution method under some regularity conditions; now, the asymptotic estimation of averages of well-behaved square-free supported arithmetic functions can be given with its critical exponent and a reasonable explicit error constant. We illustrate this new method by analyzing a particular average related to the work of Ramar\'e--Akhilesh (2017), which leads to notable improvements when imposing non-trivial coprimality conditions.Comment: Updated. Some correction