On the convergence of Fourier series of computable Lebesgue integrable functions

This paper studies how well computable functions can be approximated by their Fourier series. To this end, we equip the space of L^p‐computable functions (computable Lebesgue integrable functions) with a size notion, by introducing L^p‐computable Baire categories. We show that L^p‐computable Baire categories satisfy the following three basic properties. Singleton sets {f } (where f is L^p‐computable) are meager, suitable infinite unions of meager sets are meager, and the whole space of L^p‐computable functions is not meager. We give an alternative characterization of meager sets via Banach‐Mazur games. We study the convergence of Fourier series for L^p‐computable functions and show that whereas for every p > 1, the Fourier series of every L^p‐computable function f converges to f in the L^p norm, the set of L¹‐computable functions whose Fourier series does not diverge almost everywhere is meager (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Revisiting acido-basicity of the MgO surface by periodic density functional theory calculations: role of surface topology and ion coordination on water dissociation

Low-coordinated (LC) ions at the MgO surface (noted Mg2+LC and O2-LC with L = 1-5), located on monatomic and diatomic steps, corners, step divacancies, and kinks, have been modeled thanks to periodic density functional theory (DFT) calculations (VASP). Ions of lowest coordination induce the strongest surface geometry relaxation and the highest surface energies. The hydration energies of these sites and thermodynamic stabilities of the resulting surfaces were studied. The factors controlling the interaction strength between water and the surface are the possibility for the hydroxyl group to adopt a bridging geometry between two Mg2+ cations in concave areas of the surface, such as the bottom of the monatomic step, and at second order the surface atomic coordination, and especially the presence of three-coordinated ions. The Lewis basicity and acidity of O2-LC and Mg2+LC, respectively, increase as their coordination number decreases, which implies the same trend for the Br?nsted basicity of the Mg2+-O2- pair toward water. However, this trend can be changed if pairs leading to the formation of bridging OH groups are involved, typically on monatomic steps or in step divacancies where O2C-H and O3C-H are obtained, respectively, instead of the expected O1C-H. Thanks to thermodynamic calculations, the state of the surface as a function of temperature can be determined at a given pressure, unraveling the roles of surface topology and ions coordination.     

A synthetic entry to furo[2,3-b]pyridin-4(1H)-ones and related furoquinolinones via iodocyclization

[reaction: see text] N-Methyl-4-alkoxy-3-alkynylpyridin-2(1H)-ones readily undergo iodine-promoted 5-endo-heteroannulation under mild conditions to 3-iodofuropyridinium triiodide salts in moderate to good yields. The latter may be dealkylated in situ upon exposure to an iodide anion to provide the corresponding 3-iodofuro[2,3-b]pyridin-4(1H)-ones. The same strategy applies to the formation of furo[2,3-b]quinolin-4(9H)-ones.     

Enantioselective synthesis of ferrocenyl nucleoside analogues with apoptosis-inducing activity

[reaction: see text] As a contribution to bioorganometallic chemistry, an enantioselective synthesis of novel carbocyclic nucleoside analogues with a ferroceno-cyclopentene backbone was developed. Diastereoselective cuprate 1,4-addition or Mukaiyama-Michael addition to a planar-chiral enoate (ethyl (E)-2-[2-methoxycarbonyl-ferrocenyl]-acrylate) allowed for the introduction of different side chains (RCH(2)). Other important steps include a Dieckmann cyclization and the attachment of the nucleobase (NB) in an iron-assisted S(N)1 reaction. Some of the target compounds were shown to exhibit significant apoptosis-inducing activity (LD(50) = 10-20 microM) against tumor cells.     

Discrimination of acoustic and turbulent components from aeroacoustic wall pressure field

The investigation of the wall pressure excitations over transportation vehicle panel is of great interest to improve the knowledge of vehicle interior noise transmission and also for future noise reduction strategies. A particularly useful task concerns the characterization and the separation of both acoustic and turbulent components of the wall pressure excitation. A new application of the Proper Orthogonal Decomposition (POD) is tested from two different databases: (i) wall pressure fields synthesized from theoretical average models and (ii) wall pressure fields obtained from Lattice Boltzmann Method numerical simulation. In each case, POD application leads to an energetic partitioning of the wall pressure field that permits to well decouple both acoustic and turbulent fields, especially for mid and high frequencies under interest. To validate such separation and to demonstrate the effectiveness of the POD method, the wavenumber spectrum analysis as well as phase analysis is successively performed. Such a new splitting method provides an instantaneous acoustic–turbulent separation of an inhomogeneous wall pressure field, suggesting many useful future applications.     

SF分子基态及低激发态势能函数与光谱常数的研究

采用含Davidson修正的内收缩多参考组态相互作用的方法和考虑相对论修正, 在价态范围内的最大相关一致基 aug-cc-pV6Z 的条件下, 对SF分子的基态²∏及几个低激发态⁴∑^-, ²∑^-, ²Δ进行了势能扫描计算. 对SF分子的势能曲线进行拟合, 得到了该分子的光谱常数R_e, ω_e, ω_eχ_e, D₀, D_e, B_e和 α_e, 通过比较发现它们与已有的实验结果较为一致. 利用SF分子的势能曲线, 通过求解双原子分子核运动的径向Schrödinger方程得到J=0 时SF分子所计算各电子态的多个振动态. 对于每一振动态, 分别计算了振动能级、惯性转动常数和离心畸变常数. 关键词： SF 势能曲线 光谱常数 分子常数     

Metric stability of trees and tight spans

We prove optimal extension results for roughly isometric relations between metric ( ${\mathbb{R}}$ R -)trees and injective metric spaces. This yields sharp stability estimates, in terms of the Gromov–Hausdorff (GH) distance, for certain metric spanning constructions: the GH distance of two metric trees spanned by some subsets is smaller than or equal to the GH distance of these sets. The GH distance of the injective hulls, or tight spans, of two metric spaces is at most twice the GH distance between themselves.     

Homogeneously non-idling schedules of unit-time jobs on identical parallel machines

In this paper, we study the basic homogeneous $m$-machine scheduling problem where weakly dependent unit-time jobs have to be scheduled within the time windows between their release dates and due dates so that, for any subset of machines, the set of the time units at which at least one machine is busy, is in interval. We first introduce the notions of pyramidal structure, $k$-hole, $m$-matching, preschedule, $k$-schedule and schedule for this problem. Then we provide a feasibility criteria for a preschedule. The key result of the paper is then to provide a structural necessary and sufficient condition for an instance of the problem to be feasible. We conclude by giving the directions of ongoing works and by bringing open questions related to different variants of the basic non-idling $m$-machine scheduling problem.