The size of the set of <Emphasis Type="Italic">μ</Emphasis>-irregular points of a measure <Emphasis Type="Italic">μ</Emphasis>

Let μ be a compactly suppported positive measure on the real line. A point x∈supp?[μ] is said to be μ-regular, if, as n→∞,

$\sup_{\deg\, (P) \le n}\left(\frac{|P(x)|}{{\|P\|}_{L_{2}(d\mu)}}\right )^{1/n}\to1.$

Otherwise it is a μ-irregular point. We show that for any such measure, the set of μ-irregular points in {μ′>0} (with a suitable definition of this set) has Hausdorff \(m_{h_{\beta}}\) measure 0, for \(h_{\beta}(t) =\left(\log \frac{1}{t}\right)^{-\beta}\), any β>1.

     

Exceptional electrochemical performance of Si-nanowires in 1,3-dioxolane solutions: a surface chemical investigation

The effect of 1,3-dioxolane (DOL) based electrolyte solutions (DOL/LiTFSI and DOL/LiTFSI-LiNO(3)) on the electrochemical performance and surface chemistry of silicon nanowire (SiNW) anodes was systematically investigated. SiNWs exhibited an exceptional electrochemical performance in DOL solutions in contrast to standard alkyl carbonate solutions (EC-DMC/LiPF(6)). Reduced irreversible capacity losses, enhanced and stable reversible capacities over prolonged cycling, and lower impedance were identified with DOL solutions. After 1000 charge-discharge cycles (at 60 °C and a 6 C rate), SiNWs in DOL/LiTFSI-LiNO(3) solution exhibited a reversible capacity of 1275 mAh/g, whereas only 575 and 20 mAh/g were identified in DOL/LiTFSI and EC-DMC solutions, respectively. Transmission electron microscopy (TEM) studies demonstrated the complete and uniform lithiation of SiNWs in DOL-based electrolyte solutions and incomplete, nonuniform lithiation in EC-DMC solutions. In addition, the formation of compact and uniform surface films on SiNWs cycled in DOL-based electrolyte solutions was identified by scanning electron microscopic (SEM) imaging, while the surface films formed in EC-DMC based solutions were thick and nonuniform. X-ray photoelectron spectroscopy (XPS) and Fourier transform infrared (FTIR) spectroscopy were employed to analyze the surface chemistry of SiNWs cycled in EC-DMC and DOL based electrolyte solutions. The distinctive surface chemistry of SiNWs cycled in DOL based electrolyte solutions was found to be responsible for their enhanced electrochemical performances.     

Effect of fluoroethylene carbonate (FEC) on the performance and surface chemistry of Si-nanowire Li-ion battery anodes

The effect of FEC as a co-solvent on the electrochemical performance and surface chemistry of silicon nanowire (SiNW) anodes was thoroughly investigated. Enhanced electrochemical performance was observed for SiNW anodes in alkyl carbonates electrolyte solutions containing fluoroethylene carbonate (FEC). Reduced irreversible capacity losses accompanied by enhanced and stable reversible capacities over prolonged cycling were achieved with FEC-containing electrolyte solutions. TEM studies provided evidence for the complete and incomplete lithiation of SiNW's in FEC-containing and FEC-free electrolyte solutions, respectively. Scanning electron microscopy (SEM) results proved the formation of much thinner and compact surface films on SiNW's in FEC-containing solutions. However, thicker surface films were identified for SiNW electrodes cycled in FEC-free solutions. SiNW electrodes develop lower impedance in electrolyte solutions containing FEC in contrast to standard (FEC-free) solutions. The surface chemistry of SiNW electrodes cycled in FEC-modified and standard electrolytes were investigated using X-ray photoelectron spectroscopy (XPS) and Fourier transform infrared (FTIR) spectroscopy. The impact of FEC as a co-solvent on the electrochemical behavior of SiNW electrodes is discussed herein in light of the spectroscopic and microscopic studies.     

Automated counting of lego towers

H.N.V. Temperley's method for counting vertically convex polyominoes is modified, generalized, and most importantly, programmed (in Maple).     

How to gamble if you're in a hurry

The beautiful theory of statistical gambling, started by Dubins and Savage (for subfair games) and continued by Kelly and Breiman (for superfair games), has mostly been studied under the unrealistic assumption that we live in a continuous world, that money is indefinitely divisible and that our life is indefinitely long. Here, we study these fascinating problems from a purely discrete, finitistic and computational viewpoint, using both symbol-crunching and number-crunching (and simulation just for checking purposes).     

Bulk universality holds in measure for compactly supported measures

Let μ be a measure with compact support, with orthonormal polynomials {p _n } and associated reproducing kernels {K _n }. We show that bulk universality holds in measure in {ξ: μ′(ξ) > 0}. More precisely, given ɛ, r > 0, the linear Lebesgue measure of the set {ξ: μ′(ξ) > 0} and for which

Characterizations of self-combustion reactions (SCR) for the production of nanomaterials used as advanced cathodes in Li-ion batteries

In this work, self-combustion reactions (SCR) for the preparation of important cathode materials for rechargeable Li-ion batteries were investigated by thermal analytical tools (DSC, ARC, TGA), electron microscopy, XRD, various spectroscopies (MS, Raman, FTIR) and elemental analysis by ICP. The systems studied include solutions containing metal nitrates at the right stoichiometry and sucrose as a fuel, for the preparation of LiMn_0.5Ni_0.5O₂ (layered), LiMn_1.5Ni_0.5O₄ (spinel), LiMn_0.33Ni_0.33Co_0.33O₂ (layered), and LiMn_0.4Ni_0.4Co_0.2O₂ (layered). Similar products, which do not depend on the atmosphere of the processes (air or inert) were obtained by spontaneous SCR and the gradual heating of the same solutions by DSC, ARC, and TGA. The reactions involve the partial caramelization of sucrose, complicated by red-ox reactions with the nitrates that form solid products, whose organic part is finally decomposed around 400 °C. The presence of cobalt ions has a stabilizing effect, which is expressed by the low dissolution rates of Li ions from the solid products thus formed, into aqueous solutions. The reaction mechanisms are discussed herein.     

Photoabsorption on 4He with a realistic nuclear force

The 4He total photoabsorption cross section is calculated with the realistic nucleon-nucleon potential Argonne V18 and the three-nucleon force (3NF) Urbana IX. Final state interaction is included rigorously via the Lorentz integral transform method. A rather pronounced giant resonance with peak cross sections of 3.0 (3.2) mb is obtained with (without) the 3NF. Above 50 MeV strong 3NF effects, up to 35%, are present. Good agreement with experiment is found close to threshold. A comparison in the giant resonance region is inconclusive, since data do not show a unique picture.     

Ultrasensitive Detection of Salmonella and Listeria monocytogenes by Small‐Molecule Chemiluminescence Probes

Detection of Salmonella and L. monocytogenes in food samples by current diagnostic methods requires relatively long time to results (2–6 days). Furthermore, the ability to perform environmental monitoring at the factory site for these pathogens is limited due to the need for laboratory facilities. Herein, we report new chemiluminescence probes for the ultrasensitive direct detection of viable pathogenic bacteria. The probes are composed of a bright phenoxy‐dioxetane luminophore masked by triggering group, which is activated by a specific bacterial enzyme, and could detect their corresponding bacteria with an LOD value of about 600‐fold lower than that of fluorescent probes. Moreover, we were able to detect a minimum of 10 Salmonella cells within 6 h incubation. The assay allows for bacterial enrichment and detection in one test tube without further sample preparation. We anticipate that this design strategy will be used to prepare analogous chemiluminescence probes for other enzymes relevant to specific bacteria detection and point‐of‐care diagnostics.