Explicit estimates of sums related to the Nyman–Beurling criterion for the Riemann Hypothesis

We give an estimate for sums appearing in the Nyman–Beurling criterion for the Riemann Hypothesis. These sums contain the Möbius function and are related to the imaginary part of the Estermann zeta function. The estimate is remarkably sharp in comparison to other sums containing the Möbius function. The bound is smaller than the trivial bound – essentially the number of terms – by a fixed power of that number. The exponent is made explicit. The methods intensively use tools from the theory of continued fractions and from the theory of Fourier series.     

Ionic Conductivity of β‐Cyclodextrin–Polyethylene‐Oxide/Alkali‐Metal‐Salt Complex

Highly conductive, crystalline, polymer electrolytes, β‐cyclodextrin (β‐CD)–polyethylene oxide (PEO)/LiAsF₆ and β‐CD–PEO/NaAsF₆, were prepared through supramolecular self‐assembly of PEO, β‐CD, and LiAsF₆/NaAsF₆. The assembled β‐CDs form nanochannels in which the PEO/X⁺ (X=Li, Na) complexes are confined. The nanochannels provide a pathway for directional motion of the alkali metal ions and, at the same time, separate the cations and the anions by size exclusion.     

Multiwave interaction solutions for a (3+1)-dimensional generalized Kadomtsev-Petviashvili equation

To construct a class of new multiwave interaction solutions for the (3+1)-dimensional generalized Kadomtsev-Petviashvili equation, we calculate different types of interaction solutions among solitons, periodic waves and rational waves using the direct algebraic method together with the inheritance solving skill. Moreover, a new algorithm is proposed with the aid of the simplified Hirota method, the conjugated parameters assignment and long wave limit strategies, from which multiwave interaction solutions among solitons, breathers and lump waves are generated.     

Controlled Self-Assembly of Metallacycle-Bridged Gold Nanoparticles for Surface-Enhanced Raman Scattering

In this work, well-defined two-dimensional metallacycles have been successfully employed for the well-controlled self-assembly of gold nanoparticles (AuNPs) into discrete clusters such as dimers, trimers, tetramers, pentamers and even hexamers at the water–oil interface for the first time. Furthermore, the modular construction of metallacycle molecules allows precise control of spacing between the gold nanoparticles. Interestingly, it was found that interparticle spacing below 5 nm created by molecular metallacycles in the resultant discrete gold nanoparticle clusters led to a strong plasmon coupling, thus inducing great field enhancement inside the gap between the NPs. More importantly, different discrete clusters with precise interparticle spacing provide a well-defined system for studying the hot-spot phenomenon in surface-enhanced Raman scattering (SERS); this revealed that the SERS effects were closely related to the interparticle spacing.     

Enantioselective Synthesis of Isoxazolines Enabled by Palladium-Catalyzed Carboetherification of Alkenyl Oximes

Reported here is a highly efficient Pd/Xiang-Phos catalyzed enantioselective carboetherification of alkenyl oximes with either aryl or alkenyl halides, delivering various chiral 3,5-disubstituted and 3,5,5-trisubstituted isoxazolines in good yields with up to 97 % ee. The sterically bulky and electron-rich (S,Rs)- NMe-X2 ligand is responsible for the excellent reactivities and enantioselectivities. The salient features of this transformation include mild reaction conditions, general substrate scope, good functional-group tolerance, good yields, high enantioselectivities, easy scale-up, and application in the late-stage modification of bioactive compounds. The obtained products can be readily transformed into useful chiral 1,3-aminoalcohols.     

3D Electron Diffraction Unravels the New Zeolite ECNU-23 from the “Pure” Powder Sample of ECNU-21

A novel crystalline high-silica zeolite with 12×8-membered ring (R) channel system is prepared with the aid of the 3D electron diffraction (3D ED) technique. A crystal with the same topology as one of the predicted daughter structures of CIT-13 germanosilicate, named ECNU-23 (East China Normal University 23) was coincidentally detected by the 3D ED investigation during the structure characterization of the “pure” powder sample of existing one-dimension (1D) 10-R ECNU-21. By controlling the alkaline-assisted hydrolysis under moderate conditions, we purified the phase of ECNU-23 by selectively breaking and removing the chemically weak Ge(Si)-O-Ge and metastable Si-O-Si bonds. Its structure was determined based on the 3D ED data, and confirmed by high-resolution TEM images and powder X-ray diffraction (PXRD) data. The aluminosilicate Al-ECNU-23 shows unique catalytic properties in the isomerization/ disproportionation of m-xylene as solid-acid catalyst.     

Optimal spectral phase control of femtosecond laser-induced up-conversion luminescence in Sm^3+:NaYF4 glass

The spectral phase of the femtosecond laser field is an important parameter that affects the up-conversion(UC)luminescence efficiency of dopant lanthanide ions.In this work,we report an experi-mental study on controlling the UC lmiiinescence efficiency in Sm^3+:NaYF4 glass by 800-nm femtosec-ond laser pulse shaping using spectral phase modulation.The optimal phase control strategy efficiently enhances or suppresses the UC luminescence intensity.Based on the laser-power dependence of the UC luminescence intensity and its comparison with the luminescence spectrum under direct 266-nm fem-tosecond lciser irradiation,we propose herein an excitation model combining non-resonant two-photon absorption with resonance-media ted three-photon absorption to explain the experimental observations.     

化妆品中的肽化学*

随着科技进步和产业提升,人们不断从本源上追求美、从长效上保持美、从机制上激发美。众多肽类化合物,已被证实在人体内具有独特的生物学促进或抑制作用,也因此被广泛应用于美妆产品。以化妆品中生物活性肽的不同功效为主线,对其化学结构进行分析并阐述其中的生理作用机制。