A note on the weighted norm inequality for the one-sided maximal operator

Let be the one-sided maximal function. In this note we obtain some necessary and sufficient conditions in order that the weighted weak type inequality holds for . Meanwhile, some necessary or sufficient conditions for the weighted inequality for are given.

     

Detailed analysis of α,ω-bis(4-hydroxybutyl) poly(dimethylsiloxane) using GPC-MALDI TOF mass spectrometry

In this study the prepolymer alpha,omega-bis(4-hydroxybutyl) poly(dimethylsiloxane), used in the formulation of oxygen permeable films, is evaluated by gel permeation chromatography (GPC) combined with matrix assisted laser desorption ionization (MALDI) time of flight (TOF) mass spectrometry (MS). Two unexpected mass distributions are observed in the mass spectra. Reaction schemes for the formation of these distributions are proposed. A solution phase trimethylsilane end group modification was performed on the prepolymer to determine whether the unexpected mass distributions occur as impurities from synthesis or as artifacts from the MS process. Evaluation of the TMS modified prepolymer indicates the unexpected mass distributions indeed occur as impurities from the synthetic procedure. Average molecular weight values are determined by traditional GPC, direct MALDI-TOF MS, and GPC-MALDI-TOF MS methods and the results are compared.     

离子注入修饰电极检测硝基苯

离子注入是一种新技术，可按人们的意愿和需要，将不同的离子注入不同的基本电极表面，制成具有催化活性强，稳定性高，重现性好等特点的修饰电极。作者研究了离子注入钴和注入镍的玻碳电极在０．１ｍｏｌ／ＬＨＡｃ－ＮａＡｃ缓冲溶液中硝基苯的行为及测定。     

Chromatographic characterization of molecularly imprinted microspheres for the separation and determination of trimethoprim in aqueous buffers

Molecularly imprinted microspheres (MIMs) against trimethoprim (TMP), prepared by aqueous microsuspension polymerization, bound strongly to TMP, by electrostatic and other non-covalent interactions. The effects of pH, kind and ionic strength (I) of buffer on capacity factors (k') have been discussed in detail. The capacity factors for TMP increased with increasing pH of both acetate and phosphate buffers. The effects of ionic strength on capacity factors were very substantial and the linear relationship between logk' and logI was described by the equation logk'=0.3162-0.4420logI with R=-0.9995. The results showed that pH 3.5 acetate buffer (0.05 mol L(-1)) containing 0.1 mol L(-1) sodium chloride and a 1:9 ratio of buffer to methanol were the optimum conditions for separation and determination of TMP. The calibration plot of peak area against concentration was linear with R=0.9979.     

A unique spherical molecular host with D2d symmetry. A novel intramolecular kinetic equilibrium in metal ion complexation between two crown ethers

[formula: see text] A spherical host with D2d symmetry consisting of a tetrathia[3.3.3.3]paracyclophane and two 18-crown-6 moieties was synthesized. Its crystal structure shows a central cavity with a diameter of 1.96 A and a depth of 6.75 A. A Na+ ion could rest in the cavity center but prefers core binding to external binding in one of the crown units. An intramolecular kinetic equilibrium was reached with the Na+ ion switching between the two crown units with an energy barrier of 14.1 +/- 3 kcal/mol.     

Synthesis and Electrochemical Studies of Spinel LiNi1−xMnxVO4

Spinel compound LiNi_1−xMn_xVO₄ (0≤x≤0.4) had been prepared by using the moist chemical method. X-ray diffraction spectra showed that the lattice constant increased with x in the LiNi_1−xMn_xVO₄, XPS spectra indicating that Li1s had a chemical shift towards lesser binding energy, and manganese in LiNi_1−xMn_xVO₄ existing as the mixed valence of Mn²⁺ and Mn³⁺. The electrochemical charge and discharge testing at a current density of 0.1 mA/cm² between the potentials of 4.0 and 3.0 V vs Li/Li⁺ in 1 mol/dm³ LiPF₆/EC+DEC (1:1 by volume) at 25°C showed that LiNi_1−xMn_xVO₄ cell has a better rechargeability, but a lower cell voltage of 4.0 V vs Li/Li⁺ than that without the doping sample, and the capacity and the cycle efficiency of the Li/LiNi_1−xMn_xVO₄ cells increased with x in the LiNi_1−xMn_xVO₄.     

RNA Methylation m6A: A New Code and Drug Target?

The m⁶A‐RNA modification is a dynamic and reversible process, which has emerged as a new RNA code for the regulation of gene expression. The functional network of methyltransferases (writers), demethylases (erasers), and binding proteins (readers) modulate the level of m⁶A modification. Dysfunction of RNA methylation has been associated with various fundamental biological processes and human diseases. Herein, we briefly introduce an understanding‐enabled manipulation on m⁶A‐RNA modification with an emphasis on the use of small‐molecule intervention.      

Diffraction techniques for nonlamellar phases of phospholipids

A neutron diffraction method applicable to nonlamellar phases of substrate-supported lipid membranes is described and validated. When prepared on a flat substrate, the resulting nonlamellar phases have layered symmetry which provides some advantages over powder diffraction for detailed structure determination. This approach recently led to the detection of a rhombohedral phase and a distorted hexagonal phase of lipids. Here the determination of intensity and phase information for such phases is demonstrated by application to the hexagonal phase of diphytanoyl phosphatidylcholine (DPhPC). The hexagonal symmetry is used to verify the data reduction procedure for the intensities of the diffraction peaks. Diffraction intensities measured while varying the D2O/H2O ratio in the relative humidity was used to solve the phase problem. The neutron scattering length density distribution of the hexagonal phase was constructed and analyzed to elucidate the packing of the lipid molecules. The structure of DPhPC in the hexagonal phase is of interest in connection with its stalk structure in the rhombohedral phase. We also found that the incorporation of tetradecane into the DPhPC hexagonal phase is limited, similar to the case for dioleoyl phosphatidylethanolamine.