Integral operators commuting with dilations and rotations in generalized Morrey-type spaces

We find conditions for the boundedness of integral operators $K$ commuting with dilations and rotations in a local generalized Morrey space. We also show that under the same conditions, these operators preserve the subspace of such Morrey space, known as vanishing Morrey space. We also give necessary conditions for the boundedness when the kernel is non-negative. In the case of classical Morrey spaces, the obtained sufficient and necessary conditions coincide with each other. In the one-dimensional case, we also obtain similar results for global Morrey spaces. In the case of radial kernels, we also obtain stronger estimates of $Kf$ via spherical means of $f$. We demonstrate the efficiency of the obtained conditions for a variety of examples such as weighted Hardy operators, weighted Hilbert operator, their multidimensional versions, and others.     

Synthesis,characterization, and phase transition of an inorganic-organic hybrid compound,[(3-nitroanilinium+) (18-crown-6)] [IO4-](CH3OH)

A novel inorganic-organic hybrid supramolecular compound,[(3-nitroanilinium~+)(18-crown-6)][IO_4](CH_3OH)(1),was discovered as phase-transition materials displaying dielectric anomalous behaviors.The yellow block crystal formed by N-H…O hydrogen bonding that made contact through the cavity of 18-crown-6 was characterized by single-crystal X-ray diffraction,elemental analysis,infrared analysis,thermogravimetric analysis,differential scanning calorimetry,and potential-energy calculations.Differential scanning calorimetry measurements indicate that the compound experiences a reversible phase transition at around 220 K.Temperature-dependent dielectric measurements further confirm the phase transitions.Potential-energy calculations demonstrate that the phase transition occurs due to the molecular order-disorder rotation of CH_3OH,whereas the space grouping of the crystal remains unchanged.     

问题视角浅析

文中通过多视角分析解决数学问题,向学习者渗透了数学思想的辩证性和学习方法的灵活性,体现了"以人为本"现代理念下的数学教育.     

Measuring grain rotation at the nanoscale

In this paper, we introduced a method to measure grain rotation of nanomaterials under external stress using a high pressure diamond anvil cell and the Laue microdiffraction technique at a synchrotron facility. We used tungsten carbide marker crystals to investigate grain rotation activities of 3 and 500?nm nickel media. Our results show that the grain rotation of 3 and 500?nm nickel nanocrystals increase with pressure and finally rotation of 500?nm nickel tends to stop at a lower pressure/stress level than 3?nm nickel. 3?nm nickel nanocrystals show a higher rotation magnitude than 500?nm nickel nanocrystals. Our measurements show an effective method to study the grain rotation of nanomaterials especially in ultrafine nanocrystals.     

Synthesis and Stereochemistry of Optically Active Selenium and Tellurium Compounds

Abstract

The synthesis and stereochemistry of tricoordinated optically active selenium and tellurium compounds are described. Telluronium salts, telluronium imides, and seleninic acids were prepared and optically resolved by fractional recrystallization of diastereomeric mixtures or by chromatography using a chiral column of racemic mixtures. Diphenyl dichalcogenides also were optically resolved by chiral crystallization. Their absolute configurations were determined or estimated based on X-ray crystallographic analysis, specific rotations, and circular dichroism spectra. The kinetic studies and the mechanism for the racemization were also studied.     

A NEW SYSTEM EXHIBITING A HIGH BARRIER TO ROTATION ABOUT THE P—N BOND. SYNTHESES AND SPECTRAL STUDIES OF 1,3,2-DIAZAPHOSPHETIDIN-4-ONE DERIVATIVES

Abstract

1,3,2-Diazaphosphetidin-4-one derivatives were synthesized. Their ¹H NMR signals at ambient temperature displaed a broad doublet which eventually coalesced before becoming sharp upon warming, and the ¹³C NMR spectra also showed that the α-and β-carbons of the dialkylamino group were non-equivalent. The phenomena were ascribed to restricted rotation about the exocyclic P—N bond.     

Recent Advances of AIE-Active Conjugated Polymers: Synthesis and Application

Conjugated polymers (CPs) have long been recognized as an important class of materials. The highly conjugated backbone of the CPs will facilitate the rapid exciton migration and result in amplification of fluorescence signals. However, CPs are likely to aggregate and form excimers in solid states, directly leading to the fluorescence quenching, namely aggregation-caused quenching (ACQ), hence inhibiting their prospective utilizations in a large degree. Since the effect of aggregation-induced emission (AIE) is opposite to that of notorious ACQ, the AIE has raised great attention from scientists. CPs with AIE or aggregation-enhanced emission (AEE) features may help to solve the ACQ problem and meanwhile impart polymers with new properties and practical applications. In this review, we summarize the recent progress on the preparation of CPs with AIE or AEE characteristics, where AIE-active luminogens are located at polymer backbones or pendants. Their potential applications including fluorescent sensors, biological probes, and active layers for the fabrication of light-emitting diodes are also described.     

Preparation and Characterization of New Optically Active Poly(amide-imide)s from N,N′-(bicyclo[2,2,2]oct-7-ene-2,3,5,6-tetra carboxylic)-bis-L-isoleucine and Aromatic Diamines

Five new optically active aromatic poly(amide-imide)s (PAIs) 5a–e were prepared from a direct polycondensation reaction of a new diacid of N,N′-(bicyclo[2,2,2]oct-7-ene-2,3,5,6-tetra carboxylic)-bis-L-isoleucine 3 with various aromatic diamines 4a–e in a medium consisting of triphenyl phosphite (TPP), calcium chloride (CaCl₂), pyridine (Py) and N-methyl-2-pyrrolidone (NMP). The polycondensation reaction produced a series of novel poly(amid-imide)s 5a–e in quantitative yields with inherent viscosities of 0.39–0.51 dL/g. The resulting polymers were fully characterized by means of ¹H-NMR, FT-IR spectroscopy, elemental analyses, inherent viscosity, solubility test, specific rotation and thermal properties of them were investigated using TGA/DTG and differential scanning calorimeter (DSC). The diacid 4 was synthesized by the condensation reaction of bicyclo[2,2,2]oct-7-ene-2,3,5,6- tetracarboxylic dianhydride 1 with L-isoleucine 2 in acetic acid solution.     

Modelling phenolic and technological maturities of grapes by means of the multivariate relation between organoleptic and physicochemical properties

The ripeness of grapes at the harvest time is one of the most important parameters for obtaining high quality red wines. Traditionally the decision of harvesting is to be taken only after analysing sugar concentration, titratable acidity and pH of the grape juice (technological maturity). However, these parameters only provide information about the pulp ripeness and overlook the real degree of skins and seeds maturities (phenolic maturity). Both maturities, technological and phenolic, are not simultaneously reached, on the contrary they tend to separate depending on several factors: grape variety, cultivar, adverse weather conditions, soil, water availability and cultural practices. Besides, this divergence is increasing as a consequence of the climate change (larger quantities of CO₂, less rain, and higher temperatures).