Global existence and time decay of the non-cutoff Boltzmann equation with hard potential

This paper is concerned with the Cauchy problem on the Boltzmann equation without angular cutoff assumption for hard potential in the whole space. When the initial data is a small perturbation of a global Maxwellian, the global existence of solution to this problem is proved in unweighted Sobolev spaces $H^N\left({\mathbb{R}}_{x,v}^6\right)$ with $N\ge 2$. But if we want to obtain the optimal temporal decay estimates, we need to add the velocity weight function, in this case the global existence and the optimal temporal decay estimate of the Boltzmann equation are all established. Meanwhile, we further gain a more accurate energy estimate, which can guarantee the validity of the assumption in Chen et al. (0000).     

从知识传授到育人:高职“生活中的化学”教学实践*

深挖高职院校公选课“生活中的化学”的育人元素,精心设计教学内容,运用课堂主题辩论、趣味生活实验的设计与展示、探秘生活中的化学等理论知识传授与课内外实践相结合的教学方式,实现全过程育人,充分展现了公选课在立德树人方面的价值。     

Regularity of optimal sets for some functional involving eigenvalues of an operator in divergence form

In this paper we consider minimizers of the functional$\min \{{\lambda }_1(\mathrm{\Omega })+\cdots +{\lambda }_k(\mathrm{\Omega })+\mathrm{\Lambda }|\mathrm{\Omega }|,:\mathrm{\Omega }\subset D\text{ open}\}$ where $D\subset {\mathbb{R}}^d$ is a bounded open set and where $0<{\lambda }_1(\mathrm{\Omega })\le \cdots \le {\lambda }_k(\mathrm{\Omega })$ are the first k eigenvalues on Ω of an operator in divergence form with Dirichlet boundary condition and with Hölder continuous coefficients. We prove that the optimal sets ${\mathrm{\Omega }}^{⁎}$ have finite perimeter and that their free boundary $\partial {\mathrm{\Omega }}^{⁎}\cap D$ is composed of a regular part, which is locally the graph of a $C^{1,\alpha }$-regular function, and a singular part, which is empty if $d<d^{⁎}$, discrete if $d=d^{⁎}$ and of Hausdorff dimension at most $d-d^{⁎}$ if $d>d^{⁎}$, for some $d^{⁎}\in \{5,6,7\}$.     

Dark Energy with Phantom Crossing and the H0 Tension

We investigate the possibility of phantom crossing in the dark energy sector and the solution for the Hubble tension between early and late universe observations. We use robust combinations of different cosmological observations, namely the Cosmic Microwave Background (CMB), local measurement of Hubble constant (H0), Baryon Acoustic Oscillation (BAO) and SnIa for this purpose. For a combination of CMB+BAO data that is related to early universe physics, phantom crossing in the dark energy sector was confirmed at a 95% confidence level and we obtained the constraint H0=71.0−3.8+2.9 km/s/Mpc at a 68% confidence level, which is in perfect agreement with the local measurement by Riess et al. We show that constraints from different combinations of data are consistent with each other and all of them are consistent with phantom crossing in the dark energy sector. For the combination of all data considered, we obtained the constraint H0=70.25±0.78 km/s/Mpc at a 68% confidence level and the phantom crossing happening at the scale factor am=0.851−0.031+0.048 at a 68% confidence level.     

Portable single-sided NMR measurements at variable temperatures: Implementation of a thermo-controlled device and application to the heating of bread dough

A temperature control unit was implemented to vary the temperature of samples studied on a commercial Mobile Universal Surface Explorer nuclear magnetic resonance (MOUSE-NMR) apparatus. The device was miniaturized to fit the maximum MOUSE sampling depth (25 mm). It was constituted by a sample holder sandwiched between two heat exchangers placed below and above the sample. Air was chosen as the fluid to control the temperature at the bottom of the sample, at the interface between the NMR probe and the sample holder, in order to gain space. The upper surface of the sample was regulated by the circulation of water inside a second heat exchanger placed above the sample holder. The feasibility of using such a device was demonstrated first on pure water and then on several samples of bread dough with different water contents. For this, T1 relaxation times were measured at various temperatures and depths and were then compared with those acquired with a conventional compact closed-magnet spectrometer. Discussion of results was based on biochemical transformations in bread dough (starch gelatinization and gluten heat denaturation). It was demonstrated that, within a certain water level range, and because of the low magnetic field strength of the MOUSE, a linear relationship could be established between T1 relaxation times and the local temperature in the dough sample.     

A Far-Red Emitting Fluorescent Chemogenetic Reporter for In Vivo Molecular Imaging

Far-red emitting fluorescent labels are highly desirable for spectral multiplexing and deep tissue imaging. Here, we describe the generation of frFAST (far-red Fluorescence Activating and absorption Shifting Tag), a 14-kDa monomeric protein that forms a bright far-red fluorescent assembly with (4-hydroxy-3-methoxy-phenyl)allylidene rhodanine (HPAR-3OM). As HPAR-3OM is essentially non-fluorescent in solution and in cells, frFAST can be imaged with high contrast in presence of free HPAR-3OM, which allowed the rapid and efficient imaging of frFAST fusions in live cells, zebrafish embryo/larvae, and chicken embryos. Beyond enabling the genetic encoding of far-red fluorescence, frFAST allowed the design of a far-red chemogenetic reporter of protein–protein interactions, demonstrating its great potential for the design of innovative far-red emitting biosensors.     

Influence of Polarity and Activation Energy in Microwave–Assisted Organic Synthesis (MAOS)

The aim of this work was to determine the parameters that have decisive roles in microwave-assisted reactions and to develop a model, using computational chemistry, to predict a priori the type of reactions that can be improved under microwaves. For this purpose, a computational study was carried out on a variety of reactions, which have been reported to be improved under microwave irradiation. This comprises six types of reactions. The outcomes obtained in this study indicate that the most influential parameters are activation energy, enthalpy, and the polarity of all the species that participate. In addition to this, in most cases, slower reacting systems observe a much greater improvement under microwave irradiation. Furthermore, for these reactions, the presence of a polar component in the reaction (solvent, reagent, susceptor, etc.) is necessary for strong coupling with the electromagnetic radiation. We also quantified that an activation energy of 20–30 kcal mol⁻¹ and a polarity (μ) between 7–20 D of the species involved in the process is required to obtain significant improvements under microwave irradiation.     

地理国情普查地表覆盖内业解译的质量问题研究

地表覆盖内业解译是地理国情普查的一道重要工序。地理国情地表覆盖内业解译现存图斑平面位置精度不足、分类错误多种多样等普遍问题,问题突出典型。文中针对这些问题图文并茂、清晰明了的进行了说明,并从多方面分析问题产生的原因,提出加强对技术指标和采集原则的学习和理解,加强内业与外业的结合,充分发挥解译样本的作用等建议,以有效提高内业解译的质量。     

3维Maxwell方程局部1维多辛格式的能量恒等式

在理想导体边界条件下,对3维Maxwell方程的局部1维多辛Preissman格式的能量守恒性质进行研究.运用能量分析法推导了2个能量恒等式,这些恒等式说明了给出的格式在所定义的离散范数下是能量守恒和无条件稳定的,数值算例验证了结论的正确性.     

Plasmon Coupling-Induced Hot Electrons for Photocatalytic Hydrogen Generation

We present the fabrication of core-shell-satellite Au@SiO₂-Pt nanostructures and demonstrate that LSPR excitation of the core Au nanoparticle can induce plasmon coupling effect to initiate photocatalytic hydrogen generation from decomposition of formic acid. Further studies suggest that the plasmon coupling effect induces a strong local electric field between the Au core and Pt nanoparticles on the SiO₂ shell, which enables creation of hot electrons on the non-plasmonic-active Pt nanoparticles to participate hydrogen evolution reaction on the Pt surface. In addition, small SiO₂ shell thickness is required in order to obtain a strong plamon coupling effect and achieve efficient photocatalytic activities for hydrogen generation.