一类非线性发展方程的精确解

利用hirota双线性法,得到(3+1)维孤子方程、(3+1)维KP-Boussinesq方程、(2+1)维修正Caudrey-Dodd-Gibbon-Kotera-S awada方程、Hirota-Satsuma浅水波方程的精确解,并做出一部分解的图形,进一步研究解的结构和性质.     

A normalized solitary wave solution of the Maxwell-Dirac equations

We prove the existence of a $L^2$-normalized solitary wave solution for the Maxwell-Dirac equations in (3+1)-Minkowski space. In addition, for the Coulomb-Dirac model, describing fermions with attractive Coulomb interactions in the mean-field limit, we prove the existence of the (positive) energy minimizer.     

硅和锗纳米线的原子排布和电荷分布的密度泛函紧束缚方法研究

低维硅锗材料是制备纳米电子器件的重要候选材料，是研发高效率、低能耗和超高速新一代纳米电子器件的基础材料之一，有着潜在的应用价值。采用密度泛函紧束缚方法分别对厚度相同、宽度在0.272 nm~0.554 nm之间的硅纳米线和宽度在0.283 nm~0.567 nm之间的锗纳米线的原子排布和电荷分布进行了计算研究。硅、锗纳米线宽度的改变使原子排布，纳米线的原子间键长和键角发生明显改变。纳米线表层结构的改变对各层内的电荷分布产生重要影响。纳米线中各原子的电荷转移量与该原子在表层内的位置相关。纳米线的尺寸和表层内原子排列结构对体系的稳定性产生重要影响。     

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 $d^{⁎}\in \{5,6,7\}$.     

Well-posedness of two pseudo-parabolic problems for electrical conduction in heterogeneous media

We prove a well-posedness result for two pseudo-parabolic problems, which can be seen as two models for the same electrical conduction phenomenon in heterogeneous media, neglecting the magnetic field. One of the problems is the concentration limit of the other one, when the thickness of the dielectric inclusions goes to zero. The concentrated problem involves a transmission condition through interfaces, which is mediated by a suitable Laplace-Beltrami type equation.     

游客情感计算的文本大数据挖掘方法比较研究

旅游文本大数据以其方便、快捷和低门槛的特点为游客情感计算提供了极大便利，已经成为旅游大数据的主要来源之一。基于大数据理论和情感理论，以文本大数据为数据源，在全面梳理国内外情感计算相关成果的基础上，利用人工智能中的逻辑/算法编程方法、机器学习方法、深度学习方法对旅游文本大数据进行挖掘，探索最佳的基于文本大数据的游客情感计算方法。研究发现：（1）基于情感词典的游客情感计算模型，其核心是构建情感词典和设计情感计算规则，方法简单，容易实现，适用语料范围广。（2）机器学习，用统计学方法抽取文本中的特征项，具有非线性特征，可靠性较线性特征的情感词典方法高。（3）基于深度学习技术的游客情感计算，效果良好，准确率在85%以上。训练多领域的文本语料易于移植，实用性强，且泛化能力好，较适合大数据时代游客情感计算研究。     

High-efficient surface tailoring via reverse atom transfer radical polymerization and reversible addition-fragmentation chain-transfer polymerization in an aqueous system initiated by a monocenter redox pair

The commonly used multi-center initiation methods always lead to the formation of quantities of homopolymer in the surface tailoring based on reverse atom transfer radical polymerization (ATRP) and reversible addition-fragmentation chain-transfer (RAFT) polymerization. In this study, a monocenter redox pair constructed of silica bearing tert-butyl hydroperoxide groups and ascorbic acid (SiO₂-TBHP/AsAc) was applied to substitute the commonly used initiation method of R-supported RAFT grafting polymerization. All the propagating radicals were restricted on the surface of solid particles during the whole procedure theoretically, resulting in a higher grafting efficiency of 95.1% combined with the “controllable” feature at 10 h. This redox pair was also used to initiate the reverse ATRP in miniemulsion successfully with a grafting efficiency of 86.3% at 10 h. The grafting efficiency obtained under this monocenter initiation method was significantly higher than that of the frequently reported surface modification by reverse ATRP and RAFT polymerization. In addition, the high-efficient surface tailoring was traced and confirmed by nuclear magnetic resonance, Fourier transform infrared, X-ray photoelectron spectroscopy, thermogravimetric analysis, transmission electron microscopy, and other analysis tests. The advantage of this monocenter redox pair will open a new avenue for the potential “high-efficient” surface tailoring of various materials.     

Design consideration and modelling studies of ultrasound and ultraviolet combined approach for shelf-life enhancement of pine apple juice

Although both ultraviolet (UV) radiation and ultrasound (US) treatment have their capabilities in microbial inactivation, applying any one method alone may require a high dose for complete inactivation, which may affect the sensory and nutritional properties of pineapple juice. Hence, this study was intended to analyse and optimise the effect of combined US and UV treatments on microbial inactivation without affecting the selected quality parameters of pineapple juice. US treatment (33 kHz) was done at three different time intervals, viz. 10 min, 20 min and 30 min., after which, juice samples were subjected to UV treatment for 10 min at three UV dosage levels, viz. 1 J/cm², 1.3 J/cm², and 1.6 J/cm². The samples were evaluated for total colour difference, pH, total soluble solids (TSS), titrable acidity (TA), and ascorbic acid content; total bacterial count and total yeast count; and the standardization of process parameters was done using Response Surface Methodology and Artificial Neural Network. The results showed that the individual, as well as combined treatments, did not significantly impact the physicochemical properties while retaining the quality characteristics. It was observed that combined treatment resulted in 5 log cycle reduction in bacterial and yeast populations while the individual treatment failed. From the optimization studies, it was found that combined US and UV treatments with 22.95 min and1.577 J/cm² ensured a microbiologically safe product while retaining organoleptic quality close to that of fresh juice.     

The impact of insecticides containing deltamethrin and cyfluthrin on the composition of surface compounds in the larvae,females and males of Tenebrio molitor

This paper presents the effect of insecticides on the composition of the surface compounds of one of the most harmful insects, Tenebrio molitor, by analysis using GC–MS. As a result of the use of insecticides, the composition of the chemical compounds on the surface of insects changes, depending on the insecticides used. The most numerous groups of the marked compounds were fatty acids, alkanes, esters and sterols. The content of the identified compounds in the larvae increased at both 24 and 48 h after the application of insecticides, in comparison with the control samples. The content of identified compounds in the samples taken from the females increased 24, 48 and 72 h after the application of insecticides in comparison with the control samples. By contrast, in samples prepared from males, the content of identified compounds decreased 24 h after the application of insecticides, compared with the control samples. The highest content of chemical compounds was for fatty acids and alkanes after the use of insecticides. The content of fatty acids after the application of the insecticide with deltamethrin was 62.1 ± 3.3–466.9 ± 5.9 μg/g, and after the application of the insecticide with cyfluthrin was 49.9 ± 1.9–458.3 ± 4.2 μg/g. However, the content of alkanes after the use of deltamethrin was 115.6 ± 4.2–4672.0 ± 32.1 μg/g, and after the use of cyfluthrin was 189.4 ± 3.8–3975.0 ± 10.2 μg/g.