Global existence and blow-up of solutions of nonlocal diffusion problems with free boundaries

In this paper, we investigate some nonlocal diffusion problems with free boundaries. We first give the existence and uniqueness of local solution by the ODE basic theory and the contraction mapping principle. Then we provide a complete classification for the global existence and finite time blow-up of solutions. Moreover, estimates of blow-up rate and blow-up time are also obtained for the blow-up solution.     

基于光谱学分析的聚氨酯弹性体/聚磷酸铵/氢氧化铝复合材料阻燃机理研究

采用熔融共混技术,将聚磷酸铵(APP)和氢氧化铝(ATH)引入到聚氨酯弹性体(TPU)中,制备了一系列热塑性聚氨酯/聚磷酸铵/氢氧化铝(TPU/APP/ATH)复合材料。采用傅里叶红外光谱(FTIR)、X-射线光电子能谱(XPS)、扫描电镜(SEM)、激光拉曼光谱研究了TPU和阻燃TPU(FR-TPU)复合材料燃烧后炭渣的微观形貌、表面结构、元素组成、键合状态和石墨化程度,结合阻燃性能测试,揭示APP和ATH的协同阻燃机制。SEM分析表明相较于APP与ATH单独使用,TPU/APP/ATH炭层的空洞结构更少,炭渣的致密性更高。XPS分析表明FR-TPU的炭渣中C元素含量相比于纯TPU有所降低,O元素的含量有所上升,其中TPU/APP10/ATH10的C元素含量从88.2%降至69.24%,O元素的含量从8.07%升至17.78%,P和Al元素含量相较于单独添加分别从11.74%和16.36%下降至3.91%和3.31%。在此基础上,通过对C元素的分峰拟合发现TPU炭渣中C—C/C—H,C—O/C—N和CO/CN含量分别为61.05%,35.65%和3.30%;TPU/APP10/ATH10炭渣中三种结构含量分别为45.38%,45.00%和9.63%,说明ATH和APP复配使用有利于C元素形成酯、醚、羰基、羧酸（盐）、酯基等结构。通过对O元素的分峰拟合发现,TPU炭渣中O₂/H₂O,—O—,O三种结构含量分别为28.75%,44.36%和26.89%;TPU/APP10/ATH10炭渣中O₂/H₂O,—O—,O三种结构含量分别为44.33%,32.78%和22.89%,说明APP和ATH的加入有利于炭渣中O元素形成O₂/H₂O结构。通过对N元素的分峰拟合发现,TPU炭渣中—NH—,N结构的N元素含量分别为40.93%和59.07%;TPU/APP10/ATH10中—NH—,N结构的N元素含量分别47.17%和52.83%,说明ATH与APP复配使用促进了—NH—结构的形成。拉曼测试表明,相比于单独使用,APP和ATH复配使用,炭层的石墨化程度更好,致密性更高。以上分析结合阻燃测试可以得出TPU/APP/ATH复合材料阻燃机制：ATH受热分解生成氧化铝,吸收热量并释放大量水蒸气,有效促进APP降解,生成不燃性的氨气和聚磷酸,氨气和水蒸气稀释可燃性气体的浓度。随着温度继续升高,氧化铝可继续与聚磷酸反应生成偏磷酸铝[Al(PO₃)₃],同步催化聚氨酯基体成炭,形成高度石墨化炭层,石墨化炭层与偏磷酸铝一起覆盖在基体表面,有效抑制燃烧区域物质以及能量的输运,从而达到阻燃目的。     

一种低原子序数元素EDX RF的多次导-样条小波解析方法研究

能量色散X射线荧光（EDXRF）光谱分析待测元素的信息主要反映在能谱的特征峰峰位以及特征峰净峰面积中。对于特征峰的准确检测是EDXRF光谱分析的关键。特征X射线之间的能量在低原子序数元素中相差很小,在实际测量过程中由其他一些因素干扰会导致EDXRF光谱中特征峰产生严重重叠,以EDXRF光谱中低序列元素的重叠峰作为研究对象,提出一种四次导数结合三样条小波变换处理低序列元素重叠峰的新方法。通过数学模型模拟重叠峰检测了该方法的可行性,并仿真了实测X荧光光谱数据进行检测得到良好的效果,通过使用了CIT-3000SY X 荧光元素录井仪实测T铅黄铜数据和混合轻元素数据荧光光谱作为验证。首先,介绍导数法以及三样条小波法分解重叠的原理。导数法阶数越高信号越畸形但可以有效提高重峰分离度,而三样条小波变换对低分离度重峰处理较为无力但能有效的保持峰型。通过Tsallis峰信号模拟重叠峰,模拟出3个峰信号,第1个峰和第2个峰的分离度R=0.33,第2个峰和第3个峰的分离度R=0.67,导数处理后信号任仍具有一部分重叠,但是导数处理后不仅保留了信号的峰位值,且出现了分离度变大的现象,而三样条小波对低分离度重叠峰的分解较为无力,但是对于分离度较大的重叠峰具有较好的效果,信号通过四次导增加分离度再进行三样条小波变换,通过调节样条小波分解层次的次数,然后对分解出的高频信号采取适当的系数进行放大,最后进行信号重构。实验实现了对模拟信号的分解。验证了此方法针对重叠峰分解具有可行性。实验采用分解4层的三样条小波变换以及放大6倍的高频信号。然后,处理仿真K元素的重叠光谱,实现了重叠峰的分解,通过仿真实验表明新方法能准确的识别峰位,结果表明只有1%之内的误差,证明了新方法对X荧光光谱重叠峰分解的适用性。最后用此方法对CIT-3000SY X荧光元素录井仪实测T铅黄铜元素数据以及混合轻元素数据X荧光光谱进行处理,实现了对重叠峰的分解,且分解后的峰位误差控制在1%之内,具有较高的准确率。实验结果证明：四次导数结合三样条小波变换能有效分离重叠峰,并且在处理X荧光光谱的重叠峰分解上具有实用性。     

Some aspects of scatter search in the flow-shop problem

The flow-shop scheduling problem with the makespan criterion is a certain strongly NP-hard case from the domain of OR. This problem, having simple formulation contrasting with its troublesome, complex and time-consuming solution methods, is ideal for testing the quality of advanced combinatorial optimization algorithms. Although many excellent approximate algorithms for the flow-shop problem have been provided, up till now, in the literature, some theoretical and experimental problems associated with an algorithm’s activity still remain unexamined. In this paper, we provide a new view on the solution space and the search process. Relying upon it, we are proposing the new approximate algorithm, which applies some properties of neighborhoods, refers to the big valley phenomenon, uses some elements of the scatter search as well as the path relinking technique. This algorithm shows up to now unprecedented accuracy, obtainable within a short time on a PC, which has been confirmed in a wide variety of computer tests. Good properties of the algorithm remain scalable if the size of instances increases.     

激光驻波中运动电子的谐波自发辐射

 采用单电子模型分析了电子在线极化激光驻波中的动力学及谐波自发辐射谱,数值计算了电子在驻波中的运动情况及辐射谱。结果表明:电子在波节和波腹处入射后,其辐射谱出现不同的特征;电子在波节处垂直磁场入射后,在洛伦兹力作用下快速振动并向前运动,其向后辐射的光谱发生红移,向前辐射的光谱发生蓝移,谱线出现展宽;当激光强度或者电子初始能量增大时,这些效应更加突出,以至于产生更高阶谐波,形成连续谱;而电子在波腹处以平行电场的方向入射后,仅在电场作用下作直线运动,其自发辐射谱线没有发生移动和展宽。     

1H NMR spectral studies on the polymerization mechanism of indole and its derivatives

The existence of NH bond according to the hydrogen nuclear magnetic resonance ((1)H NMR) spectra of polyindole and its derivatives, such as poly(5-bromoindole), poly(5-cyanoindole), poly(5-nitroindole), poly(5-methylindole), proved polymerization of high-quality polyindoles, which were electrosynthesized from middle strong Lewis acid boron trifluoride diethyl etherate (BFEE) and its mixed electrolytes with additional diethyl ether, occurred at 2,3-position. The elongation of the conjugation length made the chemical shift of all the protons of polyindoles to lower field in comparison with those of monomers.     

基于博弈论视角的稀土矿区环境治理及监管策略研究

针对稀土矿区环境治理的复杂性,本文通过建立地方政府和稀土企业之间的动态演化博弈模型,分析了博弈双方在不同情形下的演化稳定策略及其影响因素,并利用matlab对其进行数值仿真。研究表明,地方政府的监管成本、执行环境规制时对稀土企业的奖惩政策、稀土企业的治污成本以及非法开采时的额外收益都会影响地方政府与稀土企业的演化稳定策略,降低地方政府的监管成本、稀土企业的治污成本等都会引导博弈双方的演化稳定策略趋向于{严格监管,合法开采},从而促进矿区环境的可持续性发展。     

Note on a conjecture for the sum of signless Laplacian eigenvalues

For a simple graph G on n vertices and an integer k with 1 ? k ? n, denote by \(\mathcal{S}^+_k\) (G) the sum of k largest signless Laplacian eigenvalues of G. It was conjectured that \(\mathcal{S}^+_k(G)\leqslant{e}(G)+(^{k+1}_{\;\;2})\) (G) ? e(G) + (k+1 2), where e(G) is the number of edges of G. This conjecture has been proved to be true for all graphs when k ∈ {1, 2, n ? 1, n}, and for trees, unicyclic graphs, bicyclic graphs and regular graphs (for all k). In this note, this conjecture is proved to be true for all graphs when k = n ? 2, and for some new classes of graphs.     

A boundary-only treatment by singular boundary method for two-dimensional inhomogeneous problems

In this study, an effective singular boundary method (SBM) in conjunction with the recursive multiple reciprocity method (MRM) is developed and validated for inhomogeneous problems. It avoids the inner nodes or domain discretizations to evaluate the particular solution, and preserves the boundary-only property of the SBM. Rather than using only polyharmonic operators in the traditional MRM, a recursive MRM is proposed to annihilate source terms with different partial differential operators recursively. Nevertheless, high-order fundamental solutions are involved in the recursive MRM. The absence of the origin intensity factors of higher order fundamental solutions is a major bottleneck in applying the SBM. In order to remedy this difficulty, the origin intensity factors of higher order fundamental solutions are derived with simple formulas. Numerical examples are presented to illustrate the accuracy and efficiency of the proposed method.