Asymptotically exact a posteriori local discontinuous Galerkin error estimates for the one‐dimensional second‐order wave equation

In this article, we analyze a residual‐based a posteriori error estimates of the spatial errors for the semidiscrete local discontinuous Galerkin (LDG) method applied to the one‐dimensional second‐order wave equation. These error estimates are computationally simple and are obtained by solving a local steady problem with no boundary condition on each element. We apply the optimal L² error estimates and the superconvergence results of Part I of this work [Baccouch, Numer Methods Partial Differential Equations 30 (2014), 862–901] to prove that, for smooth solutions, these a posteriori LDG error estimates for the solution and its spatial derivative, at a fixed time, converge to the true spatial errors in the L²‐norm under mesh refinement. The order of convergence is proved to be , when p‐degree piecewise polynomials with are used. As a consequence, we prove that the LDG method combined with the a posteriori error estimation procedure yields both accurate error estimates and superconvergent solutions. Our computational results show higher convergence rate. We further prove that the global effectivity indices, for both the solution and its derivative, in the L²‐norm converge to unity at rate while numerically they exhibit and rates, respectively. Numerical experiments are shown to validate the theoretical results. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1461–1491, 2015     

Residual symmetry reductions and interaction solutions of the (2+1)-dimensional Burgers equation

In nonlinear physics,it is very difficult to study interactions among different types of nonlinear waves.In this paper,the nonlocal symmetry related to the truncated Painleve′expansion of the(2+1)-dimensional Burgers equation is localized after introducing multiple new variables to extend the original equation into a new system.Then the corresponding group invariant solutions are found,from which interaction solutions among different types of nonlinear waves can be found.Furthermore,the Burgers equation is also studied by using the generalized tanh expansion method and a new Ba¨cklund transformation(BT)is obtained.From this BT,novel interactive solutions among different nonlinear excitations are found.     

固相萃取-气相色谱法测定饮用水中12种农药

提出了固相萃取-气相色谱法测定饮用水中12种农药残留量的方法。取水样250mL过固相萃取柱,用乙酸乙酯、正己烷各5mL洗脱,经无水硫酸钠脱水,采用DB-5MS毛细管色谱柱分离,电子捕获检测器检测。溴氢菊酯的线性范围为0.05~0.5mg·L-1,其他农药的线性范围均在0.01~0.1mg·L-1。溴氰菊酯的检出限为24.2ng·L-1,其他农药的检出限均低于10ng·L-1。12种农药的加标回收率在70.0%~110%之间,相对标准偏差(n=6)均小于10%。     

石灰岩对褐煤模拟地下气化残焦物化性质的影响

基于煤炭地下气化过程中石灰岩可能影响煤焦的组成和结构,借助煤炭地下气化模拟实验系统对不同石灰岩掺量(质量分数为0-30%)的褐煤进行水蒸气气化,并采用低温N_2吸附-脱附、XRD和FT-IR等分析手段研究石灰岩对褐煤模拟地下气化残焦的组成、比表面积及孔结构特征、微晶结构和表面官能团等物理化学性质的影响。结果表明,石灰岩对煤焦的元素组成有较大影响。石灰岩可促使煤焦中的微孔向中孔发育,增大煤焦的比表面积和孔容积;当石灰岩掺量从0增加到30%时,煤焦的比表面积增大21.91%,介孔率增加21.49个百分点。XRD分析表明,钙的存在破坏煤焦的芳香结构,使煤焦无序化程度增加,晶面间距(d_(002))增大,抑制煤焦的石墨化发展倾向。FT-IR分析表明,石灰岩存在下,煤焦的羟基官能团减少。     

Residual Dipolar-Coupling-Based Conformational Comparison of Noncovalent Ubiquitin Homodimer with Covalently Linked Diubiquitin

Although the conformation of the polymer chain of Ubiquitin (Ub) mainly depends on the type of isopeptide linkage connecting two Ub molecules, the non-covalent (noncovalent) interaction between two Ub molecules within the chain could also tune their conformational preference. Here, we studied the conformation of noncovalently formed Ub dimers in solution using residual dipolar couplings (RDCs). Comparing the RDC derived alignment tensor of the noncovalently formed dimer with the two most abundant (K11 and K48) covalent linked Ub dimers revealed that the conformation of K11 linked and noncovalent Ub dimers were similar. Between the various NMR and crystal structures of K11 linked Ub dimers, RDC tensor analysis showed that the structure of K11 linked dimer crystalized at neutral pH is similar to noncovalent dimer. Analogous to the experimental study, the comparison of predicted order matrix of various covalent Ub dimers with that of the experimentally determined order matrix of noncovalent Ub dimer also suggests that the conformation of K11 linked dimers crystalized at neutral pH is similar to the noncovalent dimer.     

以尿素为氮源合成AlN粉体过程中非晶碳的石墨化

针对有机合成过程中碳及碳化物的残余,传统方法中普遍使用除碳的工艺,而很少有文章针对非晶碳的结构和形貌进行表征。为此,本文采用高尿素含量的前驱盐体系,通过在氮气保护气氛中煅烧获得AlN粉体。采用X射线衍射分析、红外和拉曼光谱分析、扫描电子显微镜和透射电子显微镜对850~1 500 ℃温度范围内煅烧获得产物的结构和形貌进行表征,对AlN合成过程中含碳产物结构形貌的变化,以及AlN和含碳产物之间相互的依存生长关系进行分析。结果表明,AlN生长的过程中伴随着无定形碳的石墨化转变,AlN颗粒的形貌也受含碳残余产物形貌的影响而出现有规律的变化。     

Analytical and approximate solutions of(2+1)-dimensional time-fractional Burgers-Kadomtsev-Petviashvili equation

In this paper, we applied the sub-equation method to obtain a new exact solution set for the extended version of the time-fractional Kadomtsev-Petviashvili equation, namely BurgersKadomtsev-Petviashvili equation(Burgers-K-P) that arises in shallow water waves.Furthermore, using the residual power series method(RPSM), approximate solutions of the equation were obtained with the help of the Mathematica symbolic computation package. We also presented a few graphical illustrations for some surfaces. The fractional derivatives were considered in the conformable sense. All of the obtained solutions were replaced back in the governing equation to check and ensure the reliability of the method. The numerical outcomes confirmed that both methods are simple, robust and effective to achieve exact and approximate solutions of nonlinear fractional differential equations.     

铀床氚残留量的测量

分别采用直接测量法、同位素交换法和溶解法测量铀床中的氚残留量, 并分析了这三种测量方法在本实验条件下的误差. 直接测量法测量铀床的氚残留量的结果如下: 铀床的氚残留量为2.68%, 即每克铀含(0.0308±0.0003) mmol 氚气; 当压力读数在1500～133332 Pa之间时, 基于理想气体状态方程的测量方法(简称PVT法)的标准差小于0.95%. 同位素交换法测量铀床氚的结果如下: 加热充分解吸过的铀床经多次同位素交换后, 其交换效率仅为2.84%, 即不到3%(摩尔分数)的氚被氘气载带出来, 其同位素交换法测量的标准差为7.35%. 溶解法能够彻底地测量铀床中残留的氚, 其溶解法测量的标准差为6.49%.     

A Generalized Measure of Cumulative Residual Entropy

In this work, we introduce a generalized measure of cumulative residual entropy and study its properties. We show that several existing measures of entropy, such as cumulative residual entropy, weighted cumulative residual entropy and cumulative residual Tsallis entropy, are all special cases of this generalized cumulative residual entropy. We also propose a measure of generalized cumulative entropy, which includes cumulative entropy, weighted cumulative entropy and cumulative Tsallis entropy as special cases. We discuss a generating function approach, using which we derive different entropy measures. We provide residual and cumulative versions of Sharma–Taneja–Mittal entropy and obtain them as special cases this generalized measure of entropy. Finally, using the newly introduced entropy measures, we establish some relationships between entropy and extropy measures.     

浅谈黄原胶及其在农药制剂加工中的应用

黄原胶是极具发展潜力的生物多糖,独特的分子结构使其具有良好的增稠、乳化和稳定作用,已被广泛应用于日用化工、石油开采、纺织印染、食品、医药、涂料、农药等众多工业领域,拥有广阔的市场前景。本文对黄原胶的结构、特性、生产工艺以及主要应用领域等进行了简单综述,总结了黄原胶在农药制剂加工中的应用现状,指出黄原胶优越的流变特性对悬浮剂、水乳剂、悬乳剂等农药制剂悬浮稳定性的提高具有重大意义,最后展望了黄原胶未来的发展前景。