A Runge-Kutta–based WENO reconstruction on moving mesh for compressible fluids

In this paper, we construct a high-order moving mesh method based on total variation diminishing Runge-Kutta and weighted essential nonoscillatory reconstruction for compressible fluid system. Beginning with the integral form of fluid system, we get the semidiscrete system with an arbitrary mesh velocity. We use weighted essential nonoscillatory reconstruction to get the space accuracy on moving meshes, and the time accuracy is obtained by modified Runge-Kutta method; the mesh velocity is determined by moving mesh method. One- and two-dimensional numerical examples are presented to demonstrate the efficient and accurate performance of the scheme.     

富里叶级数的收敛速度

对正弦和余弦富立叶级数,通过合并相邻同号项,使其重排成交错级数.讨论了重排形成的交错级数的敛散性.指出根据自变量x的不同取值,该交错级数可能是单调递减或周期递减的级数.按照莱布尼茨判定法提出了不同精度要求的级数项数的计算公式.选取一到三阶收敛的富立叶级数计算了不同比值精度及差值精度要求的级数项数.计算表明,在x的取值为2π的等分点时,富立叶级数的部分和随项数的增加单调地逼近其收敛值.在x的取值为其它点时,富立叶级数的部分和随项数的增加围绕收敛值上下变动,周期地逼近其收敛值.低收敛阶富立叶级数的收敛速度较慢.要达到0.01%的精度,一收敛阶富立叶级数需要数万项,二收敛阶富立叶级数也需要数百项.在不同计算点处,要达到相同的计算精度,需要的级数项数差别较大.     

Rotation-Inversion Isomerization of Tertiary Carbamates: Potential Energy Surface Analysis of Multi-Paths Isomerization Using Boltzmann Statistics

Potential energy surface (PES) analyses at the SMD[MP2/6–311++G(d,p)] level and higher-level energies up to MP4(fc,SDTQ) are reported for the fluorinated tertiary carbamate N-ethyl-N-(2,2,2-trifluoroethyl) methyl carbamate ( VII ) and its parent system N,N-dimethyl methyl carbamate ( VI ). Emphasis is placed on the analysis of the rotational barrier about the CN carbamate bond and its interplay with the hybridization of the N-lone pair (NLP). All rotational transition state (TS) structures were found by computation of 1D relaxed rotational profiles but only 2D PES scans revealed the rotation-inversion paths in a compelling fashion. We found four unique chiral minima of VII , one pair each of E- and Z-rotamers, and we determined the eight unique rotational TS structures associated with every possible E/Z-isomerization path. It is a significant finding that all TS structures feature N-pyramidalization whereas the minima essentially contain sp²-hybridized nitrogen. We will show that the TS stabilities are affected by the synergetic interplay between NLP/CO₂ repulsion minimization, NLP→σ^*(CO) negative hyperconjugation, and two modes of intramolecular through-space electrostatic stabilization. We demonstrate how Boltzmann statistics must be applied to determine the predicted experimental rotational barrier based on the energetics of all eight rotamerization pathways. The computed barrier for VII is in complete agreement with the experimentally measured barrier of the very similar fluorinated carbamate N-Boc-N-(2,2,2-trifluoroethyl)-4-aminobutan-1-ol II . NMR properties of VII were calculated with a variety of density functional/basis set combinations and Boltzmann averaging over the E- and Z-rotamers at our best theoretical level results in good agreement with experimental chemical shifts δ(¹³C) and J(¹³C,¹⁹F) coupling constants of II (within 6 %).     

Channel temporal correlation-based optimization method for imperfect underwater acoustic channel state information

The rapid time variations and large channel estimation errors in underwater acoustic (UWA) channels mean that transmitters for adaptive resource allocation quickly become outdated and provide inaccurate channel state information (CSI). This results in poor resource allocation efficiency. To address this issue, this paper proposes an optimization approach for imperfect CSI based on a Gauss–Markov model and the per-subcarrier channel temporal correlation (PSCTC) factor. The proposed scheme is applicable to downlink UWA orthogonal frequency division multiple access systems. The proposed PSCTC factors are measured, and their long-term stability is verified using data recorded in real-world sea tests. Simulation and experimental results show that the optimized CSI effectively mitigates the effects of the temporal variability of UWA channels. It demonstrates that the resource allocation scheme using optimized CSI achieves a higher effective throughput and a lower bit error rate than both imperfect CSI and the CSI predicted by the recursive least-squares (RLS) algorithm.     

q value and parent energy optimization using a low-voltage ionization approach increases resolution in linear ion trap mass spectrometry

In this work, the isolation step in the linear ion trap was performed using different “q values” conditions at a low collision-induced dissociation (CID) energy leading to the parent ion resolution improvements, reasonably due to better ion energy distribution. According to the results, we obtained a greater resolution and mass accuracy operating in both traditional electrospray and low voltage ionization near the q value = 0.778 and with a CID energy of 10%. This effect was evaluated with low-molecular-mass compounds (skatole and arginine). The proposed optimization yielded a superior instrument performance without adding technological complexity to mass spectrometry analyses.     

基于改进免疫遗传算法的近红外光谱变量选择方法

该文在免疫遗传算法（IGA）的基础上,提出一种改进免疫遗传算法（iIGA）用于近红外光谱波长变量的选择。该算法舍去了原算法中固定抗体相似度阈值的思想,取而代之的是抗体相似度阈值自适应,同时引入精英保留策略和贪心算法思想,使得算法朝着正确的方向进行局部性探优。将该算法在玉米的淀粉和蛋白质含量数据集上进行实验测试,建立偏最小二乘（PLS）分析模型,并与IGA、遗传算法（GA）以及全谱方法进行了对比。结果表明,在玉米淀粉含量的预测上,iIGA相较于原IGA算法,预测集均方根误差（RMSEP）从0.312 0降至0.298 0,预测集预测精度提升4.5%;在玉米蛋白质含量的预测上,RMSEP从0.124 4降至0.110 3,预测集预测精度提升11.3%。分别对预测淀粉和蛋白质模型的RMSEP值进行显著性检验,F值分别为165.22和182.05,P值分别为9.5 × 10－23和4.5 × 10－24,P值均小于0.05,因此,iIGA能显著提升模型预测精度。     

Rethinking pedagogy for second-order differential equations: a simplified approach to understanding well-posed problems

Knowing an equation has a unique solution is important from both a modelling and theoretical point of view. For over 70 years, the approach to learning and teaching ‘well posedness’ of initial value problems (IVPs) for second- and higher-order ordinary differential equations has involved transforming the problem and its analysis to a first-order system of equations. We show that this excursion is unnecessary and present a direct approach regarding second- and higher-order problems that does not require an understanding of systems.     

Error Estimates for Semi-Discrete and Fully Discrete Galerkin Finite Element Approximations of the General Linear Second-Order Hyperbolic Equation

In this article, we derive error estimates for the semi-discrete and fully discrete Galerkin approximations of a general linear second-order hyperbolic partial differential equation with general damping (which includes boundary damping). The results can be applied to a variety of cases (e.g. vibrating systems of linked elastic bodies). The results generalize pioneering work of Dupont and complement a recent article by Basson and Van Rensburg.     

Generalized asymptotic functions in nonconvex multiobjective optimization problems

In this paper, we use generalized asymptotic functions and second-order asymptotic cones to develop a general existence result for the nonemptiness of the proper efficient solution set and a sufficient condition for the domination property in nonconvex multiobjective optimization problems. A new necessary condition for a point to be efficient or weakly efficient solution is given without any convexity assumption. We also provide a finer outer estimate for the asymptotic cone of the weakly efficient solution set in the quasiconvex case. Finally, we apply our results to the linear fractional multiobjective optimization problem.