Decay rate for viscoelastic wave equation of variable coefficients with delay and dynamic boundary conditions

In this paper, we consider a viscoelastic wave equation of variable coefficients in the presence of past history with nonlinear damping and delay in the internal feedback and dynamic boundary conditions. Under suitable assumptions, we establish an explicit and general decay rate result without imposing restrictive assumption on the behavior of the relaxation function at infinity by Riemannian geometry method and Lyapunov functional method.     

Recent Progress in the $L_p$ Theory for Elliptic and Parabolic Equations with Discontinuous Coefficients

In this paper, we review some results over the last 10-15 years on elliptic and parabolic equations with discontinuous coefficients. We begin with an approach given by N. V. Krylov to parabolic equations in the whole space with $\rm{VMO}_x$ coefficients. We then discuss some subsequent development including elliptic and parabolic equations with coefficients which are allowed to be merely measurable in one or two space directions, weighted $L_p$estimates with Muckenhoupt ($A_p$) weights, non-local elliptic and parabolic equations, as well as fully nonlinear elliptic and parabolic equations.     

贝叶斯优化卷积神经网络公共场所异常声识别*

针对公共场所异常声的感知和识别问题,提出一种基于贝叶斯优化卷积神经网络的识别方法。提取声信号的Gammatone倒谱系数、倍频程功率谱、短时能量和谱质心,组合成声信号的特征图。构建卷积神经网络作为分类器,利用递增的卷积核设置和池化操作处理不同尺度的特征。基于贝叶斯优化算法优化卷积神经网络的模型参数,对包括火苗噼啪声、婴儿啼哭声、烟花燃放声、玻璃破碎声和警报声的5种公共场所异常声进行识别。该方法的识别结果与基于不同的特征提取和分类器方案得到的识别结果进行比较,结果表明该方法的识别效果优于其他特征提取和分类器方案的识别效果。最后分析了该方法在不同信噪比噪声干扰下的识别结果,验证了该方法的有效性。     

A general analytical method for evaluation of the thermodynamic properties of matters using virial coefficients with Morse potential at high temperature

In this paper, we established an analytical formula for the second virial coefficient (SVC) with Morse potential without using any numerical methods, and the obtained formula is applied to the calculation of the speed of sound of some matter at high temperature. This approach is based on the series expansion formula and special functions, which allows the exact evaluations of any thermodynamic properties of matter using the SVC. As an application, the obtained analytical formula is used for evaluation of the SVC with Morse potential for high‐temperature gas and the plasma region of the intermolecular interactions of neutral atom gases of B, Si, Zn, H₂, N₂, O₂, NO, CO, He, Ne, Ar, Kr , and Xe . Based on the obtained formula of SVC, the speed of sound for gases of N₂, Ar , and Zn are also determined analytically. A specific maximum temperature is chosen for every gas to ensure that there are still neutral atoms in the gas, and low temperatures are avoided due to quantum effects. The results are compared with numerical data and another analytical data from the literature. The new analytical solution is shown to be in good agreement with the compared data and is verified to supply proper thermodynamic data.     

Kinetics studies of 5-methyl-2-hexanol, 2,2-dimethyl-3-hexanol,and 2,4,4-trimethyl-1-pentanol with chlorine atoms: Photooxidation mechanism of 2,4,4-trimethyl-1-pentanol

The rate constants for the reaction between chlorine atoms and either 5-methyl-2-hexanol, 2,2-dimethyl-3-hexanol, or 2,4,4-trimethyl-1-pentanol at 298 K were determined using the relative method with 2-butanol and 1-pentanol as reference compounds. The values obtained for 5-methyl-2-hexanol, 2,2-dimethyl-3-hexanol, and 2,4,4-trimethyl-1-pentanol (k × 10¹⁰ cm³ molec⁻¹ s⁻¹) were, respectively, (2.64 ± 0.5), (2.72 ± 0.5), and (2.50 ± 0.4), in agreement with the values of the rate constants reported in bibliography for similar alcohols and the values estimated by structure activity relationship methods. The photooxidation products of 2,4,4-trimethyl-1-pentanol initiated by chlorine atoms were identified (formaldehyde, 2-propanone, 2,2-dimethyl propanal, 4,4,-dimethyl-2-pentanone, and 3,3-dimethylbutanal), and the reaction mechanism was determined.     

The local ultraconvergence of high‐order finite element method for second‐order elliptic problems with constant coefficients over a rectangular partition

In this article, we will discuss the local ultraconvergence of high‐degree finite element method based on a rectangular partition for the second‐degree elliptic problem with constant coefficients in Ω ? ?² , u( y ) = 0 on ?Ω . Based on suitable regularity, ultraconvergence of the displacement of the extrapolated kth (k ≥ 3) degree finite element solution has been obtained by an extrapolation technique. Finally, numerical experiments are applied to demonstrate our theoretical findings.     

Complete Moment Convergence for the Dependent Linear Processes with Random Coefficients

In this paper, we investigate the complete moment convergence for dependent linear processes with random coefficients to form     

Elution profiles of lanthanides with α‐hydroxyisobutyric acid by ion exchange chromatography using fine resin

Experiments were carried out using a strong acid cation exchange resin with a particle size of 75–150 μm, termed as “fine resin” in hydrogen ion form for the elution of individual lanthanides Sm, Eu, Gd, Tb, and Dy that are produced as fission products in the spent nuclear fuel and generated in the effluent during reprocessing of spent nuclear fuel. Batch experiments were carried out to study the effect of concentration of nitric acid on distribution coefficient. The distribution coefficient values for these individual lanthanides were determined in nitric acid medium in the concentration range of 0.01–4.0 N. Uptake of each individual lanthanide by resin was increased with increased nitric acid concentration from 0.01 to 0.5 N and remained similar from 0.5 to 1.0 N and decreased thereafter up to 4.0 N. Column experiments were also carried out using the same resin to study the parameters like pH of the eluent, flow rate, and resin bed height under isocratic elution conditions for eluting lanthanide elements using α‐hydroxyisobutyric acid as eluent. The results of this study have indicated the possibility for the elution of individual lanthanides.