A class of time‐fractional reaction‐diffusion equation with nonlocal boundary condition

The purpose of the study is to analyze the time‐fractional reaction‐diffusion equation with nonlocal boundary condition. The proposed model is used to predict the invasion of tumor and its growth. Further, we establish the existence and uniqueness of a weak solution of the proposed model using the Faedo‐Galerkin method and compactness arguments.     

Dissolution optimization and kinetics of nickel and cobalt from iron-rich laterite ore,using sulfuric acid at atmospheric pressure

More than 70% of the world's nickel reserves are found in laterite ores. In this research, a laterite ore sample, containing Ni, Co, and Fe, was employed to study the recovery of nickel and cobalt. Thus, the effect of calcination, acid concentration, percent solids, and stirring rate on nickel and cobalt recoveries from an iron-rich laterite sample was investigated. Optimization with response surface methodology and kinetic studies were performed. The calcination of the sample prior to leaching at 500°C for 2 h provided condition for better nickel and cobalt dissolutions. At optimal conditions, the concentration of sulfuric acid, solid-to-liquid ratio, stirring speed, temperature, and time test were equal to 5 M, 0.1, 370 rpm, 90°C, and 2 h, respectively. The highest recoveries of nickel and cobalt were 65.9% and 63.1%, respectively. Solids content had a negative effect on Ni and Co recovery, whereas acid concentration was positively affected. Addition of 10% (w/v) NaCl in the presence of 5 M acid concentration, 60°C, 370 rpm, and leaching time of 2 h increased the nickel and cobalt recoveries, 15.3% and 21.4%, respectively. The high dependence of process on temperature indicates chemical control; the activation energies E_a = 59.54 and E_a = 45.74 kJ/mol, respectively, for nickel and cobalt, were also consistent with this conclusion.     

Semiclassical transition state theory/master equation kinetics of HO + CO: Performance evaluation

Previously, master equation (ME) simulations using semiclassical transition state theory (SCTST) and high-accuracy extrapolated ab initio thermochemistry (HEAT) predicted rate constants in excellent agreement with published experimental data over a wide range of pressure and temperatures ≳250 K, but the agreement was not as good at lower temperatures. Possible reasons for this reduced performance are investigated by (a) critically evaluating the published experimental data and by investigating; (b) three distinct ME treatments of angular momentum, including one that is exact at the zero- and infinite-pressure limits; (c) a hindered-rotor model for HOCO that implicitly includes the cis- and trans-conformers; (d) possible empirical adjustments of the thermochemistry; (e) possible empirical adjustments to an imaginary frequency controlling tunneling; (f) including or neglecting the prereaction complex PRC1; and (g) its possible bimolecular reactions. Improvements include better approximations to factors in SCTST and using the Hill and van Vleck treatment of angular momentum coupling. Evaluation of literature data does not reveal any specific shortcomings, but the stated uncertainties may be underestimated. All ME treatments give excellent fits to experimental data at T ≥ 250 K, but the discrepancy at T < 250 K persists. Note that each ME model requires individual empirical energy transfer parameters. Thermochemical adjustments were unable to match the experimental H/D kinetic isotope effects. Adjusting an imaginary frequency can achieve good fits, but the adjustments are unacceptably large. Whether PRC1 and its possible bimolecular reactions are included had little effect. We conclude that none of the adjustments is an improvement over the unadjusted theory. Note that only one set of experimental data exists in the regime of the discrepancy with theory, and data for DO + CO are scanty.     

Experimental and theoretical studies of Mn(II) and Co(II) metal complexes of a tridentate Schiff's base ligand and their biological activities

We have used the condensation method to synthesize 2-acetyl-5-methylsemicarbazone ligand. Manganese(II) and Cobalt(II) complexes having formula [ML₂]X₂ were synthesized where M = Mn(II) and Co(II), L = ligand, X = Cl⁻, CH₃COO⁻, NO₃⁻, ½SO₄²⁻. The characterization data suggests the octahedral geometry for all the synthesized complexes. Tridentate nature of the 2-acetyl-5-methylsemicarbazone ligand was revealed by IR studies. Molar conductance analysis suggested the electrolytic nature of the complexes. The theoretical study includes geometrical optimization, HOMO-LUMO energy gap, energetic parameters and dipole moment. These results also confirmed the tridentate nature of the ligand and the octahedral geometry of complexes. The molecular electrostatic potential (MEP) study suggested the reactive sites for an electrophilic or nucleophilic attack in the ligand. We tested the synthesized compounds for their antifungal and antibacterial action via well diffusion method and found that parent ligand after the coordination with the metal ion showed more effective inhibition against bacteria and fungi.     

An Uzawa-type algorithm for the coupled Stokes equations

An Uzawa-type algorithm is designed for the coupled Stokes equations discretized by the mixed finite element method. The velocity solved by the presented algorithm is weakly divergence-free, which is different from the one solved by the common Uzawa method. Besides, an optimal relaxation parameter of the presented algorithm is provided.     

关于不定方程x3-1=749y2

利用同余式、平方剩余、Pell方程的解的性质、递归序列证明了:不定方程x³-1=749y²仅有整数解(x,y)=(1,0).     

正负双向脉冲式爆炸及其诱导的簇发振荡

簇发振荡普遍存在.探索通向簇发振荡的可能路径是簇发研究的热点问题之一."脉冲式爆炸(pulsed-shaped explosion,PSE)"是一种最近被报道的可以诱发簇发振荡的新机制,其特征为平衡点和极限环表现出了与参数变化相关的脉冲式急剧量变.PSE会导致系统轨线急剧跃迁,从而诱发典型的簇发振荡.然而,目前报道的PSE中仅含有"单向的尖峰",未发现"双向的尖峰",且由其诱发的簇发振荡仅含单向的振荡簇.本文以多频激励Rayleigh系统为例,旨在揭示PSE的不同表现形式以及与此相关的簇发动力学.利用频率转换快慢分析法得到了Rayleigh系统的快子系统和慢变量.针对快子系统的分析表明,PSE表现出了较为复杂的动力学特性,其特征是PSE包含了正负双向两个不同的尖峰,此即所谓的正负双向PSE.其急剧量变行为,导致了系统轨线在单个振荡周期内出现正向和负向的多次跃迁,由此得到了由正负双向PSE所诱发的簇发振荡.根据吸引子类型分别揭示了点--点型和环--环型两类簇发振荡模式的产生机制.本文的研究给出了PSE的不同表现形式,丰富了多时间尺度下的簇发振荡的诱发机制.      

人行荷载下梁式结构振动分析的DQ-IQ混合法

为了评估人行荷载作用下梁式结构的振动舒适度，利用微分求积-积分求积，即DQ-IQ混合法求解移动荷载作用下梁的振动响应。人行荷载作用下梁式结构的振动控制方程是含Dirac函数的偏微分方程，首先利用IQ法离散与时间相关的Dirac函数，再利用DQ法把控制方程转化为二阶常系数微分方程，最后利用Newmark算法求解微分方程。以某钢结构连廊为例，利用DQ法计算结构自振频率并与解析解进行对比，结果验证了节点选取和边界条件施加的合理性，再利用DQ-IQ混合法和振型叠加法分别计算了不同行走步频下连廊的响应，计算结果表明，DQ-IQ混合法具有较高的可靠性和精确性。DQ-IQ混合法也可以推广到诸如车辆荷载作用下路面或桥梁的动力响应等其他移动荷载下结构的振动分析。     

基于Hopf-Cole变换的Burgers方程初边值问题的Sinc-Galerkin法

利用Sinc-Galerkin法数值求解Burgers方程的初边值问题。首先,用Hopf-Cole变换将二阶非线性的Burgers方程变换为二阶线性方程,同时把第一类边界条件变为第二类边界条件。时间上的导数采用θ加权格式离散,空间导数采用Sinc-Galerkin法离散,端点处分别引入权函数处理变换后的第二类边界条件。最后,通过数值算例验证了Sinc-Galerkin法的指数收敛性,与精确解相比,本文构造的数值格式精度高,能够有效捕捉激波等物理现象。