Curvature computations for a two-component Camassa-Holm equation with vorticity

In the present paper, a two-component Camassa-Holm (2CH) system with vorticity is studied as a geodesic flow on a suitable Lie group. The paper aims at presenting various details of the geometric formalism and a major result is the computation of the sectional curvature K of the underlying configuration manifold. As a further result, we show that there are directions for which K is strictly positive and bounded away from zero.     

A Unified Continuous Flow Assembly-Line Synthesis of Highly Substituted Pyrazoles and Pyrazolines

A rapid and modular continuous flow synthesis of highly functionalized fluorinated pyrazoles and pyrazolines has been developed. Flowing fluorinated amines through sequential reactor coils mediates diazoalkane formation and [3+2] cycloaddition to generate more than 30 azoles in a telescoped fashion. Pyrazole cores are then sequentially modified through additional reactor modules performing N-alkylation and arylation, deprotection, and amidation to install broad molecular diversity in short order. Continuous flow synthesis enables the safe handling of diazoalkanes at elevated temperatures, and the use of aryl alkyne dipolarphiles under catalyst-free conditions. This assembly-line synthesis provides a flexible approach for the synthesis of agrochemicals and pharmaceuticals, as demonstrated by a four-step, telescoped synthesis of measles therapeutic, AS-136A, in a total residence time of 31.7 min (1.76 g h⁻¹).     

Three‐dimensional printed magnetophoretic system for the continuous flow separation of avian influenza H5N1 viruses

As a result of the low concentration of avian influenza viruses in samples for routine screening, the separation and concentration of these viruses are vital for their sensitive detection. We present a novel three‐dimensional printed magnetophoretic system for the continuous flow separation of the viruses using aptamer‐modified magnetic nanoparticles, a magnetophoretic chip, a magnetic field, and a fluidic controller. The magnetic field was designed based on finite element magnetic simulation and developed using neodymium magnets with a maximum intensity of 0.65 T and a gradient of 32 T/m for dragging the nanoparticle–virus complexes. The magnetophoretic chip was designed by SOLIDWORKS and fabricated by a three‐dimensional printer with a magnetophoretic channel for the continuous flow separation of the viruses using phosphate‐buffered saline as carrier flow. The fluidic controller was developed using a microcontroller and peristaltic pumps to inject the carrier flow and the viruses. The trajectory of the virus–nanoparticle complexes was simulated using COMSOL for optimization of the carrier flow and the magnetic field, respectively. The results showed that the H5N1 viruses could be captured, separated, and concentrated using the proposed magnetophoretic system with the separation efficiency up to 88% in a continuous flow separation time of 2 min for a sample volume of 200 μL.     

Investigation of the continuous flow of the sample solution on the performance of electromembrane extraction: Comparison with conventional procedure

In this study, electromembrane extraction from a flowing sample solution, termed as continuous‐flow electromembrane extraction, was developed and compared with conventional procedures for the determination of four basic drugs in real samples. Experimental parameters affecting the extraction efficiency were further studied and optimized. Under optimum conditions, linearity of continuous‐flow procedure was within 8.0–500 ng/mL, while it was wider for conventional procedures (2.0–500 ng/mL). Moreover, repeatability (percentage relative standard deviation) was found to range between 5.6 and 10.4% (n  = 3) for the continuous‐flow procedure, with a better repeatability than that of conventional procedures (2.3–5.5% (n  = 3)). Also, for the continuous‐flow procedure, the estimated detection limit (signal‐to‐noise ratio = 3) was less than 2.4 ng/mL and extraction recoveries were within 8–10%, while the corresponding figures for conventional procedures were less than 0.6 ng/mL and 42–60%, respectively. Thus, the results showed that both continuous flow and conventional procedures were applicable for the extraction of model compounds. However, the conventional procedure was more convenient to use, and thus it was applied to determine sample drugs in real urine and wastewater samples.     

Mean flow properties for equatorially trapped internal water wave–current interactions

The aim of this paper is to provide an analysis of the mean flow velocities, and the related mass transport induced by equatorially trapped internal water waves with a constant underlying current.     

Nowhere‐Zero 5‐Flows On Cubic Graphs with Oddness 4

Tutte's 5‐flow conjecture from 1954 states that every bridgeless graph has a nowhere‐zero 5‐flow. It suffices to prove the conjecture for cyclically 6‐edge‐connected cubic graphs. We prove that every cyclically 6‐edge‐connected cubic graph with oddness at most 4 has a nowhere‐zero 5‐flow. This implies that every minimum counterexample to the 5‐flow conjecture has oddness at least 6.     

旋转流动的低模分析及仿真研究

为了探讨Couette-Taylor流从层流到湍流过渡的方式以及流动发展到湍流之后混沌吸引子的某些特征等问题,采用低模分析方法研究了Couette-Taylor流的部分动力学行为及仿真问题,讨论了Couette-Taylor流三模态类Lorenz型方程组的动力学行为,包括定态的失稳、极限环的出现、分岔与混沌的演变和全局稳定性分析等。通过线性稳定性分析和数值模拟等方法给出了此三维模型分岔与混沌等动力学行为及其演化历程,并借此解释了Couette-Taylor流试验中观察到的部分涡流的演化过程.基于系统的分岔图、Lyapunov指数谱、功率谱、Poincaré(庞加莱)截面和返回映射等揭示了系统混沌行为的普适特征.     

关于轴对称Navier-Stokes方程正则性的一个注记

建立了一个关于轴对称不可压Navier-Stokes系统的正则性准则.证明了如果局部的轴对称光滑解u满足‖ωr‖_{Lα1((0,T);Lβ1)}+‖ωθ/r‖_{Lα2((0,T);Lβ2)}<∞,其中2/α₁+3/β₁≤1+3/β₁,2/α₂+3/β₂≤2和β₁≥3, β₂>3/2,那么此强解将保持光滑性直至时刻T.     

循环取货模式下的多车场协同运输问题研究

分析循环取货模式和协同运输问题的关联性,提出了供需节点分离下的多车场一体化协同运输路线优化问题,考虑运输价值和运输成本,引入节点-弧流量的概念,通过比较流量大小确定节点集合,构建了问题的多供应点、多需求点运输模型.考虑取货的单向性和送货的闭合性,构造了求解模型的两阶段算法,运用动态规划的递推解法确定取货最优路线,然后基于余弦定理的几何法求解出发点和返回点不相同的送货路径优化问题,最后通过算例分析,说明了模型的合理性和算法的有效性.     

Amperometric detection of indapamide on glassy carbon electrode

This work describes the development of a fast, precise and reliable voltammetric method for the quantification of indapamide, an orally active diuretic sulfonamide used for hypertensive treatment. This compound acts inhibiting sodium reabsorption and increasing the elimination of water. This characteristic was responsible for its banishment by the International Olympic Committee since 1999. The study begins by finding an adequate potential range (−0.20 to 0.30 V) to avoid poisoning the working glassy carbon electrode (GCE) in phosphate buffer 0.10 mol L⁻¹ (pH=12.0). Utilizing flow injection analysis, linear responses between 2.0 × 10⁻⁶ mol L⁻¹ to 2.5 × 10⁻⁵ mol L⁻¹ of indapamide (R²=0.995), and detection limit (LOD) 3.0 × 10⁻⁷ mol L⁻¹ were obtained. This method was applied for the quantification of indapamide in tablets and in synthetic urine. The same flow system was used for the analysis of commercial drugs and the response obtained corresponded to 98 % of the concentration indicated on the drug label. These tablets were also analyzed by high performance liquid chromatography (HPLC), obtaining a recovery of 103 % and LOD 4.0 × 10⁻⁷ mol L⁻¹. The velocity of analysis using flow methods compares advantageously to the classical chromatographic methods. For synthetic urine, linear responses were obtained in samples spiked in the region from 5.0 × 10⁻⁶ mol L⁻¹ to 30 × 10⁻⁶ mol L⁻¹ (R²=0.991) and LOD 3.0 × 10⁻⁷ mol L⁻¹.