Splitting theorem, Poincaré–Hopf theorem and jumping nonlinear problems

AbstractIn this paper, we establish a Gromoll–Meyer splitting theorem and a shifting theorem for J∈C2-0E,R and by using the finite-dimensional approximation, mollifiers and Morse theory we generalize the Poincaré–Hopf theorem to J∈C1E,R case. By combining the Poincaré–Hopf theorem and the splitting theorem, we study the existence of multiple solutions for jumping nonlinear elliptic equations

Damage identification of bridge structure based on frequency domain decomposition and strain mode

Because it is difficult to determine the degree and location of damage to bridge structures under environmental excitation, a new method combining frequency domain decomposition and strain mode identification for bridge structure damage assessment is proposed and the related identification principle is derived. General variations in the strain mode parameters of different reinforced concrete beam damage states are accordingly studied under ambient excitation. The results show that the proposed strain mode identification method based on frequency domain decomposition has good anti-noise performance and can identify the strain mode parameters of a structure relying solely on the strain response information of the structure, even under strong background noise. The mutation of the strain mode was effectively used to determine the damage condition of reinforced concrete beams, and the adaptability, feasibility, and reliability of the proposed method for modal parameter and damage identification of reinforced concrete beams under environmental excitation were verified

Control of Fluid Dynamics by Nanoparticles in Laser Melting

Effective control of fluid dynamics is of remarkable scientific and practical significance. It is hypothesized that nanoparticles could offer a novel means to control fluid dynamics. In this study, laser melting was used to investigate the feasibility of tuning fluid dynamics by nanoparticles and possibly breaking existing limits of conventional laser processing techniques. Alumina nanoparticles reinforced nickel samples, fabricated through electrocodeposition, were used for laser melting experiments. Since the melt pool surface is controlled by the fluid dynamics, surface topographies were carefully studied to reveal the nanoparticle effect on the fluid dynamics. Characterizations of surface topographies and microstructures of pure Ni and Ni/Al2O3 nanocomposite were carried out before and after laser melting. The surface roughness of the Ni/Al2O3 nanocomposite sample was reduced significantly by laser melting, which broke the existing limit of laser surface polishing of pure Ni. It is believed that the nanoparticles increased the viscosity of the molten metal, thereby enhancing the viscous damping of the capillary oscillations in the melt pool, to produce a much smoother surface. Moreover, the experimental study also revealed that the viscosity enhancement by the nanoparticles effectively suppressed the thermocapillary flows which would introduce artificial asperities on a surface. The experimental results suggest that nanoparticles are effective in controlling melt pool dynamics and overcoming the existing limits of laser processing. The new methodology, fluid dynamics control by nanoparticles, opens a new pathway to enrich liquid based processes for broad applications

Effects of cardiotrophin-1 on hemodynamics and cardiomyocyte apoptosis in rats with acute myocardial infarction

The effects of cardiotrophin-1 on hemodynamics, cardiac function, cardiomyocyte apoptosis, and expression of P53, Fas, Bax and Bcl-2 proteins in myocardium were determined in a rat model of acute myocardial infarction. Twenty-four male Sprague-Dawley rats weighing approximately 310 g were subjected to left coronary artery ligation. Seven days before surgery, the rats were randomized to receive cardiotrophin-1 (treated group) or phosphate-buffered saline (control group). Recombinant rat cardiotrophin-1 (2 μg in 1 ml phosphate-buffered saline) or phosphate-buffered saline (1 ml) was administered daily via the tail vein for 7 days (n=12 for each group). Hemodynamic parameters, apoptotic index, P53, Fas, Bax and Bcl-2 expression in myocardium were measured at 24 hours after coronary ligation. As compared with control animals, rats treated with cardiotrophin-1 had significantly higher mean arterial pressure, left ventricular systolic pressure and the maximum rate of left ventricular pressure rise or fall, and significantly lower left ventricular end-diastolic pressure. Cardiotrophin-1 pretreatment did not affect the heart rate, heart weight, body weight or the ratio of heart weight to body weight. The number of apoptotic cardiomyocytes in cardiotrophin-1 treated group was less than that in control group [(15.8±5.2)% vs (34.6±7.7) %,Plt0.01]. Cardiotrophin-1 pretreatment significantly inhibited P53, Fas and Bax, and increased Bcl-2 expression in myocardium

Carbo-catalysis in Liquid Phase Selective Oxidation Reactions

This study explored the liquid phase selective oxidations with peroxymonosulfate as the oxidant activated by carbocatalysts. Various carbon materials functionalized with heteroatoms were tested to oxidize alcohol or other hydrocarbons into the desirable aldehyde or ketone product with high selectivity. The reaction pathways for the oxidant activation and the subsequent oxidations were comprehensively studied. A facile and environmentally benign approach to highly efficient selective oxidations was established by optimizing the reacting conditions