Stability of a mathematical model of tumour-induced angiogenesis

A model consisting of three differential equations to simulate the interactions between cancer cells, the angiogenic factors and endothelial progenitor cells in tumor growth is developed. Firstly, the global existence, nonnegativity and boundedness of the solutions are discussed. Secondly, by analyzing the corresponding characteristic equations, the local stability of three boundary equilibria and the angiogenesis equilibrium of the model is discussed, respectively. We further consider global asymptotic stability of the boundary equilibria and the angiogenesis equilibrium by using the well-known Liapunov–LaSalle invariance principal. Finally, some numerical simulations are given to support the theoretical results

Dark energy model with higher derivative of Hubble parameter

In this letter we consider a dark energy model in which the energy density is a function of the Hubble parameter $H$ and its derivative with respect to time $\rho_{de}=3\alpha \ddot{H}H^{-1}+3\beta\dot{H}+3\gamma H^2$. The behavior of the dark energy and the expansion history of the Universe depend heavily on the parameters of the model $\alpha$, $\beta$ and $\gamma$. It is very interesting that the age problem of the well-known three old objects can be alleviated in this models.Comment: 11 pages, 6 figures, the correct version accepted for publication in PL

Urchin-like CoCu Bimetallic Nanocomposites for Catalytic Hydrogenolysis of Glycerol to Propanediols

Bimetallic CoCu nanocomposites were synthesized in polyol by using Ru as heterogeneous nucleation agent and stearic acid as surfactant, and their catalytic properties were investigated by hydrogenolysis of glycerol to propanediols. It was found that the surfactant could induce Co nanocrystals to form nanowires as structure-directing agent, while it's ineffective for Cu because only spherical Cu particles were produced under the same condition. When Co~(2+) and Cu~(2+) coexist in polyol, Cu~(2+) is firstly reduced and forms the spherical particles, and then the Cu particles afford surface for the subsequential reduction of Co~(2+) and growth of Co nanocrystals to form the nanorods, obtaining the urchin-like CoCu nanocomposites. The catalytic performance in selective hydrogenolysis of glycerol to propanediols proposed that the CoCu urchin-like nanocomposites was superior to the Co nanowires possibly due to that the synergistic effect between Co and Cu component promoted conversion of glycerol and obtained the higher propanediol yields based on the specific surface areas of the catalysts

Optimal Design for Constraint Following Control of Tank Bi-Directional Stabilized Systems Based on Nash Game

This article proposes a robust control optimization design problem based on Nash game-theoretic for the marching tank bi-directional stabilization system of an all-electric actuator, which is accompanied by complex uncertainty (possibly fast time-varying but bounded). The task is to drive the barrel firing angle to adjust to a specified position under complex uncertainty while ensuring that multiple design parameters are optimally chosen in the controller. Firstly, the machine-electric coupled dynamics equations with uncertainty are created in the form of state space. Secondly, a robust controller with two design parameters to be chosen is given so that the constraint following error has uniform boundedness and uniform ultimate boundedness. Thirdly, a Nash game cost function consisting of three components: performance cost, time cost and control cost is proposed, and the Nash equilibrium (i.e., optimal control parameters) is obtained by minimizing the cost function. Finally, a co-simulation experimental platform is built to verify the robustness of the controller under complex uncertainty (modeling errors, uncertain disturbances and road excitation) and to demonstrate the global optimal performance of the system under optimal design parameters

Necessary and sufficient conditions for oscillation of neutral delay differential equations

In this article, we concerned with oscillation of the neutral delay differential equation $[x(t)-px(t-\tau)]'+qx(t-\sigma)=0$ with constant coefficients. By constructing several suitable auxiliary functions, we obtained some necessary and sufficient conditions for oscillation of all the solutions of the aforementioned equation for the cases $0<p<1$ and $p>1$

Study in Wire Feedability-Related Properties of Al-5Mg Solid Wire Electrodes Bearing Zr for High-Speed Train

This work offers an analysis of the wire feedability-related properties of Al-5Mg solid wire electrodes bearing Zr. Effects of Zr content on microstructures and mechanical properties of the Al-5Mg alloys were studied. Experimental results have demonstrated that α-Al dendrites of the as-cast Al-5Mg alloy are refined, and the tensile strength, microhardness and roughness of the 1.2 mm wire electrode are improved with an appropriate addition of Zr. In addition, the tensile strength and elongation of the welded joints welded using Al-5Mg wire electrodes bearing Zr reach the maximum value when 0.12% Zr is added into the wire alloy. However, when excess Zr is added, α-Al phases of the wire alloy and welded joint are coarsened, and the mechanical properties are deteriorated. Moreover, the structure and principle of a novel apparatus, which can enhance the feedability of the wire electrode, are introduced and the apparatus can achieve the rough and fine adjustments of cast and helix of the wire electrode

Efficient Hydrogenolysis of Guaiacol over Highly Dispersed Ni/MCM-41 Catalyst Combined with HZSM-5

A series of MCM-41 supported Ni catalysts with high metal dispersion was successfully synthesized by simple co-impregnation using proper ethylene glycol (EG). The acquired Ni-based catalysts performed the outstanding hydrogenolysis activity of guaiacol. The effects of the synthesis parameters including drying temperature, calcination temperature, and metal loading on the physical properties of NiO nanoparticles were investigated through the use of X-ray diffraction (XRD). The drying temperature was found to significantly influence the particle sizes of NiO supported on MCM-41, but the calcination temperature and metal loading had less influence. Interestingly, the small particle size (≤3.3 nm) and the high dispersion of NiO particles were also obtained for co-impregnation on the mixed support (MCM-41:HZSM-5 = 1:1), similar to that on the single MCM-41 support, leading to excellent hydrogenation activity at low temperature. The guaiacol conversion could reach 97.9% at 150 °C, and the catalytic activity was comparative with that of noble metal catalysts. The hydrodeoxygenation (HDO) performance was also promoted by the introduction of acidic HZSM-5 zeolite and an 84.1% yield of cyclohexane at 240 °C was achieved. These findings demonstrate potential applications for the future in promoting and improving industrial catalyst performance

Effects of Porosity, Heat Input and Post-Weld Heat Treatment on the Microstructure and Mechanical Properties of TIG Welded Joints of AA6082-T6

Various heat input conditions and post-weld heat treatments were adopted to investigate the microstructure evolution and mechanical properties of tungsten inert gas (TIG) welded joints of AA6082-T6 with porosity defects. The results show that the fracture location is uncertain when an as-welded joint has porosities in the weld zone (WZ), and overaging in the heat-affected zone (HAZ) at the same time. When the fracture of the as-welded joint occurs in the HAZ, the total heat input has a linear relation with the tensile strength of the joint. An excess heat input induces the overgrowth of Mg2Si precipitates in HAZ and the coarsening of α-Al grains in WZ, resulting in a decrease in the microhardness of the corresponding areas. After artificial aging treatment, the tensile strength of the welded joint is increased by approximately 9–13% as compared to that of as-welded joint, and fracture also occurs in HAZ. In contrast, for solution treated and artificial aging treated joint, fracture occurs suddenly at the rising phase of the tensile curve due to porosity defects throughout the weld metal. Furthermore, the eutectic Si particles of WZ coarsen and spheroidize after solution treatment and artificial aging treatment, due to the diffusion of Si to the surface of the original Si phases when soaking at high temperature

Simply packaging Ni nanoparticles inside SBA-15 channels by co-impregnation for dry reforming of methane

The highly dispersed Ni nanoparticles inside SBA-15 channels (Ni@ SBA- 15) were synthesized simply by co-impregnation using ethylene glycol (EG). During co-impregnation, the EG additive in the metal nitrate aqueous solution could successfully deliver and package the nickel species into the channels of mesoporous SBA-15. The characterization results suggest that drying after impregnation plays a critical role in the distribution of the precursor. Compared with conventional impregnation, redistribution and agglomeration of the Ni precursor were efficiently avoided due to the lower surface tension and high viscosity of the concentrated solution during drying, and super-small Ni nanoparticles with higher dispersions and narrow particle size distributions were predominantly confined over the internal surface of mesoporous channels instead of its external surface. The Ni@ SBA- 15 catalyst using co-impregnation demonstrated excellent sintering-resistance and stability in the dry reforming of methane due to its strong metal-support interaction and the confined location of Ni nanoparticles