Global stability analysis and permanence for an HIV-1 dynamics model with distributed delays

This paper mainly investigates the global asymptotic stabilities of two HIV dynamics models with two distributed intracellular delays incorporating Beddington-DeAngelis functional response infection rate. An eclipse stage of infected cells (i.e. latently infected cells), not yet producing virus, is included in our models. For the first model, it is proven that if the basic reproduction number $R_0$ is less than unity, then the infection-free equilibrium is globally asymptotically stable, and if $R_0 $ is greater than unity, then the infected equilibrium is globally asymptotically stable. We also obtain that the disease is always present when $R_0 $ is greater than unity by using a permanence theorem for infinite dimensional systems. What is more, a n-stage-structured HIV model with two distributed intracellular delays, which is the extensions to the first model, is developed and analyzed. We also prove the global asymptotical stabilities of two equilibria by constructing suitable Lyapunov functionals.     

Thermodynamically consistent modeling of granular-fluid mixtures incorporating pore pressure evolution and hypoplastic behavior

This paper presents a new, thermodynamically consistent model for granular-fluid mixtures, derived with the entropy principle of Müller and Liu. Including a pressure diffusion equation combined with the concept of extra pore pressure, and hypoplastic material behavior, thermodynamic restrictions are imposed on the constitutive quantities. The model is applied to a granular-fluid flow, using a closing assumption in conjunction with the fluid pressure. While the focal point of the work is the conceptional part, i.e. the thermodynamic consistent modeling, numerical simulations with physically reasonable results for simple shear flow are also carried out.     

HO2+HONO及其异构体抽氢反应机理

本文在CCSD(T)/aug-cc-pVTZ//M06-2X/6-311+G(3d,2p)水平上构建了HO_2与HONO及其异构体的反应势能剖面,并对各通道的速率常数进行了计算。结果表明,HONO存在cis-HONO、trans-HONO、HNO_2三种不同的异构体,其中HNO_2是最稳定的构型。HNO_2+HO_2反应(R3)能垒比其他两个反应(R1(cisHONO+HO_2)和R2(trans-HONO+HO_2))的能垒降低了8. 2～13. 8 kcal·mol~(-1)。采用传统过渡态理论结合Wigner校正对各反应在240～425 K范围内的速率常数进行了计算。结果表明,反应R3的速率常数比R1和R2的对应值大4～9个数量级,表明HO_2+HONO及其异构体的抽氢反应的速率主要取决于HNO_2+HO_2反应。     

Imaging properties of photon sieve with a large aperture

We report the optimization design and experimental results for the imaging properties of a photon sieve, which is formed on a layer of metal film supported by a thin glass substrate. As an example, we considered a micro-optical element with parameters of diameter D=50 mm, 3,564,290 hole number, and 10 μm minimum micro-hole diameter, which was designed and fabricated by means of surface machining technique in the lab. To evaluate its imaging performance, both on-axis and off-axis imaging experiments were carried out using the element. Compared to a Fresnel zone plate lens with the same feature size, the photon sieve has super imaging performance. Some quantitative analyses and initial qualitative explanations were given for the imaging characteristics.     

A thermo-mechanical continuum theory with internal length for cohesionless granular materials

This article continues Part I. Here the non-equilibrium responses of the constitutive variables t (Cauchy stress tensor), q (heat flux vector), h (equilibrated stress vector), Γ (flux term associated with the internal length ℓ), Π (production term associated with ℓ) and f (equilibrated intrinsic body force) as well as the Helmholtz free energy Ψ are postulated by use of a quasi-linear theory for three of four models deduced in Part I. In so doing, together with the equilibrium responses gained in Part I, a complete set of constitutive equations for the constitutive quantities for each model is obtained. The implemented models are applied to investigate typical isothermal steady granular shearing flows with incompressible grains, namely, simple plane shear flow, inclined gravity-driven flow and vertical channel-flow. The emphasis is on the models in which ℓ is considered a material constant (Model I) and an independent dynamic field quantity (Model III). Numerical results show that Model III is more appropriate than Model I since in the former model the effect of the motion of an individual grain can better be taken into account. Such a result is in particular significant for avalanches, since it verifies the existence of a thin layer immediately above the base of an avalanche, in which the grains are colliding strongly with one another, and provides a quantitative means to measure such a thin layer.     

对于方程a~x=x和a~(a~x)=x(a>0,a≠1)解的个数的探讨

本文讨论了两个方程a~x=x和a~(a~x)=x(a0,a≠1)解的问题,应用高等数学中的知识给出了两个方程解的存在条件和相应的个数,纠正了一些直观的错误,通过该问题的讨论可以加深学生对高数函数知识的理解和应用.     

Ethylenediamine tetramethylene phosphonic acid assisted synthesis of palladium nanocubes and their electrocatalysis of formic acid oxidation

The synthesis of Pd nanocrystals of controlled size and morphology has drawn enormous interest due to their catalytic activity. We report a new and efficient strategy for the one-step synthesis of monodispersed Pd nanocubes with ethylenediamine tetramethylene phosphonate (EDTMP) as a complex-forming and capping agent. The morphology, structure, and growth mechanism of the Pd nanocubes were fully characterized via selected area electron diffraction (SAED), transmission electron microscopy (TEM), X-ray diffraction (XRD), and X-ray photoelectron spectroscopy (XPS). It was found that the morphology of the Pd nanocrystals in the proposed EDTMP–PdCl₂ system could be changed from octahedrons to nanocubes simply by adjusting the amount of iodide used during synthesis. After UV/ozone and electrochemical cleaning, the as-prepared Pd nanocubes demonstrated excellent electrocatalytic activity and stability during formic acid oxidation, owing to their abundant {100} facets and small particle size.     

A thermo-mechanical continuum theory with internal length for cohesionless granular materials

A thermodynamically consistent continuum theory for single-phase, single-constituent cohesionless granular materials is presented. The theory is motivated by dimensional inconsistencies of the original Goodman-Cowin theory [1–3]; it is constructed by removing these inconsistencies through the introduction of an internal length ℓ. Four constitutive models are proposed and discussed in which ℓ is (i) a material constant (Model I), (ii) an independent constitutive variable (Model II), (iii) an independent dynamic field quantity (Model III) and (iv) an independent kinematic field quantity (Model IV). Expressions of the constitutive variables emerging in the systems of the balance equations in these four models in thermodynamic equilibrium are deduced by use of a thermodynamic analysis based on the Müller-Liu entropy principle. Comments on the validity of these four models are given and discussed; the results presented in the current study show a more general formulation for the constitutive quantities and can be used as a basis for further continuum-based theoretical investigations on the behaviour of flowing granular materials. Numerical results regarding simple plane shear flows will be discussed and compared in Part II of this work.     

Invariant-mass distribution of top-quark pairs and top-quark mass determination

In this study, we investigate the invariant-mass distribution of top-quark pairs near the 2m_t threshold, which strongly influences the determination of the top-quark mass m_t. Higher-order non-relativistic corrections lead to large contributions, which are not included in the state-of-the-art theoretical predictions. A factorization formula is derived to resum such corrections to all orders in the strong-coupling, and necessary ingredients are calculated to perform the resummation at next-to-leading power. We combine the resummation with fixed-order results and present phenomenologically relevant numerical results. The resummation effect significantly increases the differential cross-section in the threshold region and makes the theoretical prediction more compatible with experimental data. We estimate that using our prediction in the determination of \begin{document}$m_t $\end{document} will lead to a value closer to the direct measurement result.