Stability inL 1 of some integral operators

A class of Markov operators appearing in biomathematics is investigated. It is proved that these operators are asymptotic stable inL ¹, i.e. lim _n P ⁿ f=0 forfL ¹ and f(x) dx=0.     

LaC_3~n(n=-1,0,+1)分子簇的理论研究(英文)

用密度泛函方法研究了ＬａＣ３ｎ（ｎ＝－１，０，＋１）分子簇的结构和稳定性，对这个四原子体系，提出了５种可能构型，其中３种具有Ｃ２ｖ对称性，２种为Ｃ∞ｖ对称性．在Ｃ２ｖ对称性结构中，其中１个为Ｌａ接在弯曲的Ｃ３链上，第２个是Ｌａ通过２个键与Ｃ３环相链，第３个是Ｌａ通过１个键与Ｃ３环相连；在Ｃ∞ｖ对称性中，第１个Ｌａ接在Ｃ３链的一端，而在第２个构型中，Ｌａ被插入在Ｃ３链中．结果表明，环状结构当Ｌａ接在弯曲的Ｃ３链上的是局域极小值并且最稳定     

A central limit theorem for age- and density-dependent population processes

Consider a population consisting of one type of individual living in a fixed region with area A. In [8], we constructed a stochastic population model in which the death rate is affected by the age of the individual and the birth rate is affected by the population density P_A(t), i.e., the population size divided by the area A of the given region. In [8], we proposed a continuous deterministic model which in general is a nonlinear Volterra type integral equation and proved that under appropriate conditions the sequence P_A(t) would converge to the solution P(t) of our integral equation in the sense that

$\text{lim}\text{→∞}\text{P}\text{sup}\text{0?s?t}\text{|P}{}_{\mathrm{A}}\text{(s) ? P(s)|>ε}\text{=0}\text{for every}\text{ε > 0}$

.In this paper, we obtain a “central limit theorem” for the random element √A(P_A(t)?P(t)). We prove that under appropriate conditions √A(P_A(t)?P(t)) will converge to a Gaussian process. (See Theorem 3.4 for the explicit formula of this Gaussian process.)     

Synthesis of the four enantiomers of diethyl 1,2-di(N-Boc-amino)propylphosphonates

A simple and efficient synthetic strategy to all four enantiomerically pure diethyl 1,2-di(N-Boc-amino)propylphosphonates has been elaborated starting from the corresponding N-[(R)-(1-phenylethyl)]aziridine-(2S)- and N-[(S)-(1-phenylethyl)]aziridine-(2R)-carboxaldehydes, employing a one-pot three-components Kabachnik-Fields reaction followed by the hydrogenolytic removal of the chiral auxiliary and aziridine ring opening with simultaneous protection of the amino groups as the N-Boc derivatives.     

Dislocation-density-based constitutive modelling of tensile flow and work-hardening behaviour of P92 steel

The flow and work-hardening behaviour of tempered martensitic P92 steel have been investigated using phenomenological constitutive model in the temperature range 300–873 K for the strain rates ranging from 3.16 × 10^?5 to 1.26 × 10^?3 s^?1. The analysis indicated that the hybrid model reduced to Estrin–Mecking (E–M) one-internal-variable model at intermediate and high temperatures. Further, the analysis also indicated that dislocation dense martensite lath/cell boundaries and precipitates together act as effective barriers to dislocation glide in P92 steel. The flow behaviour of the steel was adequately described by the E–M approach for the range of temperatures and strain rates examined. Three distinct temperature regimes have been obtained for the variations in work-hardening parameters with respect to temperature and strain rate. Signatures of dynamic strain ageing in terms of the anomalous variations in work-hardening parameters at intermediate temperatures and the dominance of dynamic recovery at high temperatures have been observed. The evaluation of activation energy suggested that deformation is controlled by the dominance of cross-slip of dislocations at room and intermediate temperatures, and climb of dislocations at high temperatures.     

Interaction Products of 12·5 Deuterons with Molybdenum and their Isolation Possibilities from Worn-out Cyclotron Parts

Using chemical separations and radiometric measurements medium-half-life irradiation products of molybdenum with 12.5 MeV deuterons were determined (⁹⁰Nb, ⁹²Nb, ^95mNb, ⁹⁵Nb, ⁹⁶Nb, ⁹⁹Mo, ^95mTc, ⁹⁶Tc, ^99mTc) as well as thick target yields for some of them: ⁹²Nb (0.22 μCi/μAh), ⁹⁵Nb(0.05 μCi/μAh), ⁹⁹Mo (64 μCi/μAh), ^95mTc(0.76 μCi/μAh), ⁹⁶Tc((62.5 μCi/μAh). Moreover isolation possibiities of radioactive preparations from removed worn-cut molybdenum parts of the U-120 cycletron are discussed.     

On global stability of an HIV pathogenesis model with cure rate

In this paper, applying both Lyapunov function techniques and monotone iterative techniques, we establish new sufficient conditions under which the infected equilibrium of an HIV pathogenesis model with cure rate is globally asymptotically stable. By giving an explicit expression for eventual lower bound of the concentration of susceptible CD4⁺ T cells, we establish an affirmative partial answer to the numerical simulations investigated in the recent paper [Liu, Wang, Hu and Ma, Global stability of an HIV pathogenesis model with cure rate, Nonlinear Analysis RWA (2011) 12 : 2947–2961]. Our monotone iterative techniques are applicable for the small and large growth rate in logistic functions for the proliferation rate of healthy and infected CD4⁺ T cells. Copyright © 2014 John Wiley & Sons, Ltd.     

Large deformation of liquid capsules enclosed by thin shells immersed in the fluid

The deformation of a liquid capsule enclosed by a thin shell in a simple shear flow is studied numerically using an implicit immersed boundary method. We present a thin-shell model for computing the forces acting on the shell middle surface during the deformation within the framework of the Kirchhoff–Love theory of thin shells. This thin-shell model takes full account of finite-deformation kinematics which allows thickness stretching as well as large deflections and bending strains. For hyperelastic materials, the plane-stress assumption is used to compute the hydrostatic pressure and the incompressibility condition yields the thickness strain component and the corresponding change in the thickness. The stresses developing over the cross-section of the shell are integrated over the thickness to yield the stress and moment resultants which are then used to compute the forces acting on the shell middle surface. The immersed boundary method is employed for calculating the hydrodynamics and fluid–structure interaction effects. The location of the thin shell is updated implicitly using the Newton–Krylov method. The present numerical technique has been validated by several examples including an inflation of a spherical shell and deformations of spherical and oblate spheroidal capsules in the shear flow.