NRxx Simulation of Microflows with Shakhov Model

In this paper, we propose a method to simulate the microflows with Shakhov model using the NRxx method developed in [4, 5, 6]. The equation under consideration is the Boltzmann equation with force terms and the Shakhov model is adopted to achieve the correct Prandtl number. As the focus of this paper, we derive a uniform framework for different order moment systems on the wall boundary conditions, which is a major difficulty in the moment methods. Numerical examples for both steady and unsteady problems are presented to show the convergence in the number of moments.Comment: 31 pages, 10 figure

Effect of early exogenous supplementation of rhIGF-1 on oxygen-induced retinopathy in a mice model of prematurity, and on expressions of IGF-1 and VEGF

Purpose: To investigate the effect of early exogenous supplementation of recombinant human insulinlike growth factor (rhIGF-1) on oxygen-induced mouse model of retinopathy of prematurity (ROP). Methods: Three groups of healthy SPF grade C57BL/6 mice were used in this study, with 20 mice in each group. Hyperoxia saline (HS) and hyperoxia rhIGF-1 (HrGF) groups were placed in a closed oxygen chamber for one week and returned to the normal environment on the 15th day. The hyperoxia rhIGF-1 (HrGF) group was intraperitoneally injected with rhIGF-1 (1.5 mg/kg), while mice in high-oxygen saline (HS) group received normal saline. The air group (AG) was untreated. Changes in retinal blood vessel distributions, expression levels of serum IGF-1 and VEGF, and retinal IGF-1 and VEGF were determined. Results: On day 20, pronounced neo-vascularization was observed, but the distribution was disordered. Serum IGF-1 levels in AG and HrGF were significantly higher than that in HS group, but VEGF level was lower in HS mice (p < 0.05). VEGF level in hyperoxia rhIGF-1 group on days 11 and 15 decreased, relative to control value, while retinal IGF-1 and VEGF in AG and hyperoxia rhIGF-1 mice were elevated, relative to corresponding values in HS mice (p < 0.05). Conclusion: Early exogenous supplementation of rhIGF-1 exerts a therapeutic effect on ROP. Thus, rhIGF-1 may be a potential drug regimen for ROP in clinics

Diquark mass differences from unquenched lattice QCD

We calculate diquark correlation functions in the Landau gauge on the lattice using overlap valence quarks and 2+1-flavor domain wall fermion configurations. Quark masses are extracted from the scalar part of quark propagators in the Landau gauge. Scalar diquark quark mass difference and axial vector scalar diquark mass difference are obtained for diquarks composed of two light quarks and of a strange and a light quark. Light sea quark mass dependence of the results is examined. Two lattice spacings are used to check the discretization effects. The coarse and fine lattices are of sizes $24^3\times64$ and $32^3\times64$ with inverse spacings $1/a=1.75(4) {\rm~GeV}$ and $2.33(5) {\rm~GeV}$, respectively.Comment: 9 figure

Single-Period Two-Product Inventory Model with Substitution

In this paper we study a single-period two -product inventory model with stochastic demands, proportional revenues and costs, substitution. We focus on full downward substitution in our study. We assume that the orders have to be placed before the demands are realized. And the problem is to decide the ordering quantity for each product. We develop a general profit maximization model for single-period two -product substitution problem, and show that it is concave and submodular. And we develop the optimization condition for the problem and rewrite the solution of the problem in a perfect form, which is similar to the solution of the newsboy problem. Then we compare the solution of this problem with the solution of newsboy problem, and proof that the profit can be improved using the substitution policy. For the optimization solution, we study the effects of the parameters, such as the purchase cost, the penalty cost, the salvage value, the sale price. And we can get some interesting properties of the solution with respect to the parameters, and so we can know some instructions to adjust the order quantities while the parameters are changed. From the properties, we can find out the parameters that have stronger effects on the order quantities, and pay more attention on them while making the ordering decision