Equivalence of u–p and ζ–ψ formulations of the time-dependent Navier–Stokes equations

This paper deals with the non-stationary incompressible Navier--Stokes equations for two-dimensional flows expressed in terms of the velocity and pressure and of the vorticity and streamfunction. The equivalence of the two formulations is demonstrated, both formally and rigorously, by virtue of a condition of compatibility between the boundary and initial values of the normal component of velocity. This condition is shown to be the only compatibility condition necessary to allow for solutions of a minimal regularity, namely H¹ for the velocity, as in most current numerical schemes relying on spatial discretizations of local type.     

泛连通图定理和Ore2条件

记Ore2=min{d(y) d(x)|x,y∈V(G),d(x,y)=2}，本得到：若n阶图G的Ore2≥n 1，则G是[5;n]泛连通图。此是比Faudree等人的定理进一步的结果。     

二层多目标规划的最优性条件

本文在集值优化的框架下提出了一个二层多目标规划模型（BLMOP）.利用集值映射的相依导数和相依上导数,给出了几个有关（BLMOP）的弱有效解的必要或充分最优性条件.     

Evaluation of the drag force by integrating the energy dissipation rate in stokes flow for 2D domains using the FEM

The total drag force on the surface of a body, which is the sum of the form drag and the skin friction drag in a 2D domain, is numerically evaluated by integrating the energy dissipation rate in the whole domain for an incompressible Stokes fluid. The finite element method is used to calculate both the energy dissipation rate in the whole domain as well as the drag on the boundary of the body. The evaluation of the drag and the energy dissipation rate are post-processing operations which are carried out after the velocity field and the pressure field for the flow over a particular profile have been obtained. The results obtained for the flow over three different but constant area profiles—a circle, an ellipse and a cross-section of a prolate spheroid—with uniform inlet velocity are presented and it is shown that the total drag force times the velocity is equal to the total energy dissipation rate in the entire finite flow domain. Hence, by calculating the energy dissipation rate in the domain with unit velocity specified at the far-field boundary enclosing the domain, the drag force on the boundary of the body can be obtained.     

Synthesis of 2-methylidene-1-silacyclohexanes from 2,6-dibromohex-1-ene and polyhalosilanes

Various 2-methylidene-1-silacyclohexanes were prepared by straightforward syntheses from readily available polychloro- or polyfluorosilanes, magnesium and 2,6-dibromohex-1-ene using Barbier-type conditions or a previously synthesized Grignard reagent. Good yields were obtained considering the low stability of the products in the reaction conditions.     

Uptake and excretion of total inorganic arsenic by the freshwater alga Chlorella vulgaris

Arsenic-tolerant freshwater alga Chlorella vulgaris which had been collected from an arsenicpolluted environment were tested for uptake and excretion of inorganic arsenic. Approximately half the quantity of arsenic taken up by C. vulgaris was estimated to be adhered to the extraneous coat (10 wt %) of the cell. The remainder was bioaccumulated by the cell. Both adhered and accumulated arsenic concentrations increased with an increase in arsenic(V) concentration of the aqueous phase. Arsenic(V) accumulation was affected by the growth phse: arsenic was most actively accumulated when the cell was exposed to arsenic during the early exponential phase and then accumulation decreased with an increase in culture time exposed to arsenic. The alga grew well in the modified Detmer (MD) medium containing 1 mg As(III) dm^?3 and the growth curve was approximated by a ‘logistic equation’. Arsenic(III) was accumulated up to the second day of the culture time and arsenic(III) accumulation decreased with an increase in the culture time after that. Arsenic accumulation was also largely affected by various nutrients, especially by managanese, iron and phosphorus compounds. A modified MD medium with the three nutrients was proposed for the purpose of effective removal of arsenic from the aqueous phase. Using radioactive arsenate (Na₂H⁷⁴AsO₄), the arsenic accumulated was found to be readily excreted under conditions which were unfavourable for the multiplication of C. vulgaris.     

Trichloroisocyanuric acid as a novel oxidizing agent for the oxidation of 1,3,5-trisubstituted pyrazolines under both heterogeneous and solvent free conditions

Trichloroisocyanuric acid is used as an effective oxidizing agent for the oxidation of 1,3,5-trisubstituted pyrazolines to their corresponding pyrazoles under both heterogeneous and also solvent free conditions with good yields at room temperature.     

Calculation of impulsively started incompressible viscous flows

The paper's focus is the calculation of unsteady incompressible 2D flows past airfoils. In the framework of the primitive variable Navier–Stokes equations, the initial and boundary conditions must be assigned so as to be compatible, to assure the correct prediction of the flow evolution. This requirement, typical of all incompressible flows, viscous or inviscid, is often violated when modelling the flow past immersed bodies impulsively started from rest. Its fulfillment can however be restored by means of a procedure enforcing compatibility, consisting in a pre‐processing of the initial velocity field, here described in detail. Numerical solutions for an impulsively started multiple airfoil have been obtained using a finite element incremental projection method. The spatial discretization chosen for the velocity and pressure are of different order to satisfy the inf–sup condition and obtain a smooth pressure field. Results are provided to illustrate the effect of employing or not the compatibility procedure, and are found in good agreement with those obtained with a non‐primitive variable solver. In addition, we introduce a post‐processing procedure to evaluate an alternative pressure field which is found to be more accurate than the one resulting from the projection method. This is achieved by considering an appropriate ‘unsplit’ version of the momentum equation, where the velocity solution of the projection method is substituted. Copyright © 2004 John Wiley & Sons, Ltd.     

Point-to-Periodic and Periodic-to-Periodic Connections

In this work we consider computing and continuing connecting orbits in parameter dependent dynamical systems. We give details of algorithms for computing connections between equilibria and periodic orbits, and between periodic orbits. The theoretical foundation for these techniques is given by the seminal work of Beyn in 1994, “On well-posed problems for connecting orbits in dynamical systems”, where a numerical technique is also proposed. Our algorithms consist of splitting the computation of the connection from that of the periodic orbit(s). To set up appropriate boundary conditions, we follow the algorithmic approach used by Demmel, Dieci, and Friedman, for the case of connecting orbits between equilibria, and we construct and exploit the smooth block Schur decomposition of the monodromy matrices associated to the periodic orbits. Numerical examples illustrate the performance of the algorithms. This revised version was published online in July 2006 with corrections to the Cover Date.     

Positive periodic solution of two-species ratio-dependent predator–prey system with time delay in two-patch environment

In this paper, we are concerned with the existence of positive periodic solution to a class of two-species ratio-dependent predator–prey diffusion model with time delay. By using the continuation theorem of coincidence degree theory, we transform this problem into a problem of calculating the topological degree of a continuous mapping, and then some sufficient conditions of the existence of positive periodic solution is established for the system.