A linear convection equation with discontinuous coefficients arises in wave propagation through interfaces. An interface condition is needed at the interface to select a unique solution. An upwind scheme that builds t...A linear convection equation with discontinuous coefficients arises in wave propagation through interfaces. An interface condition is needed at the interface to select a unique solution. An upwind scheme that builds this interface condition into its numerical flux is called the immersed interface upwind scheme. An ι1-error estimate of such a scheme was first established by Wen et al. （2008）. In this paper, we provide a simple analysis on the ι1-error estimate. The main idea is to formulate the solution to the underline initial-value problem into the sum of solutions to two convection equations with constant coefficients, which can then be estimated using classical methods for the initial or boundary value problems.展开更多
The kinetics of ternary complex formation involving Cu(5-X-1, 10-phen) and threonine (CuAL, A=5-X-1, 10-phen; L=threonine or represented by O-N; X=NO_2, Cl, H, CH_3) has been studied by temperature-jump and stopped-fl...The kinetics of ternary complex formation involving Cu(5-X-1, 10-phen) and threonine (CuAL, A=5-X-1, 10-phen; L=threonine or represented by O-N; X=NO_2, Cl, H, CH_3) has been studied by temperature-jump and stopped-flow methods. The formation rate constants, k_f(M^(-1).s^(-1)), for the complexation reaction, CuA + LCuAL, are as follows; X=NO_2, 8.68×10~8; X=Cl, 7.13×10~8; X=H, 6.12×10~8; X=CH_3, 5.42×10~8. The rate constants for zwitterion attack are nil within experimental error. It has been found that a linear free energy relationship exists between the stability(logK_(CuAL)^(CuA) of the complexes CuAL and log kf as follows: IogK_(CuAL)^(CuA)=0.13 + 0.83 logk_f, r=0.99. It suggested that the formation rate governed the stability of the ternary complexes. The rates of formation of the ternary complexes increased with decreasing electron-donating property of the substituents. A linear relationship was found to exist as expressed by the following equation: log(k_f^R/k_F^O) = 0.097σ, r=0.96. A mechanism involves a rapid equilibrium between CuA and L followed by a slow ring closure of L.展开更多
基金supported by National Science Foundation of USA(Grant No.DMS1114546)
文摘A linear convection equation with discontinuous coefficients arises in wave propagation through interfaces. An interface condition is needed at the interface to select a unique solution. An upwind scheme that builds this interface condition into its numerical flux is called the immersed interface upwind scheme. An ι1-error estimate of such a scheme was first established by Wen et al. （2008）. In this paper, we provide a simple analysis on the ι1-error estimate. The main idea is to formulate the solution to the underline initial-value problem into the sum of solutions to two convection equations with constant coefficients, which can then be estimated using classical methods for the initial or boundary value problems.
文摘The kinetics of ternary complex formation involving Cu(5-X-1, 10-phen) and threonine (CuAL, A=5-X-1, 10-phen; L=threonine or represented by O-N; X=NO_2, Cl, H, CH_3) has been studied by temperature-jump and stopped-flow methods. The formation rate constants, k_f(M^(-1).s^(-1)), for the complexation reaction, CuA + LCuAL, are as follows; X=NO_2, 8.68×10~8; X=Cl, 7.13×10~8; X=H, 6.12×10~8; X=CH_3, 5.42×10~8. The rate constants for zwitterion attack are nil within experimental error. It has been found that a linear free energy relationship exists between the stability(logK_(CuAL)^(CuA) of the complexes CuAL and log kf as follows: IogK_(CuAL)^(CuA)=0.13 + 0.83 logk_f, r=0.99. It suggested that the formation rate governed the stability of the ternary complexes. The rates of formation of the ternary complexes increased with decreasing electron-donating property of the substituents. A linear relationship was found to exist as expressed by the following equation: log(k_f^R/k_F^O) = 0.097σ, r=0.96. A mechanism involves a rapid equilibrium between CuA and L followed by a slow ring closure of L.
