Convergence of linear multistep methods for two-parameter singular perturbation problems

1. IntroductionIt is well known that the IVPs of ODEs in singular perturbation form may be consideredas a special class of stab problems. But it is regrettable that they can't be satisfactorily covered by B-theory (of. [2-8]) because of their very special structure. In the recede ten yeaxslmany importallt and illteresting results on the convergence of linear multistep methods,Runge-Kutta methods, Rosenbrock methods and general linear methods applied to oneparameter singular perturbation pr…     

血红蛋白在L-半胱氨酸微银修饰电极上的电化学行为

L-半胱氨酸通过化学键结合到微银电极表面成化学修饰电极,研究表明此修饰电极对血红蛋白的氧化还原有促进作用.并用预富集和示差脉冲溶出伏安法检测血红蛋白的浓度,检测限为1.0×10~(-8)mol/L,8次测定2.0×10~(-7)mol/L血红蛋白的相对标准偏差是6.3%.     

Stability Analysis of Runge-Kutta Methods for Non-Linear Delay Differential Equations

This paper is concerned with the numerical solution of delay differential equations(DDEs). We focus on the stability behaviour of Runge-Kutta methods for nonlinear DDEs. The new concepts of GR(l)-stability, GAR(l)-stability and weak GAR(l)-stability are further introduced. We investigate these stability properties for (k, l)-algebraically stable Runge-Kutta methods with a piecewise constant or linear interpolation procedure.     

Synthesis and Characterization of 1-[2-(N,N-dimethyl-amino)ethyl]-1H-tetrazol-5-thiol

l-[2-(N,N-dimethyl-amino)ethyl]-1H-tetrazol-5-thiol is an important intermediate.It is widely used as cephalosporin C_S derivative.This paper has developed a new synthetic pathway to give it by six steps.The experimental procedures are shown the following.     

Modular-Approach Synthesis of Giant Molecule Acceptors via Lewis-Acid-Catalyzed Knoevenagel Condensation for Stable Polymer Solar Cells

The operational stability of polymer solar cells is a critical concern with respect to the thermodynamic relaxation of acceptor-donor-acceptor (A-D-A) or A-DA'D-A structured small-molecule acceptors (SMAs) within their blends with polymer donors. Giant molecule acceptors (GMAs) bearing SMAs as subunits offer a solution to this issue, while their classical synthesis via the Stille coupling suffers from low reaction efficiency and difficulty in obtaining mono-brominated SMA, rendering the approach impractical for their large-scale and low-cost preparation. In this study, we present a simple and cost-effective solution to this challenge through Lewis acid-catalyzed Knoevenagel condensation with boron trifluoride etherate (BF₃ ⋅ OEt₂) as catalyst. We demonstrated that the coupling of the monoaldehyde-terminated A-D-CHO unit and the methylene-based A-link-A (or its silyl enol ether counterpart) substrates can be quantitatively achieved within 30 minutes in the presence of acetic anhydride, affording a variety of GMAs connected via the flexible and conjugated linkers. The photophysical properties was fully studied, yielding a high device efficiency of over 18 %. Our findings offer a promising alternative for the modular synthesis of GMAs with high yields, easier work up, and the widespread application of such methodology will undoubtedly accelerate the progress of stable polymer solar cells.