例谈数形结合在高数解题中的应用

通过微分中值的等式证明、求渐近线方程、定积分中的换元法、几何图形的描绘以及曲线积分的计算等例题,说明将代数运算或证明与几何直观相结合给解高等数学问题带来的好处．     

Synthesis and structure-insecticidal activity relationship of novel phenylpyrazole carboxylic acid derivatives containing fluorine moiety

A series of novel phenylpyrazole carboxylic acid derivatives containing fluorine moiety,i.e.,diamides 11,simple aryl-bearing amides 12 and acylthioureas 14 were successfully synthesized based on the key fluo ro-containing phe nylpyrazole acid intermediate.The new compounds were identified and confirmed by melting point,1H NMR,13C NMR and elemental analysis or HRMS.The bioassay results indicated that some of the compounds possessed excellent insecticidal activities towards oriental armyworm,diamondback moth and corn borer at low concentrations.For examples,compounds 11a,11e-g and 14b exhibited remarkable larvicidal activities with LC50 values of 0.13-0.39 mg/L and 0.0002-0.0014 mg/L against oriental armyworm and diamondback moth,respectively,were comparable with those of the control chlorantraniliprole.Particularly,lie were found superior to chlorantraniliprole in oriental armyworm tests(LC50:0.23 mg/L vs.0.26 mg/L);11a,lie,11f and 14c in diamondback moth tests with LC50 values of 0.0002 mg/L,0.0002 mg/L,0.0008 mg/L and 0.0005 mg/L,respectively,we re more effective than that of chlorantraniliprole.In addition,12 a also showed a promising insecticidal potential and development/optimization advantage.Compounds 11a,lle-g,12a,14b and 14c could be considered as possible new leading structures for further study.The SAR investigation indicated that the compounds with fluorine motif(e.g.,-F,-CF2H,-CF3)held apparently favorable insecticidal potentials,which provided useful guidance for further design/development of new phenylpyrazole-containing agrochemicals.