简介：本文给出任意有限维全微分方程的判定定理与求通解的一种方法。定理的条件是充要的。判断与求通解是同步进行的,方法简单,运用方便。解决了高维全微分方程的判断与求通解的困难。

简介：本文首先给出integralfromato+∞f（x）dx收敛≠lim+∞f（x）=0的一更强的例子,然后给出一个与级数收敛的必要条件类似的,integralfromato+∞f（x）dx收敛的必要条件。在许多工科高等数学教材中,广义积分敛散性的判别,一般都在级数中讨论,因而一部分同学和个别教师往往把级数的一些重要性质,直接推广到广义积分integralfromato+∞f（x）dx上。最典型的错误是把级数收敛的必要条件推广到广义积分上,即integralfromato+∞f（x）dx收敛?lim?+∞f（x）=0.这类错误较为普遍。

简介：Effectsofself-coilingoforganicmoleculesonintramolecularexciplexformationofcompoundI,inwhichthecarbazolechromophoreandterephthalicacidmethylesteracceptorgrouparelinkedbyone(CH2)10chain,andthedecreaseofthefluorescenceintensitiesofcompoundsⅡ，Ⅲ，andⅣ,inwhichthecarbazolechromophoreand3,5-dinitrobenzoateareconnectedbyonealiphaticchainof(CH2)10(Ⅱ），（CH2）12（Ⅲ）,or(CH2)4(Ⅳ）,havebeenstudiedinthedioxane(DX)-H2Obinarysystem.Theresultsshowthatself-coilingoforganicmoleculesinDX-H2OfacilitatesintramolecularexciplexformationofIandinducesthedecreaseoffluorescenceintensitiesofⅡ,bacauseoftheproximityeffectbroughtaboutbyselfcoilingoforganicmoleculesunderhydrophobic-lipophilicinteraction(HLI)betweentheexcitedcarbazolechromophoreandtheacceptor.SincethesimilareffectsareobservedevenwhentheconcentrationoftheprobesarelessthantheirCAgCs(criticalaggregateconcentrations)intheDX-H2Omixturewiththesameφvalues,formationoftheintermolecularexciplexhasbeenexcluded.Theeffectsarefoundtobestronglydependedonφvalues,indicationthattheyaremainlydrivenbyHLI.Thepropertiesoftheacceptorscanalsoaffecttheintramolecularexciplexformation.Withterephthalicacidmethylestermoietyastheacceptor,thecarbazolechromophoreexhibitsthefluorescencespectraoftheexciplex,whilewith3,5-dinitrobenzoatemoietyastheacceptor,onlythefluorescencespectraofexcitedcarbazolylchromophoreareobserved.

简介：在不定积分的教学中,我们会碰到形如integralfromn=1（Pn（x）dx）/(（x+Px+q）q?)的积分,如同济二版高等数学