简介:本文研究了Riemann积分和Lebesgue积分的本质区别,得到了结论:从Riemann积分推广到Lebesgue积分的本质是从不完备空间R[a,b]到完备空间L[a,b]的扩充.
简介:Byapplyingiterativetechnique,weobtaintheexistenceofpositivesolutionsforasingularRiemann-Stieltjesintegralboundaryvalueprobleminthecasethatf(t,u)isnon-increasingrespecttou.
简介:摘要构造辅助函数是高中数学中一种常用的方法。所谓“构造函数法”是根据问题题设和题目的结构特征构造辅助函数,将原问题转化为研究辅助函数的性质,凭借辅助函数的性质解决问题的一种方法。近几年各地高考数学试卷中,许多涉及抽象函数与导数的题目都要运用这种方法解决问题,使得这一方法成为一个热点。本文就这一方法的应用做进一步的总结,以期为高中学生提供一定的参考价值。
简介:Thequestforneuroprotectivedrugstoslowtheprogressionofneurodegenerativediseases(NDDs),includingAlzheimer'sdisease(AD),Parkinson'sdisease(PD),andHuntington'sdisease(HD),hasbeenlargelyunrewarding.Preclinicalevidencesuggeststhatrepurposingquetiapine,lithium,valproate,fluoxetine,donepezil,andmemantineforearlyandpre-symptomaticdisease-modificationinNDDsmaybepromisingandcanspareregulatorybarriers.Theliteratureofthesepsychotropicsinearlystageandpre-symptomaticAD,PD,andHDisreviewedandpropitiousfindingsfollow.Mildcognitiveimpairment(MCI)phaseofAD:salutaryhumanrandomizedcontrolledtrialfindingsforlow-doselithiumand,inselectedpatients,donepezilawaitreplication.Pre-symptomaticAD:humanepidemiologicaldataindicatethatlithiumreducesADrisk.Animalmodelstudies(AMS)revealencouragingresultsforquetiapine,lithium,donepezil,andmemantine.EarlyPD:valproateAMSfindingsshowpromise.Pre-symptomaticPD:lithiumandvalproateAMSfindingsareencouraging.EarlyHD:uncontrolledclinicaldataindicatenon-progressionwithlithium,fluoxetine,donepezil,andmemantine.Pre-symptomaticHD:lithiumandvalproateareauspiciousinAMS.Manyotherpromisingfindingsawaitingreplication(valproateinMCI;lithium,valproate,fluoxetineinpre-symptomaticAD;lithiuminearlyPD;lithium,valproate,fluoxetineinpre-symptomaticPD;donepezilinearlyHD;lithium,fluoxetine,memantineinpre-symptomaticHD)arereviewed.Dose-andstage-dependenteffectsareconsidered.Suggestionsforsignal-enhancementinhumantrialsareprovidedforeachNDDstage.