简介：Inthispaper,weestablishanewtypeofalternationtheoryformoregeneralrestrictedrangesChebyshevapproximationwithequalities.Theuniquenessandstronguniquenesstheoremsaregiven.Applyingtheresults,weobtainthealternationtheoremanduniquenesstheoremforbestcoposiliveapproximation.

简介：让G没有固定的点在的一个集合上的一个排列组，和m是一个积极整数。然后，G的运动被定义为行动(G)：=supG{|Gg\G|g？G}行动(G)：=\mathop{\sup}\limits_\Gamma\left\{{\left|{\Gamma^g\backslash\Gamma}\right|\left|{g\inG}\right}\right\}。它被Praeger显示出如果行动(G)=m那时|3m+t1，在t是G轨道在上的数字的地方。在这份报纸，有有最大值的度3m+t1的所有不及物的排列组跳了被分类。确实，她问题的一个积极答案是否上面的界限|=3m+t1为|为每t是锋利的>1被给。

简介：Wetransformthesingularintegralequationswithsolutionssimultaneouslyhavingsingularitiesofhigherorderatinfinitepointandatseveralfinitepointsontherealaxisintoonesalongaclosedcontourwithsolutionshavingsingularitiesofhigherorder,andfortheformerobtaintheextendedNeothertheoremofcompleteequationaswellasthesolutionsandthesolvableconditionsofcharacteristicequationfromthelatter.Theconclusionsdrawnbythisarticlecontainspecialcasesdiscussedbefore.

简介：Asacontinuationof[1],theauthorstudiesthelimitcyclebifurcationaroundthefocusS1otherthanO(0,0)forthesystem(1)asδvaries.Aconjectureonthenon-existenceoflimitcyclesaroundS1,andanotheroneonthenon-coexistenceoflimitcycleswoundbothOandS1aregiven,togetherwithsomenumericalexamples.

简介：Forthequadraticsystem:x=-y+δx+lx^2+ny^21y=x(1+ax-y)undercondtions-1<1<0,n+l-1>0theauthordrawsinthe(a,b)parameterplanetheglobalbifurcationdiagramoftrajectoriesaroundO(0,0).Noticethatwhenna^2+1<0thesystemhasonesaddleN(0,1/n)andthreeantisaddles.