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简介：在这份报纸，作者定义强壮(弱)准确边界可控制性并且强壮(弱)为第一顺序quasilinear的准确边界observability夸张系统，和研究他们在他们之间的性质和关系。

简介：ThepresentpaperinvestigatesthefractalstructureoffractionalintegralsofWeierstrassfunctions.Theexactboxdimensionforsuchfunctionsmanyimportantcasesisestablished.Weneedtopointoutthat,althoughtheresultitselfachievedinthepresentpaperisinteresting,thenewtechniqueandmethodshouldbeemphasized.ThesenovelideasmightbeusefultoestablishtheboxdimensionorHausdorffdimension(especiallyforthelowerbounds)formoregeneralgroupsoffunctions.

简介：让ScR2是重申的功能系统的引起注意的人{f{，f2，f3}那么在联合起来的等边三角形上重申英尺(x)=Xtx+bhi=1,2,3，x={Xl，x2)，bx=(0,0)，b2=(1-A2,0)，b3=(-2.,-(1-A3))。这篇论文在关于收缩参数的一些条件下面决定准确Hausdorff措施，集中的盖住的措施和S的收拾行李的措施。

简介：Foraclassofmixedinitial-boundaryvalueproblemforgeneralquasilinearhyperbolicsystems,thispaperestablishesthelocalexactboundarycontrollabilitywithboundarycontrolsonlyactingononeend.Asanapplication,theauthorsshowthelocalexactboundarycontrollabilityforakindofnonlinearvibratingstringproblem.

简介：Inthispaper,thevariablecofficientKdVequationwithdissipativelossandnonuniformitytermsandthevariablecoefficientSGequationwithnonuniformitytermarestudied.TheexactsolutionsoftheKdVandSGequationsareobtained.Inparticular,thesolitonsolutionsoftwoequationsarefound.

简介：基于同质的平衡方法和试用函数方法，由指数的函数组成的几个试用函数方法被建议并且适用于非线性的分离系统。在符号的计算系统的帮助下，分离非线性的mKdV格子方程的新准确独居的波浪答案，分离非线性(2+1)维的Toda格子方程，Ablowitz-Ladik-lattice系统被构造。方法具有意义寻求准确独居的波浪解决方案到另外的非线性的分离系统。

简介：

简介：Byasingthenonclassicalmethodofsymmetryreductions,theexactsolutionsforgeneralvariable-coefficientKdVequationwithdissipativelossandnonuniformitytermsareobtained.Whenthedissipativelossandnonuniformitytermsdon'texist,themultisolitonsolutionsarefoundandthecorrespondingPainleveIItypeequationforthevariable-coefficientKdVequationisgiven.

简介：ThispapersummarizedrecentachievementsobtainedbytheauthorsabouttheboxdimensionsoftheBesicovitchfunctionsgivenbyB(t):=∞∑k=1λs-2ksin(λkt),where1＜s＜2,λk＞0tendstoinfinityask→∞andλksatisfiesλk+1/λk≥λ＞1.Theresultsshowthatlimk→∞logλk+1/logλk=1isanecessaryandsufficientconditionforGraph(B(t))tohavesameupperandlowerboxdimensions.ForthefractionalRiemann-LiouvilledifferentialoperatorDuandthefractionalintegraloperatorD-v,theresultsshowthatifλissufficientlylarge,thenanecessaryandsufficientconditionforboxdimensionofGraph(D-v(B)),0＜v＜s-1,tobes-vandboxdimensionofGraph(Du(B)),0＜u＜2-s,tobes+uisalsolimk→∞logλk+1/logλk=1.

简介：Theexactparametricrepresentationsofthetravelingwavesolutionsforanonlinearelasticrodequationareconsidered.Byusingthemethodofplanardynamicalsystems,indifferentparameterregions,thephaseportraitsofthecorrespondingtravelingwavesystemaregiven.Exactexplicitkinkwavesolutions,periodicwavesolutionsandsomeunboundedwavesolutionsareobtained.

简介：在这篇文章，作者由夸张正切功能扩大方法，夸张正割扩大方法，和Jacobi椭圆形的功能与量修正为血浆学习修改Zakharov方程的准确旅行波浪答案扩大方法。他们包括三角法的函数解决方案，合理函数解决方案，和更多获得更多的准确旅行波浪解决方案通常独居的波浪，它被称为古典明亮的soliton，塑造W的soliton，和塑造M的soliton。

简介：这份报纸使描述有弹性的字符串的一个3-dimensional网络的颤动的非线性的波浪方程的一个系统担心。作者导出方程和适当节的条件，决定平衡解决方案，并且，由使用quasilinear的方法夸张系统，证明那因为树联网天赋起始，边界值问题有古典解决方案在拉长的平衡解决方案的邻居存在。然后，这的本地可控制性近联网在某个指定时间间隔的配置被证明的如此的平衡。最后，它被证明那，给二不同平衡状态令人满意某些条件，在足够地大的时间间隔上在第二平衡的一位合适的邻居在一平衡的一位足够小的邻居从状态控制网络到任何状态是可能的。

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简介：Inthisarticle,byusingtheoryoflinearevolutionsystemandSchauderfixedpointtheorem,weestablishasufficientresultofexactnullcontrollabilityforanonautonomousfunctionalevolutionsystemwithnonlocalconditions.Inparticular,thecompactnesscondi-tionorLipschitzconditionforthefunctionginthenonlocalconditionsappearinginvariousliteraturesisnotrequiredhere.Anexampleisalsoprovidedtoshowanapplicationoftheobtainedresult.

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简介：Forfirst-orderquasilinearhyperbolicsystemswithzeroeigenvalues,theauthorestablishesthelocalexactcontrollabilityinashortertime-periodbymeansofinternalcontrolsactingonsuitabledomains.Inparticular,undercertainspecialbutreasonablehypotheses,thelocalexactcontrollabilitycanberealizedonlybyinternalcontrols,andthecontroltimecanbearbitrarilysmall.

简介：Bythemethodofdynamicalsystem,weconstructtheexacttravellingwavesolutionsofanewHamiltonianamplitudeequationandtheOstrovskyequation.Basedonthismethod,thenewexacttravellingwavesolutionsofthenewHamiltonianamplitudeequationandtheOstrovskyequation,suchassolitarywavesolutions,kinkandanti-kinkwavesolutionsandperiodictravellingwavesolutions,areobtained,respectively.

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简介：Inthispaperwegivetheexactorderof丨x-xk丨丨lk（x）丨foranyfixednonnegativeintegerssandt,whichisn-s,n-slnnandn1-fors≤t-2,s=t-1ands≥t,respectively.