简介：这篇调查文章记录unguided由在最后十年里的北京大学和他们的合作者的topologists的数学旅游。旅游从关于chirality的研究开始了并且，在引起注意的人附近由问题吸引了，越过拓扑学和动力学导致了一条之字形路径。在各种各样的阶段在这旅游加入了我们的人包括丁凡，刘毅，NiYi，潘建忠，姚建刚，郑浩和周青。与罗伯特·爱德华兹，温兰和其它一起的谈话，补充说使旅行成为了更多的趣事到扭曲和拐弯。这篇文章由这些作者得益于相关讲课，在许多会议，大学，以及高中。

简介：Analyticalsolutionsfortheelasticpropertiesofavarietyofbinarynanotubeswitharbitrarychiralityareobtainedthroughthestudyofsystematicmolecularmechanics.Thismolecularmechanicsmodelisfirstextendedtochiralbinarynanotubesbyintroducinganadditionaloutof-planeinversiontermintotheso-calledstick-spiralmodel,whichresultsfromthepolarbondsandthebucklingofbinarygraphiticcrystals.Theclosed-formexpressionsforthelongitudinalandcircumferentialYoung’smodulusandPoisson’sratioofchiralbinarynanotubesarederivedasfunctionsofthetubediameter.Theobtainedinversionforceconstantsarenegativeforalltypesofbinarynanotubes,andthepredictedtubestiffnessislowerthanthatbytheformerstick-spiralmodelwithoutconsiderationoftheinversionterm,reflectingthesofteningeffectofthebucklingontheelasticpropertiesofbinarynanotubes.Theobtainedpropertiesareshowntobecomparabletoavailabledensityfunctionaltheorycalculatedresultsandtobechiralityandsizesensitive.ThedevelopedmodelandexplicitsolutionsprovideasystematicunderstandingofthemechanicalperformanceofbinarynanotubesconsistingofIII–VandII–VIgroupelements.

简介：BasedonthemethodofseparatingvariablesandthetechniqueofMuller’scalculatingroots,thepropagationcharacteristicsofhybridmodesinhomogeneousandinhomogeneouscircularFaradaychirowaveguidesareexaminedindetail.Numericalresultsarepresentedtodemonstratethecombinedeffectsofdifferentconstitutiveparametersonthemodebifurcation,symmetryandnonreciprocity,backward-waveandattenuationofhybridmodes,whicharedifferentfromthecasesofordinarygyrotropicandreciprocalchiralwaveguides.

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简介：Thecrystalstructureoftetrakis[(pyrrol-1-yl)methyl]methanewasdeterminedbyX-raydiffractionmeasurement,andtheresultshowsthatitbelongstomonocliniccrystalsystem,spacegroupisP21/n,witha=0.9284(3)nm,b=1.0950(6)nm,c=1.8749(8)nm;α=γ=90.00(4)°,β=103.63(3)°,V=1.8523(14)nm3,Z=4,ρcalcd.=1.192kg/m3,μ=0.072nm-1,F(000)=712,R1=0.0854,wR2=0.1884.Ithasbeenfoundthatthemoleculesexistintwoenantiomericstates.Enantioselectiveself-assembliessuchasone-dimensionalmolecularstacksinasinglehandedness,homochiralmonolayersandachiralsuperlatticearespecifiedinthisracemiccrystal.Inaddition,asimpletechniqueisadvocatedtodistinguishchiralstatesfromtetrahedralmoleculesinthesolidstate.ThepresentR/Snomenclatureofthetetracooradinatedcarboncentersisusedsolelyforitsconveniencetodistinguishthetwoenantiomericstates,butnotusedtodeterminetheabsoluteconfigurations.