An expansion theorem of a class of operator matrices is set up.The symplectic orthogonality of eigen-vectors is obtaind,and a necessary and sufficient condition for the completeness of the eigen-vector system is further given.As concrete applications,the obtained results are tested for differential equations.
{"title":"Eigen-vector Expansion Theorem of a Class of Operator Matrices","authors":"Y. Qiao","doi":"10.7498/aps.61.140205","DOIUrl":"https://doi.org/10.7498/aps.61.140205","url":null,"abstract":"An expansion theorem of a class of operator matrices is set up.The symplectic orthogonality of eigen-vectors is obtaind,and a necessary and sufficient condition for the completeness of the eigen-vector system is further given.As concrete applications,the obtained results are tested for differential equations.","PeriodicalId":16190,"journal":{"name":"Journal of Inner Mongolia University","volume":"58 2-3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2015-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91475440","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Surface and interface phonon-polaritons in four layer heterostructure systems consisting of polar ternary mixed crystals are investigated with the modified random-element-isodisplacement model and the Born-Huang approximation,based on the Maxwell's equations with the usual boundary conditions.The numerical results of the surface and interface phonon-polariton frequencies as functions of the thickness of slabs in the GaAs/Al0.4Ga0.6As heterostructure systems are obtained and discussed.It is shown that there are seven branches of surface and interface phonon-polariton modes in heterostructure systems,and the energies of surface or interface modes of the slab change with the thickness of slab,however,the other polariton modes almost not change.
{"title":"Effect of Thickness of Slabs on the Surface and Interface Phonon-Polaritons in Four Layer Systems Consisting of Polar Ternary Mixed Crystals","authors":"B. Ji","doi":"10.7498/aps.63.107105","DOIUrl":"https://doi.org/10.7498/aps.63.107105","url":null,"abstract":"Surface and interface phonon-polaritons in four layer heterostructure systems consisting of polar ternary mixed crystals are investigated with the modified random-element-isodisplacement model and the Born-Huang approximation,based on the Maxwell's equations with the usual boundary conditions.The numerical results of the surface and interface phonon-polariton frequencies as functions of the thickness of slabs in the GaAs/Al0.4Ga0.6As heterostructure systems are obtained and discussed.It is shown that there are seven branches of surface and interface phonon-polariton modes in heterostructure systems,and the energies of surface or interface modes of the slab change with the thickness of slab,however,the other polariton modes almost not change.","PeriodicalId":16190,"journal":{"name":"Journal of Inner Mongolia University","volume":"86 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2015-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74954845","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
My first career in Inner Mongolia University was as a researcher in particle physics.Then my interest was turned to the theoretical biophysics.The main problems are summarized on theoretical biology and bioinformatics which were studied by my group in the past 25 years.Among others the quantum folding theory,the principle of genome evolution and the cell's entropy production are emphasized and suggested as three fields to be investigated deeply and carefully in the future.
{"title":"Commemorating the Past and Looking towards the Future","authors":"L. Liao-fu","doi":"10.1142/5068","DOIUrl":"https://doi.org/10.1142/5068","url":null,"abstract":"My first career in Inner Mongolia University was as a researcher in particle physics.Then my interest was turned to the theoretical biophysics.The main problems are summarized on theoretical biology and bioinformatics which were studied by my group in the past 25 years.Among others the quantum folding theory,the principle of genome evolution and the cell's entropy production are emphasized and suggested as three fields to be investigated deeply and carefully in the future.","PeriodicalId":16190,"journal":{"name":"Journal of Inner Mongolia University","volume":"48 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2013-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80863189","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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