Schur convexity, Schur geometrical convexity and Schur harmonic convexityof a class of symmetric functions are investigated. As consequences some knowninequalities are generalized. In addition, a class of geometric in...Schur convexity, Schur geometrical convexity and Schur harmonic convexityof a class of symmetric functions are investigated. As consequences some knowninequalities are generalized. In addition, a class of geometric inequalities involvingn-dimensional simplex in n-dimensional Euclidean space En and several matrix inequalitiesare established to show the applications of our results.展开更多
Computer-aided Design （CAD）, video games and other computer graphic related technology evolves substantial processing to geometric elements. A novel geometric computing method is proposed with the integration of des...Computer-aided Design （CAD）, video games and other computer graphic related technology evolves substantial processing to geometric elements. A novel geometric computing method is proposed with the integration of descriptive geometry, math and computer algorithm. Firstly, geometric elements in general position are transformed to a special position in new coordinate system. Then a 3D problem is projected to new coordinate planes. Finally, according to 2D/3D correspondence principle in descriptive geometry, the solution is constructed computerized drawing process with ruler and compasses. In order to make this method a regular operation, a two-level pattern is established. Basic Layer is a set algebraic packaged function including about ten Primary Geometric Functions （PGF） and one projection transformation. In Application Layer, a proper coordinate is established and a sequence of PGFs is sought for to get the final results. Examples illustrate the advantages of our method on dimension reduction, regulatory and visual computing and robustness.展开更多
By virtue of Cauchy’s integral formula in the theory of complex functions,the authors establish an integral representation for the weighted geometric mean,apply this newly established integral representation to show ...By virtue of Cauchy’s integral formula in the theory of complex functions,the authors establish an integral representation for the weighted geometric mean,apply this newly established integral representation to show that the weighted geometric mean is a complete Bernstein function,and find a new proof of the well-known weighted arithmetic-geometric mean inequality.展开更多
Sunoj et al.[(2009).Characterization of life distributions using conditional expectations of doubly(Intervel)truncated random variables.Communications in Statistics–Theory and Methods,38(9),1441–1452]introduced the ...Sunoj et al.[(2009).Characterization of life distributions using conditional expectations of doubly(Intervel)truncated random variables.Communications in Statistics–Theory and Methods,38(9),1441–1452]introduced the concept of Shannon doubly truncated entropy in the literature.Quantile functions are equivalent alternatives to distribution functions in modelling and analysis of statistical data.In this paper,we introduce quantile version of Shannon interval entropyfor doubly truncated random variable and investigate it for various types of univariate distribution functions.We have characterised certain specific lifetime distributions using the measureproposed.Also we discuss one fascinating practical example based on the quantile data analysis.展开更多
基金The Doctoral Programs Foundation(20113401110009) of Education Ministry of Chinathe Natural Science Research Project(2012kj11) of Hefei Normal Universitythe NSF(KJ2013A220) of Anhui Province
文摘Schur convexity, Schur geometrical convexity and Schur harmonic convexityof a class of symmetric functions are investigated. As consequences some knowninequalities are generalized. In addition, a class of geometric inequalities involvingn-dimensional simplex in n-dimensional Euclidean space En and several matrix inequalitiesare established to show the applications of our results.
基金National Natural Science Foundation of China（No.61073986）
文摘Computer-aided Design （CAD）, video games and other computer graphic related technology evolves substantial processing to geometric elements. A novel geometric computing method is proposed with the integration of descriptive geometry, math and computer algorithm. Firstly, geometric elements in general position are transformed to a special position in new coordinate system. Then a 3D problem is projected to new coordinate planes. Finally, according to 2D/3D correspondence principle in descriptive geometry, the solution is constructed computerized drawing process with ruler and compasses. In order to make this method a regular operation, a two-level pattern is established. Basic Layer is a set algebraic packaged function including about ten Primary Geometric Functions （PGF） and one projection transformation. In Application Layer, a proper coordinate is established and a sequence of PGFs is sought for to get the final results. Examples illustrate the advantages of our method on dimension reduction, regulatory and visual computing and robustness.
文摘By virtue of Cauchy’s integral formula in the theory of complex functions,the authors establish an integral representation for the weighted geometric mean,apply this newly established integral representation to show that the weighted geometric mean is a complete Bernstein function,and find a new proof of the well-known weighted arithmetic-geometric mean inequality.
基金The first author wishes to acknowledge the Science and Engineering Research Board(SERB)Government of India,for the financial assistance(Ref.No.ECR/2017/001987)for carrying out this research work.
文摘Sunoj et al.[(2009).Characterization of life distributions using conditional expectations of doubly(Intervel)truncated random variables.Communications in Statistics–Theory and Methods,38(9),1441–1452]introduced the concept of Shannon doubly truncated entropy in the literature.Quantile functions are equivalent alternatives to distribution functions in modelling and analysis of statistical data.In this paper,we introduce quantile version of Shannon interval entropyfor doubly truncated random variable and investigate it for various types of univariate distribution functions.We have characterised certain specific lifetime distributions using the measureproposed.Also we discuss one fascinating practical example based on the quantile data analysis.
