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- W2364995801 abstract "In this paper,making use of algebraic inequalities and mathematical induction, a class of parametric inequalities of the dihedral angles of simplex∑(E,n)in n-dimensional Eu- clidean space E~n are gerenalized,a class of parametric inequalities without constraint condition about 2-mθ_(ij)~(E)(m∈N)are established.As their applications,some triangle inequalities are gerenalized to higher dimensional Euclidean space E~n,and a unsolved problem is introduced. The concept of all lateral face of simplex∑(H,n)in a hypersphere is introduced by the model of n-dimensional hyperbolic space H~n,then the quadratic form I(x)=∑_(i=0)~n∑_(j=0)~ncosθ_(ij)~(H)x_ix_j with constraint condition x_0+x_1+…+x_n=0 is positive definite form when all lateral face of simplex∑(H,n)is in a hypersphere,a extremal representation of the radius of inscribed sphere of∑(H,n)is given,a class of parametric inequalities with constraint condition are established." @default.
- W2364995801 created "2016-06-24" @default.
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- W2364995801 date "2008-01-01" @default.
- W2364995801 modified "2023-09-26" @default.
- W2364995801 title "Some New Progress in the Conditional Extremum of the Dihedral Angles of Simplex" @default.
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