Optimization of Schur-convex functions

Zhang, Xin-Min

doi:10.7153/mia-01-31

Cited by 9 publications

(4 citation statements)

References 3 publications

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“…We can find the second order partial derivatives of D via implicit differentiation on Eqs. (9) and (10). Through a lengthy but direct calculation, we find that at the point (x, y) = (π/3, π/3),…”

Section: Fractal Dimension Of Sptmentioning

confidence: 87%

Sierpiński Pedal Triangles

Zhang

Hitt²,

Wang

et al. 2008

Fractals

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We generalize the construction of the ordinary Sierpiński triangle to obtain a two-parameter family of fractals we call Sierpiński pedal triangles. These fractals are obtained from a given triangle by recursively deleting the associated pedal triangles in a manner analogous to the construction of the ordinary Sierpiński triangle, but their fractal dimensions depend on the choice of the initial triangles. In this paper, we discuss the fractal dimensions of the Sierpiński pedal triangles and the related area ratio problem, and provide some computer-generated graphs of the fractals. Fractals 2008.16:141-150. Downloaded from www.worldscientific.com by MCGILL UNIVERSITY on 02/03/15. For personal use only. Fractals 2008.16:141-150. Downloaded from www.worldscientific.com by MCGILL UNIVERSITY on 02/03/15. For personal use only.

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Section: Fractal Dimension Of Sptmentioning

confidence: 87%

Sierpiński Pedal Triangles

Zhang

Hitt²,

Wang

et al. 2008

Fractals

Self Cite

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“…Zhang [23] proved that every Schur-convex function f : D ⊂ R n → R is a symmetric function, that is, f (x) = f x σ(1) , . .…”

Section: The Dual Cone Of the Cone R Nmentioning

confidence: 99%

An Infinite Dimensional Version of the Schur Convexity Property and Applications

Vallée

Rădulescu

2007

Anal. Appl.

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We extend to infinite dimensional separable Hilbert spaces the Schur convexity property of eigenvalues of a symmetric matrix with real entries. Our framework includes both the case of linear, selfadjoint, compact operators, and that of linear selfadjoint operators that can be approximated by operators of finite rank and having a countable family of eigenvalues. The abstract results of the present paper are illustrated by several examples from mechanics or quantum mechanics, including the Sturm–Liouville problem, the Schrödinger equation, and the harmonic oscillator.

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“…Every Schur-convex function is a symmetric function [18]. But it is not hard to see that not every symmetric function can be a Schur-convex function [15, …”

Section: Some Definitions and Lemmasmentioning

confidence: 99%