Derivatives of Spectral Functions

Some Results on Convex Spectral Functions: I

In this paper, we give a fundamental convexity preserving for spectral functions. Indeed, we investigate infimal convolution, Moreau envelope and proximal average for convex spectral functions, and show that this properties are inherited from the properties of its corresponding convex function. This results have many applications in Applied Mathematics such as semi-definite programmings and eng...

Theoretical Structural and Spectral Analyses of TEMPO Radical Derivatives of Fullerene

The spectroscopic properties of the 2,2,6,6-tetramethyl-piperidine-1-oxyl (TEMPO) radicalderivatives of the fullerene (C60) were theoretically investigated. The ground state optimizedstructures of the radical adducts of the fullerene were calculated by using DFT (B3LYP) with 6-31G(d) level. It was concluded that a 6-6 ring junction of C60 moiety generally covalently links to thepiperidine ring ...

Arylazo derivatives of some fluorinated β-diketones and their metal complexes

Phenylazo and benzothiazolylazo derivatives of trifluoroacetylacetone andhexafluoroacetylacetone have been synthesized and characterized. Analytical and spectral datarevealed the existence of phenylazo derivatives in the intramolecularly hydrogen-bonded ketohydrazoneform while the benzothiazolylazo derivatives in the azo-enol form. The monobasicbidentate coordination of the phenylazo derivative...

Rings of functions with integer derivatives at x=1

Some Perturbed Inequalities of Ostrowski Type for Functions whose n-th Derivatives Are Bounded

We firstly establish an identity for $n$ time differentiable mappings Then, a new inequality for $n$ times differentiable functions is deduced. Finally, some perturbed Ostrowski type inequalities for functions whose $n$th derivatives are of bounded variation are obtained.

Some Observations on the Sensitivity Analysis of Spectral Functions

We examine the formulae for the first and second derivatives of spectral functions of real symmetric matrices to understand why they have the form that they do. The development, which involves only elementary linear algebra and calculus, is based on computing directional derivatives of the spectral function and its gradient along a canonical set of orthonormal matrices. A particular aim of our ...