On the Spectral Properties of Symmetric 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...

Some Properties of Certain Subclasses of Close-to-Convex and Quasi-convex Functions with Respect to 2k-Symmetric Conjugate Points

Buckling Behaviors of Symmetric and Antisymmetric Functionally Graded Beams

The present study investigates buckling characteristics of both nonlinear symmetric power and sigmoid functionally graded (FG) beams. The volume fractions of metal and ceramic are assumed to be distributed through a beam thickness by the sigmoid-law distribution (S-FGM), and the symmetric power function (SP-FGM). These functions have smooth variation of properties across the boundary rather tha...

Properties of eigenvalue function

For the eigenvalue function on symmetric matrices, we have gathered a number of it’s properties.We show that this map has the properties of continuity, strict continuity, directional differentiability, Frechet differentiability, continuous  differentiability. Eigenvalue function will be extended to a larger set of matrices and then the listed properties will prove again.

Theoretical study of the influence of solvent polarity on the structure and spectral properties in the interaction of C20 and Si2H2

In this investigation, the interaction of C20 and Si2H2 molecules was explored in the M06-2X/6-311++G(d,p)level of theory in gas solution phases. The obtained interaction energy values with standard method werecorrected by basis set superposition error (BSSE) during the geometry optimization for all molecules atthe same level of theory. Also, the bonding interaction between th...

Prox-Regularity of Spectral Functions and Spectral Sets

Important properties such as differentiability and convexity of symmetric functions in Rn can be transferred to the corresponding spectral functions and vice-versa. Continuing to built on this line of research, we hereby prove that a spectral function F : Sn → R ∪ {+∞} is prox-regular if and only if the underlying symmetric function f : Rn → R ∪ {+∞} is prox-regular. Relevant properties of symm...