‎Many optimization problems can be reduced to a problem with an increasing and co-radiant objective function by a suitable transformation of variables. Functions, which are increasing and co-radiant, have found many applications in microeconomic analysis. In this paper, the abstract convexity of positive valued affine increasing and co-radiant (ICR) functions are discussed. Moreover, the ...

In this paper, we study the properties of Gerstewitz nonlinear scalar functional with respect to coradiant set and radiant in real linear space. With help nonconvex separation theorem co-radiant set, first obtain that is a special co-radiant(radiant) when corresponding set. Based on subadditivity property convex calculate its Fenchel(approximate) subdifferential. As applications, derive optimal...

An open question in the study of quasiconvex function is the characterization of the class of functions which are sum of quasiconvex functions. In this paper we restrict attention to quasiconvex radiant functions, i.e. those whose level sets are radiant as well as convex and deal with the claim that a function can be expressed as the sum of quasiconvex radiant functions if and only if it is rad...

In this paper, we first give a characterization of sub-topical functions with respect to their lower level sets and epigraph. Next, by using two different classes of elementary functions, we present a characterization of sub-topical functions with respect to their polar functions, and investigate the relation between polar functions and support sets of this class of functions. Finally, we obtai...

Recently, Hermite-Hadamard-type inequalities and their applications have attracted considerable interest, as shown in the book [1], for example. These inequalities have been studied for various classes of functions such as convex functions [1], quasiconvex functions [2–4], p-functions [3, 5], Godnova-Levin type functions [5], r-convex functions [6], increasing convex-along-rays functions [7], a...

Normal modes, quasi-normal modes and super-radiant modes are studied to clarify the total dynamics for complex scalar fields in Kerr anti-de Sitter black hole spacetime. Orthonormal relations and quasi-orthonormal relations are obtained for normal modes and quasi-normal modes. Mode expansions are done and the conserved quantities are studied. Any modes are shown to be separated into two groups,...

The problem of reconstructing the coherent-mode structure of an optical field with unknown crossspectral density function is solved by means of optimal approximating the measured radiant intensity. An alternative field is defined with the coherent-mode structure calculated for the chosen orthonormal basis. An effciency of the proposed technique is illustrated with the results of a numerical sim...

This study presents an optimization problem for shape design of a 2-D radiant enclosure with transparent medium and gray-diffuse surfaces. The aim of the design problem is to find the optimum geometry of a radiant enclosure from the knowledge of temperature and heat flux over some parts of boundary surface, namely the design surface. The solution of radiative heat transfer is based on the net r...