A kind of generalized convex set, called as local star-shaped E-invex set with respect to η, is presented, and some of its important characterizations are derived. Based on this concept, a new class of functions, named as semilocal E-preinvex functions, which is a generalization of semi-Epreinvex functions and semilocal E-convex functions, is introduced. Simultaneously, some of its basic proper...

Motivated by typical questions from computational geometry (visibility and art gallery problems) and combinatorial geometry (illumination problems) we present an analogue of the Krein-Milman theorem for the class of star-shaped sets. If S ⊆ R is compact and star-shaped, we consider a fixed, nonempty, compact, and convex subset K of the convex kernel K0 = ck(S) of S, for instance K = K0 itself. ...

The equilibrium contact angles and line tensions of macroscopic droplets, composed of star-shaped polystyrene (PS) macromolecules, on silicon oxide substrates, are shown to be smaller than their linear analogs, by up to approximately 1 and 2 orders of magnitude, respectively, depending on the size and functionality of the star-shaped molecule. A precursor layer, of lateral dimensions and of thi...

Bacteriophage T4 consists of a head for protecting its genome and a sheathed tail for inserting its genome into a host. The tail terminates with a multiprotein baseplate that changes its conformation from a "high-energy" dome-shaped to a "low-energy" star-shaped structure during infection. Although these two structures represent different minima in the total energy landscape of the baseplate as...