We present the method introduced by Neeman of generalized side conditions with two types of models. We then discuss some applications: a variation of the Friedman-Mitchell poset for adding a club with finite conditions, the consistency of the existence of an ω2 increasing chain in (ω1 1 , <fin), originally proved by Koszmider, and the existence of a thin very tall superatomic Boolean algebra, o...

Generalized algebraic operations introduced by Ben-Tal [5] are used to define new classes of generalized convex functions, namely (h,?)?(b,F,?) -convex functions and (h,?)?(b,F,?)-convex in the vectorial case. Further, optimality duality results proved for considered (h,?)- nondifferentiable multiobjective programming problem under assumptions that involved (generalized) (b,F,?)-convex.

Harmonic univalent mappings have attracted the serious attention of complex analysts only after the appearance of a basic paper by Clunie and Sheil-Small [4] in 1984. These researchers laid the foundation for the study of harmonic univalent mappings over the unit disk as a generalization of analytic univalent functions. Interestingly, almost at the same time, the famous Bieberbach conjecture wh...