Under some non-degeneracy condition we show that sequences of entropy solutions of a nonlinear ultra-parabolic equation are strongly pre-compact in the general case of a Caratheodory flux vector. The proofs are based on localization principles for H-measures corresponding to sequences of measure-valued functions.

Let G and f : [0,1]×R4 → R be two functions satisfying Caratheodory conditions. This paper is concerned with the problems of existence and uniqueness of solutions for the nonlinear fourth-order ordinary differential equation y′′′′ +λy′′ +ky+G(x,y,y′,y′′,y′′′)= f (x,y,y′,y′′,y′′′) with one of a particular set of boundary conditions.

In this paper we introduce certain analytic functions of boundary rotation bounded by k1r which are of Caratheodory origin. With them we study two classes of analytic and univalent functions in the unit disk E = {z E C Izi < I} , which are also of bounded boundary rotation.

In this paper, we will show how one is able to construct a lattice on the completion of an algebra and to obtain an isomorphism to its Caratheodory Extension. In addition, it will be shown that the lattice form a σ-algebra and a complete Heyting algebra of countable type.

Iran is the biggest pistachio producer and exporter in the world. Surely, one of the most problems of pistachio industry is Aflatoxin contamination in recent years that treated exportation this valuable crop. This research was done in order to evaluate Aflatoxin contamination in indehiscence and mechanical splitting pistachios of Ouhadi cultivars in Rafsanjan region. Treatments of this research...

Here and in what follows we assume S is a finite multiset in R d. This means tha t the points in S have "multiplicity". Strict ly speaking, a multiset is a map S : F --, R d and in our case F is finite. Then corekS = M{convS(E) : E C_ F, IF \ El _< k}. From now on we do not say explicitly tha t the sets in question are multisets. This will make the no ta t ion simpler and will not cause confusi...