applying two definitions of the union of if-events, p. grzegorzewski gave two generalizations of the inclusion-exclusion principle for if-events.in this paper we prove an inclusion-exclusion principle for if-states based on a method which can also be used to prove grzegorzewski's inclusion-exclusion principle for probabilities on if-events.finally, we give some applications of this principle by...

In this paper we study discrete approximations of continuous-time evolution sy~tems governed by differential inclusions with nonconvex compact values in infinite-dimensional spaces. Our crucial result ensures the possibility of a strong Sobolev space approximation of every feasible solution to the continuous-time inclusion by its discrete-time counterparts extended as Euler's "bro~ ken lines." ...

We establish some Filippov type existence theorems for solutions of fractional semilinear differential inclusions involving Caputo’s fractional derivative in Banach spaces.

background: vascular endothelial growth factor (vegf) is a coordinate regulator of physiological angiogenesis during embryogenesis, skeletal growth and reproductive functions. there are several types of vegf, including vegf165. vegfs stimulate endothelial cell growth, angiogenesis, and capillary permeability. low induction temperature is a major factor for expression of the recombinant vegf165 ...

The size and length effects of an inclusion on multi-pass copper shaped-wire drawing were investigated. For this purpose, an experimental investigation on optimal die half-angle was conducted. Based on experimental data of optimal die half-angle, wire and inclusion deformations, drawing and hydrostatic stress of copper shaped-wires that contain an inclusion were calculated by two-dimensional fi...

The sequential morphological and cytochemical alterations in HeLa cells infected with adenovirus types 1 to 4 are described. Each of the four viruses studied led to consistent and reproducible cytological changes not observed in uninfected control cultures. All four agents produced striking and characteristic changes in the nuclei of infected cells. Alterations in the cytoplasm, though present,...

We survey and announce some current results on the existence, the viability, and the topological structure of the viable solutions of differential equations and inclusion in Banach spaces under set constraints. Some new results concerning semilinear differential inclusions with state variables constrained to the so-called regular and strictly regular sets, together with their applications, are ...

In this paper we present an existence result for a first order impulsive differential inclusion with periodic boundary conditions and impulses at the fixed times under the convex condition of multi-functions.