The recent boom in multifunction portable electronic equipments requires the development of compact and miniaturized electronic circuits with high efficiencies, low costs and long lasting time. For the operation of most line-powered electronics, alternating current (ac) line-filters are used to attenuate the leftover ac ripples on direct current (dc) voltage busses. Today, aluminum electrolytic...

It is shown that for every annulus P = {z 6 Cn : 6 < \z\ < r}, b > 0, there exists a set-valued correspondence z —> K{z): P —> 2C , whose graph is a bounded relatively closed subset of the manifold {(z,w) 6 Px Cn : ziwi + ■ ■ ■ + ZnWn = 1} which can be covered by n-dimensional analytic manifolds. The analytic set-valued selection K obtained thereby is then applied to several problems in complex...

n be a continuous multifunction with compact, not necessarily convex values. If F is Lipschitz continuous, it was shown in [4] that there exists a measurable selection f of F such that, for every x 0 , the Cauchy problem ˙ x(t) = f (t, x(t)), x(0) = x 0 has a unique Caratheodory solution, depending continuously on x 0. In this paper, we prove that the above selection f can be chosen so that f (...

We investigate aspects of effectivity and computability on open, closed and quasi-compact sets as well as partial continuous functions in computable T0spaces. A computable T0-space is a second countable T0-spaces with a notation of a base whose domain is recursive and computable intersection on the base. As we do not suppose our space to be a Hausdorff space, we don’t talk about compact subsets...

We first show that a bounded linear operator $ T $ on a real Banach space $ E $ is quasicompact (Riesz, respectively) if and only if $T': E_{mathbb{C}}longrightarrow E_{mathbb{C}}$ is quasicompact  (Riesz, respectively), where the complex Banach space $E_{mathbb{C}}$ is a suitable complexification of $E$ and $T'$ is the complex linear operator on $E_{mathbb{C}}$ associated with $T$. Next, we pr...

This paper investigates the approximation of set-valued functions with compact images (not necessarily convex), by adaptations of the Schoenberg spline operators and the Bernstein polynomial operators. When replacing the sum between numbers in these operators, by the Minkowski sum between sets, the resulting operators approximate only set valued functions with compact-convex images [10]. To obt...