We study the integrability of Banach space valued strongly measurable functions defined on [0, 1]. In the case of functions f given by ∑ ∞ n=1 xnχEn , where xn are points of a Banach space and the sets En are Lebesgue measurable and pairwise disjoint subsets of [0, 1], there are well known characterizations for Bochner and Pettis integrability of f. The function f is Bochner integrable if and only if the series ∑∞ n=1 xn|En| is absolutely convergent. Unconditional convergence of the series is equivalent to Pettis integrability of f. In this paper we give some conditions for variational Henstock integrability of a certain class of such functions.
We study properties of variational measures associated with certain conditionally convergent integrals in ${\mathbb R}^m$. In particular we give a full descriptive characterization of these integrals.
Some properties of absolutely continuous variational measures associated with local systems of sets are established. The classes of functions generating such measures are described. It is shown by constructing an example that there exists a $\mathcal{P}$-adic path system that defines a differentiation basis which does not possess Ward property.
We compare alternative definitions of undirected graphical models for discrete, finite variables. Lauritzen \cite{Lauritzen:1996} provides several definitions of such models and describes their relationships. He shows that the definitions agree only when joint distributions represented by the models are limited to strictly positive distributions. Heckerman et al. \cite{Heckerman_et_al:2000}, in their paper on dependency networks, describe another definition of undirected graphical models for strictly positive distributions. They show that this definition agrees with those of Lauritzen \cite{Lauritzen:1996} again when distributions are strictly positive. In this paper, we extend the definition of Heckerman et al. \cite{Heckerman_et_al:2000} to arbitrary distributions and show how this definition relates to those of Lauritzen \cite{Lauritzen:1996} in the general case.
Idempotent slim groupoids are groupoids satisfying $xx\=x$ and $x(yz)\=xz$. We prove that the variety of idempotent slim groupoids has uncountably many subvarieties. We find a four-element, inherently nonfinitely based idempotent slim groupoid; the variety generated by this groupoid has only finitely many subvarieties. We investigate free objects in some varieties of idempotent slim groupoids determined by permutational equations.
A-kinase interacting protein 1 (AKIP1) has been shown to interact
with a broad range of proteins involved in various cellular
processes, including apoptosis, tumorigenesis, and oxidative
stress suggesting it might have multiple cellular functions. In this
study, we used an epitope-tagged AKIP1 and by combination of
immunochemical approaches, microscopic methods and reporter
assays we studied its properties. Here, we show that various
levels of AKIP1 overexpression in HEK-293 cells affected not only
its subcellular localization but also resulted in aggregation. While
highly expressed AKIP1 accumulated in electron-dense
aggregates both in the nucleus and cytosol, low expression of
AKIP1 resulted in its localization within the nucleus as a free,
non-aggregated protein. Even though AKIP1 was shown to
interact with p65 subunit of NF-κB and activate this transcription
factor, we did not observe any effect on NF-κB activation
regardless of various AKIP1 expression level.
Vascular stenosis is often described only by its percentage in both clinical and scientific praxis. Previous studies gave inconclusive results regarding the effect of stenosis eccentricity on its hemodynamic effect. The aim of this experimental study was to investigate and quantify the effect of stenosis severity and eccentricity on the pressure drop. A combination of pressure and flow measurements by Par ticle Imaging Velocimetry (PIV) method was used. Models of the same stenosis significance but with different levels of eccentricity were studied in vitro by PIV. This study has shown that stenosis asymmetry is associated with more profound pressure drop an d flow volume decrease. On the contrary, pressure drop and flow volume decrease were not further significantly influenced by the level of asymmetry. Hemodynamic changes associated with stenosis eccentricity must be taken into account in both clinical and s cientific studies., L. Novakova, J. Kolinsky, J. Adamec, J. Kudlicka, J. Malik., and Obsahuje bibliografii