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.
Paper deals with derivation of mathematical relationships of dry friction force versus relative velocity in friction contact of two bodies. It is focused on such main types of dry friction characteristics, which frequently occur in dynamic mechanical systems. New models of modified Coulomb friction law and spring - friction elements are determined. For easy application in computing programs used in technical practice and based on linear equations, the equivalent linear stiffness and damping expressions are formulated and analysed in detail. and Obsahuje seznam literatury
The purpose of this study was to determine the role of lipotoxicity in vascular smooth muscle (VSM). C1-BODIPY 500/510 C12 used to assess the ability of VSM A7r5 cells to transport long-chain fatty acids showed that lipid transport did not appear to limit metabolism. Thin layer chromatography revealed that storage of transported fatty acid occurred primarily as mono- and diglycerides and fatty acids but not as triglycerides. We used lipid-induced apoptosis as a measure of lipotoxicity and found that 1.5 mM palmitate (6.8:1) bound to albumin resulted in a 15-fold increase in the number of apoptotic cells compared to the control at 24 hours. This apoptosis did not seem to be due to an increase in reactive oxygen species (ROS) since VSM cells incubated in palmitate showed less ROS production than cells incubated in albumin only. Similar exposure to oleate did not significantly increase the number of apoptotic cells compared to the control. Oleate actually significantly attenuated the apoptosis induced by palmitate, suggesting that unsaturated fatty acids have a protective effect on cells undergoing palmitate-induced apoptosis. These results suggest that vascular smooth muscle is vulnerable to lipotoxicity and that this lipotoxicity may play a role in the development of atherosclerosis., H. M. Mattern, C. D. Hardin., and Obsahuje bibliografii a bibliografické odkazy