Extremal Lipschitz functions in the deviation inequalities from the mean

We obtain an optimal deviation from the mean upper bound \begin{equation} D(x)\=\sup_{f\in \F}\mu\{f-\E_{\mu} f\geq x\},\qquad\ \text{for}\ x\in\R\label{abstr} \end{equation} where \F is the class of the integrable, Lipschitz functions on probability metric (product) spaces. As corollaries we get exact solutions of \eqref{abstr} for Euclidean unit sphere $S^{n-1}$ with a geodesic distance and a normalized Haar measure, for $\R^n$ equipped with a Gaussian measure and for the multidimensional cube, rectangle, torus or Diamond graph equipped with uniform measure and Hamming distance. We also prove that in general probability metric spaces the $\sup$ in \eqref{abstr} is achieved on a family of distance functions.Comment: 7 page

Двигательная активность студентов

В статье рассмотрены теоретические аспекты двигательной активности студентов, возможности увеличения ее объема. The article considers theoretical aspects of physical activity of students, the possibility of increasing its volume

Thin Film Deposition Using Spray Pyrolysis

Spray pyrolysis has been applied to deposit a wide variety of thin films. These films were used in various devices such as solar cells, sensors, and solid oxide fuel cells. It is observed that often the properties of deposited thin films depend on the preparation conditions. An extensive review of the effects of spray parameters on film quality is given to demonstrate the importance of the process of optimization. The substrate surface temperature is the most critical parameter as it influences film roughness, cracking, crystallinity, etc. Processes involved in the spray pyrolysis technique are discussed in this review as wel

Complexity of the frog intracardiac neurons. Intracellular injection study

The goal of this study was to determine the structure of intracardiac neurons in the frog Rana temporaria. Fifty-six intracardiac neurons from 8 animals were labelled ionophoretically by the intracellular markers AlexaFluor 586 and Lucifer Yellow CH. Among the labelled neurons, we found the cells of unipolar, bipolar, multipolar and pseudounipolar types. Multiple neuronal processes originated from the soma, the axon hillock and the initial segment of axon. With respect to the soma, the neuron contained (Mean ± SE) 3.5 ± 0.3 long and 5.5 ± 0.6 short processes. Most neurons had the spine, the bubble or the flake like extensions on their soma surface and were classified as Golgi I typeneurons. Few Golgi II type neurons, the presumptive interneurons, were also found. Our findings contradict to a general view that the frog intracardiac ganglia contain only the adendritic neurons of the unipolar type. Our findings demonstrate that the frog intracardiac neurons are structurally complex and diverse. This diversity may account for the complicated integrative functions of the frog intrinsic cardiac ganglia

Molecular mechanisms behind progressing chronic inflammatory dilated cardiomyopathy

Background: Inflammatory dilated cardiomyopathy (iDCM) is a common debilitating disease with poor prognosis that often leads to heart failure and may require heart transplantation. The aim of this study was to evaluate sera and biopsy samples from chronic iDCM patients, and to investigate molecular mechanism associated with left ventricular remodeling and disease progression in order to improve therapeutic intervention. Methods: Patients were divided into inflammatory and non-inflammatory DCM groups according to the immunohistochemical expression of inflammatory infiltrates markers: T-lymphocytes (CD3), active-memory T lymphocyte (CD45Ro) and macrophages (CD68). The inflammation, apoptosis, necrosis and fibrosis were investigated by ELISA, chemiluminescent, immunohistochemical and histological assays. Results: The pro-inflammatory cytokine IL-6 was significantly elevated in iDCM sera (3.3 vs. 10.98 μg/ml; P < 0.05). Sera levels of caspase-9, −8 and −3 had increased 6.24-, 3.1- and 3.62-fold, (P  < 0.05) and only slightly (1.3-, 1.22- and 1.03-fold) in biopsies. Significant release of Hsp60 in sera (0.0419 vs. 0.36 ng/mg protein; P < 0.05) suggested a mechanistic involvement of mitochondria in cardiomyocyte apoptosis. The significant MMP9/TIMP1 upregulation in biopsies (0.1931 - 0.476, P < 0.05) and correlation with apoptosis markers show its involvement in initiation of cell death and ECM degradation. A slight activation of the extrinsic apoptotic pathway and the release of hsTnT might support the progression of chronic iDCM. Conclusions: Data of this study show that significant increase of IL-6, MMP9/TIMP1 and caspases-9, −8, −3 in sera corresponds to molecular mechanisms dominating in chronic iDCM myocardium. The initial apoptotic pathway was more activated by the intramyocardial inflammation and might be associated with extrinsic apoptotic pathway through the pro-apoptotic Bax. The activated intrinsic form of myocardial apoptosis, absence of necrosis and decreased fibrosis are most typical characteristics of chronic iDCM. Clinical use of anti-inflammatory drugs together with specific anti-apoptotic treatment might improve the efficiency of therapies against chronic iDCM before heart failure occurs

VU studentų matematikos olimpiadai praėjus

Some problems of the olympiad are considered. One of them is solved.Santraukos nėra