Multiscale expansions of difference equations in the small lattice spacing regime, and a vicinity and integrability test. I

We propose an algorithmic procedure i) to study the ``distance'' between an integrable PDE and any discretization of it, in the small lattice spacing epsilon regime, and, at the same time, ii) to test the (asymptotic) integrability properties of such discretization. This method should provide, in particular, useful and concrete informations on how good is any numerical scheme used to integrate a given integrable PDE. The procedure, illustrated on a fairly general 10-parameter family of discretizations of the nonlinear Schroedinger equation, consists of the following three steps: i) the construction of the continuous multiscale expansion of a generic solution of the discrete system at all orders in epsilon, following the Degasperis - Manakov - Santini procedure; ii) the application, to such expansion, of the Degasperis - Procesi (DP) integrability test, to test the asymptotic integrability properties of the discrete system and its ``distance'' from its continuous limit; iii) the use of the main output of the DP test to construct infinitely many approximate symmetries and constants of motion of the discrete system, through novel and simple formulas.Comment: 34 pages, no figur

Long-Term Results of the Etiotropic Therapy of Subcompensed Liver Cirrhosis in the Outcome of Chronic Hepatitis C

Aim. The evaluation of long-term results of antiviral therapy (AVT) with ombitasvir/paritaprevir/ritonavir and dasabuvir in patients with noncompensated liver cirrhosis (LC) in the outcome of chronic hepatitis C.Material and methods. A retrospective analysis included the data from patients with subcompensated liver cirrhosis (LC) of HCV etiology (genotype 1b) (7–9 points of the Child-Pugh score) having received interferon-free antiviral therapy (AVT) with ombitasvir/paritaprevir/ritonavir and dasabuvir during 12 weeks from September to December 2015. In total, 66 patients (27 men and 39 women) received such a therapy, the median age was 56.4 years.Results. 147 weeks (IQR 56–156) following AVT completion, the long-term results were evaluated. At that time, 27 patients were available for observation. The assessment of liver function compensation using the Child-Pugh score showed improvement in 25 (93 %) patients. The assessment of laboratory data revealed a decrease in the median of total bilirubin by 13.6 μmol/l, as well as an increase in the median of serum albumin by 9.7 g/L and the median of platelets by 41,700/μl. Two deaths were reported due to hepatocellular cancer (HCC) and bleeding from esophageal varices. HCC was detected in 8 patients. Two patients underwent liver transplantation.Conclusion. AVT in patients with LC of HCV etiology is associated with a high frequency of virologic response. Longterm follow-up results indicate a significant improvement of liver function, but also a continuing high risk of developing complications of underlying disease, primarily HCC

Comparative analysis of oxidative metabolism indicators at acute alcohol and acute surrogate alcohol intoxication

High level of population alcoholization is the cause of many cases of acute alcohol and alcoholic surrogate intoxication. The number of alcohol intoxication cases in Kazakhstan in 2014 amounted to 13891 (80.3 per 100 000 people), the number of fatal intoxication cases amounted to 882 (5.1 per 100 000 people). The problem of alcoholization in Russia remains urgent as well: according to the statistics of 2014,152 551 cases of acute intoxication of chemical etiology were registered, 33.9 % of cases occurred due to alcohol intoxication. Alcoholic beverages in the course of their biotransformation to acetic acid can form oxygen free radicals in particular superoxide anion as a byproduct of acetic aldehyde oxidation reaction. Studies on oxidative metabolism of ethanol intoxication are currently being conducted. At the same time, the state of oxidative metabolism during alcoholic surrogate intoxication was not practically investigated. Evaluation of oxidative metabolism depending on the severity of alcohol or its surrogate intoxication is of special interest. The aim was to compare oxidative metabolism indicators among patients with acute alcohol and alcoholic surrogate intoxication of different severity. The object of the study was blood of 62 people with diagnosed moderate or severe degrees of acute alcohol and alcoholic surrogate intoxication. Indicators of oxidative metabolism in erythrocytes and blood plasma were estimated. Significant differences were found in product concentration of protein oxidation containing bityrosine crosslinks in blood plasma under increase of alcohol intoxication degree

Characterization of the oxidative metabolism of erythrocytes in patients with community-acquired pneumonia

Free radical oxidation plays an important role in the development and exacerbation of the pathological process. Oxidative stress causes a disturbance of the rheological properties of red blood cells and modification of their membrane. Activation of processes of peroxidation of lipids disturbs the integrity of the erythrocyte membrane. In community-acquired pneumonia the study of oxidative metabolism of red blood cells, especially the oxidative modification of their proteins, dedicated to a limited number of studies. Oxidative modification of hemoglobin dissipate a key role in the development of inflammation induced by hypoxia. The aim of the research was to study indicators of oxidative stress, the content of oxidized modified proteins in the red blood cells and the permeability of their membranes to low-molecular-weight hydrophilic substances in patients with community-acquired pneumonia. The object of the study were the erythrocytes of blood of 33 patients with community-acquired pneumonia and 19 practically healthy persons of young and middle age from 27 to 42 years. Evidence of oxidative processes in red blood cells was a significant increase of the oxidized-modified proteins (carbonyl derivatives) in erythrocytes. The increase in the content of membrane-bound hemoglobin may also be due to the high level of lipid peroxidation in erythrocyte membranes. The results of the study showed the presence of intracellular oxidative stress in erythrocytes of patients with community-acquired pneumonia, which leads to damage to their membranes and release of hemoglobin into the blood plasma

Five types of blow-up in a semilinear fourth-order reaction-diffusion equation: an analytic-numerical approach

Five types of blow-up patterns that can occur for the 4th-order semilinear parabolic equation of reaction-diffusion type u_t= -\Delta^2 u + |u|^{p-1} u \quad {in} \quad \ren \times (0,T), p>1, \quad \lim_{t \to T^-}\sup_{x \in \ren} |u(x,t)|= +\iy, are discussed. For the semilinear heat equation $u_t= \Delta u+ u^p$, various blow-up patterns were under scrutiny since 1980s, while the case of higher-order diffusion was studied much less, regardless a wide range of its application.Comment: 41 pages, 27 figure

Continuous Symmetries of Difference Equations

Lie group theory was originally created more than 100 years ago as a tool for solving ordinary and partial differential equations. In this article we review the results of a much more recent program: the use of Lie groups to study difference equations. We show that the mismatch between continuous symmetries and discrete equations can be resolved in at least two manners. One is to use generalized symmetries acting on solutions of difference equations, but leaving the lattice invariant. The other is to restrict to point symmetries, but to allow them to also transform the lattice.Comment: Review articl

Synthesis and Biological Activity of 2,5-Bisubstituted Derivatives of 1,3,4-Thiadiazol-2,5-dithiol

By reaction of 1,3,4-thiadiazol-2,5-dithiol with different organohalogens, chlorides of carboxylic acids, acrylic acid derivatives, alkaloids, and secondary amines, various derivatives of 2,5-bi-substituted 1,3,4-thiadiazole were synthesized, and biological properties of some of them were studied