Analytic approximation of solutions of parabolic partial differential equations with variable coefficients

A complete family of solutions for the one-dimensional reaction-diffusion equation $$u_{xx}(x,t)-q(x)u(x,t) = u_t(x,t)$$ with a coefficient $q$ depending on $x$ is constructed. The solutions represent the images of the heat polynomials under the action of a transmutation operator. Their use allows one to obtain an explicit solution of the noncharacteristic Cauchy problem for the considered equation with sufficiently regular Cauchy data as well as to solve numerically initial boundary value problems. In the paper the Dirichlet boundary conditions are considered however the proposed method can be easily extended onto other standard boundary conditions. The proposed numerical method is shown to reveal good accuracy.Comment: 8 pages, 1 figure. Minor updates to the tex

Lidar investigations of M-zone

The creation of pulse dye lasers tuned to resonant line of meteor produced admixtures of atmospheric constituents has made it possible to begin lidar investigations of the vertical distribution of mesospheric sodium concentration and its dynamics in the upper atmosphere. The observed morning increase of sodium concentration in the vertical column is probably caused by diurnal variations of sporadic meteors. The study of the dynamics of the sodium column concentration in the period of meteor streams activity confirms the suggestion of cosmic origin of these atoms. The short lived increase of sodium concentration brought about by a meteor stream, however, exceeds by one order the level of the sporadic background

Transmutations for Darboux transformed operators with applications

We solve the following problem. Given a continuous complex-valued potential q_1 defined on a segment [-a,a] and let q_2 be the potential of a Darboux transformed Schr\"odinger operator. Suppose a transmutation operator T_1 for the potential q_1 is known such that the corresponding Schr\"odinger operator is transmuted into the operator of second derivative. Find an analogous transmutation operator T_2 for the potential q_2. It is well known that the transmutation operators can be realized in the form of Volterra integral operators with continuously differentiable kernels. Given a kernel K_1 of the transmutation operator T_1 we find the kernel K_2 of T_2 in a closed form in terms of K_1. As a corollary interesting commutation relations between T_1 and T_2 are obtained which then are used in order to construct the transmutation operator for the one-dimensional Dirac system with a scalar potential

Global validation of the WSES Sepsis Severity Score for patients with complicated intra-abdominal infections : a prospective multicentre study (WISS Study)

Background: To validate a new practical Sepsis Severity Score for patients with complicated intra-abdominal infections (cIAIs) including the clinical conditions at the admission (severe sepsis/septic shock), the origin of the cIAIs, the delay in source control, the setting of acquisition and any risk factors such as age and immunosuppression. Methods: The WISS study (WSES cIAIs Score Study) is a multicenter observational study underwent in 132 medical institutions worldwide during a four-month study period (October 2014-February 2015). Four thousand five hundred thirty-three patients with a mean age of 51.2 years (range 18-99) were enrolled in the WISS study. Results: Univariate analysis has shown that all factors that were previously included in the WSES Sepsis Severity Score were highly statistically significant between those who died and those who survived (p <0.0001). The multivariate logistic regression model was highly significant (p <0.0001, R-2 = 0.54) and showed that all these factors were independent in predicting mortality of sepsis. Receiver Operator Curve has shown that the WSES Severity Sepsis Score had an excellent prediction for mortality. A score above 5.5 was the best predictor of mortality having a sensitivity of 89.2 %, a specificity of 83.5 % and a positive likelihood ratio of 5.4. Conclusions: WSES Sepsis Severity Score for patients with complicated Intra-abdominal infections can be used on global level. It has shown high sensitivity, specificity, and likelihood ratio that may help us in making clinical decisions.Peer reviewe

Prospective Observational Study on acute Appendicitis Worldwide (POSAW)

Acute appendicitis (AA) is the most common surgical disease, and appendectomy is the treatment of choice in the majority of cases. A correct diagnosis is key for decreasing the negative appendectomy rate. The management can become difficult in case of complicated appendicitis. The aim of this study is to describe the worldwide clinical and diagnostic work-up and management of AA in surgical departments.info:eu-repo/semantics/publishedVersio

A complex method for prophylaxis of laparoscopic cholecystectomy complications

The clinical examination and treatment results were analyzed in 1282 patients, in whom laparoscopic cholecystectomy, using complex method of the complications prophylaxis, was performed for calculous cholecystitis. The complications have had occurred in 21 (1.64%) patients, the conversion necessity--in 10 (0.78%), 3 (0.23%) patients died

Presowing treatment of spring wheat seeds by a pulsed electron beam in the atmosphere

The purpose of this work is to optimize the conditions of presowing treatment of spring wheat seeds with a low-energy pulsed electron beam