Medical rehabilitation of blood flow disorders in patients with one-sided pathological kidney lever

The release of vasoactive substances into the bloodstream causes a number of vascular reactions, alternating vasoconstriction and vasodilation disrupt the course of adequate adaptive responses to the restoration of blood circulation in the kidneys [3, 5]. The additional impact of surgery also affects the adequate restoration of total renal function [3]. There are two ways to positively affect the state of blood circulation: improving the rheological properties of blood and preventing or reducing vascular spasm of the renal parenchyma, which should be effectively performed during the perioperative period and in the long term after surgery [6]. The aim of the study. To analyze and clinically evaluate the method of perioperative correction of renal blood flow in patients with unilateral kidney damage. Material and methods of research. The clinical study was performed in 58 patients aged 18 to 65 years with unilateral kidney damage who received surgical treatment according to the protocols of medical care for a specific pathology, as well as additional measures of perioperative improvement of blood flow in the parenchyma of both kidneys

Reaction-diffusion systems with constant diffusivities: conditional symmetries and form-preserving transformations

Q-conditional symmetries (nonclassical symmetries) for a general class of two-component reaction-diffusion systems with constant diffusivities are studied. Using the recently introduced notion of Q-conditional symmetries of the first type (R. Cherniha J. Phys. A: Math. Theor., 2010. vol. 43., 405207), an exhaustive list of reaction-diffusion systems admitting such symmetry is derived. The form-preserving transformations for this class of systems are constructed and it is shown that this list contains only non-equivalent systems. The obtained symmetries permit to reduce the reaction-diffusion systems under study to two-dimensional systems of ordinary differential equations and to find exact solutions. As a non-trivial example, multiparameter families of exact solutions are explicitly constructed for two nonlinear reaction-diffusion systems. A possible interpretation to a biologically motivated model is presented

On elliptic solutions of the quintic complex one-dimensional Ginzburg-Landau equation

The Conte-Musette method has been modified for the search of only elliptic solutions to systems of differential equations. A key idea of this a priory restriction is to simplify calculations by means of the use of a few Laurent series solutions instead of one and the use of the residue theorem. The application of our approach to the quintic complex one-dimensional Ginzburg-Landau equation (CGLE5) allows to find elliptic solutions in the wave form. We also find restrictions on coefficients, which are necessary conditions for the existence of elliptic solutions for the CGLE5. Using the investigation of the CGLE5 as an example, we demonstrate that to find elliptic solutions the analysis of a system of differential equations is more preferable than the analysis of the equivalent single differential equation.Comment: LaTeX, 21 page

Management of an Advertising Campaign Based on the Model of the Enterprise's Logistic System

The study is devoted to solving the scientific problem of optimal expansion of the enterprise's market niche, taking into account potential demand and the formation of an effective advertising campaign. An economic-mathematical model of the enterprise's production activity has been developed taking into account logistics and market demand.The problem of determining the optimal advertising costs is solved in two formulations:a) the enterprise produces homogeneous goods and the wholesale warehouse can fulfill the retail order for any quantity of goods in the wholesale warehouse;b) the enterprise produces some products in assortment. In this case, a certain minimum stock of products should be available at the wholesale warehouse.The study found that the optimal advertising costs are determined by the value of all the main parameters of the enterprise's logistics system.This conclusion was obtained as a result of careful model accounting of the structure of the enterprise's logistics system. All the main links (flows) between the elements of the logistics system were also taken into account. The simulation was performed in such a way that non-physical phenomena (for example, storage overflow, etc.) did not appear at the intermediate stages of modeling. The calculations found that with the planned capacity of 4.1 (units per day), the annual profit will be 3975.5 (units) with an optimal advertising cost of 44.8 (units). The practical significance of the study is that scientific ideas about the relationship of the advertising campaign with the production potential of the enterprise can serve as the basis for more efficient management of the budget process at the enterprise, namely: more informed planning of production volumes and expenses for its advertising campaig

The influence of electric fields and surface tension on Kelvin-Helmholtz instability in two-dimensional jets

We consider nonlinear aspects of the flow of an inviscid two-dimensional jet into a second immiscible fluid of different density and unbounded extent. Velocity jumps are supported at the interface, and the flow is susceptible to the Kelvin–Helmholtz instability. We investigate theoretically the effects of horizontal electric fields and surface tension on the nonlinear evolution of the jet. This is accomplished by developing a long-wave matched asymptotic analysis that incorporates the influence of the outer regions on the dynamics of the jet. The result is a coupled system of long-wave nonlinear, nonlocal evolution equations governing the interfacial amplitude and corresponding horizontal velocity, for symmetric interfacial deformations. The theory allows for amplitudes that scale with the undisturbed jet thickness and is therefore capable of predicting singular events such as jet pinching. In the absence of surface tension, a sufficiently strong electric field completely stabilizes (linearly) the Kelvin–Helmholtz instability at all wavelengths by the introduction of a dispersive regularization of a nonlocal origin. The dispersion relation has the same functional form as the destabilizing Kelvin–Helmholtz terms, but is of a different sign. If the electric field is weak or absent, then surface tension is included to regularize Kelvin–Helmholtz instability and to provide a well-posed nonlinear problem. We address the nonlinear problems numerically using spectral methods and establish two distinct dynamical behaviors. In cases where the linear theory predicts dispersive regularization (whether surface tension is present or not), then relatively large initial conditions induce a nonlinear flow that is oscillatory in time (in fact quasi-periodic) with a basic oscillation predicted well by linear theory and a second nonlinearly induced lower frequency that is responsible for quasi-periodic modulations of the spatio-temporal dynamics. If the parameters are chosen so that the linear theory predicts a band of long unstable waves (surface tension now ensures that short waves are dispersively regularized), then the flow generically evolves to a finite-time rupture singularity. This has been established numerically for rather general initial conditions