The model equation of soliton theory

We consider an hierarchy of integrable 1+2-dimensional equations related to Lie algebra of the vector fields on the line. The solutions in quadratures are constructed depending on $n$ arbitrary functions of one argument. The most interesting result is the simple equation for the generating function of the hierarchy which defines the dynamics for the negative times and also has applications to the second order spectral problems. A rather general theory of integrable 1+1-dimensional equations can be developed by study of polynomial solutions of this equation under condition of regularity of the corresponding potentials.Comment: 17

Equivalence classes of the second order ODEs with the constant Cartan invariant

Second order ordinary differential equations that possesses the constant invariant are investigated. Four basic types of these equations were found. For every type the complete list of nonequivalent equations is issued. As the exampes the equivalence problem for the Painleve II equation, Painleve III equation with three zero parameters, Emden equations and for some other equations is solved

On Darboux Integrable Semi-Discrete Chains

Differential-difference equation $\frac{d}{dx}t(n+1,x)=f(x,t(n,x),t(n+1,x),\frac{d}{dx}t(n,x))$ with unknown $t(n,x)$ depending on continuous and discrete variables $x$ and $n$ is studied. We call an equation of such kind Darboux integrable, if there exist two functions (called integrals) $F$ and $I$ of a finite number of dynamical variables such that $D_xF=0$ and $DI=I$, where $D_x$ is the operator of total differentiation with respect to $x$, and $D$ is the shift operator: $Dp(n)=p(n+1)$. It is proved that the integrals can be brought to some canonical form. A method of construction of an explicit formula for general solution to Darboux integrable chains is discussed and for a class of chains such solutions are found.Comment: 19 page

Ассоциация Gln27Glu полиморфизма гена β2-адренорецептора с особенностями каскада иммунорегуляторных цитокинов и продукцией IgE у больных бронхиальной астмой

The objective: to study the level of serum cytokines IL-4, IFN-γ and the activity of IgE production in patients with bronchial asthma (BA) with the consideration of the Gln27Glu-polymorphism of the β2-AR gene.Subjects and Methods. 130 people of Uzbek ethnicity were examined including 83 patients with BA. BA patients were divided into groups according to the international classification of the World Health Organization and the GINA 2006 diagnostic criteria. Genotyping was performed by polymerase chain reaction technology and restriction fragment analysis.Results. In the group with allergic BA, patients with the Gln27Gln-polymorphic variant of the β2-adrenergic receptor gene had an average IgE value (1,664.20 ± 293.29 pg/ml) higher versus patients with the Gln27Glu genotype (338.40 ± 121.33 pg/ml; p < 0.01). No significant relationship between the Gln27Glu polymorphism of the β2-adrenergic receptor gene and the activity of inductor cytokines was found. The Gln27Gln genotype of the β2-adrenergic receptor gene in patients with bronchial asthma, especially in the allergic form of the disease, is associated with hyperproduction of IgE.Цель исследования: изучить уровень сывороточных цитокинов IL-4, IFN-γ и активность продукции IgE у больных бронхиальной астмой (БА) с учетом Gln27Glu-полиморфизма гена β2-АР.Материал и методы. Обследовано 130 человек узбекской национальности, из них 83 больных БА. Больные БА распределялись по группам согласно международной классификации Всемирной организации здравоохранения и в соответствии с диагностическими критериями GINA 2006 г. Проведено генотипирование с использованием технологии полимеразной цепной реакции и анализа рестрикционных фрагментов.Результаты. В группе с аллергической БА у больных с Gln27Gln-полиморфным вариантом гена β2-адренорецептора средний показатель IgE (1 664,20 ± 293,29 пг/мл) превышал уровень такового у больных с Gln27Glu-генотипом (338,40 ± 121,33 пг/мл; p < 0,01). Достоверной взаимосвязи полиморфизма Gln27Glu гена β2-адренорецептора с активностью индукторных цитокинов не обнаружено. Генотип Gln27Gln гена β2-адренорецептора у пациентов с бронхиальной астмой, особенно при аллергической форме заболевания, ассоциирует с гиперпродукцией IgE

Conditional Lie-B\"acklund symmetry and reduction of evolution equations.

We suggest a generalization of the notion of invariance of a given partial differential equation with respect to Lie-B\"acklund vector field. Such generalization proves to be effective and enables us to construct principally new Ans\"atze reducing evolution-type equations to several ordinary differential equations. In the framework of the said generalization we obtain principally new reductions of a number of nonlinear heat conductivity equations $u_t=u_{xx}+F(u,u_x)$ with poor Lie symmetry and obtain their exact solutions. It is shown that these solutions can not be constructed by means of the symmetry reduction procedure.Comment: 12 pages, latex, needs amssymb., to appear in the "Journal of Physics A: Mathematical and General" (1995

Mathematical Modeling of the Combined Heat Supply System of a Solar House

Today, increasing energy efficiency in residential heating systems, saving fuel and energy resources, and improving the efficiency of using devices based on renewable energy sources is an urgent issue. The purpose of the article is to develop a mathematical model of the heat balance and conduct a theoretical study of one-story rural houses based on the use of solar energy in a non-stationary mode. To achieve this goal, an experimental one-story solar house with autonomous heat supply was built. The heat supply of the experimental solar house mainly uses solar energy, and when the heat supply load exceeds this load, the traditional boiler device is used. The power supply of the experimental solar house is provided by a solar panel (photovoltaic converter). A heat balance scheme for a solar house with autonomous heat supply and an electrothermal scheme of a physical model are proposed. Based on the proposed schemes, a mathematical model of heat balance and a calculation algorithm based on the heat balance equation of the dynamic state of the heat supply system of a one-story experimental solar house in a non-stationary mode have been developed. On the basis of mathematical modeling, the influence of the heat capacity of the wall structure on the temperature regime of the building was studied. On the basis of the MATLAB-Simulink program, the main temperature characteristics were built, on which the change in the temperature of the internal air of the building was analyzed depending on the ambient temperature. On the basis of the program, a modular scheme of the dynamic model was built. Based on the modular scheme, the results of the experiment on changing the air inside the solar house and the outdoor temperature are presented in the form of a graph. The mathematical model of the thermal balance of the building in dynamic mode and the obtained calculation results are recommended for use in the development of energy-efficient solar houses

Математическое моделирование комбинированной системы теплоснабжения солнечного дома)

Today, increasing energy efficiency in residential heating systems, saving fuel and energy resources, and improving the efficiency of using devices based on renewable energy sources is an urgent issue. The purpose of the article is to develop a mathematical model of the heat balance and conduct a theoretical study of one-story rural houses based on the use of solar energy in a non-stationary mode. To achieve this goal, an experimental one-story solar house with autonomous heat supply was built. The heat supply of the experimental solar house mainly uses solar energy, and when the heat supply load exceeds this load, the traditional boiler device is used. The power supply of the experimental solar house is provided by a solar panel (photovoltaic converter). A heat balance scheme for a solar house with autonomous heat supply and an electrothermal scheme of a physical model are proposed. Based on the proposed schemes, a mathematical model of heat balance and a calculation algorithm based on the heat balance equation of the dynamic state of the heat supply system of a one-story experimental solar house in a non-stationary mode have been developed. On the basis of mathematical modeling, the influence of the heat capacity of the wall structure on the temperature regime of the building was studied. On the basis of the MATLAB-Simulink program, the main temperature characteristics were built, on which the change in the temperature of the internal air of the building was analyzed depending on the ambient temperature. On the basis of the program, a modular scheme of the dynamic model was built. Based on the modular scheme, the results of the experiment on changing the air inside the solar house and the outdoor temperature are presented in the form of a graph. The mathematical model of the thermal balance of the building in dynamic mode and the obtained calculation results are recommended for use in the development of energy-efficient solar houses.Вопросы экономии топливно-энергетических ресурсов, повышения эффективности систем теплоснабжения жилых помещений, а также использования устройств на основе возобновляемых источников энергии на сегодняшний день имеют особую актуальность. Цель статьи – разработать математическую модель теплового баланса и провести теоретическое исследование одноэтажных сельских домов, использующих солнечную энергию в нестационарном режиме. Для ее реализации построен экспериментальный одноэтажный солнечный дом с автономным теплоснабжением на основе преимущественно солнечной энергии. В случаях, если нагрузка на теплоснабжение превышает солнечную нагрузку, применяется традиционное котельное устройство. Электроснабжение экспериментального дома обеспечивается солнечной панелью (фотоэлектрическим преобразователем). Предложены схема теплового баланса солнечного дома с автономным теплоснабжением и электротепловая схема физической модели. На их основе разработаны математическая модель и алгоритм расчета, базирующийся на уравнении теплового баланса динамического состояния системы теплоснабжения экспериментального дома в нестационарном режиме. Исследовано влияние теплоемкости стеновой конструкции на температурный режим здания. В среде моделирования MATLAB-Simulink построены основные температурные характеристики, на которых проанализировано изменение температуры внутреннего воздуха здания в зависимости от температуры окружающей среды. Построена модульная схема динамической модели, результаты эксперимента по изменению воздуха внутри солнечного дома и температуры наружного воздуха представлены в виде графика. Математическая модель теплового баланса здания в динамическом режиме и результаты расчетов могут использоваться при разработке энергоэффективных солнечных домов

On the classification of Darboux integrable chains

Cataloged from PDF version of article.We study differential-difference equation (d/dx) t (n+1,x) =f (t (n,x),t (n+1,x), (d/dx) t (n,x)) with unknown t (n,x) depending on continuous and discrete variables x and n. Equation of such kind is called Darboux integrable, if there exist two functions F and I of a finite number of arguments x, { t (n+k,x) } k=-∞ ∞, {(dk /d xk) t (n,x) } k=1 ∞, such that Dx F=0 and DI=I, where D x is the operator of total differentiation with respect to x and D is the shift operator: Dp (n) =p (n+1). Reformulation of Darboux integrability in terms of finiteness of two characteristic Lie algebras gives an effective tool for classification of integrable equations. The complete list of Darboux integrable equations is given in the case when the function f is of the special form f (u,v,w) =w+g (u,v). © 2009 American Institute of Physics

ЛЕЧЕНИЕ ГИПЕРВОЛЕМИИ МАЛОГО КРУГА ПОСЛЕ ОПЕРАЦИИ РАСТЕЛЛИ У БОЛЬНОЙ С ТЕТРАДОЙ ФАЛЛО И АТРЕЗИЕЙ ЛЕГОЧНОЙ АРТЕРИИ

17yearold patient with hypervolemia of lesser (pulmonary) circulation was operated for tetralogy of Fallout with pulmonary atresia. She was successfully treated by intensive therapy using techniques of noninvasive ventilation with regard to clinical status of hypovolemia of the lesser (pulmonary) circulatory system in the early post operative period.Пациентка, 17 лет, была оперирована по поводу тетрады Фалло с атрезией легочной артерии. В раннем послеоперационном периоде наблюдалась клиника гиперволемии малого круга кровообращения. После проведения интенсивной терапии с применением методов неинвазивной вентиляции легких пациентка в удовлетворительном состоянии переведена из ОРИТ на 5е сутки

Efficacy of Videoendoscopic Inguinal Femoral Lymphadenectomy for Management of Metastatic Skin Melanoma

Aim. Assessment of the utility and advantage of videoendoscopic inguinal femoral lymphadenectomy (VE-LAD) over the standard open technique (OLAD) in patients with malignant skin melanoma and metastatic lesions of regional inguinal and/or femoral lymph nodes.Materials and methods. The Saint-Petersburg Clinical Research Centre for Specialty Medical Aid in Oncology managed 86 inguinal femoral LADs in melanoma patients over 2013–2016. VE-LAD was rendered in 48 (54.7 %) cases, and OLAD otherwise.Results and discussion. A total of 72 patients were included in the study. VE-LAD was performed in 48 (54.7 %) cases, and OLAD otherwise. An average VE-LAD duration was 90 (60 to 160) min. Severe complications were observed in 4/48 (8 %) VE-LAD and 16/24 (66 %) OLAD cases, which reveals a significantly lower complication rate in the study cohort (chi-square p > 0.000). Lymphorrhoea was shorter in the study cohort (> 7 days in 5 patients vs. 3/24 and > 14 days only in 11/24 OLAD cases; chi-square p > 0.000). No significant differences in relapse-free survival were observed between the cohorts, with higher absolute values of 22.6 months in the VE-LAD (95 % CI 14.8–30.4, p = 0.087) vs. 9.4 months (95 % CI 0.0–18.9, p = 0.087) in OLAD cohort. A median OS was 52.3 months (95 % CI 30.5–74.1, p = 0.996) in the VE-LAD vs. 39.9 months (95 % CI 30.6–49.2, p = 0.996) in OLAD cohort.Conclusion. Videoendoscopic inguinal femoral lymphadenectomy allows a radical inguinal femoral lymph node removal alike in conventional surgical dissection. Our results indicate the method performance towards reduced postoperative wound complications. The oncological indicators are comparable to the traditional surgery cohort