Group classification of variable coefficient KdV-like equations

The exhaustive group classification of the class of KdV-like equations with time-dependent coefficients $u_t+uu_x+g(t)u_{xxx}+h(t)u=0$ is carried out using equivalence based approach. A simple way for the construction of exact solutions of KdV-like equations using equivalence transformations is described.Comment: 8 pages; minor misprints are corrected. arXiv admin note: substantial text overlap with arXiv:1104.198

New Solutions for Solar Absorption Refrigeration Systems and Air Conditioning Systems

The mission of the research includes the following objectives: the development of new circuit decisions for the alternate refrigerating systems based on the use of an open absorptive circuit and on the use of solar energy for absorbent solution regeneration; an assessment of the energy and environmental characteristics of the developed systems; obtaining of the experimental data for an assessment of the principal capabilities of the proposed new solar air-conditioning systems. The multistage principle of the creation of drying and cooling contours with the increase of concentration of absorbent on cooler steps is offered. The absorber with internal steam cooling allowing the improvement of the scheme of the alternate refrigerating system is developed. On the basis of the obtained experimental data the analysis of the main opportunities of the developed solar air-conditioning systems was made which showed that the created systems: provide the required comfortable parameters indoors without engaging of traditional refrigerating technics; allow to use only one - or two-stage option of refrigerating system for application in the conditions of Ukraine and of Europe. In comparison with traditional vapor-compression systems, the developed solar systems provide the considerable decrease in energy consumption (to 30%), their use leads to the decrease of exhaustion of natural resources, influences less global climate change

Equivalence of conservation laws and equivalence of potential systems

We study conservation laws and potential symmetries of (systems of) differential equations applying equivalence relations generated by point transformations between the equations. A Fokker-Planck equation and the Burgers equation are considered as examples. Using reducibility of them to the one-dimensional linear heat equation, we construct complete hierarchies of local and potential conservation laws for them and describe, in some sense, all their potential symmetries. Known results on the subject are interpreted in the proposed framework. This paper is an extended comment on the paper of J.-q. Mei and H.-q. Zhang [Internat. J. Theoret. Phys., 2006, in press].Comment: 10 page

Дослідження м’ясного продукту з додаванням кверцетинвмісної сировини в середовищі in vivo

The purpose of the work was to study antioxidants of natural origin, which are not inferior to the effectiveness of synthetic analogues. Natural antioxidants, in contrast to chemically synthesized, do not show any negative side effects on the human body, improving the quality of the product; have low toxicity and have a positive effect on the physiological processes of the human body, increasing its resistance. For this purpose, a preliminary selection of antioxidants of natural origin was carried out; meat technology improved; а number of studies have been conducted in the in vivo environment. As a source of substances with antioxidant characteristics, husk is selected, which contains a powerful antioxidant flavanoid quercetin. The work was devoted to the study of the effect of onion husk extract in a composite with a meat product on a number of physiological and biochemical parameters in an experimental model of the state of an approaching metabolic syndrome in animals with genetically determined arterial hypertension. In this work, glucose levels in the blood and parameters of changes in temperature and body weight of rats were studied in the process of feeding with the improved meat product. Measurements of glucose levels in rat arterial blood showed double-fold (59%, P < 0.01) increase in glucose content in spontaneously hypertensive rats. Adding fructose to drinking water increased glucose content by only 5%. Feeding rats with meat products containing quercetin did not reduce glucose levels. However, feeding on fructose animals, a meat product with onion husk extract, lowered glucose levels by 14%. Indicators of changes in body mass and body temperature of white male rats when using meat product with onion husk extract, quercetin, in comparison with control groups, showed that the percentage of survival was 100%. Measurements of mass and temperature showed the following: in the control group with normal feed, the rats did not gain weight at all, but the temperature at the end of the study decreased; The largest amount of rats in the diet was added to the meat product with quercetin. The temperature remained within the normal limits only in the groups that ate the meat product with the extract of husk of onion or quercetin.  Метою роботи було дослідження антиоксидантів природного походження, які не поступаються за ефективністю синтетичним аналогам. Природні антиоксиданти на відміну від хімічно синтезованих не проявляють негативного побічного впливу на організм людини, поліпшуючи якісні характеристики продукту; мають низьку токсичність і позитивно впливають на фізіологічні процеси людського організму, підвищуючи його резистентність. Для поставленої мети попередньо було проведено підбір антиоксидантів природного походження; удосконалено технологію м’ясних продуктів; проведено ряд досліджень в середовищі in vivo. Як джерело речовин з антиокиснюючими характеристиками вибрано лушпиння цибулі, яке містить потужний антиосидант флаваноїд кверцетин. Робота була присвячена дослідженню впливу екстракту лушпиння цибулі в композиті з м’ясним продуктом на ряд фізіологічних і біохімічних параметрів в експериментальній моделі стану, наближеного до метаболічного синдрому, у тварин з генетично детермінованою артеріальної гіпертензією. Вивчали показники вмісту глюкози в крові та показники зміни температури і маси тіла щурів в процесі згодовування удосконаленим м’ясним продуктом. Вимірювання рівнів глюкози в артеріальній крові щурів показали двократне (на 59%, Р < 0,01) збільшення вмісту глюкози у спонтанногіпертензивних щурів. Додавання фруктози до питної води збільшило вміст глюкози всього на 5%. Годування щурів м’ясним продуктом із вмістом кверцетину не знизило рівень глюкози. Однак годування тварин, що утримувались на фруктозі, м’ясним продуктом з екстрактом лушпиння цибулі знизило рівень глюкози на 14%. Показники зміни маси і температури тіла білих щурів самців при вживанні м’ясного продукту з екстрактом лушпиння цибулі, кверцетином, порівняно з контрольними групами показали, що процент виживання склав 100%. Заміри маси і температури показали таке: в контрольній групі зі звичайним кормом щурі майже не набрали ваги, але температура наприкінці дослідження знизилась; найбільше маси набрали щурі, в раціон яких додаткового було включено м’ясний продукт з кверцетином. Температура залишилась в межах норми лише у групах, які з’їдали м’ясний продукт з екстрактом лушпиння цибулі чи кверцетину. &nbsp

Enhanced Group Analysis and Exact Solutions of Variable Coefficient Semilinear Diffusion Equations with a Power Source

A new approach to group classification problems and more general investigations on transformational properties of classes of differential equations is proposed. It is based on mappings between classes of differential equations, generated by families of point transformations. A class of variable coefficient (1+1)-dimensional semilinear reaction-diffusion equations of the general form $f(x)u_t=(g(x)u_x)_x+h(x)u^m$ ($m\ne0,1$) is studied from the symmetry point of view in the framework of the approach proposed. The singular subclass of the equations with $m=2$ is singled out. The group classifications of the entire class, the singular subclass and their images are performed with respect to both the corresponding (generalized extended) equivalence groups and all point transformations. The set of admissible transformations of the imaged class is exhaustively described in the general case $m\ne2$. The procedure of classification of nonclassical symmetries, which involves mappings between classes of differential equations, is discussed. Wide families of new exact solutions are also constructed for equations from the classes under consideration by the classical method of Lie reductions and by generation of new solutions from known ones for other equations with point transformations of different kinds (such as additional equivalence transformations and mappings between classes of equations).Comment: 40 pages, this is version published in Acta Applicanda Mathematica

Multicultural sources and analogies of the visual system of wooden architecture of Zaural′e

The article is dedicated to the study of multicultural sources and analogies of the visual system of Russian wooden architecture of Zaural′e. The history of formation of traditions of wooden construction is overviewed. Peculiarities of volume, relief and hand carving are pointed out. Types of window casing mouldings, their structural basis and main decorative elements are analyzed. The visual motifs of geometrical, vegetal, anthropomorphic and ornithomorphic types of ornament of window casing mouldings are introduced. Historical and cultural ties of Zaural`e, which were reflected in the eclecticism of wooden architecture are described. S-shaped curves and heart-shaped figures, vortex rosaces, and vegetative ornament were actively used by carvers in the visual system of wooden architecture of Zaural′e in the late XIX — early XX centuries. The most widely distributed ornament in the regional architecture was the one of vegetable cruciform of plaited stems. Images of ancient Byzantine-Romanesque origin (paired birds, heraldic motifs, crowns) can be found in the house carving of Zaural′e. These elements can be related to the genesis of the Slavic culture, which is an integral part of the Orthodox Byzantine tradition. Manifestations of Baroque and Сlassicism stylistic traits in wooden construction of the region are studied. Multicultural analogies are pointed out in the ornamental motifs of the visual system of wooden architecture. Traditions of folk regional architecture related to the decorative plasticity of the facades are generalized. An ornament is characterized as a historical source for the study of the formation of the cultural landscape. The eclecticism of the visual system of the Russian wooden regional architecture is connected to ethno-cultural interactions, the waves of colonization of Zaural′e. The article contains extensive illustrative material, which represents analogies in the decoration of the wooden housing construction and the archeological artifacts from ornitho-, anthropomorphic and floral ornaments