Note on Moufang-Noether currents

The derivative Noether currents generated by continuous Moufang tranformations are constructed and their equal-time commutators are found. The corresponding charge algebra turns out to be a birepresentation of the tangent Mal'ltsev algebra of an analytic Moufang loop.Comment: LaTeX2e, 6 pages, no figures, presented on "The XVth International Colloquium on Integrable Systems and Quantum Symmetries, Prague, 15-17 June, 2006

On classification of discrete, scalar-valued Poisson Brackets

We address the problem of classifying discrete differential-geometric Poisson brackets (dDGPBs) of any fixed order on target space of dimension 1. It is proved that these Poisson brackets (PBs) are in one-to-one correspondence with the intersection points of certain projective hypersurfaces. In addition, they can be reduced to cubic PB of standard Volterra lattice by discrete Miura-type transformations. Finally, improving a consolidation lattice procedure, we obtain new families of non-degenerate, vector-valued and first order dDGPBs, which can be considered in the framework of admissible Lie-Poisson group theory.Comment: 24 page

Automated construction of the boundaries of basin geosystems for the Volga Federal District

© 2014, Pleiades Publishing, Ltd. Using the Volga (Privolzhskii) Federal District as an example, we offer the solution of such a currently central scientific and methodological problem as automated identification of the boundaries of basin geosystems under different landscape and geomorphological conditions in terms of multiresolution digital elevation models. The main stages of work are described, namely the development of the digital elevation model, its hydrological adjustment, identification of the boundaries of basin geosystems, and validity assessment of results obtained. The technique has been developed for constructing a hydrologically valid digital elevation model with the purpose of identifying the boundaries of basin geosystems

Cartographic model of river basins of European Russia

© 2017, Pleiades Publishing, Ltd. An analysis made of the worldwide existing geoinformation systems (HydroSHEDS, CCM, Ecrins, WBD, etc.) suggests that there are as yet no models of adequate quality for the basin boundaries of small rivers in the European part of Russia. For the territory of the European part of Russia with a total area of more than 4 mln. km2 the GIS technology tools were used to construct the electron vector map of river basins and their interbasin spaces. The map thus obtained displays the basins of first-order rivers for a given level of generalization (sc 1:1 000 000). The GMTED2010 model was used as the digital elevation model. A total of 63 553 basin geosystems were identified on the map, averaging 68 km2 in area. Accuracy verification of identifying the basin boundaries showed a good agreement of areal and geometric characteristics of the method used with expert approach. In test areas, the men difference of the indicators of the area of the basins identified automatically and by use of the expert approach made up 3.6%. For areas with weakly dissected lowland topography this error does not exceed 5% while it is about 2% in areas with relatively dissected elevated topography. The basin geosystems thus identified are operational-territorial units with respect to which the geospatial data base is generated to characterize the natural-resource potential of the European territory of Russia. An example is provided for the generation of the geospatial database containing hydrological information covering 1763 hydrological stations collecting streamflow data

Free-algebra functors from a coalgebraic perspective

Given a set $\Sigma$ of equations, the free-algebra functor $F_{\Sigma}$ associates to each set $X$ of variables the free algebra $F_{\Sigma}(X)$ over $X$. Extending the notion of \emph{derivative} $\Sigma'$ for an arbitrary set $\Sigma$ of equations, originally defined by Dent, Kearnes, and Szendrei, we show that $F_\Sigma$ preserves preimages if and only if $\Sigma \vdash \Sigma'$, i.e. $\Sigma$ derives its derivative $\Sigma'$. If $F_\Sigma$ weakly preserves kernel pairs, then every equation $p(x,x,y)=q(x,y,y)$ gives rise to a term $s(x,y,z,u)$ such that $p(x,y,z)=s(x,y,z,z)$ and $q(x,y,z)=s(x,x,y,z)$. In this case n-permutable varieties must already be permutable, i.e. Mal'cev. Conversely, if $\Sigma$ defines a Mal'cev variety, then $F_\Sigma$ weakly preserves kernel pairs. As a tool, we prove that arbitrary $Set-$endofunctors $F$ weakly preserve kernel pairs if and only if they weakly preserve pullbacks of epis

On n-ary Hom-Nambu and Hom-Nambu-Lie algebras

It is observed that the category of n-ary Hom-Nambu(-Lie) algebras is closed under twisting by self-weak morphisms. Constructions of ternary Hom-Nambu algebras from Hom-associative algebras, Hom-Lie algebras, ternary totally Hom-associative algebras, and Hom-Jordan triple systems are given. Every multiplicative n-ary Hom-Nambu algebra gives rise to a sequence of Hom-Nambu algebras of exponentially higher arities. Under some conditions, an n-ary Hom-Nambu(-Lie) algebra gives rise to an (n-1)-ary Hom-Nambu(-Lie) algebra.Comment: 23 page

НАВЧАЛЬНА ДЕМОНСТРАЦІЯ АВТОПСІЇ ЯК МЕТОД ПРОВЕДЕННЯ ПРАКТИЧНОГО ЗАНЯТТЯ З ПАТОМОРФОЛОГІЇ

The aim of the work – to develop a methodology for conducting classes in a sectional room, which will allow students to be involved and motivated to study a clinical case involving an autopsy, and to more objectively evaluate theoretical training and practical skills at its completion; evaluate the opinion of students of the rst and second course, regarding their attitude to different methods of conducting classes on pathomorphology. In addition, to conduct a survey of students, who taught the subject “Pathomorphology”, regarding their attitude to various methods of conducting lessons from the subject, and to analyze its results.The main body. We proposed the technique of laboratory class with evaluation of achieved knowledge and skills. The general purpose of this approval was the improving of students’ observing work quality in an autopsy room. We developed the methodological materials in form of simpli ed questionnaire blank for autopsy report, which in its turn was adapted for third-year students.Conclusions. This method stimulates the observation skills during the autopsy. It either comprises the writing assessment of knowledge and skills that are related to the current case. Attendance of educational autopsies helps medical students in clinical-pathological comparison, in more profound understanding of pathologies, and improves their quali cation.Мета роботи – розробити методику проведення заняття у секційному залі, що дозволить залучити та мотивувати студентів до вивчення клінічного випадку, пов’язаного із розтином, а також більш об’єктивно оцінити теоретичну підготовку та практичні навички по його завершенні. Оцінити думку студентів першого та другого курсів щодо їх ставлення до різних методів проведення заняття з патоморфології. Окрім того, провести опитування студентів, яким викладався предмет “Патоморфологія”, щодо їх ставлення до різних методик проведення занять із предмета, та проаналізувати його результати.Основна частина. Для підвищення якості роботи студентів у секційному залі ми запропонували техніку проведення заняття та оцінки отриманих знань і навичок, розробивши методичні матеріали у вигляді бланка навчального протоколу розтину, адаптованого для студентів третього року навчання медичного факультету.Висновки. Дана методика стимулює навичку спостереження в процесі автопсії, а також включає у себе виконання письмового завдання для перевірки теоретичних знань та вмінь, пов’язаних із макроскопічним описом патологічних змін. Навчальне відвідування автопсій допомагає майбутнім лікарям провести клініко-морфологічні паралелі, глибше зрозуміти зміст нозологій та підвищити власний кваліфікаційний рівень