Bases in the solution space of the Mellin system

Local holomorphic solutions z=z(a) to a univariate sparse polynomial equation p(z) =0, in terms of its vector of complex coefficients a, are classically known to satisfy holonomic systems of linear partial differential equations with polynomial coefficients. In this paper we investigate one of such systems of differential equations which was introduced by Mellin. We compute the holonomic rank of the Mellin system as well as the dimension of the space of its algebraic solutions. Moreover, we construct explicit bases of solutions in terms of the roots of p and their logarithms. We show that the monodromy of the Mellin system is always reducible and give some factorization results in the univariate case

A Graceful Basis in the Solution Space of an ODE with Constant Coefficients

We revisit the classical problem of construction of a fundamental system of solutions to a linear ODE whose elements remain analytic and linearly independent for all values of the roots of the characteristic polynomial.Comment: 3 page

Didactic software for chemistry education at the ISCED 2 level

1 ABSTRACT The current chemistry education solves problems related primarily to the setting of the curriculum contents, which would be professionally correct, appropriately extensive, and at the same time connected with current aspects of life in modern society, and to problems of teaching strategies that would stimulate the students into an interest in science and commitment to it. The main goal of this dissertation is to create an educational website with an interactive chemistry course for lower secondary schools (ISCED 2) and verify its effectiveness in school practice. The first part of the dissertation describes methods of interactive chemistry teaching supporting the increase of the students' cognitive activity and the effectiveness of the learning process using ICT. The second part characterizes the chemistry course thus created and lists various ways to apply interactive teaching in it. Our interactive course contains a total of 14 thematic units, each with 2-6 subthemes. All themes are processed with respect to the practical application of the subject matter using the listed interactive education methods. This course was tested in 2018-2020 during chemistry lessons in Kazakhstan and Czech Republic, and the students' opinions toward interactive teaching in this study were tested using a simple...1 ABSTRAKT Současné chemické vzdělávání řeší problémy spojené především se stanovením obsahu učiva, který bude odborně správný, přiměřeně rozsáhlý a zároveň spojený s aktuálními aspekty života současné společnosti, a problémy strategie výuky, která bude podněcovat zájem a zaujetí žáků pro přírodní vědy. Hlavním cílem disertační práce je vytvořit vzdělávací webovou stránku s interaktivním kurzem chemie pro 2. stupeň základních škol a nižší ročníky víceletých gymnázií a ověřit její účinnost ve školní praxi. V první části práce jsou popsány vybrané způsoby interaktivní výuky chemie podporující zvýšení kognitivní aktivity žáků a účinnosti učebního procesu s využitím ICT. Ve druhé části práce je charakterizován vytvořený kurz chemie a uvedeny možné způsoby aplikace interaktivní výuky v tomto kurzu. Kurz obsahuje celkem 14 tematických bloků, dále dělených na 2-6 dílčích témat. Všechny tematické bloky jsou vytvořeny s přihlédnutím k praktickému použití oboru chemie a využití uvedených interaktivních výukových metod. Vytvořený kurz byl pilotně ověřován ve výuce chemie v Kazachstánu a České republice v letech 2018-2020, a to především z hlediska zjištění zájmu žáků o tento způsob výuky formou dotazníkového šetření. První ověřování vzdělávacích materiálů interaktivního kurzu chemie bylo provedeno v Karagandě...Department of teaching and Didactics of ChemistryKatedra učitelství a didaktiky chemiePřírodovědecká fakultaFaculty of Scienc

Bivariate hypergeometric D-modules

AbstractWe undertake the study of bivariate Horn systems for generic parameters. We prove that these hypergeometric systems are holonomic, and we provide an explicit formula for their holonomic rank as well as bases of their spaces of complex holomorphic solutions. We also obtain analogous results for the generalized hypergeometric systems arising from lattices of any rank

The polymorphism and tradition of funerary practices of medieval Turks in light of new findings from Tuva Republic.

The medieval Turks of the eastern Asian steppe are known for funerary finds exalting horsemanship and military heroism that thrived on intertribal warfare. Existing bodies of research on various categories of objects-which include architecture, stelae, grave goods and inhumations-are in depth but highly regionalized. As a result, our understanding of the archaeological culture of the Turks on a spatio-temporal scale commensurate with territorial shifts in their political dominion throughout the period of the Turk khaganates (mid-6th to mid-8th centuries CE) remains disjunct. The present paper addresses this problem of disparate data. We present a synthesis of the archaeological research of medieval Turks spanning Mongolia, southern Siberia, and Xinjiang in view of results of the excavation of medieval burials at Tunnug 1 in Tuva Republic-where Turkic remains are dispersed and not easily distinguishable from other funerary cultures of connecting time periods. We argue that Turkic funerary culture can be better characterized as polymorphic-the presence of different regional amalgams of burial traditions. The horse-and-human burials and commemorative ogradka known to be quintessentially Turkic are but one of the more dominant amalgams. This pattern of differential practices is congruent with the history of medieval Turks evolving as peoples of mixed lineages and political groupings, rather than people of a unitary culture

Comparing analysis of pretreatment methods of wood and bone materials for the chronology of peripheral burials at Tunnug 1, Tuva Republic, Russia

Nine burials from Tunnug 1 site in Tuva Republic, which contained human and animal bones as well as remains of wood, were chosen for intercomparison study of preparation methods. Nine human bones, nine animal bones and 11 pieces of wood were prepared. Gelatin extracted from bones was purified using the UF method but the extraction from bones was modified with respect to acid and base treatment. Wood samples were treated as whole using acid-base-acid and cellulose was extracted for comparison. The results confirmed a highly consistent chronology of the sites centered at 200–400 CE, however, a few bones resulted in an offset between ages obtained by different methods. The extraction of cellulose was limited due to the poor preservation of wood. Our results highlight problems of dating poorly preserved bones and wood