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

Group analysis and exact solutions of a class of variable coefficient nonlinear telegraph equations

A complete group classification of a class of variable coefficient (1+1)-dimensional telegraph equations $f(x)u_{tt}=(H(u)u_x)_x+K(u)u_x$, is given, by using a compatibility method and additional equivalence transformations. A number of new interesting nonlinear invariant models which have non-trivial invariance algebras are obtained. Furthermore, the possible additional equivalence transformations between equations from the class under consideration are investigated. Exact solutions of special forms of these equations are also constructed via classical Lie method and generalized conditional transformations. Local conservation laws with characteristics of order 0 of the class under consideration are classified with respect to the group of equivalence transformations.Comment: 23 page

Symmetries of Differential Equations via Cartan's Method of Equivalence

We formulate a method of computing invariant 1-forms and structure equations of symmetry pseudo-groups of differential equations based on Cartan's method of equivalence and the moving coframe method introduced by Fels and Olver. Our apparoach does not require a preliminary computation of infinitesimal defining systems, their analysis and integration, and uses differentiation and linear algebra operations only. Examples of its applications are given.Comment: 15 pages, LaTeX 2.0

Group Analysis of Variable Coefficient Diffusion-Convection Equations. I. Enhanced Group Classification

We discuss the classical statement of group classification problem and some its extensions in the general case. After that, we carry out the complete extended group classification for a class of (1+1)-dimensional nonlinear diffusion--convection equations with coefficients depending on the space variable. At first, we construct the usual equivalence group and the extended one including transformations which are nonlocal with respect to arbitrary elements. The extended equivalence group has interesting structure since it contains a non-trivial subgroup of non-local gauge equivalence transformations. The complete group classification of the class under consideration is carried out with respect to the extended equivalence group and with respect to the set of all point transformations. Usage of extended equivalence and correct choice of gauges of arbitrary elements play the major role for simple and clear formulation of the final results. The set of admissible transformations of this class is preliminary investigated.Comment: 25 page

Juchi Khan Mausoleum: realities, legends and rituals

Lore and folk legends designate the burial of Jochi Khan, the eldest son of Genghis Khan, in the eponymous mausoleum in Ulytau, Kazakhstan. The mausoleum was built according to Islamic architecture of the 14th-15th centuries. A.Kh. Margulan, the author of archeological excavations, relying mostly on the folk legends designated the mausoleum’s burial to Jochi Khan. Radiocarbon dating of mausoleum determines two stages of its construction throughout the 14th century and the burial box age later than the death of Jochi Khan in 1225. New evidence from the mausoleum architecture and artifacts suggests that Jochi's burial is not in the mausoleum but a secret place prescribed by the Chinggisid canon. The assembly of Islamic and pre-Islamic traditions and the camel skull found in the burial indicates that the burial was made for a person of Islamic faith from the Golden Horde. Whereas the mausoleum was named in the honor of Jochi Khan

Ancient genomic time transect from the Central Asian Steppe unravels the history of the Scythians

The Scythians were a multitude of horse-warrior nomad cultures dwelling in the Eurasian steppe during the first millennium BCE. Because of the lack of first-hand written records, little is known about the origins and relations among the different cultures. To address these questions, we produced genome-wide data for 111 ancient individuals retrieved from 39 archaeological sites from the first millennia BCE and CE across the Central Asian Steppe. We uncovered major admixture events in the Late Bronze Age forming the genetic substratum for two main Iron Age gene-pools emerging around the Altai and the Urals respectively. Their demise was mirrored by new genetic turnovers, linked to the spread of the eastern nomad empires in the first centuries CE. Compared to the high genetic heterogeneity of the past, the homogenization of the present-day Kazakhs gene pool is notable, likely a result of 400 years of strict exogamous social rules.Introduction Results - The IA transition in the Kazakh Steppe - Admixture modeling of IA steppe populations - Post-IA genetic turnovers in the Kazakh Steppe - Dating ancient admixture - Present-day Kazakhs Discussion Material and methods - Radiocarbon dating - DNA extraction, library preparations, and sequencing - Modern DNA genotyping and quality controls - Ancient DNA data processing -- Raw data -- Authentication and contamination estimate -- Genotyping -- Sex determination -- Genetic relatedness estimation - Uniparental haplogroup assignment - Population structure analyses - Individual labeling and population grouping criteria - F-statistics and ancestry modeling - Admixture dating - CHROMOPAINTER and fineSTRUCTURE analyse

Observation of Bright Yellow Luminescence in Lead Bromide Perovskite Single Crystals

We report the results of photoluminescence (PL) studies in organic-inorganic hybrid perovskite CH3NH3PbBr3. The PL was registered with the 455 nm laser over temperatures from 5 to 320 K in increments 5-10 K.Работа выполнена при поддержке ключевого центра превосходства УрФУ “Радиационные и ядерные технологии” и при финансовой поддержке РФФИ и Свердловской области в рамках научного проекта № 20-42-660004