Akademii Nauk SSSR Research Articles

Thermal inertia effect of reactive sources on one-dimensional discrete combustion wave propagation

In the present work, the discrete flame model developed by Shoshin et al. (Doklady Akademii Nauk SSSR, 1986) and further scrutinized by Tang et al. (Combustion Theory and Modelling, 2009) is augmented by introducing the thermal inertia of particles in the preheating zone. The effect of particle thermal inertia on the speeds, propagation limits, and near-limits dynamics of one-dimensional discrete combustion waves is studied using the new model. It is found that, with the increase of particle thermal inertia, the propagation velocity of the discrete flame decreases due to the smaller heating rate of the particles. Besides, particle thermal inertia extends the propagation limits compared to the prediction of the old model. Furthermore, it is mathematically proven that the nonphysical branch of the solutions for the discrete flame speeds, found using the old discrete model, is a set of solutions for the propagation limits of steady-state discrete flames with particle thermal inertia included. The flame speed predicted using the new model is also compared with that determined analytically using a continuum model considering the thermal inertia of the condensed phase, attributed to Goroshin et al. (Combustion and Flame, 1996). We find that the discrete flame speeds predicted by the both models become closer to each other with increasing particle thermal inertia. Finally, the two models converge regardless of the discrete nature of the heat sources when particle thermal inertia is large enough so that can limit the flame propagation. The particle thermal inertia controlled flames could be regarded as a new kind of combustion regime.

Nekotorye voprosy obshchego nadzora prokuratury: rezul'taty nauchnoj diskussii, provedennoj v Institute prava Akademii nauk SSSR i Voenno-yuridicheskoj akademii Krasnoj armii v 1945 g.

In modern conditions, the importance of the activities of the Prosecutor's office in solving the entire complex of tasks of state and social development of the country is increasing. One of the most important activities of the Prosecutor's office is the activity covered by the concept of “general supervision of the Prosecutor's office”, which is currently presented mainly as a scientific category, which, however, has not received its legislative consolidation. In order to get a more complete picture of the general supervision of the Prosecutor's office in the historical and legal aspect, it is proposed to consider the results of a discussion on some issues of general supervision of the prosecutor's office held at the Institute of Law of the Academy of Sciences of the USSR and the Military Law Academy of the Red Army in 1945, where the issues of the correlation between the supervisory activities of the Prosecutor's office and state control; the powers of the prosecutor in the field of general supervision; forms of prosecutorial response; requirements imposed on employees of the Prosecutor's office; and also raised the question of the existence of general supervision of the Prosecutor's office in the military, especially in wartime conditions.

Модель роста нитевидных кристаллов, контролируемого гетерогенной химической реакцией, с учетом размерного эффекта

Нитевидные кристаллы имеют важное практическое применение в машиностроении позволяя улучшать прочностные, эксплуатационные и физические характеристики конструкционных материалов при создании композитов армированных усами. Модель роста усов кремния, контролируемого химической реакцией на границе жидкостьгаз, дополнена учетом давления насыщенного пара кремния в расплаве на вершине кристалла. Для кристаллов достаточно малых размеров давление насыщенного пара кристаллизующегося вещества становится столь значительным, что рост кристалла прекращается. Модель предполагает диффузионную доставку исходных веществ и отвод продуктов реакции в тонкий приповерхностный слой газа у поверхности раздела жидкость-газ, где концентрации реагентов остаются постоянными. Концентрации реагентов в этом слое определяют скорость химической реакции выделения кристаллизующегося вещества.Учтён поток, возникающий за счет давления насыщенного пара кремния над расплавом,при условии, что испаряющиеся атомы практически полностью вступают во взаимодействие с реагентами в газовой фазе. Баланс диффузионных, химических потоков и потоков испарения позволяет найти скорость роста нитевидного кристалла в зависимости от его радиуса и технологических параметров процесса. Зависимость скорости роста нитевидного кристалла от его радиуса имеет максимум, а при достаточно малых поперечных размерах кристалла обращается в нуль. Получено выражение для радиуса кристалла, при котором скорость роста обращается в нуль. Рост кристалла прекращается при достаточно больших радиусах. Получено выражение, определяющее максимальный радиус кристалла, при котором рост становится невозможным. Результаты работы будут полезны при анализе роста нитевидных кристаллов различных веществ, который сопровождается химической реакцией. Модель, предложенная в работе, будет востребована для разработки технологических процессов массового производства кристаллов с целью получения композиционных материалов.
 
 
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T-x-диаграмма системы Ga – Se в диапазоне составов 48.0 – 61.5 мол. % Se по данным термического анализа

Целью настоящей работы было термографическое исследование T-x диаграммы системы Ga – Se в диапазоне температур от 500 до 1100 °С и в диапазоне составов от 48.0 до 61.5 mol % Se. Методом исследования являлся дифференциальный термический анализ c компьютерной регистрацией данных. Получены свидетельства о наличии ретроградного солидуса фазы g-GaSe со стороны селена (с областью гомогенности в несколько десятых mol % при температурах выше эвтектической) и о независимом существовании близких по составу фаз e-GaSe и g-GaSe. При этом более богатая галлием фаза e-GaSe испытывает перитектический распад с образованием расплава (L2) и g-GaSe. Для темпера-туры предполагаемой перитектической реакции получено значение 921 ±2 °С. Вместе стем, на данном этапе работ не получено никаких данных в пользу существования ожидавшейся (по аналогии с системой Ga – S) высокотемпературной модификации, близкой по составу к сесквиселениду галлия (Ga2S3). Другие результаты, полученные в настоящей работе (характер и температуры плавления промежуточных фаз, температуры эвтектического и монотектического превращений, а также координата эвтектического состава), хорошо согласуются с литературными данными по исследованной системе
 
 
 
 
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THE 2018 NICOLSON FELLOW: TARGOL CHATRENOOR

THE 2018 NICOLSON FELLOW: TARGOL CHATRENOOR

СРАВНИТЕЛЬНЫЙ АНАЛИЗ СРЕДНЕАЗИАТСКИХ ВЕРСИЙ ЭПОСА «ГЁРОГЛЫ»

В статье исследуются среднеазиатские версии эпоса «Гёроглы», проводится их сравнительный анализ в историческом, этнографическом, культурологическом аспектах. Актуальность данного исследования обусловлена необходимостью комплексного исследования данного цикла с определением его исторической основы, а также культурных взаимовлияний для более точного определения основы и времени образования эпоса данного цикла. Цель исследования – найти сходство и индивидуальные отличия между версиями, проследить последовательность культурного взаимовлияния народов региона, а также объяснить причину столь широкого распространения эпоса. Задачами исследования являются рассмотрение каждого эпоса данной версии, анализ их содержания и выявление пути культурных отношений между народами. Научная новизна исследования отразилась в идее возможности исторической основы среднеазиатских версий, истоки которой скрыты в туркменском варианте героического эпоса.В данной статье эпос рассматривается как индикатор культурных отношений между народами среднеазиатского региона. К среднеазиатским версиям эпоса «Гёроглы» относятся версии героического эпоса туркменского, узбекского, каракалпакского, казахского, таджикского и татарского (тобольские татары) народов. Проведённые сравнения этих версий эпоса дают определённые представления о диапазоне давних взаимных контактов и культурных связей народов региона. Особенно много параллелей между версиями обнаруживается у народов, живущих в соседстве друг с другом. Многочисленность национальных версий эпоса и их сюжетная близость говорит об единых культурных корнях, основы которой начали складываться ещё в далёкие времена. А окончательное утверждение и приобретение ими некоторых локально-национальных черт произошло уже в процессе формирования их каждой в своей национальной среде. Несмотря на то, что изучением среднеазиатских версий героического эпоса занималось большое количество исследователей и каждой из них посвящено много публикаций, всё же самобытные и бесконечно разнообразные по сюжетам, вариантам, идейно-художественным качествам сказания о Гёроглы заслуживают ещё более внимательного и специального изучения. Потому что, отражая в высокохудожественной форме светлые идеалы и стремления народов, эпос «Гёроглы», несомненно, играл и продолжает играть значительную роль в сближении народов региона, в формировании национальных культур, продолжает служить делу воспитания молодого поколения.

ВОССТАНОВЛЕНИЕ РАСТИТЕЛЬНОСТИ И ПОЧВЕННОГО ПОКРОВА НА НАЧАЛЬНОЙ СТАДИИ ЗАРАСТАНИЯ ГАРЕЙ НА ВЫРАБОТАННЫХ ТОРФЯНИКАХ, "Лесоведение"

RUSSIAN JOURNAL OF FOREST SCIENCE. 2018. NO. 2. P. 119-129. VEGETATION AND SOIL COVERS AT EARLY STAGE OF POST-FIRE RECOVERY IN EXTRACTED PEATLANDS N. P. Akhmet’eva 1 , A. V. Mikhailova 2 , L. P. Fedorova 3 1 Water Problems Institute, Russian Academy of Sciences Gubkin st. 3, Moscow, 119333, Russia E-mail: nakhmeteva@rambler.ru 2 Vernadsky Institute of Geochemistry and Analytical Chemistry, Russian Academy of Sciences Kosygin st. 19, Moscow, 119991, Russia 3 Berg State Researh Institute on Lake and River Fisheries Gagarina st. 14, Konakovo, Tver Oblast, 171254, Russia Received 12 April 2016 Recovery of vegetation and soil covers after fire in 2010 was studied during summer on drained peatland sites Galitskii Mokh (Tver Oblast) and Radovitskii Mokh (Moscow Oblast), which has been filled with water in 2012-13. By the year 2015 we have found the following. Grass and wooden vegetation recovered intensively for 2-3 years after fire. Birch, willow and cottongrass community with alder and aspen, and little abundance of pine on Radovitskii Mokh, have formed by the time of study. Chemical composition of peat ash and pyrogenic peat has changed essentially and differently on the sites. However concentration of chemical elements under study has not reached the pre-fire values. Chemical composition of wetland waters on Radovitskii Mokh has become similar to pre-fire. On the other hand, wetland waters on Galitskii Mokh still have contained high concentrations of sulfates and phosphorus. Keywords: drained wetlands, peat fires, vegetation recovery, hydrochemical indicators in ash, pyrogenic peat, wetland waters. DOI: 10.7868/S0024114818020043 REFERENCES Akhmet'eva N.P., Belova S.E., Dzhamalov R.G., Kulichevskaya I.S., Lapina E.E., Mikhailova A.V., Natural post-fire bog recovery, Water Resources , 2014, Vol. 41, No. 4, pp. 353–363. Akhmet'eva N.P., Mikhailova A.V., Pozhary 2010-2011 gg. na bolote Radovitskii Mokh i ikh posledstviya (Consequences of 2010-11 fires on Radovitskii Mokh bog), Monitoring i sokhranenie osobo tsennykh prirodnykh territorii i obektov Vladimirskoi oblasti i sopredel'nykh regionov: problemy, opyt i perspektivy (Monitoring and conservation of outstanding natural resources lands and sites in Vladimir Oblast and the neighbouring regions: Challenges, experience and perspectives) Vladimir, 14-15 December 2012, Vladimir: Tranzit-IKS, 2013, pp. 14-18. Atrokhin V.G., Kuznetsov G.V., Lesovodstvo (Silviculture), Moscow: Agropromizdat, 1989, 400 p. Gromtsev A.N., Dinamika korennykh taezhnykh lesov Evropeiskoi chasti Rossii pri estestvennykh narusheniyakh (Dynamics of intact forests in taiga of European part of Russia under natural disturbance), Aktual'nye problemy geobotaniki (Urgent challenges of geobotany), Petrozavodsk, 24-28 September 2007, Petrozavodsk: Izd-vo KarNTs RAN, 2007, pp. 283-301. Gubanov I.A., Novikov V.S., Tikhomirov V.N., Opredelitel' vysshikh rastenii srednei polosy Evropeiskoi chasti SSSR (Key to higher plants of the Center of the European part of the USSR), Moscow: Prosveshchenie, 1981, 287 p. Korchagin A.A., Vliyanie pozharov na rastitel'nost' i vosstanovlenie ee posle pozhara na Evropeiskom Severe (The effect of fires on vegetation: recovery after fire in Northern Europe), Trudy Botanicheskogo instituta im. V.L. Komarova Akademii nauk SSSR. Seriya 3: Geobotanika , 1954, No. 9, pp. 75-149. P'yavchenko N.I., Lesnoe bolotovedenie: osnovnye voprosy (Forest paludology: basic issues), Moscow: Izd-vo AN SSSR, 1963, 192 p. Panov V.V., Tsymlyakova S.S., Prostranstvennaya struktura pozharov i gari na tekhnogenno narushennykh torfyanykh bolotakh (Spatial structure of fires and burnt areas in the technologically disturbed peat bogs), Izvestiya Russkogo geograficheskogo obshchestva , 2013, Vol. 145, No. 1, pp. 80-90. Sirin A.A., Minaeva T.Y., Vozbrannaya A.E., Bartalev S.A., Kak izbezhat' torfyanykh pozharov? (How to avoid peat fires?), Nauka v Rossii , 2011, No. 2, pp. 13-21.

Scientific legacy of Georgy K. Boreskov: bibliometric and thematic analysis

Year 2017 is momentous by the 110th anniversary of Prof. Georgy K. Boreskov’s birth. Prof. Georgy K. Boreskov (1907–1984) was a great scientist who made invaluable contribution to the theory of catalysis, kinetics and mechanisms of catalytic reactions. In 1958 he founded the Institute of Catalysis within the structure of Siberian Branch of Academy of Sciences, USSR. The Institute was headed by him until his death in 1984. Bibliometric and thematic analysis of scientific legacy of Prof. Georgy K. Boreskov represented by his publications 1929–1988 referred in the Web of Science, Scopus, Chemical Abstracts Plus and Russian Science Citation Index databases has been performed to highlight his unique contribution into the field of fundamental and applied catalysis. Among the widest areas of his expertise, heterogeneous oxidation catalysis significantly predominates. In patent publications authored by G. K. Boreskov, sulfur oxides are the most frequent compounds. The journal Reaction Kinetics and Catalysis Letters occupies third position (after Kinetics and Catalysis and Doklady Akademii Nauk SSSR) among the most frequent journal titles, where research works of G. K. Boreskov were published.

Yury Borisovich Rumer and his 'biological papers' on the genetic code.

Yury Borisovich Rumer was one of the most important theoretical physicists of the former Soviet Union in the early 1930s. However, he also wrote a few 'biological papers' on the standard genetic code after he read Crick's and Nirenberg's pioneering papers on the topic. Rumer's articles on the 'Systematization of Codons in the Genetic Code' (Rumer 1966 Doklady Akademii nauk SSSR 167, 1393-1394); Rumer 1968 Doklady Akademii nauk SSSR 183, 225-226; Rumer 1969 Doklady Akademii nauk SSSR 187, 937-938, where he suggested the idea of partitioning codons depending on their redundancy-the first mention of symmetry in the genetic code-were published in Russian only. Due to their importance and their frequent citation, we here present translations of these articles into English in order to make them accessible to a broader community.

Translation of 'Systematization of Codons in the Genetic Code [III]' by Yu. B. Rumer (1969).

Translation of 'Systematization of Codons in the Genetic Code [III]' by Yu. B. Rumer (1969).

On predicate provability logics and binumerations of fragments of Peano arithmetic

Solovay proved (Israel J Math 25(3---4):287---304, 1976) that the propositional provability logic of any ?2-sound recursively enumerable extension of PA is characterized by the propositional modal logic GL. By contrast, Montagna proved in (Notre Dame J Form Log 25(2):179---189, 1984) that predicate provability logics of Peano arithmetic and Bernays---Godel set theory are different. Moreover, Artemov proved in (Doklady Akademii Nauk SSSR 290(6):1289---1292, 1986) that the predicate provability logic of a theory essentially depends on the choice of a binumeration of the theory which is used to construct the provability predicate. In this paper, we compare predicate provability logics of I? n 's. For a binumeration ?(x) of a recursive theory T, let PL ?(T) be the predicate provability logic of T defined by ?(x). We prove that for any natural numbers i, j such that 0 < i < j, there exists a ?1 binumeration ?(x) of some recursive axiomatization of I? i such that $${{\sf PL}_\alpha({\rm I \Sigma}_i) \nsupseteq \bigcap_{\beta(x)}{\sf PL}_\beta({\rm I \Sigma}_j)}$$ PL ? ( I Σ i ) ? ? β ( x ) PL β ( I Σ j ) and $${{\sf PL}_\alpha({\rm I \Sigma}_i) \nsubseteq \bigcup_{\beta(x)}{\sf PL}_\beta({\rm I \Sigma}_j)}$$ PL ? ( I Σ i ) ? ? β ( x ) PL β ( I Σ j ) , where β(x) ranges over all ?1 binumerations of recursive axiomatizations of I? j .

Singular Integral Operators on an Open Arc in Spaces with Weight

The aim of this work is to study a singular integral operator \({\mathbf{A}=aI+bS_\Gamma}\) with the Cauchy operator SΓ (SIO) and Holder continuous coefficients a, b in the space \({\mathbb{H}^0_\mu(\Gamma,\rho)}\) of Holder continuous functions with an power “Khvedelidze” weight. The underlying curve is an open arc. It is well known, that such operator is Fredholm if and only if, along with the ellipticity condition \({a^2(t)-b^2(t)\not=0,\, t\in\Gamma}\), the “Gohberg–Krupnik arc condition” is fulfilled (see Duduchava, in Dokladi Akademii Nauk SSSR 191:16–19, 1970). Based on the Poincare–Beltrami formula for a composition of singular integral operators and the celebrated Muskhelishvili formula describing singularities of Cauchy integral, the formula for a composition of weighted singular integral operators is proved. Using the obtained composition formula and the localization, the Fredholm criterion of the SIO is derived in a natural way, by looking for the regularizer of the operator \({\mathbf{A}}\) and equating to 0 non-compact operators. The approach is space-independent and this is demonstrated on similar results obtained for SIOs with continuous coefficients in the Lebesgue spaces with a “Khvedelidze” weight \({\mathbb{L}_p(\Gamma,\rho)}\), investigated earlier by Gohberg and Krupnik (Studia Mathematica 31:347–362, 1968; One Dimensional Singular Integral Operators II, Operator Theory, Advances and Applications, vol. 54, chapter IX, 1979) with a different approach.

To the theory of total reflection**Fedorov F I 1955 To the theory of total reflection Doklady Akademii Nauk SSSR, 105, # 3, 465–8; received 9 December 1949. Presented by academician Lebedev A A on 27 May 1955. Translated by D I Pustakhod 2012.

To the theory of total reflection**Fedorov F I 1955 To the theory of total reflection Doklady Akademii Nauk SSSR, 105, # 3, 465–8; received 9 December 1949. Presented by academician Lebedev A A on 27 May 1955. Translated by D I Pustakhod 2012.

Approximation properties for generalized Baskakov-type operators

In this paper, we give a generalization of the Baskakov-type operators introduced by Baskakov (Doklady Akademii Nauk SSSR 113:249–251, 1957 (in Russian)) and obtain some direct and inverse results for these new operators. MSC: 41A35, 41A36

Maria Szymanowska (1789-1831): A Bio-Bibliography (review)

Maria Szymanowska (1789-1831): A Bio-Bibliography. By Anna Kijas. Lanham, MD: Scarecrow Press 2010. [xvii, 201 p. ISBN 9780810876842. $55.] Illustrations, music examples, tables, index, annotated bibliography, discography. Polish pianist-composer Maria Szyman - owska (1789-1831) is one of the most fascinating figures of the early-nineteenthcentury musical scene. She was one of the earliest international performing artists of the time, influential as performer and composer, and, perhaps most incredibly, she advanced her career despite being divorced woman with three young children. Respected by the foremost musicians of her day (including Johann Nepomuk Hummel, Gioacchino Rossini, and Luigi Cherubini), admired by aristocracy, she was also muse of the great romantic poets Johan Wolfgang Goethe and Adam Mickiewicz. Szymanowska scholarship in Polish and Russian is rather extensive, with major biographies on the composer already half century old (in Russian by Igor Belza, Mariia Shimanovskaia [Moscow: Izd-vo Akademii nauk SSSR, 1956]; in Polish by Teofil Syga and Stanislaw Szenic, Maria Szymanowska i jej czasy [Warsaw: Panstwowy Instytut Wydawniczy, 1960]). The same cannot be said about Anglo-American musicology, where interest in the Polish virtuosa began only in the late 1980s and early 1990s. Only recently, in 2006, has an English biography of the composer appeared: Maria Szymanowska: Pianist and Composer by Slawomir Dobrzanski (Los Angeles, CA: Polish Music Center at USC: Figuero Press, 2006). Anna Kijas's biobibliography is thus an important new research tool for scholars of Szymanowska, providing an indispensable up-to-date guide for anyone interested in investigating the sources related to her, including her compositions and correspondence. Unlike Dobrzanski's work, Kijas's book is not an attempt at comprehensive biography of the artist. Her approach also differs from what we see in Polish studies, which often consider Szymanowska in relation to other great Polish composers including Chopin, Elsner, and Oginski. Instead, in the 128-page biography section the author focuses on two specific areas of Szymanow - ska's professional life: the daily aspects of her grand tours in the 1820s and the last three years of her life (1828-31) spent in Russia. The treatment of touring is particularly illuminating. Engaged in such trivia as transportation, lodging, and finances, it offers valuable insight into the day-to-day aspects of the careers of nineteenth century performers. Kijas discusses not only the repertoire, ticket prices, and critical reception of Szymanowska's concerts, but also more broadly considers the crucial role patrons and musicians' networks played in performer's life. Kijas brings sources to her work that were unavailable at the time of the classic Polish and Russian biographies, or earlier American studies. The rediscovered diary of Szymanowska's daughter Helena, considered lost until the 1980s (published as Malewska, Dziennik: 1827-1857, ed. Zbigniew Sudolski [Warsaw: Ancher, 1999]), as well as Kijas's own recent discovery of Helena's correspondence with Eliza Middleton (a daughter of Henry Middle - ton, American Ambassador to Russia), shed light on the period between Szymanowska's leaving Warsaw and her premature death from cholera in St. Petersburg in the summer of 1831. The letters, comprising the time period 1830-46 and located at the Historical Society in Charleston, South Carolina, include passages written by Maria Szymanowska, Celina Szymanowska, and other members of their circle (p. 126). These newly discovered sources are able to offer us, as Kijas writes, a vivid portrayal of Szymanowska's life as performer, composer, teacher, and mother as viewed and experienced by her daughter Helena (p. 112). The engrossing chapter on Szymanowska as concert pianist (which includes table with her concert repertoire) is preceded by short presentation of her musical background, education, and life prior to her international concert tours. …

Solution of a linear pursuit-evasion game with integral constraints

A linear two player zero-sum pursuit-evasion differential game is considered. The control functions of players are subject to integral constraints. In the game, the first player, the Pursuer, tries to force the state of the system towards the origin, while the aim of the second player, the Evader, is the opposite. We construct the optimal strategies of the players when the control resource of the Pursuer is greater than that of the Evader. The case where the control resources of the Pursuer are less than or equal to that of the Evader is studied to prove the main theorem. For this case a new method for solving of the evasion problem is proposed. We assume that the instantaneous control employed by the Evader is known to the Pursuer. For construction, the strategy of the Evader information about the state of the system and the control resources of the players is used. References R. Isaacs. Differential games. John Wiley and Sons, New York, 1965. L. S. Pontryagin. Collected works. Nauka, Moscow, 1988. (Russian) L. D. Berkovitz. Necessary conditions for optimal strategies in a class of differential games and control problems. SIAM Journal on Control , 5 , 1--24, 1967. L. D. Berkovitz. A survey of differential games. Mathematical Theory of Control , Edited by A. V. Balakrishnan and L. W. Neustadt, Academic Press, New York, 373--385, 1967. N. N. Krasovskii and A. I. Subbotin. Game-theoretical control problems. New York, Springer, 1988. W. H. Fleming. The convergence problem for differential games. Journal of Mathematical Analysis and Applications . 3 , 102--116, 1961. W. H. Fleming. The convergence problem for differential games, Part 2. Advances in Game Theory, Annals of Mathematics Studies , (52), Princeton University Press, Princeton, New Jersey,195--210, 1964. A. Friedman. Differential games. Wiley-Interscience, New York, 1971. R. J. Elliott and N. J. Kalton. The existence of value in differential games. Memoirs of the American Mathematical Society , 126 , 1--67, 1972. L. A. Petrosyan. Differential games of pursuit. World Scientific, Singapore, London, 1993. O. Hajek. Pursuit games. Academic Press, New York, San Francisco, 1975. A. Ya. Azimov. Linear differential pursuit game with integral constraints on the control. Differentsial'nye Uravneniya, 11 (10), 1975, 1723--1731; English transl. in Differential Equations 11 , 1283--1289, 1975. A. Ya. Azimov. A linear differential evasion game with integral constraints on the controls. USSR Computational Mathematics and Mathematical Physics, 14 (6), 56--65, 1974. M. S. Nikolskii. The direct method in linear differential games with integral constraints. Controlled systems, IM, IK, SO AN SSSR, (2), 49--59, 1969. A. I. Subbotin and V. N. Ushakov. Alternative for an encounter-evasion differential game with integral constraints on the playersi controls. PMM 39 (3), 387--396, 1975. V. N. Ushakov. Extremal strategies in differential games with integral constraints. PMM , 36 (1), 15--23, 1972. B. N. Pshenichnii and Yu. N. Onopchuk. Linear differential games with integral constraints. Izvestige Akademii Nauk SSSR, Tekhnicheskaya Kibernetika , (1), 13--22, 1968. A. A. Azamov, B. Samatov. $\pi $-strategy. An elementary introduction to the theory of differential games. National University of Uzbekistan. Tashkent, Uzbekistan, 2000. G. I. Ibragimov. A game problem on a closed convex set. Siberian Advances in Mathematics . 12 (3), 16--31, 2002. G. I. Ibragimov. A problem of optimal pursuit in systems with distributed parameters. J. Appl. Math. Mech, 66 (5), 719--724, 2003. E. B. Lee and and L. Markus. Foundations of optimal control theory, John Wiley and Sons Inc., New York, 1967.

Radiogenic argon distribution within a mineral grain: implications for dating of hydrothermal mineral-forming event in Sludyanka complex, Siberia, Russia

Usually, in age-determination procedures, the experimenter is interested in the mean concentrations of parent and daughter substances. However, the structure of a solution of the Fick’s diffusion equation enables one to specify a procedure, allowing, through macroscopic experiments, one to determine the distribution of radiogenic argon (as well as any of other isotopes) within a mineral grain. Argon, influenced in the geological past by a metamorphic event, has a half-sinusoidal distribution, whereas argon preserved in geological time has a rectangular distribution. The ratio of the quantity of argon of the first type to the total argon is called an α-factor. It is believed that this coefficient can be of great interest for geochronological studies, being a symptom of virtual Ar losses and the time instant, at which they happened. A laboratory procedure and a mathematical algorithm to determine the α-factor are developed. As an example, a determination of the α-factor on a vein-phlogopite from the well-studied Sludyanka deposit, Southern Baikal, Siberia, Russia, is described. Rb–Sr isochron age on phlogopite–calcite–apatite paragenetic assemblage yielded 460±7 Ma and is constrained by U–Pb zircon ages of 471±1 and 447±2 Ma, respectively, on an emplacement of early syenites and monzonites and later ‘post-phlogopitic’ pegmatites [E.B. Salnikova, S.A. Sergeev, A.B. Kotov, S.Z. Yakovleva, R.H. Steiger, L.Z. Reznitskiy, E.P. Vasil’ev. U–Pb zircon dating of granulite metamorphism in the Sludyanskiy complex, Eastern Siberia. Gondwana Res., 1, 195–205 (1998). L.Z. Reznitskii, G.P. Sandimirova, Y.A. Pakhol’chenko, S.V. Kuznetsova. The Rb–Sr age of phlogopite deposits in Sludyanka, southern Baikal region. Dokl. Earth Sci., 367, 711–713 (1999). L.Z. Reznitskii, A.B. Kotov, E.B. Salnikova, E.P. Vasil’ev, S.Z. Yakovleva, V.P. Kovach, A.M. Fedoseenko. The age and time span of the origin of phlogopite and lazurite deposits in the Southwestern Baikal area: U–Pb geochronology. Petrology, 8, 66–76 (2000).]. In this study, the phlogopite gave an apparent K–Ar age of 365.6±10.4 Ma which has no geological meaning. The α-factor of 0.27 was derived from a laboratory kinetic experiment. The age determined by the rectangularly distributed argon corresponded to α×0.129 nmm3/g (total radiogenic argon in the sample)=94.17 nmm3/g, and an age of ∼274 Ma (e.g. a period without any argon losses). Here, at the first sight, we deal with common argon losses not conjugated with any geological event, because after 447 Ma only lower temperature (in a range of 50–300 °C) hydrothermal processes were recorded. A paragenetic phlogopite-bearing vein mineral, hyalophane, having a disturbed Rb–Sr isotopic system, however, yielded 40Ar/39Ar subplateau age of 271±2 Ma [V.V. Ivanenko, M.I. Karpenko, M.A. Litsarev. Age of the Sludyanka phlogopite deposits (in Russian; data of the 39Ar–40Ar method). In Geological Series 5, pp. 92–98, Izvestiya Akademii Nauk SSSR, Moskva (1990).], marking similar timing of the K–Ar isotopic system closure. This indicates that K–Ar isotopic system in the phlogopite was not closed (or was partially reset) long after its crystallisation and closing of the Rb–Sr system, in spite of the fact that the crystal was not affected by processes having temperatures above the accepted closure temperatures for micas. There seems to have acted an exchange mechanism of OH-groups between surrounding fluid and hydrocrystal structure. Thus the argon loss did not occur, spontaneously, but argon particles seem to have been captured and carried to the mineral surface by vacancies formed during displacements of OH-groups.

Malacosoma parallela

<i>Malacosoma parallela</i>

Ips hauseri

<i>Ips hauseri</i>

Nobel Lecture: Type-II superconductors and the vortex lattice

Nobel Lecture: Type-II superconductors and the vortex lattice