There is no doubt that periodization is a rather effective method of data ordering and analysis, but it deals with exceptionally complex types of processual and temporal phenomena and thus it simplifies historical reality. Many scholars emphasize the great importance of periodization for the study of history. In fact, any periodization suffers from one-sidedness and certain deviations from reality. However, the number and significance of such deviations can be radically diminished as the effectiveness of periodization is directly connected with its author's understanding of the rules and peculiarities of this methodological procedure. In this paper we would like to suggest a model of periodization of history based on our theory of historical process. We shall also demonstrate some possibilities of mathematical modeling for the problems concerning the macroperiodization of the world historical process. This analysis identifies a number of cycles within this process and suggests its generally hyperexponential shape, which makes it possible to propose a number of forecasts concerning the forthcoming decades. 

With regard to social disciplines, a question contin­ually arises: are mathematical methods fit for analyzing historical and social processes? Obviously, we should not absolutize differences between fields of knowledge, but the division of sciences into two opposite types, made by W. Windelband and H. Rickert, is still valid. As is known, they singled out sciences involving nomo-thetic methods, i.e., looking for general laws and gener­alizing phenomena, and those applying idiographic methods, i.e., describing individual and unique events and objects. Rickert attributed history to the second type. In his opinion, history always aims at picturing an isolated and more or less wide course of development in all its uniqueness and individuality 

One of natural combinations of Kripke complete modal logics is the product, an operation that has been extensively investigated over the last 15 years. In this paper we consider its analogue for arbitrary modal logics: to this end, we use product-like constructions on general frames and modal algebras. This operation was first introduced by Y. Hasimoto in 2000; however, his paper remained unnoticed until recently. In the present paper we quote some important Hasimoto’s results, and reconstruct the product operation in an algebraic setting: the Boolean part of the resulting modal algebra is exactly the tensor product of original algebras (regarded as Boolean rings). Also, we propose a filtration technique for Kripke models based on tensor products and obtain some decidability results.

The recent decade has witnessed remarkable success in various aspects of socioeconomic development in Tropical Africa. However, contrary to the “development is the best contraceptive” expectations, fertility in many countries remains stalled, frequently at very high levels of 5 and more children per woman. This actualizes the risks of population explosions, which are particularly sharp, and can bear truly dramatic consequences for national and even regional development, in the largest countries. In order to foresee such risks, valid population projections are necessary. The only widely recognized comprehensive series of such forecasts is currently developed by the UN Population Division; however, the method underlying their forecast has a number of limitations. We offer a different method for modelling the scenarios of demographic future of a given country. We apply this method to the case of Mozambique and reveal that the population projections calculated for Mozambique by the UN Population Division in 2012 – 2013 seem to be overly optimistic. 

Статья о взаимоотношениях двух групп художников (Артели Крамского и Товарищества Передвижников) с Академией Художеств. Акцент сделан на социокультурных аспектах русского искусства второй половины 19 в. – государственной поддержке и влиянию, стремлении к независимости и о методах, которыми пользовались Передвижники их стремлении к коммерциализации оборота произведений искусства.

This paper is the first in a series that describe a conjectural analog of the geometric Satake isomorphism for an affine Kac-Moody group (in this paper for simplicity we consider only untwisted and simply connected case). The usual geometric Satake isomorphism for a reductive group G identifies the tensor category Rep(G_) of finitedimensional representations of the Langlands dual group G_ with the tensor category PervG(O)(GrG) of G(O)-equivariant perverse sheaves on the affine Grassmannian GrG = G(K)/G(O) of G (here K = C((t)) and O = C[[t]]). As a byproduct one gets a description of the irreducible G(O)-equivariant intersection cohomology sheaves of the closures of G(O)-orbits in GrG in terms of q-analogs of the weight multiplicity for finite dimensional representations of G_. The purpose of this paper is to try to generalize the above results to the case when G is replaced by the corresponding affine Kac-Moody group Gaff (we shall refer to the (not yet constructed) affine Grassmannian of Gaff as the double affine Grassmannian). More precisely, in this paper we construct certain varieties that should be thought of as transversal slices to various Gaff(O)-orbits inside the closure of another Gaff (O)-orbit in GrGaff . We present a conjecture that computes the IC sheaf of these varieties in terms of the corresponding q-analog of the weight multiplicity for the Langlands dual affine group G_aff and we check this conjecture in a number of cases. Some further constructions (such as convolution of the corresponding perverse sheaves, analog of the Beilinson-Drinfeld Grassmannian etc.) will be addressed in another publication.

 

 

We introduce and study deformations of finite-dimensional modules over rational Cherednik algebras. Our main tool is a generalization of usual harmonic polynomials for each Coxeter group — the so-called quasiharmonic polynomials. A surprising application of this approach is the construction of canonical elementary symmetric polynomials and their deformations for all Coxeter groups.

We describe a family of calibrations arising naturally on a hyperk¨ahler manifoldM. These calibrations calibrate the holomorphic Lagrangian, holomorphic isotropic and holomorphic coisotropic subvarieties. When M is an HKT (hyperk¨ahler with torsion) manifold with holonomy SL(n,H), we construct another family of calibrations i, which calibrates holomorphic Lagrangian and holomorphic coisotropic subvarieties. The calibrations i are (generally speaking) not parallel with respect to any torsion-free connection on M.

The article presents the possible role of consciousness in quantum-mechanical description of physical reality. The widely spread interpretations of quantum phenomena are considered as indicating the apparent connection between conscious processes (such as observation) and the properties of the microcosm. The reasons for discrepancies between the results of observations of the microcosm and macrocosm and the potential association of consciousness with these reasons are closely investigated. The mentioned connection is meant to be interpreted in the sense that the probable requirement for a complete understanding of quantum theory is the adequate description of consciousness within it and that the correct theory of consciousness should include quantum-mechanical theoretical apparatus. In this context, the question about the methods of scientific cognition is discussed, in particular, the problem of the place and the importance of intellectual intuition in science and philosophy of science. The author draws the conclusiions about the current state of the “measuring” problem in its relationship with consciousness. 

Наследие Ханны Арендт в России достаточно хорошо изучено, в академических дискуссиях чувствуется влияние ее мысли. Но ее теоретические позиции едва ли помогают существенно изменить сегодняшнюю локальную ситуацию в политике и философии. В силу одной той же причины ее идеи популярны в России и не ведут к практическим переменам. Ее оригинальный подход к политике прекрасно ложится на традиционные шаблоны российской политической жизни, которые не менее далеки от устойчивых форм западной политической культуры. Некритически пересаженный на иную почву, ее нетрадиционный способ мышления о политике встречает в России непосредственный и живой отклик, но не столь же суровую критическую проверку, как в странах Запада. Парадоксальным образом это доказывает, что взгляды Арендт могут скорее подтверждать, чем оспаривать локальный статус-кво. В этой статье я привожу объяснение этому парадоксу, указав как элементы ее теории, ускользающие от внимания ее российских последователей, так и догматические положения, присущие в целом ее школе мысли, которые можно выявить благодаря прочтению ее текстов в контексте российской истории. Так, неявно, но различимо в теории Арендт содержатся элитистские и либеральные тенденции, что отчасти согласуется с макиавеллиевским характером современной российской политики. Но как только ее взгляды неожиданно сближаются с позицией Исайи Берлина, эти нормативные решения по большей части оставляются без внимания. В то же время чтение ее текстов в свете российского опыта позволяет выявить ее собственные презумпции относительно человеческого бытия, смысла политического существования и нашего отношения к истории, ослабляющие практическую релевантность ее размышлений.

The so-called Syriac Julian Romance is preserved in two manuscripts from the British Library, BL Add 14641 (6th c.) and BL Rich Rich 7192 (9th c.). T. Nöldeke was first to propose the idea that the mss. constitute one literary piece. However it consists of three different stories which were copied from different protographa. The story of Eusebius was written by a certain deacon Epainetos of whom only a rubric survived in the text. However the story of the Persian expedition of Julian the Apostate is a different case. It is possible that it has preserved parts of the original colophon from the protograph at the beginning and at the end of the Expedition narrative. The first part of this ‘circum-colophon’ introduces the abbot ‘Abdel and his addressee certain Apolinarius. At the end we see what has remained from the colophon and that is written by Apolinarius himself. This circular structure could be called circum-colophon in the sense that it frames the single literary piece, which once formed a manuscript. In this article the structure of the colophon is exposed and the explanation for the person of Apolinarius is proposed. In addition the colophon of the Sinai Arabic version of the same text is analyzed.

Цель – Цель этой статьи – представить результаты сравнительного анализа и различных моделей, основанных на ресурсах культурного наследия, способствующих региональному развитию.

Дизайн/методология/подход – сравнение оперативных схем, рыночных позиций и брендинга трех центров успешного культурного наследия в Германии, Великобритании и России, демонстрирующие разнообразие моделей регионального развития, основанных на культурных ресурсах, развитии туризма, и показывающие преимущества и недостатки.

 Выводы - в статье доказывается, что потенциал культурных ресурсов и сектор туризма являются драйверами регионального развития, и сформулированы основные рекомендации для ситуации в России, требующие разработки адекватных финансовых и социальных инструментов. 

Оригинальность/значение – в статье приведен комплексный анализ различных оперативных моделей в трех европейских странах при конкретных национальных ситуациях и специфичности оперативного управления в отношении культурного наследия.

In his “Difference and Repetition” Deleuze reveals an aporia: repetition is singular, solitary, it is torn away from any original or source; nevertheless it preserves a genetic tie with certain event to which it is a repetition. This solitariness of the repetition is not however confined to mere difference between the act of repetition and the repeated source that cancels the original just to differentiate two performative procedures. An act of repetition is solitary only when it evolves in specific time-regime, which even ontically diverges from the regular ontology of time. Deleuze calls such temporality “empty”, Nietzsche defines it as amor fati, Heidegger sees in it convergence of eternity and an instant. The stake in this case is a specific kind of repetitive regime which unfolds as the performative syndrome of ‘dying’ – a “repetition into death” (Deleuze) which paradoxically executes itself as performative plenitude. But who is the Subject undergoing such a syndrome and what should have happened to her/him so as to impose the regime of dying on any act of repetition?

 

Реплика в дискуссии о современном состоянии философии в России по сравнению с Советским Союзом.

Это мой краткий ответ на возражения Адониса Франгеску на мою рецензию его книги (2017). Я подробно разбираю фрагмент из Левинаса, который Франгеску использует, чтобы возразитьмне, и обсуждаю, каким именно образом идея-Бога-во-мне связана с проблемами чувственности, ранимости и страдания. Я утверждаю, что рассмотрение философии Левинаса в контексте кантовской аналитики возвышенного совершенно необходимо, так как позволяет выявить катастрофическое измерение левинасовского подхода к субъективности.