Development of the trade project and its role in Russian-french relations in the early 1680s

Introduction. The article considers the problems of Russian-French negotiations on the organization of trade between Russia and France in the first half of the 1680s.Materials and methods. The uniqueness of the study is facilitated by the use of materials from both Russian (Russian State Archive of Ancient Documents) and French archives (Archives du ministère des affaires étrangères), which have not previously been widely used in research. Thanks to the comprehensive use of documents from both sides, the study clarifies the details of the events that took place in the embassies and the specifics of their perception by the Russian and French courtiers. The analysis of the negotiations, their preparation and their procurement is conducted in the context of the methodology of new diplomatic history in order to establish the role of the trade question in the development of diplomatic relations between Russia and France.Results. The results of the study show the essential role of the Russian-French trade project in establishing direct connections between Russia and France, independent of changes in both countries policies towards the Polish-Lithuanian Commonwealth and Sweden. In the context of Russian court politics of the early 1680s, it is shown that both supporters of confrontation with Sweden and their adversaries, focusing on Russian participation in the anti-Ottoman coalition, were interested in rapprochement with France. At the same time, the preparation of the trade project led to analytical work in both countries that broadened their perceptions of each other, intensified contacts between representatives of both states, and led to the emergence of conjugate foreign policy projects.Conclusion. The work supplements the established in historiography conceptions of the organization of Russian diplomatic missions to France, the information about the role of the management of the Ambassador's office in this process, as well as the envoys and interpreters sent to France and their own perceptions of their place in this process

Social and Cultural Development of the Southwestern Peripheries of the Russian State in the 17th Century: New Aspects

This work is dedicated to the analysis of the monograph by the renowned regional historian D. A. Lyapin, titled “On the Empire’s Edge: Everyday Life of the Southern Population of Russia in the 17th Century,” published in 2020. The study offers a refreshed perspective on the history of the southwestern districts of the Russian State during the 17th century. This review aims to reinvigorate the exploration of regional social history and draws scholars’ attention to D. A. Lyapin’s work, which encapsulates his extensive research on regional issues. The author’s insights significantly augment prevailing perceptions of Russia’s regional history in the 17th century and advocate for its enhanced prominence within the academic community. D.A. Lyapin’s monograph proves invaluable not only for specialists in the social history of southwestern Russia but also for researchers beginning to delve deeply into the history of this region. © The Author(s) 2023

Formation of Social Ties in P. I. Potemkin's Embassy to France (1680–1682)

The article was submitted on 29.11.2023.На основе сохранившихся комплексов русских и французских источников проанализированы механизмы формирования социальных связей русского посольства во Франции 1681 г. Посольство имело как внешнеполитическое, так и дипломатическое значение для репрезентации царской власти и рус- ской культуры во Франции: посланники должны были не только уведомить Людовика XIV о событиях в Восточной Европе, но и получить представления о позиции Франции по вопросам подготовки Вечного мира России с Речью Посполитой, заключения русско-французского торгового договора и обеспечить найм иностранных специалистов. Формирование связей рассмотрено в контексте новой дипломатической истории с особым вниманием к проблемам репрезентации власти, личности дипломатов и культурной стороне их миссии. Впервые на основе всего комплекса архивных документов о посольстве характеризуются особенности формирования социальных связей участников посольства, необходимых для успешной реализации задач дипломатической миссии. В основу исследования легли французские придворные отчеты о церемониях, записки придворных, внутренняя переписка дипломатических ведомств России и Франции, материалы парижской периодической печати и отчетные документы русских посланников. Сделаны выводы о специфике стратегий посланника П. И. Потемкина по формированию социальных связей, об их значении для развития русской дипломатии, внешней политики и культурных контактов с Западной Европой, а также об особенностях отражения рассмотренных связей в сохранившихся источниках.Based on the extant complex of Russian and French sources, this article analyses the mechanisms of the formation of social ties of the Russian embassy in France in 1681. The embassy had both foreign policy and diplomatic significance for the representation of tsarist power and Russian culture in France: the envoys had not only to inform Louis XIV about the events in Eastern Europe, but also to get an overview of the French position on the preparation of the Perpetual Peace of Russia with the Polish-Lithuanian Commonwealth, the conclusion of the Russian-French trade treaty, and to ensure the recruitment of foreign specialists. The author examines the formation of relations in the context of the new diplomatic history, paying special attention to the problems of power representation, the personalities of diplomats and the cultural side of their mission. For the first time in historiography, the article characterises the whole complex of archival documents about the embassy, the peculiarities of the formation of social ties of the embassy participants necessary for the successful implementation of the tasks of the diplomatic mission. The study is based on French court reports on ceremonies, notes of courtiers, internal correspondence of Russian and French diplomatic departments, materials of the Parisian periodical press, and reports of Russian envoys. Conclusions are drawn on the peculiarities of the strategies of the envoy P. I. Potemkin in establishing social relations, their significance for the development of Russian diplomacy, foreign policy, and cultural contacts with Western Europe, as well as on the peculiarities of the reflection of these relations in the surviving sources.Исследование выполнено за счет гранта Российского научного фонда № 23-78-01059 «Механизмы функционирования социальных связей в контексте государственного реформирования в России во второй половине XVII – начале XVIII в.»

Russia on the French Roads to China in the second half of the XVII Century

The article examines the main attempts of French expansion into China, through the land route through Russia. To analyze the process, the author identifies areas associated with the diplomatic, cultural, religious and economic expansion of the kingdom of Louis XIV and the French nation (in its current meaning for the 17th century). Conclusions are drawn about the peculiarities of the geographical ideas about Russia in France, the process of perception of this knowledge through the space of the historical experience of the French, as well as the importance of the overland route to China for France in the 17th century are analyzed.В статье рассматриваются основные попытки французской экспансии в Китай посредством сухопутного пути через Россию. Для анализа процесса автором выделяются направления, связанные с дипломатической, культурно-религиозной и экономической экспансией королевства Людовика XIV и французской нации (в актуальном для XVII в., значении). Сделаны выводы об особенностях географических представлений о России во Франции, проанализирован процесс восприятия этих знаний через пространство исторического опыта французов, а также значение сухопутного пути в Китай для Франции XVII в

A representation formula for maps on supermanifolds

In this paper we analyze the notion of morphisms of rings of superfunctions which is the basic concept underlying the definition of supermanifolds as ringed spaces (i.e. following Berezin, Leites, Manin, etc.). We establish a representation formula for all morphisms from the algebra of functions on an ordinary manifolds to the superalgebra of functions on an open subset of R^{p|q}. We then derive two consequences of this result. The first one is that we can integrate the data associated with a morphism in order to get a (non unique) map defined on an ordinary space (and uniqueness can achieved by restriction to a scheme). The second one is a simple and intuitive recipe to compute pull-back images of a function on a manifold by a map defined on a superspace.Comment: 23 page

Cohomology Groups of Deformations of Line Bundles on Complex Tori

The cohomology groups of line bundles over complex tori (or abelian varieties) are classically studied invariants of these spaces. In this article, we compute the cohomology groups of line bundles over various holomorphic, non-commutative deformations of complex tori. Our analysis interpolates between two extreme cases. The first case is a calculation of the space of (cohomological) theta functions for line bundles over constant, commutative deformations. The second case is a calculation of the cohomologies of non-commutative deformations of degree-zero line bundles.Comment: 24 pages, exposition improved, typos fixe

Menelaus relation and Fay's trisecant formula are associativity equations

It is shown that the celebrated Menelaus relation and Fay's trisecant formula similar to the WDVV equation are associativity conditions for structure constants of certain three-dimensional algebra.Comment: Talk given at the Conference " Mathematics and Physics of Solitons and Integrable Systems", Dijon, 28.6-2.7, 2009. Minor misprints correcte

Minkowski superspaces and superstrings as almost real-complex supermanifolds

In 1996/7, J. Bernstein observed that smooth or analytic supermanifolds that mathematicians study are real or (almost) complex ones, while Minkowski superspaces are completely different objects. They are what we call almost real-complex supermanifolds, i.e., real supermanifolds with a non-integrable distribution, the collection of subspaces of the tangent space, and in every subspace a complex structure is given. An almost complex structure on a real supermanifold can be given by an even or odd operator; it is complex (without "always") if the suitable superization of the Nijenhuis tensor vanishes. On almost real-complex supermanifolds, we define the circumcised analog of the Nijenhuis tensor. We compute it for the Minkowski superspaces and superstrings. The space of values of the circumcised Nijenhuis tensor splits into (indecomposable, generally) components whose irreducible constituents are similar to those of Riemann or Penrose tensors. The Nijenhuis tensor vanishes identically only on superstrings of superdimension 1|1 and, besides, the superstring is endowed with a contact structure. We also prove that all real forms of complex Grassmann algebras are isomorphic although singled out by manifestly different anti-involutions.Comment: Exposition of the same results as in v.1 is more lucid. Reference to related recent work by Witten is adde

Deformed Minkowski spaces: clasification and properties

Using general but simple covariance arguments, we classify the `quantum' Minkowski spaces for dimensionless deformation parameters. This requires a previous analysis of the associated Lorentz groups, which reproduces a previous classification by Woronowicz and Zakrzewski. As a consequence of the unified analysis presented, we give the commutation properties, the deformed (and central) length element and the metric tensor for the different spacetime algebras.Comment: Some comments/misprints have been added/corrected, to appear in Journal of Physics A (1996

Physically Realistic Solutions to the Ernst Equation on Hyperelliptic Riemann Surfaces

We show that the class of hyperelliptic solutions to the Ernst equation (the stationary axisymmetric Einstein equations in vacuum) previously discovered by Korotkin and Neugebauer and Meinel can be derived via Riemann-Hilbert techniques. The present paper extends the discussion of the physical properties of these solutions that was begun in a Physical Review Letter, and supplies complete proofs. We identify a physically interesting subclass where the Ernst potential is everywhere regular except at a closed surface which might be identified with the surface of a body of revolution. The corresponding spacetimes are asymptotically flat and equatorially symmetric. This suggests that they could describe the exterior of an isolated body, for instance a relativistic star or a galaxy. Within this class, one has the freedom to specify a real function and a set of complex parameters which can possibly be used to solve certain boundary value problems for the Ernst equation. The solutions can have ergoregions, a Minkowskian limit and an ultrarelativistic limit where the metric approaches the extreme Kerr solution. We give explicit formulae for the potential on the axis and in the equatorial plane where the expressions simplify. Special attention is paid to the simplest non-static solutions (which are of genus two) to which the rigidly rotating dust disk belongs.Comment: 32 pages, 2 figures, uses pstricks.sty, updated version (October 7, 1998), to appear in Phys. Rev.