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On the Existence and Uniqueness of a Positive Solution to a Boundary Value Problem for One Nonlinear Functional - Differential Equation of Even Order
No full textIn this article, we consider a two-point boundary value problem for one nonlinear functional differential equation of even order with strong non-linearity on segment [0,1] with homogeneous boundary conditions. With the use of special topological means, sufficient conditions for the existence and uniqueness of a positive solution to the problem under consideration. Existence of a positive solution proved using the well-known Krasnoselsky theorem on a fixed point in a cone, uniqueness is respectively established using the contraction mapping principle. A non-trivial example is given, illustrating the fulfillment of sufficient conditions unique solvability of the problem
Mean-square Approximation of Iterated Ito and Stratonovich Stochastic Integrals: Method of Generalized Multiple Fourier Series. Application to Numerical Integration of Ito Sdes and Semilinear Spdes (third Edition)
No full textThis is the third edition of the monograph (first edition 2020, second edition 2021) devoted to the problem of mean-square approximation of iterated Ito and Stratonovich stochastic integrals with respect to components of the multidimensional Wiener process. The mentioned problem is considered in the book as applied to the numerical integration of non-commutative Ito stochastic differential equations and semilinear stochastic partial differential equations with nonlinear non-commutative trace class noise. The book opens up a new direction in researching of iterated stochastic integrals. For the first time we use the generalized multiple Fourier series converging in the sense of norm in Hilbert space for the expansion of iterated Ito stochastic integrals of arbitrary multiplicity k with respect to components of the multidimensional Wiener process (Chapter 1). Sections 1.11-1.13 (Chapter 1) are new and generalize the results of Chapter 1 obtained earlier by the author and are also closely related to the multiple Wiener stochastic integral introduced by Ito in 1951. The convergence with probability 1 as well as the convergence in the sense of n-th (n=2, 3,...) moment for the expansion of iterated Ito stochastic integrals have been proved (Chapter 1). Moreover, the rate of both types of convergence has been established. The main difference between the third and second editions of the book is that the third edition includes original material (Chapter 2, Sections 2.10-2.19) on a new approach to the series expansion of iterated Stratonovich stochastic integrals of arbitrary multiplicity k with respect to components of the multidimensional Wiener process. The above approach allowed us to generalize some of the author's earlier results and also to make significant progress in solving the problem of series expansion of iterated Stratonovich stochastic integrals. In particular, for iterated Stratonovich stochastic integrals of the fifth and sixth multiplicity, series expansions based on multiple Fourier-Legendre series and multiple trigonometric Fourier series are obtained. In addition, expansions of iterated Stratonovich stochastic integrals of multiplicities 2 to 4 were generalized. These results (Chapter 2) adapt the results of Chapter 1 for iterated Stratonovich stochastic integrals. Two theorems on expansion of iterated Stratonovich stochastic integrals of arbitrary multiplicity k based on generalized iterated Fourier series with pointwise convergence are formulated and proved (Chapter 2). The results of Chapters 1 and 2 can be considered from the point of view of the Wong-Zakai approximation for the case of a multidimensional Wiener process and the Wiener process approximation based on its series expansion using Legendre polynomials and trigonometric functions. The integration order replacement technique for iterated Ito stochastic integrals has been introduced (Chapter 3). Exact expressions are obtained for the mean-square approximation error of iterated Ito stochastic integrals of arbitrary multiplicity k (Chapter 1) and iterated Stratonovich stochastic integrals of multiplicities 1 to 4 (Chapter 5). Furthermore, we provided a significant practical material (Chapter 5) devoted to the expansions and mean-square approximations of specific iterated Ito and Stratonovich stochastic integrals of multiplicities 1 to 6 from the unified Taylor-Ito and Taylor-Stratonovich expansions (Chapter 4). These approximations were obtained using Legendre polynomials and trigonometric functions. The methods constructed in the book have been compared with some existing methods (Chapter 6). The results of Chapter 1 were applied (Chapter 7) to the approximation of iterated stochastic integrals with respect to the finite-dimensional approximation of the Q-Wiener process (for integrals of multiplicity k) and with respect to the infinite-dimensional Q-Wiener process (for integrals of multiplicities 1 to 3)
The evolution of the Russian state in the context of formational views on the structure of the world history
No full textThe approach to history in general and the history of Russia in particular, which points to the
presence of the necessary historical stages, is primarily associated with various trends in Marxism.
In the case of the last centuries of Russian history, the most important point is the question
of the nature of the 1917 Revolution. More generally, it is a question of the extent to which
Marxist theory is able to substantiate the possibility of a “jump” through historical steps. We
have chosen two Marxists from different periods as an example the attitude to the topic. The
first example is G. V. Plekhanov, an outstanding Russian theorist and polemist. His reaction to
the revolutionary events was twofold. The February Revolution of 1917 fully met his aspirations
both in the medium term (the overthrow of “tsarism” and the continuation of the struggle
against Germany) and in the long term (creation in Russia of prerequisites for economic development,
and, therefore, a socialist revolution). On the contrary, the October Revolution was
regarded by him as a tragic mistake. Another position on the October Revolution was expressed
by a modern proponent of the formational approach, the Japanese philosopher Kajio Karatani.
He significantly changed the understanding of how the social development of mankind takes
place. The most important reason for historical change is the relationship of the three modes of
economic exchange, which dictate those types of state system that are relevant in different historical
eras. Karatani believes that the Russian Revolution was the reaction of an imperial-type
state to pressure from national states. The idea of class reorganization, on which the teachings
of the Bolsheviks were based, allowed the imperial, supranational structure of Russia to survive.
After the Civil War it received the supranational name of the Soviet Union.The research was carried out thanks to funding of Russian Science Foundation (project no. 21-18-
00153, St. Petersburg State University)
Sculpture of the Christ of Sorrows from Belarus
No full textThe article discusses the history and style, the levels of the addition of the cult of the statue of
the Christ of Sorrows (also known as the Man of Sorrows) from the Holy Trinity Church in
the town of Ros’ in Belarus (Grodno Region). This church is a well-known sanctuary of Christ
of Sorrows, a place of worship for believers from all over Belarus and other countries. Based
on the analysis of archival documents, the issue of dating the sculpture within the boundaries
of 1611–1618 has been resolved and its Neo-Gothic style, which developed in the symbiosis
of the late Renaissance and early Baroque, with the Neo-Gothic accent characteristic for the
early 17th century, which was considered the “new style” in Northern Europe at that time, has
been determined. The sculpture was a reflection of the concept of Andachtsbild — a specific
genre of art, the purpose of which is to excite the pious thoughts and intentions of the believer.
Today, a sufficient number of sculptures of the Christ of Sorrows are known in museums and
the existing churches of Belarus. There are even more indications of their presence in archival
documents, both in Catholic and Orthodox shrines. This material is intended to show the
meanings that affirm the obligatory nature of the images of the Christ of Sorrows in Eastern
European art and the inevitability of its appearance (acceptance) at certain points in a
large area from Western Europe to Eastern Europe in historical time. Sculpture in Ros’ is that
unique example of a transitional time, when the art of Eastern Europe turned to the creation
of early Baroque forms, synthesizing the forms of Gothic and Renaissance (Mannerism) in a
certain conceptual direction of internal meditative practice, personal prayer
Trusts in mixed jurisdictions
Full text linkClosed legal systems are gone in modern world, “mixed” legal systems have become the norm.
That has made so-called “transplants” easier but, contrary to a widely held view, legal institutions
cannot be transplanted. English trust rules even less, for they are not a coherent set of
rules. The British attempted to legislate on trusts for their colonies, for instance for Ceylon (the
present-day Sri Lanka), and were thus obliged to be coherent. That made it necessary to introduce
new legal concepts with unforeseeable consequences. A wave of legislation followed the
adoption of the convention “On The Law Applicable To Trusts And On Their Recognition” by the
15th session of the Hague Conference on private international law (1985); it gave birth to the “international
model” of trusts that quickly became the favourite setting of the rich and ultra-rich.
Jersey in the Channel Islands was the leading jurisdiction, many others followed but it was not
until the establishment of the International Finance Centres in the Gulf and later in Kazakhstan
where “the laws of England and Wales” are taken as a source of law and local courts are staffed
by former English judges or in any event by lawyers brought up in the common law that a proper
transplant of the English trust took place. A totally different legal setting witnessed attempts to
create imitations that had to run against well-established civil law conceptual attitudes that did
not allow the existence of more than one patrimony per person or the segregation of assets
within one person’s patrimony. In 2022 France decreed that each businessman is automatically
the owner of two patrimonies; that open the way to a radical re-thinking of civil law notions.
Québec and Louisiana are taken as examples of civil law legislation on trusts but Québec
has followed its own idea that the assets that form the object of a fiducie belong to nobody,
while Louisiana’s Trust Code is a deft admixture of civil law and common law elements based
on the civilian notion of “fiduciary”. Luxembourg, France and other civil law countries are then
examined: the focus then is on South Africa and Scotland, two countries which have a common
past in a shared period of the European ius commune and a common present in being both orphaned
from a cultural lineage that provided answers to current matters by drawing on Roman
law. Now they both solve the problem of the patrimony by holding that a trustee has more than
one patrimony, his own and then one for each trust of which he is the trustee
BIBLICAL PRECEDENT UNITS AS INTERTEXTUAL ELEMENTS IN CONTEMPORARY MEDIA DISCOURSE
Full text linkModern media discourse is featured by a certain freedom of choice of linguistic means to
express the author’s intention or to draw attention to the event covered. Globalisation of the information space initiates dynamic processes of image perception and reinterpretation
of universal concepts under the conditions of intercultural communication. The
article deals with the analysis of biblical precedent units as intertextual inclusions for linguistic
expressiveness with a profound pragmatic component in the language of modern
media and the Internet. The research is devoted to investigation ofbiblicism functioning
specifics in media discourse which is considered a driving force of modern language. Correlations
of global bible concepts in different linguistic communities are also considered.
For contextual interpretation of biblical precedent units in modern media discourse the
following methods were implemented: descriptive-comparative method, the method of
continuous sampling, the method of contextual analysis, the method of interpretation. It
was found that the rich internal form of the biblical concept increases the pragmatic potential
of intertextual context, performing the following functions: expressiveness, philosophical
reconsideration, symbolism, provocation, initiation of semantic association,
and text quintessence. On the example of illustrative material, taken from a corpus of
media — Russian, British, American periodicals and the information space of the Internet,
it is shown that the main biblical meanings and concepts are universal in terms of associative
chains, formed in the consciousness of the recipient. On this basis, the conclusion
is made that some correlations exist between different forms of presentation of religious
doctrine and their modern interpretation, which found expression in a certain connection
of some concepts and evaluations. Refs 15
Severus of Antioch’s idea of transforming the theological language from Triadology to Christology and its critique in Leontius of Byzantium’s treatise “Refutation of syllogisms of Severus”. Part two
No full textThe given study is the second part of the article, which scrutinizes the idea of
Severus of Antioch concerning which way, in the event of Christ’s incarnation, the
meanings of the concepts of essence, nature, hypostasis, and person, which are the
most important for representation of the theological sense of this event, are mystically
transformed. Along with that, the polemics between the Chalcedonites and Severian Monophysites deployed on this idea, which is immediately represented
in the third chapter of Leontius’ of Byzantium treatise “Refutation of syllogisms of
Severus”, is taken into consideration. By its content, this chapter is split into two
parts, each consisting of an argument of a Severian adversary of the Chalcedonite
confession and a detailed refutation of this argument proposed by Leontius. While
the content of the first half of the text is focused on the philosophical analysis of the
problem of methodological adequacy of the very formulation of Severus’ idea both
from the viewpoint of external philosophical wisdom and of theology, the second
half is dedicated to the problem of the grammatical and philosophical status of the
exegesis of ambiguous expressions of the Fathers. In this section of the study, a detailed
interpretation is proposed of the first part of the third chapter of Leontius’
treatise, and, on the grounds of addressing the models of philosophical and theological
argumentation authentic for the first half of the 6th century, an analysis is
performed of the logico-philosophical and theological sense of the polemical arguments
applied by the opponents.The present research was funded by the Russian Foundation for Basic Research, project
no. 21-011-44263 “Formation of the concept of ‘theology’ as a science and its conceptual
apparatus in the Byzantine Christian theological thought of the late 5th — early 8th centuries in
the context of scientific and philosophical knowledge of late antiquity”
Suleiman of Gazza on the Ecumenical Councils
No full textThe article discusses the ideas about the history and deeds of the Ecumenical Councils
of the Melkite writer of the 10th–11th centuries Suleiman, Bishop of Gaza, the
first Arabic-speaking Christian poet and author of a number of theological and
philosophical treatises. Although Suleiman was not a historian, he nonetheless
wrote two noteworthy texts on the history of the Ecumenical Councils. According
to a number of formal criteria, these texts may well be attributed to “the synopsis
of the Councils” genre, which was very popular in Byzantium and was widely used
in Byzantine doctrinal and catechetical literature. At the same time, this genre was
not in demand in Melkite literature, and the Bishop of Gaza was actually the only
Arabic-speaking Melkite writer who created works in “the synopsis of the Councils”
genre, which was widely used in Byzantine doctrinal and catechetical literature. The
author notes that, unlike most Melkite writers of the 8th–13th centuries (St John of
Damascus, Theodore Abu Qurrah, Agapius of Manbij, Macarius of Sinai), who had quite adequate ideas about the history of the Ecumenical Councils and their deeds,
Suleiman in his treatises makes many mistakes, both purely historical and concerning
the theological essence of some heresies condemned by the Councils. The article
attempts to establish the reasons for the mistakes made by Suleiman of Gazza and
find logical explanations for some of them. The author comes to the conclusion that
Suleiman’s knowledge of Church history cannot be considered satisfactory. Because
of this, it is absolutely impossible to call the Bishop of Gazza a writer who knew the
history of the Church well, as some researchers do