The Dirichlet problem for the Poisson type equations in the plane

We present a new approach to the study of semilinear equations of the form div[A(z)▽u]=f(u), the diffusion term of which is the divergence uniform elliptic operator with measurable matrix functions A(z), whereas its reaction term f(u) is a continuous non-linear function. We establish a theorem on the existence of weak C(Ḋ)∩W¹′²loc(D) solutions of the Dirichlet problem with arbitrary continuous boundary data in any bounded domains D without degenerate boundary components and give applications to equations of mathematical physics in anisotropic media.Запропоновано новий підхід до вивчення напівлінійних рівнянь виду div[A(z)∇u]=f(u), дифузний член яких є дивергентним рівномірно еліптичним оператором з вимірними матричними функціями A(z), тоді як його реакційний член f(u) є неперервною нелінійної функцією. Доведено теорему про існування слабких C(Ḋ)∩W¹′²loc(D) розв'язків задачі Діріхле з довільними неперервними граничними даними в довільних обмежених областях D без вироджених граничних компонент і дано застосування до рівнянь математичної фізики в анізотропних середовищах.Предложен новый подход к изучению полулинейных уравнений вида div[A(z)∇u]=f(u) , диффузионный член которых является дивергентным равномерно эллиптическим оператором с измеримыми матричными функциями A(z) , тогда как его реакционный член f(u) является непрерывной нелинейной функцией. Доказана теорема о существовании слабых C(Ḋ)∩W¹′²loc(D) решений задачи Дирихле с произвольными непрерывными граничными данными в любых ограниченных областях D без вырожденных граничных компонент и даны приложения к уравнениям математической физики в анизотропных средах

Human adaptation in the information environment: individual characteristics and mechanisms

The article deals with the problem of human adaptation in the modern information environment. The rationale for the approach to the study and prediction of adaptation based on the identification of humanspecific variant of the orienting reflex is givenВ статье рассматривается проблема адаптации человека в современной информационной среде. Приводится обоснование подхода к изучению и прогнозированию адаптации на основе выявления характерного для человека варианта ориентировочного рефлекс

Semilinear equations in a plane and quasiconformal mappings

We consider generalizations of the Bieberbach equation with nonlinear right parts, which makes it possible to study many problems of mathematical physics in inhomogeneous and anisotropic media with smooth characteristics. We establish interconnections of these semilinear equations with quasiconformal mappings, obtain on this basis, a series of theorems on the existence of their solutions that blow-up on the boundary of a unit disk, as well as on punctured unit disks and rings, and give their explicit representations.Розглянуто узагальнення рівняння Бібербаха з нелінійними правими частинами, які дають можливість вивчати багато проблем математичної фізики в неоднорідних та анізотропних середовищах з гладкими характеристиками. Встановлено взаємозв'язки цих напівлінійних рівнянь з квазіконформними відображеннями і на цій основі отримано ряд теорем існування їх розв'язків, що вибухають на границі одиничного круга, проколотих одиничних кіл та кільцях, а також наведено їх явні зображення.Рассмотрены обобщения уравнения Бибербаха с нелинейными правыми частями, которые позволяют изучать многие проблемы математической физики в неоднородных и анизотропных средах с гладкими характеристиками. Установлены взаимосвязи этих полулинейных уравнений с квазиконформными отображениями и на этой основе получен ряд теорем существования их решений, взрывающихся на границе единичного круга, проколотых единичных кругах и кольцах, а также приведены их явные представления

THE IMAGE OF SIR ARTHUR CONAN DOYLE IN J. BARNES NOVEL ARTHUR AND GEORGE

Abstract. The article analyzes the novel of the famous British author Julian Barnes Arthur and Georgededicated to the life of Sir Arthur Conan Doyle, the creator of Sherlock Holmes. The novel, being a work of fiction, is based on the real events from the biography of Sir Doyle. Using the method of comparative analysis, we compare the facts known about the life of Conan Doyle with their artistic interpretation presented by Julian Barnes in the novel in order to reveal the author's understanding of the historical figure and its relation to the depiction of history in general. In the process of the study it was established that even though the novel strictly adheres to historical facts on the level of the plot and the author even uses the historical documents, Barnes does not seek to recreate either the historical truth objectively or the historical personality close to what she most likely was. The novel is both a psychological prose on ahistorical subject and a metafiction, a statement about history, how the reality, the life of a person and their literary creativity are correlated, how they influence each other.Keywords: J. Barnes, “Arthur and George”, A.C. Doyle, postmodernism, history, metafiction

To the theory of semi-linear equations in the plane

In two dimensions, we present a new approach to the study of the semilinear equations of the form div[A(z)∇u] = f(u), the diffusion term of which is the divergence uniform elliptic operator with measurable matrix functions A(z),whereas its reaction term f(u) is a continuous non-linear function. Assuming that f(t)/t → 0 as t → ∞, we establish a theorem on existence of weak C(Ď )∩ W¹,² loc (D) solutions of the Dirichlet problem with arbitrary continuous boundary data in any bounded domains D without degenerate boundary components. As consequences, we give applications to some concrete model semi-linear equations of mathematical physics, arising from modelling processes in anisotropic and inhomogeneous media. With a view to further development of the theory of boundary value problems for the semi-linear equations, we prove a theorem on the solvability of the Dirichlet problem for the Poisson equation in Jordan domains with arbitrary boundary data that are measurable with respect to the logarithmic capacity

On quasiconformal maps and semi-linear equations in the plane

Assume that Ω is a domain in the complex plane C and A(z) is symmetric 2× 2 matrix function with measurable entries, det A = 1 and such that 1/K|ξ|²≤ 〈A(z)ξ, ξ〉 ≤ K|ξ|², ξ ∊ R², 1 ≤ K < ∞. In particular, for semi-linear elliptic equations of the form div (A(z)∇u(z)) = f(u(z)) in Ω we prove Factorization Theorem that says that every weak solution u to the above equation can be expressed as the composition u = T ◦ ω, where ω : Ω → G stands for a K−quasiconformal homeomorphism generated by the matrix function A(z) and T(w) is a weak solution of the semi-linear equation △T(w) = J(w)f(T(w)) in G. Here the weight J(w) is the Jacobian of the inverse mapping ω⁻¹. Similar results hold for the corresponding nonlinear parabolic and hyperbolic equations. Some applications of these results in anisotropic media are given

SELF-IDENTIFICATION IN CROSS-CULTURAL SPACE: WOMEN’S PERSPECTIVE IN MONICA ALI’S BRICK LANE

Abstract. The paper deals with self-identification as one of the most topical problems in view of Britishpostcolonial literature. Women’s multicultural prose, being a bright combination of gender and ethnic discourses, gives an opportunity to form even more interesting ground for discussion. In this regard Brick Lane (2003), the debut novel of half-English half-Bangladeshi Monica Ali is particularly appropriate. Nazneen, a young woman, is in the center of the novel’s narrative. At the age of 18 she and her husband Chanu move from Guripur, a Sylhetian village, to Tower Hamlets, a borough inhabited by the biggest East Pakistani diaspora in London. The novel covers 17 years, from 1985 to 2002. During the period described the main heroine does not only mature, take death of the son, become a mother of2 daughters, but also finds her city and female self. The story presents a peculiar example of cross-cultural and gender issues’ interaction which is reflected through the depiction of the female protagonist in search of identity.Keywords: Monica Ali, Brick Lane, self-identification, multicultural, cross-cultural space, postcolonial novel,female

TRADITIONS OF PURITANISM IN THE MID-20 TH CENTURY AMERICAN NOVEL: LEGACY, DIALOGUE AND DEBATE

Abstract. The paper explores the evolution and transformation of Puritan ethical and moral principles in themid-20 th century American literature as represented by novels of John Cheever and John Updike providing both idealized and revisionist insight into traditional Puritan values that form the foundation of American culture. The key tenets of Puritanism underwent profound rethinking and revision throughout the history of American literature. The interpretation of the worldly asceticism concept in the new historical context is discussed as the key component in the revision of Puritan legacy. The analysis of alternative perspectives on desacralization of daily life in the works of heever and Updike reveals different paths they take for a continued dialogue with the tradition. John Cheever is nostalgic about the long lost simplicity and meaning of the bygone life, while John Updike turns to Karl Barth’s theology to prove the moral ineptitude of worldly asceticism in the modern world.Key words: tradition, Puritanism, worldly asceticism, John Updike, John Cheever