To the theory of semi-linear Beltrami equations

The present paper is devoted to the study of semi-linear Beltrami equations which are closely relevant to the corresponding semi-linear Poisson type equations of mathematical physics on the plane in anisotropic and inhomogeneous media. In its first part, applying completely continuous ope\-ra\-tors by Ahlfors-Bers and Leray--Schauder approach, we prove existence of regular solutions of the semi-linear Beltrami equations with no boundary conditions. Moreover, here we derive their representation through solutions of the Vekua type equations and generalized analytic functions with sources. As consequences, it is given a series of applications of these results to semi-linear Poisson type equations and to the corresponding equations of mathematical physics describing such phenomena as diffusion with physical and chemical absorption, plasma states and stationary burning in anisotropic and inhomogeneous media. The second part of the paper contains existence, representation and regularity results for nonclassical solutions to the Hilbert (Dirichlet) boundary value problem for semi-linear Beltrami equations and to the Poincare (Neumann) boundary value problem for semi-linear Poisson type equations with arbitrary boundary data that are measurable with respect to logarithmic capacity.Comment: 28 pages. arXiv admin note: text overlap with arXiv:2107.1066

On Dirichlet problem for degenerate Beltrami equations with sources

The present paper is devoted to the study of the Dirichlet problem ${\rm{Re}}\,\omega(z)\to\varphi(\zeta)$ as $z\to\zeta,$ $z\in D,\zeta\in \partial D,$ with continuous boundary data $\varphi :\partial D\to\mathbb R$ for Beltrami equations $\omega_{\bar{z}}=\mu(z) \omega_z+\sigma (z)$, $|\mu(z)|<1$ a.e., with sources $\sigma :D\to\mathbb C$ in the case of locally uniform ellipticity. In this case, we establish a series of effective integral criteria of the type of BMO, FMO, Calderon-Zygmund, Lehto and Orlicz on singularities of the equations at the boundary for existence, representation and regularity of solutions in arbitrary bounded domains $D$ of the complex plane $\mathbb C$ with no boun\-da\-ry component degenerated to a single point for sources $\sigma$ in $L_p(D)$, $p>2$, with compact support in $D$. Moreover, we prove in such domains existence, representation and regularity of weak solutions of the Dirichlet problem for the Poisson type equation ${\rm div} [A(z)\nabla\,u(z)] = g(z)$ whose source $g\in L_p(D)$, $p>1$, has compact support in $D$ and whose mat\-rix valued coefficient $A(z)$ guarantees its locally uniform ellipticity.Comment: 31 pages. arXiv admin note: substantial text overlap with arXiv:2111.1037

Сравнительная оценка сортов тыквы в Удмуртской Республике

Relevance. Pumpkin is a food, medicinal and fodder crop of the Cucurbitaceae family. It is valued for its high content of vitamins, minerals, organic acids. At present, thanks to the huge variety of species and modern selection, it is possible to select pumpkin varieties for cultivation in almost any region, including areas with short and not too hot summers. Udmurtia belongs to the zone of risky farming, the end of spring frosts is observed on average in the first ten days of June, and autumn frosts on the soil are possible at the end of August. Due to the short frost-free period, it is necessary to choose earlier maturing varieties, grow the crop through seedlings and use temporary shelters. The pumpkin fruit is usually large in size, is a thick layer of pulp, covered with a dense peel. When cutting such a fruit, the pumpkin is not stored in the future, it requires urgent processing. In this connection, in recent years, portioned varieties of pumpkin, the size of the fruit of which does not exceed 1.5–3.0 kg, have become increasingly in demand.Materials and Methods. The purpose of the research: a comparative assessment of varietal characteristics of growth and productivity of pumpkin species. In 2020–2021 in the conditions of the Udmurt Republic, experiments were carried out to study the characteristics of growth and productivity of pumpkin varieties. We studied varieties of pumpkin: Pearl, Crumb, Honey Tale, Marble, Rossiyanka, Smile, Candied fruit.Results and its discussion. Within two years, pumpkin varieties of large-fruited and nutmeg were studied. On average, for two years, the pumpkin Medovaya skazka distinguished itself with the highest yield. In 2021, the yield for the Medovaya Skazka variety was 64.7 t/ha. The yield increase was obtained due to an increase in fruit weight, which in 2020 amounted to 2.9 kg, in 2021 - 6.5 kg. The studied varieties of pumpkin differed in quality indicators of fruits. On average, over two years, the varieties Rossiyanka and Mramornaya showed an increase in the content of water-soluble sugars in fruits. The fruits of the pumpkin Candied fruit and Kroshka were distinguished by a high content of dry matter.Актуальность. Тыква – пищевая, лекарственная и кормовая культура семейства Тыквенные (Cucurbitaceae). Ценится за высокое содержание витаминов, минералов, органических кислот. В настоящее время, благодаря огромному разнообразию видов и современной селекции можно подобрать сорта тыквы для выращивания практически в любом регионе, в том числе и для районов с коротким и не слишком жарким летом. Удмуртия относится к зоне рискованного земледелия, окончание весенних заморозков отмечается в среднем в первой декаде июня, а осенние заморозки на почве возможны в конце августа. В связи с коротким беззаморозковым периодом необходимо выбирать более раннеспелые сорта, выращивать культуру через рассаду и использовать временные укрытия. Плод тыквы, обычно, отличается большими размерами, представляет собой толстый слой мякоти, покрытый плотной кожурой. При разрезании такого плода, тыква в дальнейшем не хранится, требует срочной переработки. В связи с чем в последние годы все большим спросом начали пользоваться порционные сорта тыквы, размер плода которых не превышает 1,5–3,0 кг.Материалы и методы. Цель исследований: сравнительная оценка сортовых особенностей роста и продуктивности видов тыквы. В 2020–2021 гг. в условиях Удмуртской Республики были проведены опыты по изучению особенностей роста и урожайности сортов тыквы. Изучали сорта тыквы: Жемчужина, Крошка, Медовая сказка, Мраморная, Россиянка, Улыбка, Цукат.Результаты и их обсуждение. В течение двух лет были изучены сорта тыквы крупноплодной и мускатной. В среднем за два года наибольшей урожайностью отличилась тыква Медовая сказка. В 2021 г. по сорту Медовая сказка урожайность составила 64,7 т/га. Прибавка урожайности получена за счет увеличения массы плода, которая в 2020 г. составила 2,9 кг, в 2021 г. – 6,5 кг. Изучаемые сорта тыквы отличались по качественным показателям плодов. В среднем за два года по сортам Россиянка и Мраморная отмечено увеличение содержания водорастворимых сахаров в плодах. Плоды тыквы Цукат и Крошка отличались повышенным содержанием сухого вещества

Hamlet revisited: Adaptations of shakespeare in recent Russian drama

© 2019 Shamina et al. Shakespeare has always been among the most popular foreign playwrights staged in Russia. Among them, Hamlet has always been definitely the most widely liked and often staged play. Its protagonist was for a long time perceived by Russians as a symbol of nonconformism and rebellion. Nowadays its reception as a heroic play ending in elevating catharsis has given way to all sorts of deconstruction, which is reflected both in its stage adaptations as well as in creating remakes of the famous play. However, one of the first playwrights, who introduced a new theatrical form and did it on Shakespeare's material, was Tom Stoppard. In Rosencrantz and Guildenstern are Dead the playwright laid the basic principles of the approach to the classical Canon, which were further developed in the dramaturgy of the second half of the twentieth century, Russian drama including. It became a "precedent play" for the pieces written by recent Russian playwrights, such as Boris Akunin, Ludmila Petrushevskaya, Victor Korkia and the Presnyakov brothers addressed in the essay. They successfully exploited and further developed Stoppard's techniques such as intertextuality, actualisation of metaphors, parcellation and contamination of popular idioms, deheroisation, decentralisation and other types of deconstruction

Hamlet revisited: Adaptations of shakespeare in recent Russian drama

© 2019 Shamina et al. Shakespeare has always been among the most popular foreign playwrights staged in Russia. Among them, Hamlet has always been definitely the most widely liked and often staged play. Its protagonist was for a long time perceived by Russians as a symbol of nonconformism and rebellion. Nowadays its reception as a heroic play ending in elevating catharsis has given way to all sorts of deconstruction, which is reflected both in its stage adaptations as well as in creating remakes of the famous play. However, one of the first playwrights, who introduced a new theatrical form and did it on Shakespeare's material, was Tom Stoppard. In Rosencrantz and Guildenstern are Dead the playwright laid the basic principles of the approach to the classical Canon, which were further developed in the dramaturgy of the second half of the twentieth century, Russian drama including. It became a "precedent play" for the pieces written by recent Russian playwrights, such as Boris Akunin, Ludmila Petrushevskaya, Victor Korkia and the Presnyakov brothers addressed in the essay. They successfully exploited and further developed Stoppard's techniques such as intertextuality, actualisation of metaphors, parcellation and contamination of popular idioms, deheroisation, decentralisation and other types of deconstruction

On boundary value problems for inhomogeneous Beltrami equations

We give here results on the existence of nonclassical solutions of the Hilbert boundary value problem in terms of the so-called angular limits (along nontangent curves to the boundary) for Beltrami equations with sources in Jordan domains satisfying the quasihyperbolic boundary condition by Gehring-Martio, generally speaking, without $(A)-$condition by Ladyzhenskaya-Ural'tseva and, in particular, without the known outer cone condition that were standard for boundary value problems in the PDE theory. Assuming that the coefficients of the problem are functions of countable bounded variation and the boundary data are measurable with respect to the logarithmic capacity, we prove the existence of locally H\"older continuous solutions of the problem. Moreover, we prove similar results on the Hilbert boundary value problem with its arbitrary measurable boundary data as well as coefficients in finitely connected Jordan domains along the so-called general Bagemihl-Seidel systems of Jordan arcs to their boundaries. In the same terms, we formulate theorems on the existence of regular solutions of the known Riemann boundary value problems, including nonlinear, with arbitrary measurable coefficients for the nonhomogeneous Beltrami equations. We give also the representation of obtained solutions through the so-called generalized analytic functions with sources. Finally, we formulate similar results on Poincare and Neumann problems for the Poisson type equations that are main in hydromechanics (mechanics of incompressible fluids) in anisotropic and inhomogeneous media. We give here the representation of their solutions through the so-called generalized harmonic functions with sources that describe the corresponding physical processes in iso\-tro\-pic and homogeneous media.Comment: 22 page

The folding of the specific DNA recognition subdomain of the sleeping beauty transposase is temperature-dependent and is required for its binding to the transposon DNA.

The reaction of DNA transposition begins when the transposase enzyme binds to the transposon DNA. Sleeping Beauty is a member of the mariner family of DNA transposons. Although it is an important tool in genetic applications and has been adapted for human gene therapy, its molecular mechanism remains obscure. Here, we show that only the folded conformation of the specific DNA recognition subdomain of the Sleeping Beauty transposase, the PAI subdomain, binds to the transposon DNA. Furthermore, we show that the PAI subdomain is well folded at low temperatures, but the presence of unfolded conformation gradually increases at temperatures above 15°C, suggesting that the choice of temperature may be important for the optimal transposase activity. Overall, the results provide a molecular-level insight into the DNA recognition by the Sleeping Beauty transposase