Научный архив: статьи

We obtain a number of spectral and functional inequalities related to Schr ̈odinger operators defined on antisymmetric functions. Among them are Lieb — Thirring and CLR inequalities. Besides, we find new constants for the Sobolev and the Gagliardo — Nirenberg inequalities restricted to antisymmetric functions

The modern theory of development includes such concepts as entropy, dissipative and conservative structures, equilibrium systems, etc. But what is behind these concepts?

Are they not quite correct, which leads to a misunderstanding of the development process? How, on their basis, can a more general process diagram be constructed that would give a complete description of social dynamics?

Having non-linear equations share properties is useful, but when it comes to measurements and calculations, every non-linear system is a thing in itself. Comprehension of one of them gave absolutely nothing for penetration into the other. The Lorenz attractor revealed the stability and hidden structure of a system that, otherwise, seemed completely unstructured. But how could this double helix help specialists study objects that have nothing to do with it? No one knew.

The discoverers of new forms compromised the rigor of the scientific style. Ruelle wrote: “I have not mentioned the aesthetic impact of strange attractors. These tangles of curves and swarms of dots sometimes conjure up magnificent fireworks or mysterious galaxies, sometimes they resemble a bizarre riot of plants. Before us is a vast realm of undiscovered forms and unknown perfection.

At the turn of the 19th and 20th centuries, the scientific community was in a rosy mood - and not without reason: it seemed that a few more strokes, and the picture of the world would be built. By the end of the 19th century, classical science could rightfully be proud of its achievements. Since the time of Newton, the world, which the ancients divided into the sublunar and supralunar spheres, has become a single. Uniform cognizable (and, as the representatives of natural science and philosophical circles believed, largely cognized) laws acted in it.

The role of bifurcation or structural-phase transitions in the evolution of complex systems is analyzed using a phenomenological algorithm and formalized concepts of adaptability and stability. It is shown that the algorithm makes it possible to estimate the degree of transition harmonicity and the stability of the new state. Knowledge of the features of the most critical zones of structural-phase transitions makes it possible to change the trajectory, pace and ultimate goal of the evolution of various dangerous natural processes by small energy impacts, preventing their development to extreme states. The knowledge of the functional significance of such “acupuncture” points of evolutionary processes makes it possible to control them with minimal energy costs for the purpose of preventive protection.

The polyfunctionality of complex evolving systems is analyzed. It is shown that not only living objects, but also various inert, bio-inert systems have numerous functions in the general natural organism. The functions of a dual nature systems - bioinert soil and biosocial man - turned out to be especially numerous. Such functions turned out to be the basic objects of study of the existing world system polyfunctionality.

Приводится описание нового межвидового гибрида Salix × jessenii O. V. Epanch. et I. V. Belyaeva. Этот гибрид культивируется в ботанических садах и частных коллекциях в Европе и России. Предложено возможное использование этой необычной декоративной ивы.

This article revises current perspectives on the generic status, composition, and subject matter of Phoenician Women by Seneca. It adopts a new approach, focusing on selected elements of text organisation. In particular, emphasis is given to the construction of characters and the analogies and contrasts between them which were already of interest to ancient poetics and rhetoric. Moreover, the article refers to observations, accurate but isolated and largely ignored, made by scholars who recognised Seneca’s originality and suggested that his plays might have been inspired by the declamatory tradition and should be read in the context of evolving postclassical literature. By adopting this perspective, it becomes possible to bring together a large number of partial conclusions that are related to Phoenician Women as well as other plays by Seneca. What is more important, the work brings to light the purposeful composition of the drama and its thematic unity, allowing us to return to the MS versions that until now have been replaced by conjectures, which often distort the meaning of the text. After dismissing the emendations and adopting a new method of reading, Seneca’s Phoenician Women can be regarded as complete and well-organised. The play has certain characteristic features of a tragedy, of all Seneca’s dramas, it is the one most inspired by the genre of declamation and the poetics of Seneca the Elder’s anthology, and it is an example of the use of plot material typical of tragedy for presenting the problem of pietas in all its complexity

This piece is a fresh take on the crux philologorum in Sappho fr. 96,8, an extended moon simile, where Aeolic σελάννα, a commonplace of Sapphic poetry, easily restituted ex coniectura by W. Schubart in his editio princeps of PBerol. 9722 in 1902, was ousted by an unmetrical, if poetic, μήνα. The author offers an overview of the past and most recent scholarly effort along with an attempt (albeit a speculative one) to approach the issue of the irrational ratio corruptelae from the part of the resonant adjective βροδοδάκτυλος, an altogether uncommon epithet of the moon, paying close attention to the fact that the intruding word is disyllabic. The dactylic feel of the weighty adjective βροδοδάκτυλος is deemed at some point to have prevailed in a scribe’s dictation interne to the result that ἠώς could have landed in the text proper, or could have found its way there gradually from an intrusive marginal gloss left by a learned scribe unable to keep the Homeric clausula ῥοδοδάκτυλος ἠώς to himself. At some point another, no less learned scribe, attentive to the context of the simile, picked up μήνα, not σελήνη, as his remedy of choice, sticking to the number of syllables in the now resident ἠώς

This article opens a series devoted to investigating the sources of the ample zoological excursus (vv. 916–1223) in the Hexaemeron by George of Pisidia, a 7th-century Byzantine poet. Since the two attempts to find a general formula for George of Pisidia’s treatment of his models have led to directly opposite results (according to Max Wellmann, the poet distanced himself from pagan zoologists; according to Luigi Tartaglia, on the contrary, he drew material from them, favouring Aelian), it seems that the question of the poem’s sources should be addressed by a step-by-step examination of passages, paying attention to such evidence as the coincidence of minor details or words. In v. 1116 the unusual metaphor “aithyia, bending its winged cloud” (in the sense of “spreading its wings”) makes one think of an (unconscious?) association with Arat. Phaen. 918–920, where “a stretching cloud” is mentioned in the catalogue of storm’s signs in immediate juxtaposition to the flapping of the wings of seabirds. In vv. 1117–1124 (the self-cleansing of the ibis) the reference to Galen is not a mere metonymy (= “the most skillful physician”), as interpreters have hitherto thought, but points to the poet’s source: in the Galenic corpus this story is attested three times, and the passage closest to George of Pisidia’s account is [Galen.] Introd. 1.2. In vv. 1154–1159 (the structure of the web) the confused sequence of the stages of the spider’s work (first concentric circles, then radial threads), that contradicts both reality and (which is more important) the ancient tradition going back to Book IX of Historia animalium, seems to betray the influence of John Philoponus (De opif. mundi, p. 257, 24 sqq. Reinhardt). In Philoponus’ text this sequence is justified by the fact that his rhetorical passage describes, strictly speaking, not the web itself, but a drawing of it made by a “diligent geometer”.

Проблема профессионального самоопределения является актуальной для большинства обучающихся, в том числе в старших классах. Практика показывает, что учителю необходим инструментарий, способствующий осознанному выбору будущей профессии, знакомству с данной сферой деятельности. Авторы рассматривают STEM-кейсы как инструменты решения поставленных задач, средство профориентации обучающихся. Целью исследования, описанного в статье, является разработка и апробация учебно-методических материалов (кейсов), направленных на мотивирование обучающихся к изучению естественно-научных дисциплин, математики и технологии, способствующих профориентации. Разработанные учебно-методические материалы представляют собой кейсы (материалы для учеников) и методические рекомендации по их применению для учителей. Предлагаемые кейсы содержат элементы исследования или проектирования, раскрывают реальные проблемы и задачи, решаемые на производстве. Результаты апробации показали, что разработанные материалы могут стать эффективным инструментом профориентации, позволяющим обучающимся «примерить» на себя различные профессии и сделать осознанный выбор.

This article continues the series devoted to the study of an extensive zoological excursus in Hexaemeron by George of Pisidia, a 7th-century Byzantine poet. It deals with two accounts of the miraculous properties of vultures which offer their author(s) an opportunity to engage in anti-pagan polemics and to assert the truth of the virgin birth of Jesus (vv. 1077–1086, 1124a–r). The second of these passages is attested only in part of the paradosis, and it is placed differently in different MSS, which indicates that at least for some time it was transmitted in the margins. The question of whether these verses should be considered an interpolation or an author’s variant has been raised twice by Fabrizio Gonnelli, with opposite results. A doxographic commentary on both passages permits a cautious decision for the authenticity of vv. 1124a–r, since it involves a sophisticated and highly original theological development (or even a correction) of a phrase from Homilies in Hexaemeron of Basil the Great (8. 6. 76DE). At the same time, the second passage should be regarded as a later version of the first, since the position of vv. 1077–1086 in the poem seems to point to a hidden polemic with the famous story from Physiologus (ch. 4 of the oldest recension) about the pelican resurrecting its chicks with its own blood; vv. 1124a–r, where nothing is said about vultures feeding their chicks, could not fulfil this role. Incidentally, two unnoticed quotations from Hexaemeron are identified, namely in the scholia recentiora to Aristophanes’ Plutus (v. 63i Chantry) and in the anonymous Byzantine text Παράδειγμα περὶ τοῦ ἀλέκτορος