THE ARCHAIC LAYER IN THE PLOT OF B. GURZHIBEKOV’S POEM «ENCHANTED BEAUTY»

В статье критически пересмотрены сложившиеся в отечественной филологии оценки поэмы «Сахи рæсугъд» классика осетинской литературы Б. Гуржибекова. В противовес идеологическим трактовкам в русле дискурса соцреализма предлагается новая интерпретация произведения как реализации в нем (возможно, на подсознательном уровне) идеи агональности миров — универсального мотива в древнейших мифологических системах. Реконструкция архаического пласта образности позволяет с уверенностью говорить о сюжетном ядре поэмы, выдержанном в духе зороастрийских понятий дуализма, в свою очередь унаследованных от древней иранской религии. Речь идет о признании во вселенной двух равновеликих сил: Добра и Зла, их борьба и есть условие существования вселенной. Агонистика персоносферы представлена в поэме противостоянием Сказителя и Авдеуа — персонажей, наделенных способностью проникать во все сферы мироздания, но с разнополярными функциями. Такая трактовка героев дает возможность раскрыть в произведении потаенную символику феномена сказителя, а состязанию соперников придать статус космической битвы, выводя его за рамки личной мотивации. Равным образом мотив дистанционного контроля Авдеуом девушки из башни, передаваемый идиомой «дæндаг хъæртун», позволяет адекватно семантизировать заглавие поэмы: эпитет «сах» в нем акцентирует не исключительную красоту, а состояние зачарованности героини. Все остальное: вопросы происхождения, родовых корней протоперсонажа, линия любви — то, что позиционируется исследователями как свобода проявления чувств, и даже волшебные дары (зеркало, меч) суть не что иное, как временные наслоения, социальные и этические рефлексии писателя, наложившиеся на структуру древнего мифа. The article critically reviews the traditional for Russian philology assessments of the poem «Enchanted Beauty» («Sahy Beauty») by B. Gurzhibekov, classic of the Ossetian literature. In contrast to the ideological interpretations in line with the discourse of social realism, a new interpretation of the work is presented as realization (perhaps at a subconscious level) of the ideas of the agonality of worlds — a universal motive in the ancient mythological systems. The reconstruction of the archaic reservoir of imagery allows discuss the plot core of the poem, sustained in the spirit of the Zoroastrian concepts of dualism, inherited in their turn from the ancient Iranian religion. It is about the recognition of two equal forces in the universe: the Good and the Evil, their struggle being the very condition for the existence of the universe. The agonistics of the personal sphere is represented in the poem by the confrontation between the Storyteller and Avdeu, characters with the ability to penetrate into all spheres of the universe, but with opposite or polar functions. Such an interpretation of the characters makes it possible to reveal the hidden symbolism of the narrator’s phenomenon in the work, and to give the status of a space battle to the competition of the rivals, outwarding it beyond personal motivation. Equally, the remote control motive by Avdeu of the girl from the tower makes it possible to adequately semanticize the title of the poem: the epithet «sahy» in its original title emphasizes not exceptional beauty, but the state of enchantment of the heroine. Everything else: questions of origin, generic roots of the proto-character, the line of love — that is positioned by researchers as freedom of expression of feelings, and even magic gifts (mirror, sword) are nothing but temporal stratifications, social and ethical reflections of the writer, superimposed on the structure of the ancient myth.

Conic Connections with Polar Functions

Encourage investigation of the conic-section attributes of focus, eccentricity, directrix, and semi-latus rectum using polar coordinates and projective geometry.

Polar Functions for Anisotropic Gaussian Random Fields

LetXbe an (N,d)-anisotropic Gaussian random field. Under some general conditions onX, we establish a relationship between a class of continuous functions satisfying the Lipschitz condition and a class of polar functions ofX. We prove upper and lower bounds for the intersection probability for a nonpolar function andXin terms of Hausdorff measure and capacity, respectively. We also determine the Hausdorff and packing dimensions of the times set for a nonpolar function intersectingX. The class of Gaussian random fields that satisfy our conditions includes not only fractional Brownian motion and the Brownian sheet, but also such anisotropic fields as fractional Brownian sheets, solutions to stochastic heat equation driven by space-time white noise, and the operator-scaling Gaussian random field with stationary increments.

Technology Tips: Using FluidMath to Explore Recursive and Explicit Functions

luidMath™ (www.fluiditysoftware.com), a new mathematics software tool for Tablet devices, computers, and interactive whiteboards, can create a dynamic graph or table with a simple gesture and recognize written expressions as the mathematical relationship they intend. The software uses a stylus as its input device. By changing constant values in an equation to parameters, the user can create sliders instantly and see graphs and tables change dynamically. The CAS (Computer Algebra System) functionality allows simplification of algebraic expressions and solution of equations and can perform all the calculations from algebra through calculus. FluidMath uses standard mathematical notation to explore explicitly and implicitly defined functions, parametric functions, polar functions, and recursively defined functions.

Functorial polar functions

W∞ denotes the category of archimedean ℓ-groups with designated weak unit and complete ℓ-homomorphisms that preserve the weak unit. CmpT2,∞ denotes the category of compact Hausdorff spaces with continuous skeletal maps. This work introduces the concept of a functorial polar function on W∞ and its dual a functorial covering function on CmpT2,∞.We demonstrate that functorial polar functions give rise to reflective hull classes in W ∞ and that functorial covering functions give rise to coreflective covering classes in CmpT 2,∞. We generate a variety of reflective and coreflecitve subcategories and prove that for any regular uncountable cardinal α, the class of α-projectable ℓ-groups is reflective in W ∞, and the class of α-disconnected compact Hausdorff spaces is coreflective in CmpT 2,∞. Lastly, the notion of a functorial polar function (resp. functorial covering function) is generalized to sublattices of polars (resp. sublattices of regular closed sets).