Algebraic Structures of Quantum Projective Field Theory Related to Fusion and Braiding. Hidden Additive Weight

The interaction of various algebraic structures describing fusion, braiding and group symmetries in quantum projective field theory is an object of an investigation in the paper. Structures of projective Zamolodchikov al- gebras, their represntations, spherical correlation functions, correlation characters and envelopping QPFT-operator algebras, projective \"W-algebras, shift algebras, braiding admissible QPFT-operator algebras and projective G-hypermultiplets are explored. It is proved (in the formalism of shift algebras) that sl(2,C)-primary fields are characterized by their projective weights and by the hidden additive weight, a hidden quantum number discovered in the paper (some discussions on this fact and its possible relation to a hidden 4-dimensional QFT maybe found in the note by S.Bychkov, S.Plotnikov and D.Juriev, Uspekhi Matem. Nauk 47(3) (1992)[in Russian]). The special attention is paid to various constructions of projective G-hyper- multiplets (QPFT-operator algebras with G-symmetries).Comment: AMS-TEX, amsppt style, 16 pages, accepted for a publication in J.MATH.PHYS. (Typographical errors are excluded

A spinor-like representation of the contact superconformal algebra K'(4)

In this work we construct an embedding of a nontrivial central extension of the contact superconformal algebra K'(4) into the Lie superalgebra of pseudodifferential symbols on the supercircle S^{1|2}. Associated with this embedding is a one-parameter family of spinor-like tiny irreducible representations of K'(4) realized just on 4 fields instead of the usual 16.Comment: 19 pages, TeX. Corrections to the references in the paper to be published in J. Math. Phys. v 42, no 1, 200

Classical N=2 W-superalgebras From Superpseudodifferential Operators

We study the supersymmetric Gelfand-Dickey algebras associated with the superpseudodifferential operators of positive as well as negative leading order. We show that, upon the usual constraint, these algebras contain the N=2 super Virasoro algebra as a subalgebra as long as the leading order is odd. The decompositions of the coefficient functions into N=1 primary fields are then obtained by covariantizing the superpseudodifferential operators. We discuss the problem of identifying N=2 supermultiplets and work out a couple of supermultiplets by explicit computations.Comment: 19 pages (Plain TeX), NHCU-HEP-94-1

Idempotent convexity and algebras for the capacity monad and its submonads

Idempotent analogues of convexity are introduced. It is proved that the category of algebras for the capacity monad in the category of compacta is isomorphic to the category of $(\max,\min)$-idempotent biconvex compacta and their biaffine maps. It is also shown that the category of algebras for the monad of sup-measures ($(\max,\min)$-idempotent measures) is isomorphic to the category of $(\max,\min)$-idempotent convex compacta and their affine maps

Нейромережева ідентифікація двох схем розв’язання задачі оптимізації кородуючих балок

By adjusting and training an artificial neural network has been set up simple and at the same time an effective approximation model of determining the coefficient of influence of the perimeter of cross-section. The analysis of factors, influencing on the choice of the coefficient of influence of the perimeter, has been conducted. Proposed and justified method of obtaining training and test sample specimens. As a result of testing the trained network, high efficiency and accuracy of the scheme solving the optimization problem with two consecutive single-circuit connections and neural network module compared to traditional circuit solutions has been shown.Путём настройки и обучения искусственной нейронной сети была создана простая и, в то же время, эффективная апроксимационная модель определения коэффициента влияния периметра сечения. Проведён анализ факторов, влияющих на выбор коэффициента влияния периметра. Предложена и обоснована методика получения обучающей и тестовой выборки образцов. В результате тестирования обученной сети сделан вывод о высокой эффективности и точности схемы решения задачи оптимизации с двумя последовательными одноконтурными связями и нейросетевым модулем по сравнению с традиционной схемой решения.Шляхом налаштування і навчання штучної нейронної мережі була створена проста і, в той же час, ефективна апроксимаційна модель визначення коефіцієнта впливу периметра перетину. Проведено аналіз факторів, що впливають на вибір коефіцієнта впливу периметра. Запропоновано й обґрунтовано методику отримання навчальної та тестової вибірки зразків. У результаті тестування навченої мережі зроблено висновок про високу ефективність і точність схеми розв’язання задачі оптимізації з двома послідовними одноконтурними зв'язками і нейромережевим модулем, порівняно з традиційною схемою розв’язання

Integrability of the Frobenius algebra-valued Kadomtsev-Petviashvili hierarchy

We introduce a Frobenius algebra-valued Kadomtsev-Petviashvili (KP) hierarchy and show the existence of Frobenius algebra-valued τ-function for this hierarchy. In addition, we construct its Hamiltonian structures by using the Adler-Dickey-Gelfand method. As a byproduct of these constructions, we show that the coupled KP hierarchy, defined by Casati and Ortenzi [J. Geom. Phys. 56, 418-449 (2006)], has at least n-“basic” different local bi-Hamiltonian structures. Finally, via the construction of the second Hamiltonian structures, we obtain some local matrix, or Frobenius algebra-valued, generalizations of classical W-algebras