Proceedings of the National Academy of Sciences of Belarus. Series of Physical-Mathematical Sciences / Известия Национальной академии наук Беларуси. Серия физико-математических наук
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К ОПТМ ИЗАЦИИ ПРОЦЕССОВ ПОСЛЕДОВАТЕЛЬНОЙ ОБРАБОТКИ ПАРТИЙ ДЕТАЛЕЙ
Get PDFA problem of optimal design of processes of sequential machining of multiple parts on rotary table machines is considered. Batches are processed in a given sequence. Parts of the same batch are located at the working positions of rotary table and are machined simultaneously. Operations are divided into groups which are performed by spindle heads or by turrets. Constraints on the design of spindle heads, turrets, and working positions, as well as on the order of operations are given. The problem is to minimize the estimated cost of machine equipment while reaching a given output. The proposed method to solve the problem is based on its formulation in terms of mixed integer linear programming. Computational results are reported.Рассматривается задача оптимального проектирования процессов последовательной обработки партий деталей на станках с поворотным столом. Последовательность обработки партий задана. Детали одной и той же партии устанавливаются на рабочих позициях станка и обрабатываются одновременно. Множество технологических переходов для обработки всех деталей разбивается на группы, которые выполняются с помощью шпиндельных или револьверных головок. Заданы ограничения, связанные с разбиением переходов по шпиндельным и револьверным головкам, рабочим позициям станка, а также порядком выполнения переходов. Задача заключается в минимизации оценки стоимости оборудования станка при обеспечении заданной производительности. Предлагаемый метод решения задачи основан на ее формулировке в терминах смешанного целочисленного линейного программирования. Приводятся результаты вычислительных экспериментов
АЛГОРИТМ СЖАТИЯ ГИПЕРСПЕКТРАЛЬНЫХ ДАННЫХ ДИСТАНЦИОННОГО ЗОНДИРОВАНИЯ ЗЕМЛИ
Get PDFThe evaluation results of hyperspectral data correlation in spatial and spectral domains are presented by the example of the hypercube AVIRIS Moffett Field, and the key features of hyperspectral data are formulated. The basic approaches to lossless compression and the algorithms, which can be applied in Earth remote sensing, are considerеd. They are the prediction (linear prediction, fast lossless, spectral oriented least squares, correlation-based conditional average prediction, M-CALIC), the lookup tables (lookup table, locally averaged interband scaling lookup tables), the 3D wavelets (3D-SPECK). A compression algorithm of hyperspectral data is proposed with regard to the advantages and disadvantages of specific implementations of the analyzed algorithms in remote sensing. The main algorithm stages are the preprocessing (for each spectral channel, it is executed independently), the reduction of a correlation level in the spectral area and the entropy coder. The test results of the developed algorithm are given in comparison to the alternative codecs on the AVIRIS test set (Cuprite, Jasper Ridge, Low Altitude, Moffet Field) that prove the efficiency of the proposed algorithm: parallel processing, low computing cost (low latency instructions are used, no division and multiplication), small random access memory requirements (the memory is used only for storage of the hypercube). In the context of the above advantages, the hardware implementation of the algorithm is allowed for on board the aircraft.
СТАТИСТИЧЕСКОЕ ОТНЕСЕНИЕ РЕАЛИЗАЦИЙ НЕСТАЦИОНАРНЫХ ВРЕМЕННЫХ РЯДОВ К ЗАДАННЫМ ТРЕНДОВЫМ МОДЕЛЯМ
Get PDFThe problem of statistical assignment of realizations of non-stationary time series to the fixed trend models is investigated. The decision rule in a space of trend coefficients determined on the same orthogonal basis is proposed and its efficiency is analytically studied. As an example the case of two alternative trends is studied.Исследуется проблема статистического отнесения реализаций нестационарных временных рядов к заданным трендовым моделям. Предлагается использовать решающее правило в пространстве коэффициентов трендов, определенных в одном и том же ортогональном базисе. В качестве меры эффективности принимаемых решений аналитически вычислен риск (вероятность ошибочно определить ближайший к реализации тренд). Как пример рассмотрен случай двух альтернативных трендов.
БЕЗУСЛОВНО МОНОТОННЫЕ РАЗНОСТНЫЕ СХЕМЫ ВТОРОГО ПОРЯДКА АППРОКСИМАЦИИ НА РАВНОМЕРНЫХ СЕТКАХ ДЛЯ ГАММ А-УРАВНЕНИЯ
Get PDFIn this article we consider the initial boundary-value problem for the so-called Gamma equation, which can be derived by transforming the nonlinear Black – Scholes equation for option price into a quasi-linear parabolic equation for the second derivativeof option price, and for its exact solution the two-side estimates are obtained. By means of the regularization principle, the previous results are generalized to construct an unconditionally monotone finite-difference scheme (the maximum principle is satisfied without limitations on the relations between the coefficients and the grid parameters) of second-order approximation on uniform grids for this equation. With the help of the difference maximum principle, the two-side estimates for a difference solution are obtained using the arbitrary non-sign-constant input data of the problem. The a priori estimate in the maximum norm C is proved. It is interesting to note that the proven two-side estimates for the difference solution are fully consistent with the differential problem, and the maximal and minimal values of the difference solution do not depend onthe diffusion and convection coefficients. Computational experiments confirming the theoretical conclusions are given
ОДНОРОДНАЯ КРАЕВАЯ ЗАДАЧА РИМАНА С МЕРОМОРФНЫМИ КОЭФФИЦИЕНТАМИ ДЛЯ БЕСКОНЕЧНО СВЯЗНЫХ ОБЛАСТЕЙ
Get PDFHomogeneous Riemann boundary value problem with meromorphic coefficients for infinitely connected domains is considered. In the closed form the problem is solved in the class of piece-wise analytic functions, possessing meromorphic continuation to the whole complex plane. Special attention is paid to the existence of doubly periodic solutions to the problem with elliptic coefficients. The example of the problem having a unique solution up to an arbitrary constant multiplier is presented, as well as of the problem with a solution depending on a number of arbitrary parameters. The obtained results can be used for solving of an inhomogeneous Riemann boundary value problem with meromorphic coefficients in an infinitely connected domain in the general statement
АБ НАБЛІЖЭННІ ФУНКЦЫІ|sin x| РАЦЫЯНАЛЬНЫМІ АПЕРАТАРАМІ ФЕЕРА
Get PDFРацыянальныя шэрагі Фур’е былі пабудаваны М. М. Джрбашанам у 1956 г. У прыватнасці, знойдзе-на кампактнае прадстаўленне іх ядра Дзірыхле. На гэтай аснове В. М. Русак увёў рацыянальныя аператары Феера, Джэксана і Вале Пусэна. Частковыя сумы рацыянальных шэрагаў Фур’е, аператары Вале Пусэна і Джэксана знайшлі шырокае прымяненне для адшукання класаў функцый, рацыянальная апраксімацыя якіх лепшая за палінаміяльную ў сэнсе парадку. Рацыянальныя аператары Феера заставаліся недаследаванымі. Таму ўяўляе інтарэс даследаваць іх апраксімацыйныя характарыстыкі для элементарных функцый. Перыядычная функцыя | sin x | адыгрывае практычна такую жа ролю, што і функцыя |x| . У дадзенай рабоце з дапамогай метаду вываду параметра ў камплексную плоскасць атрыманы некаторыя дакладныя і асімптатычныя судачыненні для набліжэнняў функцыі | sin x | з дапамогай рацыянальных аператараў Феера. Паказана ў прыватнасці, што такія набліжэнні адлюстроўваюць асаблівасці рацыянальнай апраксімацыі. Rational Fourier series were constructed by M. M. Dzhrbashian in 1956. A compact representation of their Dirichlet kernel was also found. Later V. N. Rusak introduced rational operators of Fejér, de la Vallée Poussin and Jackson type. Partial sums of rational Fourier series, operators of de la Vallée Poussin and Jackson type are widely used for finding classes of functions, for which rational approximation is better than polynomial approximation. But in our opinion, rational operators of Fejér type are still unexpolred, so it’s interesting to investigate their approximation characteristics for elementary functions. The periodic function | sin | x plays almost the same role in approximation theory as the function |x |. In this article, we have obtained some exact and asymptotic ratios for approximation of | sin x | by Fejér-type rational operators. Рацыянальныя шэрагі Фур’е былі пабудаваны М. М. Джрбашанам у 1956 г. У прыватнасці, знойдзе-на кампактнае прадстаўленне іх ядра Дзірыхле. На гэтай аснове В. М. Русак увёў рацыянальныя аператары Феера, Джэксана і Вале Пусэна. Частковыя сумы рацыянальных шэрагаў Фур’е, аператары Вале Пусэна і Джэксана знайшлі шырокае прымяненне для адшукання класаў функцый, рацыянальная апраксімацыя якіх лепшая за палінаміяльную ў сэнсе парадку. Рацыянальныя аператары Феера заставаліся недаследаванымі. Таму ўяўляе інтарэс даследаваць іх апраксімацыйныя характарыстыкі для элементарных функцый. Перыядычная функцыя | sin x | адыгрывае практычна такую жа ролю, што і функцыя |x| . У дадзенай рабоце з дапамогай метаду вываду параметра ў камплексную плоскасць атрыманы некаторыя дакладныя і асімптатычныя судачыненні для набліжэнняў функцыі | sin x | з дапамогай рацыянальных аператараў Феера. Паказана ў прыватнасці, што такія набліжэнні адлюстроўваюць асаблівасці рацыянальнай апраксімацыі.
ЧАСТИЦА КОКСА ВО ВНЕШНЕМ МАГНИТНОМ ПОЛЕ: АНАЛИЗ В ПРОСТРАНСТВЕ ЛОБАЧЕВСКОГО
Get PDFThe generalized Schrődinger equation for a scalar Cox particle is studied in the presence of a magnetic field on the background of Lobachevsky space. Separation of variables is performed. An equation describing the particle motion along the z axis appears to be much more complex than that when describing the Cox particle in Minkowski space. The form of the effective potential curve says that we have a quantum-mechanical problem of tunneling type. The derived equation has 6 regular singular points. Singular points 0 and 1 of the derived equation correspond to the physical domains z = ±∞. The solutions of the equation are constructed with the help of power series. Convergence of the series is examined by the Poincare – Perrone method. These series are convergent within the whole physical domain z ∈ (-∞,+∞). When considering an ordinary particle in Lobachevsky space, a simpler problem of tunneling type arises, which is exactly solved in terms of hypergeometric functions.
ВЫЧИСЛЕНИЕ ФУНКЦИОНАЛЬНЫХ ИНТЕГРАЛОВ С ПОМОЩЬЮ ПОСЛЕДОВАТЕЛЬНОСТЕЙ ШТУРМА
Get PDFThe present work deals with two directions of the theory of functional integration. The first is the representation of physical quantities, in particular the evolution operator kernel in the form of functional integrals. The second is concerned with the methods for calculation of functional integrals. A new method for approximate evaluation of functional integrals with respect the conditional Wiener measure is proposed in this work. This method is based both on the use of the Feynman – Kac formula giving the integral representation of the evolution operator kernel and on the representation of the kernel using eigenvaluesand eigenvectors of operator. The proposed method is effective for calculation of functional integrals over a space of functions defined on the intervals of large length.Данная работа касается двух направлений теории функционального интегрирования: представления физических величин, в частности ядра оператора эволюции, в виде функциональных интегралов и методов вычисления функциональных интегралов. Предложен новый метод приближенного вычисления функциональных интеграловпо условной мере Винера, который основывается на использовании формулы Фейнмана – Каца, дающей интегральное представление для ядра оператора эволюции, и на представлении ядра с помощью собственных значений и собственных векторов оператора. Предлагаемый подход эффективен при вычислении функциональных интегралов по пространству функций, заданных на отрезках большой длины