The allowance for various defects including cracks represents a critical issue related to structural risk analysis. The complexity and the ambiguity involved with such allowance for the amount and growth of defects (cracks) is demonstrated on the real structure of a metallurgical overhead crane. The problem of distribution function conversion must be solved to allow for any variations in defects starting from the point of time when the initial (technological) defectiveness is determined and ending with the estimated time of risk analysis. Due to the lack of data on cyclic resistance to cracking for Вст3сп5 steel, it does not yet seem possible to construct the distribution functions and to determine the estimated theoretical average and dispersion of crack sizes. However, by using the previously obtained calculated data on active stresses and strains, it is now possible to simulate growth of cracks based on Weibull distribution. Different engineering solutions can be accepted at various stages of operating large structures, according to the obtained results.
Mathematics and architecture have always been closely interrelated, the main methods of design in architecture has always belonged to mathematics. At the present stage in connection with the development of computer technology and the Internet began a new round in the relationship between mathematics and architecture. A competent architect should have excellent skills in painting and sculpture, as well as a good knowledge of mathematics. We came to the conclusion that the purpose of mathematical training in the University of students of construction specialties is the development of their mathematical competence. This requires: 1) students should be able to solve applied mathematical problems; 2) students should carry out projects related to their future professional activities; 3) students should be able to create mathematical models. We have developed criteria, indicators and levels of development of mathematical competence of students of the University, which allows you to organize control and measuring materials to assess the level of mathematical training of students.
This article describes mathematical modelling of reliability, safety and risk indicators related to load bearing structural elements. The number of this type of cranes used at a modern iron and steel enterprise constitutes more than half of the total number of cranes. Therefore, the concerned issue and the problems addressed in this case represent current interest. Due to the impossibility of conducting a laboratory or a full-scale experiment, a numerical experiment is conducted using model distribution. Benchmark data used for calculations and based on previous studies performed by the author and available statistical data about incidents and damages are systematized and proposed. Hypotheses about addition and multiplication of damages related to elements of the equipment under study are made. Modelling adequacy is observed when the experiment findings match with available data. Classification of incidents arising when metallurgical cranes are operated beyond the expiry of their warranty period is identified. These calculations and procedure develop the theory of structural risk analysis of complex technical systems and allow making correct engineering-related managerial decisions.
Обучение способам составления задач как основа развития профессиональной компетентности будущих учителей математики На основе анализа педагогического опыта авторами показано, что для эффективного усвоения метода решения задачи, необходимо овладение учащимися способами создания задач, решаемых этим методом. Помимо этого система математического образования в школе требует от будущих учителей владения способами составления задач, что дает возможность формулировки большого и разнообразного круга задач, позволяющих учителю реализовывать различные образовательные цели.Ключевые слова: методика высшей школы, содержание образования студентов педагогических специальностей, компетенции, задачи по математике, методы решения задач Перспективы Науки и Образования Международный электронный научный журнал
Очевидно, что трудности возникающие в применении теории вихревых течений, во многом обусловлены самой вычислительной процедурой нахождения собственных чисел оператора Орра -Зоммерфельда, который относится к несамосопряженным операторам. В работах авторов статьи разработан численный метод вычисления первых собственных чисел дискретных полуограниченных операторов, который получил наименование метод регуляризованных следов (РС). В статье описана методика использования этого метода РС для определения собственных чисел соответствующей краевой задачи. Напрямую применять метод РС к решению прямой задачи Орра -Зоммерфельда нельзя. Поэтому с вспомогательной целью нами была поставлена спектральная задача, в которой просматривается аналогия с задачей Орра -Зоммерфельда в части совпадения собственных чисел. Получены новые оценки регуляризованных следов дискретного оператора. Найдены формулы, по которым можно вычислить поправки теории возмущений необходимого порядка. Для проведения вычислительных экспериментов в среде математического пакета Maple написаны программы, позволяющие находить приближенные значения первых собственных чисел исследуемой задачи. Выбор математической среды Maple обусловлен тем, что при численной реализации разработанного алгоритма необходимо производить операции с действительными числами с большой мантиссой. Ключевые слова: спектральная теория, численные методы, собственные числа, регуляризованные следы, краевые задачиIt is known that difficulties appearing in the linear theory of viscous fluid flow stability are much interconnected with computational problems of finding eigenvalues of non-self-adjoint operators including Orr-Sommerfeld operator. The numerical calculation method of the first eigenvalues of discrete semibounded operators has been developed in the works of the article authors. This method has been called regularized tracks method (RT). The technique of this method usage for findingapproximate values of the first eigenvalues of Orr-Sommerfeld boundaryvalue problem is described in the article. This method (RT) cannot be used directly to solve Orr-Sommerfeld direct task. Consequently the auxiliary spectral task has been built where the array of eigenvalues coincide with the array of eigenvalues of Orr-Sommerfeld task. New regularized tracks estimations of discrete operator have been obtained. Formulae to calculate amendments to the theory of necessary order perturbation have been found. For conducting calculation experiments in mathematical package medium Maple the programs that allow to find approximate values of the first eigenvalues of Orr-Sommerfeld spectral task have been written. The choice of mathematical medium Maple has been made due to the necessity to make operations with real numbers with large mantissa.
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