319 research outputs found

    Determination of the Optimum Chemical Composition and Temperature Interval of Hot Deformation for Steels of Supermartensity Class

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    The formation problem of the “banded microstructure” defect in low-carbon steels of the supermartensitic class was described. Options for reducing the likelihood of this defect are proposed. For this, thermodynamic calculations were carried out in order to select the optimal chemical composition and temperature range of hot deformation.В работе описана проблема образования дефекта «полосчатости микроструктуры» в низкоуглеродистых сталях супермартенситного класса. Предложены варианты снижения вероятности образования данного дефекта. Для этого проведены термодинамические расчеты с целью подбора оптимального химического состава и температурного интервала горячей деформации

    Determination of Temperature of (γ → α)-Transformation Using the Software Thermo-Calc for Small Carbon Low Alloy Steel

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    In this paper, we considered the capabilities of the Thermo-Calc program, which allows us to calculate equilibrium phase diagrams, the number and composition of phases, liquidus temperatures, equilibrium and nonequilibrium solidus, and phase formation under nonequilibrium conditions. Thermodynamic calculations were carried out to determine the temperature A3 for mild low-alloy steel for controlled thermomechanical processing (TMCP).В работе рассмотрены возможности программы Thermo-Calc, позволяющей проводить расчеты равновесных диаграмм состояния, количества и состава фаз, температур ликвидуса, равновесного и неравновесного солидуса, образования фаз в слабо неравновесных условиях. Проведены термодинамические расчеты по определению температуры А3 для малоуглеродистой низколегированной стали для контролируемой термомеханической обработки (TMCP).Работа выполнена при финансовой поддержке стипендии Президента Российской Федерации (проект СП-259.2018.1)

    Two factor saturated designs: cycles, Gini index and state polytopes

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    In this paper we analyze and characterize the saturated fractions of two-factor designs under the simple effect model. Using Li et al.ear algebra, we define a criterion to check whether a given fraction is saturated or not. We also compute the number of saturated fractions, providing an alternative proof of the Cayley's formula. Finally we show how, given a list of saturated fractions, Gini indexes of their margins and the associated state polytopes could be used to classify them

    Nonlinear Integer Programming

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    Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject to integrality requirements for the variables. This chapter is dedicated to this topic. The primary goal is a study of a simple version of general nonlinear integer problems, where all constraints are still linear. Our focus is on the computational complexity of the problem, which varies significantly with the type of nonlinear objective function in combination with the underlying combinatorial structure. Numerous boundary cases of complexity emerge, which sometimes surprisingly lead even to polynomial time algorithms. We also cover recent successful approaches for more general classes of problems. Though no positive theoretical efficiency results are available, nor are they likely to ever be available, these seem to be the currently most successful and interesting approaches for solving practical problems. It is our belief that the study of algorithms motivated by theoretical considerations and those motivated by our desire to solve practical instances should and do inform one another. So it is with this viewpoint that we present the subject, and it is in this direction that we hope to spark further research.Comment: 57 pages. To appear in: M. J\"unger, T. Liebling, D. Naddef, G. Nemhauser, W. Pulleyblank, G. Reinelt, G. Rinaldi, and L. Wolsey (eds.), 50 Years of Integer Programming 1958--2008: The Early Years and State-of-the-Art Surveys, Springer-Verlag, 2009, ISBN 354068274
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