The paper presents theoretical results on the interaction of cubically nonlinear harmonic elastic plane waves in a nonlinear material described by the Murnaghan potential. The interaction of two harmonic transverse waves is studied using the method of slowly varying amplitude. Reduced and evolution equations and the Manley-Rowe relations are derived. An analysis is made of the mechanism of energy transfer from the strong pumping wave, which has frequency ω, to the weak signal wave, which has frequency 3ω because of this interaction. A switching mechanism for hypersonic waves in a nonlinear elastic material is described, which is similar to the switching mechanism observed in transistors Keywords: cubic nonlinearity, elastic transverse plane harmonic wave, method of slowly varying amplitude, reduced and evolution equations, Manley-Rowe relations, pumping and signal waves, two-wave interaction, self-switchingThe paper discusses theoretical results on the interaction of two vertically polarized transverse plane harmonic waves in a nonlinear elastic material. The nonlinearity of the material is modeled based on the Murnaghan potential. This elastic potential is cubically nonlinear with respect to the strain components and offers several advantages in wave analysis: adequate accounting for the features of deformation through all the three first invariants of the strain tensor and fairly simple analytic representation and, consequently, satisfactory and numerically convenient description of the main nonlinear wave phenomena. Of the previous studies, noteworthy are those concerned with the laws of propagation of quadratically nonlinear harmonic plane waves (see [4,6,8,15,16]). The nonlinear properties of a material are described in these studies by transforming the Murnaghan potential cubically nonlinear with respect to the components of the strain tensor to a form cubically nonlinear with respect to the components of the strain gradient. Doing this yields coupled wave equations quadratically nonlinear with respect to the displacement components of a plane wave propagating along the abscissa axis,

Аннотация. Цель. Выявить содержательные элементы технологии проектирования многооконного приложения SDI стиля в среде программирования Delphi, проиллюстрировать на конкретном примере основные этапы и технологические приемы.Методы. Анализ и синтез специальной литературы по проблеме исследования, обобщение и систематизация, моделирование.

The paper presents a novel discourse-based approach to argument quality assessment defined as a graph classification task, where the depth of reasoning (argumentation) is evident from the number and type of detected discourse units and relations between them. We successfully applied state-of-the-art discourse parsers and machine learning models to reconstruct argument graphs with the identified and classified discourse units as nodes and relations between them as edges. Then Graph Neural Networks were trained to predict the argument quality assessing its acceptability, relevance, sufficiency and overall cogency. The obtained accuracy ranges from 74.5% to 85.0% and indicates that discourse-based argument structures reflect qualitative properties of natural language arguments. The results open many interesting prospects for future research in the field of argumentation mining.

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