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## Применение принципов механики Лагранжа для анализа электрических цепей с сосредоточенными параметрами

In this paper, the application of Lagrangian mechanic principles is introduced for dynamic analysis of lumped-element electric circuits containing resistors and sources of independent voltages and currents. It was discussed that formal analogy between the generalized coordinates of masses in classical mechanics and charges in electric circuit theory allows making up a clear qualitative interpretation of the proposed analytical method that paves the way for its further application to analysis of complex physical systems.

We prove a Darboux theorem for derived schemes with symplectic forms of degree k<0, in the sense of Pantev, Toën, Vaquié, and Vezzosi. More precisely, we show that a derived scheme X with symplectic form omega' of degree k is locally equivalent to (Spec A, omega) for Spec(A) an affine derived scheme in which the cdga A has Darboux-like coordinates with respect to which the symplectic form omega is standard, and in which the differential in A is given by a Poisson bracket with a Hamiltonian function Phi of degree k+1.

When k=-1, this implies that a -1-shifted symplectic derived scheme (X,omega') is Zariski locally equivalent to the derived critical locus Crit(Phi) of a regular function Phi: U --> A^1 on a smooth scheme U. We use this to show that the classical scheme t_0(X) has the structure of an algebraic d-critical locus,* *in the sense of Joyce.

In a series of works, the authors and their collaborators extend these results to (derived) Artin stacks, and discuss a Lagrangian neighbourhood theorem for shifted symplectic derived schemes, and applications to categorified and motivic Donaldson-Thomas theory of Calabi-Yau 3-folds, and to defining new Donaldson-Thomas type invariants of Calabi-Yau 4-folds, and to defining Fukaya categories of Lagrangians in algebraic symplectic manifolds using perverse sheaves.

Liénard-type equations are used for the description of various phenomena in physics and other fields of science. Here we find a new family of the Liénard-type equations which admits a non-standard autonomous Lagrangian. As a by-product we obtain autonomous first integrals for each member of this family of equations. We also show that some of the previously known conditions for the existence of a non-standard Lagrangian for the Liénard-type equations follow from the linearizability of the corresponding equation via nonlocal transformations.

Generalized error-locating codes are discussed. An algorithm for calculation of the upper bound of the probability of erroneous decoding for known code parameters and the input error probability is given. Based on this algorithm, an algorithm for selection of the code parameters for a specified design and input and output error probabilities is constructed. The lower bound of the probability of erroneous decoding is given. Examples of the dependence of the probability of erroneous decoding on the input error probability are given and the behavior of the obtained curves is explained.

The dynamics of a two-component Davydov-Scott (DS) soliton with a small mismatch of the initial location or velocity of the high-frequency (HF) component was investigated within the framework of the Zakharov-type system of two coupled equations for the HF and low-frequency (LF) fields. In this system, the HF field is described by the linear Schrödinger equation with the potential generated by the LF component varying in time and space. The LF component in this system is described by the Korteweg-de Vries equation with a term of quadratic influence of the HF field on the LF field. The frequency of the DS soliton`s component oscillation was found analytically using the balance equation. The perturbed DS soliton was shown to be stable. The analytical results were confirmed by numerical simulations.

Radiation conditions are described for various space regions, radiation-induced effects in spacecraft materials and equipment components are considered and information on theoretical, computational, and experimental methods for studying radiation effects are presented. The peculiarities of radiation effects on nanostructures and some problems related to modeling and radiation testing of such structures are considered.

This volume presents new results in the study and optimization of information transmission models in telecommunication networks using different approaches, mainly based on theiries of queueing systems and queueing networks .

The paper provides a number of proposed draft operational guidelines for technology measurement and includes a number of tentative technology definitions to be used for statistical purposes, principles for identification and classification of potentially growing technology areas, suggestions on the survey strategies and indicators. These are the key components of an internationally harmonized framework for collecting and interpreting technology data that would need to be further developed through a broader consultation process. A summary of definitions of technology already available in OECD manuals and the stocktaking results are provided in the Annex section.