Popov's Method Research Articles

Stability of nonlinear electromechanical systems with a magnetic gearbox

On the basis of the block diagram of an open-loop electromechanical system with a radial magnetic gearbox, its absolute stability is proved, taking into account the nonlinearity of the magnetic coupling. In the Simulink MatLab objectvisual modeling environment, a dynamic model of an electromechanical system is implemented. The transient response confirms the presence of significant speed fluctuations at the output of an open loop system. Keywords: magnetic reducer, two-mass system, elastic connection, block diagram, transfer function, stability, Popov's method. sapsalevav@ngs.ru, kharit1@yandex.ru, achitaevaa@gmail.com

Weak and strong convergence of a modified adaptive generalized Popov's algorithm for solving variational inequality problems

In this paper, we introduce a modified adaptive step-size algorithm by basing a generalized Popov's method to solve variational inequality problems in a real Hilbert space. The algorithm only needs to act on the operator once time in each iteration, which greatly reduces the calculation time and calculation difficulty. Of particular interesting, by using our new same generalized Popov's method, we also weaken the conditions of the operator about weak continuity and quasi-monotone property. Of particular interesting, by using our new same generalized Popov's method, we can obtain a weak convergence result under the condition that the operator A is quasi-monotone and a R-linear convergence result under the condition that the operator A is strongly pseudo-monotone in the variational inequality, respectively. Finally, the feasibility and effectiveness of the algorithm are verified by some numerical experiments.

Refined frequency estimates for stability domains of synchronization systems

n this paper we examine stability of Lur’e-type systems arising as a feedback superpositions of infinite-dimensional linear blocks, described by integrodifferential Volterra equations, and periodic nonlinearities. Such systems have multiple equilibria, so traditional methods of stability investigation, defined for systems with single equilibrium are no good here. In the paper traditional Popov method of a priori integral indices is combined with two special techniques: Leonov’s nonlocal reduction method and the Bakaev-Guzh procedure. As a result new frequency–algebraic stability criteria are established, yielding tightened estimates of stability domains in the space of the system’s parameters.

Saturation of Energy Levels of the Hydrogen Atom in Strong Magnetic Field

We demonstrate that the finiteness of the limiting values of the lower energy levels of a hydrogen atom under an unrestricted growth of the magnetic field, into which this atom is embedded, is achieved already when the vacuum polarization (VP) is calculated in the magnetic field within the approximation of the local action of Euler–Heisenberg. We find that the mechanism for this saturation is different from the one acting, when VP is calculated via the Feynman diagram in the Furry picture. We study the effective potential that appears when the adiabatic (diagonal) approximation is exploited for solving the Schrödinger equation for the longitudinal degree of freedom of the electron on the lowest Landau level in the atom. We find that the (effective) potential of a point-like charge remains nonsingular thanks to the growing screening provided by VP. The regularizing length turns out to be α/3π¯λC, where ¯λC is the electron Compton length. The family of effective potentials, labeled by growing values of the magnetic field condenses towards a certain limiting, magnetic-field-independent potential-distance curve. The limiting values of even ground-state energies are determined for four magnetic quantum numbers using the Karnakov–Popov method.

A new Popov's subgradient extragradient method for two classes of equilibrium programming in a real Hilbert space

In this paper, we proposed two different methods for solving pseudomonotone and strongly pseudomonotone equilibrium problems. We can examine these methods as an extension and improvement of the Popov's extragradient method. We replaced the second minimization problem onto a closed convex set in the Popov's extragradient method, with a half-space minimization problem that is updated on each iteration and also formulates a useful method for determining the appropriate stepsize on each iteration. The weak convergence theorem of the first method and strong convergence theorem for the second method is well-established based on a standard assumption on a cost bifunction. We also consider various numerical examples to support our well-established convergence results, and we can see that the proposed methods depict a significant improvement in terms of the number of iterations and execution time.

New methods of local medical treatment of purulent wounds

Purpose of the study. To study experimental model of purulent wounds efficiency of the combined effects of benzalkonium chloride and metronidazole immobilized on various bases.Materials and methods. The material was in vitro studies and experimental animals (Wistar rats), which was modeled a purulent wound and then divided into 3 groups according to the treatment method with the three studied combinations, each of which contained benzalkonium chloride and metronidazole, the combinations differed in bases, which were polyethylene oxide or sodium salt of carboxymethylcellulose, or polymethylsiloxane polyhydrate. Research methods: in an in vitro experiment, growth retardation zones were determined for the most common pathogens of wound infection using the standard disc method. In an in vivo experiment the healing process was evaluated by Popov's planimetric method, the contamination of the wounds was studied by sowing the biopsy of wounds on nutrient media with subsequent counting of the grown up colonies. The data were processed statistically, the reliability of the differences was assessed by the Kruskal-Wallis test.Results. All test combinations showed high growth retardation areas for all test strains of microorganisms. Objectively, the highest results were observed with a combination of polyethylene oxide (Staphylococcus aureus 30 (29; 30), Bacillus cereus 27 (27; 28), Escherichia coli 20.5 (20; 21), Proteus vulgaris 21.5 (20; 22), Pseudomonas aeruginosa 17 (16; 17), Candida albicans 25.5 (25; 26)). In determining the healing rate, it was noted that the maximum values in the groups when using combinations based on the sodium salt of carboxymethylcellulose and polymethylsiloxane polyhydrate occurred on day 1–3 (29.6 (27.6; 31) and 20.2 (18.8; 24.2) mm2/day, respectively), and in the group using a combination on polyethylene oxide — for 3–5 days (20.6 (17.3; 22.8) mm2/day).Conclusion. Our studies have shown the high antimicrobial activity of all the developed combinations for all the strains of microorganisms studied. It is also possible to recommend combinations on polyethylene oxide and sodium salt of carboxymethylcellulose for further preclinical studies at all times of treatment, and a combination based on polymethylsiloxane polyhydrate only in the first phase of the wound process.

Development of a design load patch for the consideration of ice loads

ABSTRACT Ships operating in ice-covered waters may experience structural damage due to ice-induced loads. This can occur even though the ship structure is designed according to rules considering ice loading. The basis of these design rules can be empirical, e.g. measured loads from full-scale trials and observed damages or energy based, which is known as the Popov Method. The rules propose to apply the design ice load as a uniformly loaded rectangular pressure patch. This simplification is, however, not in line with spatial variations of local ice loads and does not account for high pressure zones directly. Therefore, this paper proposes a method for identifying a representative ice load distribution under consideration of local pressure maxima based on a spatial and temporal varying ice load sequence. This identified load is applied to an example structure and the response is compared to the response using a current rule-based patch load. .

Analysis of a Collision-Energy-Based Method for the Prediction of Ice Loading on Ships

Ships designed for operation in Polar waters must be approved in accordance with the International Code for Ships Operating in Polar Waters (Polar Code), adopted by the International Maritime Organization (IMO). To account for ice loading on ships, the Polar Code includes references to the International Association of Classification Societies’ (IACS) Polar Class (PC) standards. For the determination of design ice loads, the PC standards rely upon a method applying the principle of the conservation of momentum and energy in collisions. The method, which is known as the Popov Method, is fundamentally analytical, but because the ship–ice interaction process is complex and not fully understood, its practical applications, including the PC standards, rely upon multiple assumptions. In this study, to help naval architects make better-informed decisions in the design of Arctic ships, and to support progress towards goal-based design, we analyse the effect of the assumptions behind the Popov Method by comparing ice load predictions, calculated by the Method with corresponding full-scale ice load measurements. Our findings indicate that assumptions concerning the modelling of the ship–ice collision scenario, the ship–ice contact geometry and the ice conditions, among others, significantly affect how well the ice load prediction agrees with the measurements.

Semi-empirical methods for estimation/prediction of metal matrices behavior during thermochemical processing

Abstract Series of solutions for estimations/predictions of the behavior of metal matrices during thermochemical treatments are described on basis on minimal number of experimental results under relatively random chosen processing conditions. Three methods were considered: Popov, Kazeev and Baram. The Popov method is based on the solutions of the second differential equation of diffusion (Fick’s second law), obtained by analytical and criterial solving under third boundary conditions; in this way, the kinetic parameters D, h*, and k are estimated. The Kazeev method is based on the correct hypothesis that besides the atomic diffusion takes place also other phenomena/interactions in the metallic matrix. All these complex processes can be described by specific equations whose solutions allow to determine certain parameters which change continuously during the diffusion process. The Baram method considers the generalized equation of kinetics of heterogeneous chemical reactions. This was resulted by taking into account the law of mass action and the phenomenological dependence of change over time of the inter-phases separation surfaces positions in solid materials subjected to thermochemical processing. It was thus possible to describe the phenomena occurred during thermochemical processing. The algorithms for the utilization of these methods are exemplified by experimental data resulted from the gaseous nitriding of the pure technical iron (ARMCO).

Quantized gauged massless Rarita-Schwinger fields

We study the quantization of a minimally gauged massless Rarita--Schwinger field, by both the Dirac bracket and functional integral methods. The Dirac bracket approach in the covariant radiation gauge leads to an anticommutator that has a nonsingular limit as gauge fields approach zero, is manifestly positive semidefinite, and is Lorentz invariant. The constraints also have the form needed to apply the Faddeev--Popov method for deriving a functional integral, using the same constrained Hamiltonian and inverse constraint matrix that appear in the Dirac bracket approach.

Generalized Faddeev–Popov method for a deformed supersymmetric Yang–Mills theory

In this paper, we will study the deformation of a three dimensional N=2 supersymmetry gauge theory. We will deform this theory by imposing non-anticommutativity. This will break the supersymmetry of the theory from N=2 supersymmetry to N=1 supersymmetry. We will address the problem that occurs in the Landau gauge due to the existence of multiple solutions to the gauge fixing condition. This problem will be addressed using a formalism that has been motivated by topological field theories. Finally, we will study the extended BRST symmetry that occurs in this theory.

Asymptotic Properties of Nonlinear Singularly Perturbed Volterra Equations

In this paper we examine asymptotic behavior of dynamics systems in the Lur'e form, that can be decomposed into feedback interconnection of a linear part and a time-varying nonlinearity. The linear part obeys a singularly perturbed integro-differential Volterra equation of the convolutional type, whereas the nonlinearity is sector-bounded. For such a system we propose frequency-domain criteria of the stability and the “gradient-like” behavior, i.e. the attraction of any solution to one of equilibria points. Those criteria, based on the V.M. Popov's method of a priori integral indices, are uniform with respect to the small parameter.

The (IR-)relevance of the Gribov ambiguity in [formula omitted] gauge theories with fundamental Higgs matter

It is well accepted that dealing with the Gribov ambiguity has a major impact on correlation functions in gauge-fixed Yang–Mills theories, in particular in the low momentum regime where standard perturbation theory based on the Faddeev–Popov approach fails. Recent results, derived from functional tools (Dyson–Schwinger equations or exact RG) or the effective Gribov–Zwanziger action method, pointed towards e.g. gauge boson correlation functions that are not compatible with the properties of observable degrees of freedom. Although such an observation is a welcome feature for gauge theories exhibiting confinement, it would be a discomfort for gauge theories supplemented with Higgs fields, cf. the experimental success of the electroweak model based on a SU(2)×U(1) gauge group. The purpose of this short note is to assure that the effective action resolution to the Gribov ambiguity reduces to the standard Faddeev–Popov method in the perturbative regime of sufficiently small coupling/large Higgs condensate, thereby not compromising the physical particle spectrum of massive gauge bosons and a massless photon for the SU(2)×U(1) gauge–Higgs model. The closer the theory gets to the limit of vanishing Higgs condensate, the more the Gribov problem resurfaces with all its consequences. We give some speculations w.r.t. the Fradkin–Shenker insights about the phase diagram.

General Formalism for the BRST Symmetry

In this paper we will discuss Faddeev—Popov method for gauge theories with a general form of gauge symmetry in an abstract way. We will then develope a general formalism for dealing with the BRST symmetry. This formalism will make it possible to analyse the BRST symmetry for any theory.

Physical state condition in quantum general relativity as a consequence of BRST symmetry

Quantization of systems with constraints can be carried out with several methods. In the Dirac formulation the classical generators of gauge transformations are required to annihilate physical quantum states to ensure their gauge invariance. Carrying on BRST symmetry it is possible to get a condition on physical states which, different from the Dirac method, requires them to be invariant under the BRST transformation. Employing this method for the action of general relativity expressed in terms of the spin connection and tetrad fields with path integral methods, we construct the generator of the BRST transformation associated with the underlying local Lorentz symmetry of the theory and write a physical state condition following from BRST invariance. This derivation is based on the general results on the dependence of the effective action used in path integrals and consequently of Green's functions on the gauge-fixing functionals used in the DeWitt–Faddeev–Popov method. The condition we gain differs from the one obtained within Ashtekar's canonical formulation, showing how we recover the latter only by a suitable choice of the gauge-fixing functionals. Finally we discuss how it should be possible to obtain all of the requested physical state conditions associated with all the underlying gauge symmetries of the classical theory using our approach.

ARITHMETICAL RESULTS ON CERTAIN q-SERIES, I

Entire transcendental solutions of certain mth order linear q-difference equations with polynomial coefficients are considered. The aim of this paper is to give, under appropriate arithmetical conditions, lower bounds for the dimension of the K-vector space generated by 1 and the values of these solutions at m successive powers of q, where K is the rational or an imaginary quadratic number field. The main ingredients of the proofs are, first, Nesterenko's dimension estimate and its various generalizations, and secondly, Popov's method (in Töpfer's version) for the asymptotic evaluation of certain complex integrals.

Regimes pluviais, estação chuvosa e probabilidade de ocorrência de veranicos no Estado do Ceará

Um método de regionalização pluvial proposto foi aplicado a dados pluviais mensais de 175 postos do Estado do Ceará e identificou três grupos pluvialmente homogêneos: grupo 1 (105 postos) predominantemente semi-árido, grupo 2 (56 postos) e grupo 3 (14 postos). Compararam-se esses grupos com as sete regiões climáticas reconhecidas pela Fundação Cearense de Meteorologia e Recursos Hídricos (FUNCEME) e constatou-se que o método foi capaz de identificar as regiões Ibiapaba e Cariri, bem como a área composta pelas regiões Centro-Leste e Centro-Oeste e a área formada pelas regiões Litoral Norte e Litoral Sul. Identificou-se também, a estação chuvosa (EC) em cada posto do Estado do Ceará, mediante a utilização do método de Frère & Popov (1979), e constatou-se que em 143 (81,71%) dos 175 postos a EC ocorre de janeiro a maio e que em 69 (65,71%) dos 105 postos do grupo 1, ela ocorre de fevereiro a maio. Verificou-se a probabilidade de ocorrência de veranicos nos três decêndios (1 a 10, 11 a 20 e 21 ao último dia do mês) dos meses de janeiro a junho nos 105 postos do grupo 1. Observou-se, ainda, probabilidades grupais médias de 51, 39 e 25%, respectivamente no primeiro, segundo e terceiro decêndio de janeiro; 20, 18 e 21% em fevereiro; 10, 7 e 6% em março; 9, 10 e 11% em abril; 25, 25 e 28% em maio e de 38, 43 e 51% em junho.

Popov's Method and its Subsequent Development

A simple proof of the quadratic criterion for absolute stability is given for the nondegenerate case. A similar result was proved earlier (for both degenerate and nondegenerate cases) by the author (1967) by using completely different methods. The proof given has some similarities with the ideas used by Popov (1959-1961) in the proof of his now widely known frequency-domain criterion of absolute stability. The new frequency-domain criterion of absolute stability is given for the system with the periodic coefficient. One illustrative example is considered.

Absolute Stability for Neutral Differential Systems

This paper is aimed to show that Popov's method for absolute stability, based on the frequency domain approach and the use of Volterra integral equations, can be applied to the case of neutral differential systems of the form (1). The operator A appearing in (1) is formally given by (2), and it is acting on various function spaces under hypothesis H 1 and H 2 below. The absolute stability for the system (1), (8) is obtained from the corresponding integral equation (15).

The path integral quantization and the construction of theS-matrix operator in the Abelian and non-Abelian Chern - Simons theories

The covariant path integral quantization of the theory of the scalar and spinor fields interacting through the Abelian and non-Abelian Chern - Simons gauge fields in 2 + 1 dimensions is carried out using the De Witt - Fadeev - Popov method. The mathematical ill-definiteness of the path integral of theories with pure Chern - Simons' fields is remedied by the introduction of the Maxwell or Maxwell-type (in the non-Abelian case) terms, which make the resulting theories super-renormalizable and guarantees their gauge-invariant regularization and renormalization. The generating functionals are constructed and shown to be the same as those of quantum electrodynamics (quantum chromodynamics) in 2 + 1 dimensions with the substitution of the Chern - Simons propagator for the photon (gluon) propagator. By constructing the propagator in the general case, the existence of two limits; pure Chern - Simons and quantum electrodynamics (quantum chromodynamics) after renormalization is demonstrated.