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## Periodic compensation of Polarization mode dispersion

Polarization mode dispersion is the effect of signal broadening in a fiber with birefringent disorder. The disorder, frozen into the fiber, is characterized by the so-called vector of birefringence (VB). In a linear medium a pulse broadens as the two principal states of polarization split. It is well-known that, under the action of short-correlated disorder, naturally present in fibers, the dispersion vector (DV), characterizing the split, performs a Brownian random walk. We discuss a strategy of passive (i.e., pulse-independent) control of the DV broadening. The suggestion is to pin (compensate) periodically or quasi-periodically the integral of VB to zero. As a result of the influence of pinning, the probability distribution function of the DV becomes statistically steady in the linear case. Moreover, pinning improves confinement of the pulse in the weakly nonlinear case. The theoretical findings are confirmed by numerical analysis

The conference “2021 Systems of signals generating and processing in the field of on board communications” is organized with technical sponsorship of Russian (Moscow) IEEE Circuits and Systems (CAS04) Chapter IEEE Region 8, Russian Section Chapter, MTT/ED and Institute of Radio and Information Systems Association (IRIS), Vienna, Austria. The conference featured invited researchers, educators, managers, and graduate students, whose research activity, case studies or best practices, are shedding light on the theory or practice of engineering, include modern digital transportation systems design and technical operation, radio waves propagation, transmitting, receiving and processing signals in television and radio broadcasting devices, information technologies in transport. The main areas of the conference “Systems of signals generating and processing in the field of on board communications” include modern digital transportation systems design and technical operation, radio waves propagation, transmitting, receiving and processing signals in television and radio broadcasting devices, information technologies in transport. FIELD OF INTEREST: Components, Circuits, Devices and Systems; General Topics for Engineers; Signal Processing and Analysis. Reports presented at the conference are grouped in 6 sections: 1. Antennas and Radio Waves Propagation. 2. Navigation and Mathematical Algorithms of an Object Space Orientation. 3. Radiofrequency Applications. 4. Wire and Optical Communication and Control Systems. 5. Intelligent Transport Systems (ITS): Sub-section 1: Use of digital ITS infrastructure in telematic control systems on urban passenger transport Sub-section 2: Peculiarities of data exchange in cooperative ITS Sub-section 3: Theoretical Aspects of Artificial Intelligence Systems Development for Transportation Engineering Sub-section 4: Test methods of motor vehicles integrated into an intelligent transport environment 6. Digital signal processing in on-board radio systems

The authors of [1, 2] suggested a model of information distortion by white noise. The present work discusses the asymptotic behavior of CRC error probabilities at low values of p, which is the probability of distortion of transferred information bits. On the basis of the theoretical results in two specific protocols—Е1 and ETSI EN 302307—as well as in the examples, the probability values for the error in recognizing the given packet as nondistorted in the presence of at least one distortion are assessed.

We study the value distributions for the control cyclic redundancy check (CRC) of length *k*, drawn at the data section of volume *n*. The behavior of CRC value distribution is examined at large *n* and fixed values of *k* (*k* = const, *n* → ∞). With the application of the character theory, we find the conditions of asymptomatic uniformity of the CRC distribution. The asymptomatic results can be applied during the assessment of errors of a series of protocols such as USB, X.25, HDLC, Bluetooth, Ethernet, etc.

The paper considers certain probability-theoretic models of packet mode-transferred information distortions. Attention is drawn mainly to distortions, including possible interferences influencing multiple transfer cycles. Distortions are modeled by a consequential impacts that are defined by dependent random variables. *K*-dimensioned values of CRC, respectively allow representation as a sum of *k*-dimensioned independent random variables.

In some cases it is possible to bring them to a sum of independent terms in a *k*-dimensioned vector space over a two-element field and, afterwards, apply to them existing limit theorems dealing with convergence to uniform distributions.

The paper discusses prospects for impacts stretching to *m* cycles of acquiring convergence conditions for CRC distribution as a sum of *m*-dependent terms or ones not interconnected to a non-homogeneous Markov chain.

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.

Let k be a field of characteristic zero, let G be a connected reductive algebraic group over k and let g be its Lie algebra. Let k(G), respectively, k(g), be the field of k- rational functions on G, respectively, g. The conjugation action of G on itself induces the adjoint action of G on g. We investigate the question whether or not the field extensions k(G)/k(G)^G and k(g)/k(g)^G are purely transcendental. We show that the answer is the same for k(G)/k(G)^G and k(g)/k(g)^G, and reduce the problem to the case where G is simple. For simple groups we show that the answer is positive if G is split of type A_n or C_n, and negative for groups of other types, except possibly G_2. A key ingredient in the proof of the negative result is a recent formula for the unramified Brauer group of a homogeneous space with connected stabilizers. As a byproduct of our investigation we give an affirmative answer to a question of Grothendieck about the existence of a rational section of the categorical quotient morphism for the conjugating action of G on itself.

Let G be a connected semisimple algebraic group over an algebraically closed field k. In 1965 Steinberg proved that if G is simply connected, then in G there exists a closed irreducible cross-section of the set of closures of regular conjugacy classes. We prove that in arbitrary G such a cross-section exists if and only if the universal covering isogeny Ĝ → G is bijective; this answers Grothendieck's question cited in the epigraph. In particular, for char k = 0, the converse to Steinberg's theorem holds. The existence of a cross-section in G implies, at least for char k = 0, that the algebra k[G]G of class functions on G is generated by rk G elements. We describe, for arbitrary G, a minimal generating set of k[G]G and that of the representation ring of G and answer two Grothendieck's questions on constructing generating sets of k[G]G. We prove the existence of a rational (i.e., local) section of the quotient morphism for arbitrary G and the existence of a rational cross-section in G (for char k = 0, this has been proved earlier); this answers the other question cited in the epigraph. We also prove that the existence of a rational section is equivalent to the existence of a rational W-equivariant map T- - - >G/T where T is a maximal torus of G and W the Weyl group.