106 research outputs found

    Spontaneous polarization and piezoelectricity in boron nitride nanotubes

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    Ab initio calculations of the spontaneous polarization and piezoelectric properties of boron nitride nanotubes show that they are excellent piezoelectric systems with response values larger than those of piezoelectric polymers. The intrinsic chiral symmetry of the nanotubes induces an exact cancellation of the total spontaneous polarization in ideal, isolated nanotubes of arbitrary indices. Breaking of this symmetry by inter-tube interaction or elastic deformations induces spontaneous polarization comparable to those of wurtzite semiconductors.Comment: 5 pages in PRB double column format, 3 figure

    Tight-binding study of structure and vibrations of amorphous silicon

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    We present a tight-binding calculation that, for the first time, accurately describes the structural, vibrational and elastic properties of amorphous silicon. We compute the interatomic force constants and find an unphysical feature of the Stillinger-Weber empirical potential that correlates with a much noted error in the radial distribution function associated with that potential. We also find that the intrinsic first peak of the radial distribution function is asymmetric, contrary to usual assumptions made in the analysis of diffraction data. We use our results for the normal mode frequencies and polarization vectors to obtain the zero-point broadening effect on the radial distribution function, enabling us to directly compare theory and a high resolution x-ray diffraction experiment

    Predicting polarization enhancement in multicomponent ferroelectric superlattices

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    Ab initio calculations are utilized as an input to develop a simple model of polarization in epitaxial short-period CaTiO3/SrTiO3/BaTiO3 superlattices grown on a SrTiO3 substrate. The model is then combined with a genetic algorithm technique to optimize the arrangement of individual CaTiO3, SrTiO3 and BaTiO3 layers in a superlattice, predicting structures with the highest possible polarization and a low in-plane lattice constant mismatch with the substrate. This modelling procedure can be applied to a wide range of layered perovskite-oxide nanostructures providing guidance for experimental development of nanoelectromechanical devices with substantially improved polar properties.Comment: 4 pages, submitted to PR

    Liquid-liquid phase transition in Stillinger-Weber silicon

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    It was recently demonstrated that the Stillinger-Weber silicon undergoes a liquid-liquid first-order phase transition deep into the supercooled region (Sastry and Angell, Nature Materials 2, 739 (2003)). Here we study the effects of perturbations on this phase transition. We show that the order of the liquid-liquid transition changes with negative pressure. We also find that the liquid-liquid transition disappears when the three-body term of the potential is strengthened by as little as 5 %. This implies that the details of the potential could affect strongly the nature and even the existence of the liquid-liquid phase.Comment: 13 page

    Π‘ΠΌΠ΅Ρ‰Π΅Π½ΠΈΠ΅ уровня значимости ΠΈ мощности критСрия ΠΏΡ€ΠΈ ΠΊΠΎΠ½Π΅Ρ‡Π½ΠΎΠΉ ΠΊΡ€ΡƒΡ‚ΠΈΠ·Π½Π΅ ΠΏΠ΅Ρ€Π΅Ρ…ΠΎΠ΄Π½ΠΎΠΉ характСристики

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    Π˜ΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½Ρ‹ смСщСния уровня значимости ΠΈ мощности критСрия, ΠΊΠΎΠ³Π΄Π° ΠΏΡ€ΠΈ ΠΏΡ€ΠΎΠ²Π΅Ρ€ΠΊΠ΅ статистичСских Π³ΠΈΠΏΠΎΡ‚Π΅Π· с использованиСм ΠΏΡ€Π°Π²ΠΈΠ»Π° НСймана – ΠŸΠΈΡ€ΡΠΎΠ½Π° Π² качСствС ΠΌΠΎΠ΄Π΅Π»ΠΈ ΠΏΠ΅Ρ€Π΅Ρ…ΠΎΠ΄Π½ΠΎΠΉ характСристики логичСской схСмы ΠΈΡΠΏΠΎΠ»ΡŒΠ·ΡƒΠ΅Ρ‚ΡΡ простая функция ошибок. БмСщСния рассчитаны для рэлССвских Ρ„ΡƒΠ½ΠΊΡ†ΠΈΠΉ распрСдСлСния. Π’ качСствС ΠΎΠ΄Π½ΠΎΠ³ΠΎ ΠΈΠ· Π²Π°Ρ€ΡŒΠΈΡ€ΡƒΠ΅ΠΌΡ‹Ρ… ΠΏΠ°Ρ€Π°ΠΌΠ΅Ρ‚Ρ€ΠΎΠ² ΠΈΡΠΏΠΎΠ»ΡŒΠ·ΡƒΠ΅Ρ‚ΡΡ ΠΎΠ±ΠΎΠ±Ρ‰Π΅Π½Π½ΠΎΠ΅ ΠΎΡ‚Π½ΠΎΡˆΠ΅Π½ΠΈΠ΅ сигнал-ΠΏΠΎΠΌΠ΅Ρ…Π°. Нахмансон Π“. Π‘., ΠšΠΎΡΡ‚Π΅Π½Π½ΠΈΠΊΠΎΠ² Π’. Π‘., Ницак Π”. А. Π‘ΠΌΠ΅Ρ‰Π΅Π½ΠΈΠ΅ уровня значимости ΠΈ мощности критСрия ΠΏΡ€ΠΈ ΠΊΠΎΠ½Π΅Ρ‡Π½ΠΎΠΉ ΠΊΡ€ΡƒΡ‚ΠΈΠ·Π½Π΅ ΠΏΠ΅Ρ€Π΅Ρ…ΠΎΠ΄Π½ΠΎΠΉ характСристики. Ural Radio Engineering Journal. 2022;6(4):378–389. DOI: 10.15826/urej.2022.6.4.002

    Raman Study of Oxygen Reduced and Re-Oxidized Strontium Titanate

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    We report Raman study of oxygen-reduced single crystal strontium titanate. Oxygen reduction leads to the appearance of the forbidden first order Raman peaks, as well as new spectral features attributed to the local vibrational modes associated with oxygen vacancies. This assignment is supported by ab initio calculations of phonon modes in SrTiO3 with introduced oxygen vacancies. Raman studies of re-oxidized samples show the same spectra as the initial single crystals. Comparison of Raman spectra of SrTiO3 thin films and reduced SrTiO3 single crystals demonstrates the importance of other factors such as polar grain boundaries in the lattice dynamical behavior of thin films

    ΠžΠ±Π½Π°Ρ€ΡƒΠΆΠ΅Π½ΠΈΠ΅ Ρ‚Ρ€Π°Π΅ΠΊΡ‚ΠΎΡ€ΠΈΠΉ двиТущихся прямолинСйно Π²ΠΎΠ·Π΄ΡƒΡˆΠ½Ρ‹Ρ… Ρ†Π΅Π»Π΅ΠΉ ΠΏΡ€ΠΈ Π²Ρ‚ΠΎΡ€ΠΈΡ‡Π½ΠΎΠΉ ΠΎΠ±Ρ€Π°Π±ΠΎΡ‚ΠΊΠ΅ Ρ€Π°Π΄ΠΈΠΎΠ»ΠΎΠΊΠ°Ρ†ΠΈΠΎΠ½Π½ΠΎΠΉ ΠΈΠ½Ρ„ΠΎΡ€ΠΌΠ°Ρ†ΠΈΠΈ

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    Introduction. The primary functions of secondary processing of radar information are to detect and maintain the trajectories of air targets (AT). The AT trajectory detection can be characterised by the probability of detecting trajectory and average autocapture time. When the target moves, its distance from the radar station changes, leading to a change in the signal/noise ratio and the probability of detecting AT.Aim. To assess the impact of a change in the probability of detection of a straight and evenly moving target at consecutive time intervals of radar observation upon the characteristics of trajectory detection during secondary processing of radar information.Methods and materials. The research aim was achieved using the methods of mathematical statistics, including verification of statistical hypotheses, assessment of distribution parameters and theory of perturbations by small parameters. The ratio of the distance travelled by the AT during the review period to the target range at the initial moment of its detection was chosen as a perturbation parameter.Results. Analytical expressions were established for the probability of detecting a straight-moving AT and the probability of detecting the trajectory of its movement at interval multiples during the study period. The study illustrated the probability of detecting AT moving away from radar by means of consistent radar observations with reduced signal/noise ratios and angles between the velocity vector and the AT vector radius relative to the radar. The increase in AT speed which causes the z parameter to change from 0.01 to 0.07 reduces the probability of AT detection from 0.727 to 0.52 and leads to a corresponding change in the probability of detecting the trajectory. If the observation time is reduced by one time interval, the probability of detecting the trajectory is from 0.03 to 0.04…0.07 for signal/noise 40 ratio and from 0.06 to 0.08…0.11 for signal/noise 25 ratio (with the probability of false alarm 10–4 ).Conclusion. The resulting expressions allow for the calculation of directly moving AT trajectory detection, considering changes in the probability of detecting targets in successive time intervals of radar observations.Π’Π²Π΅Π΄Π΅Π½ΠΈΠ΅. ΠžΡΠ½ΠΎΠ²Π½Ρ‹ΠΌΠΈ Π·Π°Π΄Π°Ρ‡Π°ΠΌΠΈ Π²Ρ‚ΠΎΡ€ΠΈΡ‡Π½ΠΎΠΉ ΠΎΠ±Ρ€Π°Π±ΠΎΡ‚ΠΊΠΈ Ρ€Π°Π΄ΠΈΠΎΠ»ΠΎΠΊΠ°Ρ†ΠΈΠΎΠ½Π½ΠΎΠΉ ΠΈΠ½Ρ„ΠΎΡ€ΠΌΠ°Ρ†ΠΈΠΈ ΡΠ²Π»ΡΡŽΡ‚ΡΡ ΠΎΠ±Π½Π°Ρ€ΡƒΠΆΠ΅Π½ΠΈΠ΅ ΠΈ сопровоТдСниС Ρ‚Ρ€Π°Π΅ΠΊΡ‚ΠΎΡ€ΠΈΠΉ двиТСния Π²ΠΎΠ·Π΄ΡƒΡˆΠ½Ρ‹Ρ… Ρ†Π΅Π»Π΅ΠΉ (Π’Π¦). ΠŸΡ€ΠΈ этом процСсс обнаруТСния Ρ‚Ρ€Π°Π΅ΠΊΡ‚ΠΎΡ€ΠΈΠΉ двиТСния Π’Π¦ принято Ρ…Π°Ρ€Π°ΠΊΡ‚Π΅Ρ€ΠΈΠ·ΠΎΠ²Π°Ρ‚ΡŒ вСроятностями ΠΈΡ… обнаруТСния ΠΈ срСдним Π²Ρ€Π΅ΠΌΠ΅Π½Π΅ΠΌ ΠΈΡ… Π°Π²Ρ‚ΠΎΠ·Π°Ρ…Π²Π°Ρ‚Π°. ΠŸΡ€ΠΈ Π΄Π²ΠΈΠΆΠ΅Π½ΠΈΠΈ Ρ†Π΅Π»ΠΈ Π΅Π΅ Π΄Π°Π»ΡŒΠ½ΠΎΡΡ‚ΡŒ ΠΎΡ‚ Ρ€Π°Π΄ΠΈΠΎΠ»ΠΎΠΊΠ°Ρ†ΠΈΠΎΠ½Π½ΠΎΠΉ станции (Π Π›Π‘) измСняСтся, Ρ‡Ρ‚ΠΎ ΠΏΡ€ΠΈΠ²ΠΎΠ΄ΠΈΡ‚ ΠΊ измСнСнию ΠΎΡ‚Π½ΠΎΡˆΠ΅Π½ΠΈΡ сигнал/ΡˆΡƒΠΌ ΠΈ вСроятности обнаруТСния Π’Π¦.ЦСль Ρ€Π°Π±ΠΎΡ‚Ρ‹. ΠžΡ†Π΅Π½ΠΊΠ° влияния измСнСния вСроятности обнаруТСния прямолинСйно двиТущСйся Ρ†Π΅Π»ΠΈ ΠΏΡ€ΠΈ Ρ€Π°Π΄ΠΈΠΎΠ»ΠΎΠΊΠ°Ρ†ΠΈΠΎΠ½Π½Ρ‹Ρ… Π½Π°Π±Π»ΡŽΠ΄Π΅Π½ΠΈΡΡ… Π½Π° характСристики обнаруТСния Ρ‚Ρ€Π°Π΅ΠΊΡ‚ΠΎΡ€ΠΈΠΈ Π΅Π΅ двиТСния ΠΏΡ€ΠΈ Π²Ρ‚ΠΎΡ€ΠΈΡ‡Π½ΠΎΠΉ ΠΎΠ±Ρ€Π°Π±ΠΎΡ‚ΠΊΠ΅ Ρ€Π°Π΄ΠΈΠΎΠ»ΠΎΠΊΠ°Ρ†ΠΈΠΎΠ½Π½ΠΎΠΉ ΠΈΠ½Ρ„ΠΎΡ€ΠΌΠ°Ρ†ΠΈΠΈ.ΠœΠ΅Ρ‚ΠΎΠ΄Ρ‹. Π˜ΡΠΏΠΎΠ»ΡŒΠ·ΡƒΡŽΡ‚ΡΡ ΠΌΠ΅Ρ‚ΠΎΠ΄Ρ‹ матСматичСской статистики: ΠΏΡ€ΠΎΠ²Π΅Ρ€ΠΊΠ° статистичСских Π³ΠΈΠΏΠΎΡ‚Π΅Π·, ΠΎΡ†Π΅Π½ΠΊΠ° ΠΏΠ°Ρ€Π°ΠΌΠ΅Ρ‚Ρ€ΠΎΠ² распрСдСлСний ΠΈ тСория Π²ΠΎΠ·ΠΌΡƒΡ‰Π΅Π½ΠΈΠΉ ΠΏΠΎ ΠΌΠ°Π»ΠΎΠΌΡƒ ΠΏΠ°Ρ€Π°ΠΌΠ΅Ρ‚Ρ€Ρƒ. Π’ качСствС Π²ΠΎΠ·ΠΌΡƒΡ‰Π°ΡŽΡ‰Π΅Π³ΠΎ ΠΏΠ°Ρ€Π°ΠΌΠ΅Ρ‚Ρ€Π° Π²Ρ‹Π±Ρ€Π°Π½ΠΎ ΠΎΡ‚Π½ΠΎΡˆΠ΅Π½ΠΈΠ΅ расстояния, ΠΏΡ€ΠΎΡ…ΠΎΠ΄ΠΈΠΌΠΎΠ³ΠΎ Π’Π¦ Π·Π° ΠΏΠ΅Ρ€ΠΈΠΎΠ΄ ΠΎΠ±Π·ΠΎΡ€Π°, ΠΊ Π΄Π°Π»ΡŒΠ½ΠΎΡΡ‚ΠΈ Ρ†Π΅Π»ΠΈ Π² Π½Π°Ρ‡Π°Π»ΡŒΠ½Ρ‹ΠΉ ΠΌΠΎΠΌΠ΅Π½Ρ‚ Π΅Π΅ обнаруТСния.Π Π΅Π·ΡƒΠ»ΡŒΡ‚Π°Ρ‚Ρ‹. ΠŸΠΎΠ»ΡƒΡ‡Π΅Π½Ρ‹ аналитичСскиС выраТСния для вСроятности обнаруТСния прямолинСйно двиТущСйся Π’Π¦ ΠΈ вСроятности обнаруТСния Ρ‚Ρ€Π°Π΅ΠΊΡ‚ΠΎΡ€ΠΈΠΈ Π΅Π΅ двиТСния Π½Π° ΠΈΠ½Ρ‚Π΅Ρ€Π²Π°Π»Π°Ρ…, ΠΊΡ€Π°Ρ‚Π½Ρ‹Ρ… ΠΏΠ΅Ρ€ΠΈΠΎΠ΄Ρƒ ΠΎΠ±Π·ΠΎΡ€Π°. ΠŸΡ€ΠΎΠΈΠ»Π»ΡŽΡΡ‚Ρ€ΠΈΡ€ΠΎΠ²Π°Π½ΠΎ ΡƒΠΌΠ΅Π½ΡŒΡˆΠ΅Π½ΠΈΠ΅ вСроятности обнаруТСния Π’Π¦, ΡƒΠ΄Π°Π»ΡΡŽΡ‰Π΅ΠΉΡΡ ΠΎΡ‚ Π Π›Π‘, ΠΏΡ€ΠΈ ΠΏΠΎΡΠ»Π΅Π΄ΠΎΠ²Π°Ρ‚Π΅Π»ΡŒΠ½Ρ‹Ρ… Ρ€Π°Π΄ΠΈΠΎΠ»ΠΎΠΊΠ°Ρ†ΠΈΠΎΠ½Π½Ρ‹Ρ… Π½Π°Π±Π»ΡŽΠ΄Π΅Π½ΠΈΡΡ… с ΡƒΠΌΠ΅Π½ΡŒΡˆΠ΅Π½ΠΈΠ΅ΠΌ ΠΎΡ‚Π½ΠΎΡˆΠ΅Π½ΠΈΠΉ сигнал/ΡˆΡƒΠΌ ΠΈ ΡƒΠ³Π»Π° ΠΌΠ΅ΠΆΠ΄Ρƒ Π²Π΅ΠΊΡ‚ΠΎΡ€ΠΎΠΌ скорости ΠΈ радиусом-Π²Π΅ΠΊΡ‚ΠΎΡ€ΠΎΠΌ Π’Π¦ ΠΎΡ‚Π½ΠΎΡΠΈΡ‚Π΅Π»ΡŒΠ½ΠΎ Π Π›Π‘. Π£Π²Π΅Π»ΠΈΡ‡Π΅Π½ΠΈΠ΅ скорости Π’Π¦, Π²Ρ‹Π·Ρ‹Π²Π°ΡŽΡ‰Π΅Π΅ ΠΈΠ·ΠΌΠ΅Π½Π΅Π½ΠΈΠ΅ ΠΏΠ°Ρ€Π°ΠΌΠ΅Ρ‚Ρ€Π° z с 0.01 Π΄ΠΎ 0.07, ΠΏΡ€ΠΈΠ²ΠΎΠ΄ΠΈΡ‚ ΠΊ ΡƒΠΌΠ΅Π½ΡŒΡˆΠ΅Π½ΠΈΡŽ вСроятности обнаруТСния Π’Π¦ с 0.727 Π΄ΠΎ 0.52 ΠΈ ΠΊ ΡΠΎΠΎΡ‚Π²Π΅Ρ‚ΡΡ‚Π²ΡƒΡŽΡ‰Π΅ΠΌΡƒ измСнСнию вСроятности обнаруТСния Ρ‚Ρ€Π°Π΅ΠΊΡ‚ΠΎΡ€ΠΈΠΈ. ΠŸΡ€ΠΈ сокращСнии Π²Ρ€Π΅ΠΌΠ΅Π½ΠΈ наблюдСния Π½Π° ΠΎΠ΄ΠΈΠ½ Π²Ρ€Π΅ΠΌΠ΅Π½Π½ΠΎΠΉ ΠΈΠ½Ρ‚Π΅Ρ€Π²Π°Π» ΡƒΠΌΠ΅Π½ΡŒΡˆΠ΅Π½ΠΈΠ΅ вСроятности обнаруТСния Ρ‚Ρ€Π°Π΅ΠΊΡ‚ΠΎΡ€ΠΈΠΈ составляСт ΠΎΡ‚ 0.03 Π΄ΠΎ 0.04...0.07 для ΠΎΡ‚Π½ΠΎΡˆΠ΅Π½ΠΈΡ сигнал/ΡˆΡƒΠΌ 40 ΠΈ ΠΎΡ‚ 0.06 Π΄ΠΎ 0.08...0.11 для ΠΎΡ‚Π½ΠΎΡˆΠ΅Π½ΠΈΡ сигнал/ΡˆΡƒΠΌ 25 (ΠΏΡ€ΠΈ вСроятности Π»ΠΎΠΆΠ½ΠΎΠΉ Ρ‚Ρ€Π΅Π²ΠΎΠ³ΠΈ 10–4 ).Π—Π°ΠΊΠ»ΡŽΡ‡Π΅Π½ΠΈΠ΅. ΠŸΠΎΠ»ΡƒΡ‡Π΅Π½Π½Ρ‹Π΅ выраТСния ΠΏΠΎΠ·Π²ΠΎΠ»ΡΡŽΡ‚ Ρ€Π°ΡΡΡ‡ΠΈΡ‚Ρ‹Π²Π°Ρ‚ΡŒ характСристики обнаруТСния Ρ‚Ρ€Π°Π΅ΠΊΡ‚ΠΎΡ€ΠΈΠΉ Π²ΠΎΠ·Π΄ΡƒΡˆΠ½Ρ‹Ρ… Ρ†Π΅Π»Π΅ΠΉ, двиТущихся прямолинСйно, с ΡƒΡ‡Π΅Ρ‚ΠΎΠΌ ΠΈΠ·ΠΌΠ΅Π½Π΅Π½ΠΈΠΉ вСроятностСй обнаруТСния Ρ†Π΅Π»Π΅ΠΉ Π² ΠΏΠΎΡΠ»Π΅Π΄ΠΎΠ²Π°Ρ‚Π΅Π»ΡŒΠ½Ρ‹Ρ… Π²Ρ€Π΅ΠΌΠ΅Π½Π½Ρ‹Ρ… ΠΈΠ½Ρ‚Π΅Ρ€Π²Π°Π»Π°Ρ… ΠΎΠ±Π·ΠΎΡ€Π° Ρ€Π°Π΄ΠΈΠΎΠ»ΠΎΠΊΠ°Ρ†ΠΈΠΎΠ½Π½Ρ‹Ρ… наблюдСний

    Π­Ρ„Ρ„Π΅ΠΊΡ‚ΠΈΠ²Π½ΠΎΡΡ‚ΡŒ ΠΏΡ€ΠΈΠ΅ΠΌΠ° Ρ„Π°Π·ΠΎΠΌΠ°Π½ΠΈΠΏΡƒΠ»ΠΈΡ€ΠΎΠ²Π°Π½Π½ΠΎΠ³ΠΎ ΡˆΠΈΡ€ΠΎΠΊΠΎΠΏΠΎΠ»ΠΎΡΠ½ΠΎΠ³ΠΎ сигнала с ΠΊΠ²Π°Π΄Ρ€Π°Ρ‚ΡƒΡ€Π½ΠΎΠΉ Ρ„Π°Π·ΠΎΠ²ΠΎΠΉ модуляциСй Π² условиях Π²Π·Π°ΠΈΠΌΠ½Ρ‹Ρ… ΠΏΠΎΠΌΠ΅Ρ… ΠΈ Π²Π½ΡƒΡ‚Ρ€Π΅Π½Π½ΠΈΡ… ΡˆΡƒΠΌΠΎΠ² Π°ΠΏΠΏΠ°Ρ€Π°Ρ‚ΡƒΡ€Ρ‹

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    Receiving of the broadband phase modulated signal with quadrature phase-shift keying in case of multiple access in-terference and internal Gaussian noise has been considered. Bit error rate of broadband phase modulated signal with quadrature phase-shift keying has been obtained in case amplitudes of receiving signal and interferences have both regu-lar and fluctuating components. Broadband phase modulated signal bit error rate as a function of signal-to-noise ratio, signal-to-interference ratio, number of interferences and false positive probability has been analyzed.РассмотрСн ΠΏΡ€ΠΈΠ΅ΠΌ Ρ„Π°Π·ΠΎΠΌΠ°Π½ΠΈΠΏΡƒΠ»ΠΈΡ€ΠΎΠ²Π°Π½Π½Ρ‹Ρ… ΡˆΠΈΡ€ΠΎΠΊΠΎΠΏΠΎΠ»ΠΎΡΠ½Ρ‹Ρ… сигналов с ΠΊΠ²Π°Π΄Ρ€Π°Ρ‚ΡƒΡ€Π½ΠΎΠΉ модуляциСй Ρ„Π°Π· псСвдослучайными ΠΏΠΎΡΠ»Π΅Π΄ΠΎΠ²Π°Ρ‚Π΅Π»ΡŒΠ½ΠΎΡΡ‚ΡΠΌΠΈ Π² условиях Π²Π·Π°ΠΈΠΌΠ½Ρ‹Ρ… ΠΏΠΎΠΌΠ΅Ρ…, обусловлСнных многостанционным доступом, ΠΈ Π²Π½ΡƒΡ‚Ρ€Π΅Π½Π½ΠΈΡ… ΡˆΡƒΠΌΠΎΠ² Π°ΠΏΠΏΠ°Ρ€Π°Ρ‚ΡƒΡ€Ρ‹. ΠŸΠΎΠ»ΡƒΡ‡Π΅Π½Ρ‹ аналитичСскиС выраТСния для срСднСй вСроятности ошибки оцСнивания Π·Π½Π°Ρ‡Π΅Π½ΠΈΠΉ ΠΈΠ½Ρ„ΠΎΡ€ΠΌΠ°Ρ†ΠΈΠΎΠ½Π½Ρ‹Ρ… символов ΠΏΡ€ΠΈ ΠΏΡ€ΠΈΠ΅ΠΌΠ΅ сигналов со случайными Π½Π°Ρ‡Π°Π»ΡŒΠ½Ρ‹ΠΌΠΈ Ρ„Π°Π·Π°ΠΌΠΈ ΠΈ Π°ΠΌΠΏΠ»ΠΈΡ‚ΡƒΠ΄Π°ΠΌΠΈ, содСрТащими рСгулярныС ΠΈ Ρ„Π»ΡƒΠΊΡ‚ΡƒΠ°Ρ†ΠΈΠΎΠ½Π½Ρ‹Π΅ ΡΠΎΡΡ‚Π°Π²Π»ΡΡŽΡ‰ΠΈΠ΅, с ΡƒΡ‡Π΅Ρ‚ΠΎΠΌ Ρ„Π°Π·ΠΎΠ²Ρ‹Ρ… Ρ„Π»ΡƒΠΊΡ‚ΡƒΠ°Ρ†ΠΈΠΉ ΠΊΠ°Π½Π°Π»Π° синхронизации. ΠŸΡ€ΠΎΠ°Π½Π°Π»ΠΈΠ·ΠΈΡ€ΠΎΠ²Π°Π½Ρ‹ зависимости вСроятности ошибки ΠΎΡ‚ ΠΎΡ‚Π½ΠΎΡˆΠ΅Π½ΠΈΠΉ "сигнал/ΡˆΡƒΠΌ" ΠΈ "ΠΏΠΎΠΌΠ΅Ρ…Π°/ΡˆΡƒΠΌ", числа ΠΏΠΎΠΌΠ΅Ρ… ΠΈ качСства синхронизации
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