145 research outputs found
ΠΠ΅ΡΠΎΠ΄ΠΈ Π΅ΠΊΠΎΠ½ΠΎΠΌΡΡΠ½ΠΈΡ Π΄ΠΎΡΠ»ΡΠ΄ΠΆΠ΅Π½Ρ Π²ΠΈΡΠΎΠ±Π½ΠΈΡΠΎ-Π³ΠΎΡΠΏΠΎΠ΄Π°ΡΡΡΠΊΠΎΡ Π΄ΡΡΠ»ΡΠ½ΠΎΡΡΡ ΠΏΡΠ΄ΠΏΡΠΈΡΠΌΡΡΠ² ΡΠ· Π²ΠΈΡΠΎΠ±Π½ΠΈΡΡΠ²Π° Π±ΡΠ΄ΡΠ²Π΅Π»ΡΠ½ΠΈΡ ΠΌΠ°ΡΠ΅ΡΡΠ°Π»ΡΠ²
Π£ ΡΡΠ°ΡΡΡ ΡΠΎΠ·Π³Π»ΡΠ½ΡΡΠΎ ΠΎΡΠ½ΠΎΠ²Π½Ρ ΡΡΡΠ°ΡΠ½Ρ ΠΏΡΠ΄Ρ
ΠΎΠ΄ΠΈ Π΄ΠΎ Π΄ΡΠ°Π³Π½ΠΎΡΡΠΈΠΊΠΈ ΠΏΡΠ΄ΠΏΡΠΈΡΠΌΡΡΠ² ΡΠ· Π²ΠΈΡΠΎΠ±Π½ΠΈΡΡΠ²Π° Π±ΡΠ΄ΡΠ²Π΅Π»ΡΠ½ΠΈΡ
ΠΌΠ°ΡΠ΅ΡΡΠ°Π»ΡΠ² Π· ΡΡΠ°Ρ
ΡΠ²Π°Π½Π½ΡΠΌ ΠΎΡΠΎΠ±Π»ΠΈΠ²ΠΎΡΡΠ΅ΠΉ Π³Π°Π»ΡΠ·Ρ ΡΡ
ΡΡΠ½ΠΊΡΡΠΎΠ½ΡΠ²Π°Π½Π½Ρ. ΠΠ° ΠΏΡΠ΄ΡΡΠ°Π²Ρ ΠΏΡΠΎΠ²Π΅Π΄Π΅Π½ΠΎΠ³ΠΎ Π°Π½Π°Π»ΡΠ·Ρ Π²ΠΈΠ·Π½Π°ΡΠ΅Π½ΠΎ ΠΎΡΠ½ΠΎΠ²Π½Ρ Π½Π°ΠΏΡΡΠΌΠΊΠΈ ΠΏΡΠΎΠ²Π΅Π΄Π΅Π½Π½Ρ Π΄ΡΠ°Π³Π½ΠΎΡΡΡΠ²Π°Π½Π½Ρ ΡΠ° Π·Π°ΠΏΡΠΎΠΏΠΎΠ½ΠΎΠ²Π°Π½ΠΎ ΠΎΡΠ½ΠΎΠ²Π½Ρ ΠΌΠ΅ΡΠΎΠ΄ΠΈΡΠ½Ρ ΠΏΡΠ΄Ρ
ΠΎΠ΄ΠΈ Π΄Π»Ρ ΠΏΡΠΎΠ²Π΅Π΄Π΅Π½Π½Ρ Π²ΡΠ΄ΠΏΠΎΠ²ΡΠ΄Π½ΠΎΡ Π΄ΡΠ°Π³Π½ΠΎΡΡΠΈΠΊΠΈ.In the article the basic modern approaches to diagnostics of construction materials enterprises are examined, in view of specificity of branch of theirfunctioning. On the basis of the lead analysis the basic directions of diagnosing are determined and the basic methodical approaches, for corresponding diagnostics are offered
Fractional Analytic QCD beyond Leading Order in timelike region
In this paper we show that, as in the spacelike case, the inverse logarithmic
expansion is applicable for all values of the argument of the analytic coupling
constant. We present two different approaches, one of which is based primarily
on trigonometric functions, and the latter is based on dispersion integrals.
The results obtained up to the 5th order of perturbation theory, have a
compact form and their acquiring is much easier than the methods that have been
used before. As an example, we apply our results to study the Higgs boson decay
into a bb pair.Comment: 30 pages, 9 figures. arXiv admin note: substantial text overlap with
arXiv:2203.0930
On Fractional Analytic QCD
We present a brief overview of fractional analytic QCD.Comment: 7 pages, 1 figure, contribution to the proceedings of the XXVth
International Baldin Seminar on High Energy Physics Problems Relativistic
Nuclear Physics and Quantum Chromodynamics (September 18-23, Dubna, Russia
Investigation of the Method of Dynamic Microwave Power Redistribution in a Resonator-Type Plasmatron
The investigation results of a dynamic microwave power fmicrowave = 2, 45 Β± 0,05 GHz redistribution in a 9000 cm3 reaction-discharge chamber of a microwave resonator-type plasmatron are presented. In order to redistribute the microwave power, a rotating metallic four-blade L-form dissector placed above the reaction-discharge chamber was used. The microwave power in the local points at the axis of the chamber with plasma and without it was measured applying the "active probe" method. During the experiments the chamber contained silicon plates. Periodical interchange of maximum and minimum microwave power values along the chamber axis was established experimentally. Note, when the dissector was rotating, the range of maximum and minimum "active probe" values dispersion decreased. It has been established that during the dissector rotation the microwave power in the local discharge areas changes with periodic repetition every quarter of revolution
Neutron star inner crust: reduction of shear modulus by nuclei finite size effect
The elasticity of neutron star crust is important for adequate interpretation
of observations. To describe elastic properties one should rely on theoretical
models. The most widely used is Coulomb crystal model (system of point-like
charges on neutralizing uniform background), in some works it is corrected for
electron screening. These models neglect finite size of nuclei. This
approximation is well justified except for the innermost crustal layers, where
nuclei size becomes comparable with the inter-nuclear spacing. Still, even in
those dense layers it seems reasonable to apply the Coulomb crystal result, if
one assumes that nuclei are spherically symmetric: Coulomb interaction between
them should be the same as interaction between point-like charges. This
argument is indeed correct, however, as we point here, shear of crustal lattice
generates (microscopic) quadrupole electrostatic potential in a vicinity of
lattice cites, which induces deformation on the nuclei. We analyze this problem
analytically within compressible liquid drop model, using ionic spheroid model
(which is generalization of well known ion sphere model). In particular, for
ground state crust composition the effective shear modulus is reduced for a
factor of , where u is the filling factor (ratio
of the nuclei volume to the volume of the cell). This result is universal and
does not depend on the applied nucleon interaction model. For the innermost
layers of inner crust u~0.2 leading to reduction of the shear modulus by ~25%,
which can be important for correct interpretation of quasi-periodic
oscillations in the tails of magnetar flares.Comment: 7 pages, submitted to MNRAS on Sept.
Semiclassical Inequivalence of Polygonalized Billiards
Polygonalization of any smooth billiard boundary can be carried out in
several ways. We show here that the semiclassical description depends on the
polygonalization process and the results can be inequivalent. We also establish
that generalized tangent-polygons are closest to the corresponding smooth
billiard and for de Broglie wavelengths larger than the average length of the
edges, the two are semiclassically equivalent.Comment: revtex, 4 ps figure
Π‘ΠΈΠ½ΡΠ΅Π· Π΄ΠΈΠΌΠ΅ΡΠ½ΠΈΡ n-Π°ΡΠ΅ΡΠΈΠ»Π³Π»ΡΠΊΠΎΠ·Π°ΠΌΡΠ½ΡΠ΄ΡΠ²
Glycosylation of aliphatic and aromatic Ξ±,Ο-diols by the oxazoline method and by peracetylated Ξ±-D-glucosaminylchloride in the presence of zinc chloride and co-promoters (quaternary ammonium salts or trityl chloride) have been investigated. The highest yield of bis-glucosaminides in the conditions of oxazoline synthesis (the solvent is dichloroethane, the temperature of the reaction mixture is ~100Β°C, catalytic quantities of p-toluenesulfonic acid) has been observed for octane-1,8-diol. The products of monoglycosylation of butane-1,4-diol and dodecane-1,12-diol have been also obtained. The influence of the nature of a ΡΠΎ-promoter has been studied on the model glycosylation reaction of octane-1,8-diol with peracetylated Ξ±-D-glucosaminylchloride in reflux dichloromethane (the ratio of glycosyl-acceptor : glycosyl-donor : zinc chloride : quaternary ammonium salt = 1 : 2,5 : 2,5 : 2,5). The best yields of dimeric glycoside have been obtained using tetrabutylammonium bromide. Increase of the amount of zinc chloride up to 1.5 equivalents in relation to the glycosyl donor has not led to significant changes of the reaction product yield. The yields of bis-glycosylation have been increased using peracetylated Ξ±-D-glucosaminylchloride as a glycosyl-donor for all aglycones. The corresponding mono- and bis-glucosaminides of 2,2β-(1,2-phenylenedioxy)diethanole have been synthesized by glycosylation in these conditions. The structure of the glycosides synthesized has been proven by 1H-NMR-spectroscopy.ΠΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΎ Π³Π»ΠΈΠΊΠΎΠ·ΠΈΠ»ΠΈΡΠΎΠ²Π°Π½ΠΈΠ΅ Ξ±,Ο-Π΄ΠΈΠΎΠ»ΠΎΠ² Π°Π»ΠΈΡΠ°ΡΠΈΡΠ΅ΡΠΊΠΎΠΉ ΠΈ Π°ΡΠΎΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΎΠΉ ΠΏΡΠΈΡΠΎΠ΄Ρ Ρ ΠΏΠΎΠΌΠΎΡΡΡ ΠΎΠΊΡΠ°Π·ΠΎΠ»ΠΈΠ½ΠΎΠ²ΠΎΠ³ΠΎ ΠΌΠ΅ΡΠΎΠ΄Π° ΠΈ ΠΏΠ΅ΡΠ°ΡΠ΅ΡΠ°ΡΠ° Ξ±-D-Π³Π»ΡΠΊΠΎΠ·Π°ΠΌΠΈΠ½ΠΈΠ»Ρ
Π»ΠΎΡΠΈΠ΄Π° Π² ΠΏΡΠΈΡΡΡΡΡΠ²ΠΈΠΈ Ρ
Π»ΠΎΡΠΈΠ΄Π° ΡΠΈΠ½ΠΊΠ° ΠΈ ΡΠΎΠΏΡΠΎΠΌΠΎΡΠΎΡΠΎΠ² (ΡΠ΅ΡΠ²Π΅ΡΡΠΈΡΠ½ΡΠ΅ Π°ΠΌΠΌΠΎΠ½ΠΈΠΉΠ½ΡΠ΅ ΡΠΎΠ»ΠΈ ΠΈΠ»ΠΈ ΡΡΠΈΡΠΈΠ»Ρ
Π»ΠΎΡΠΈΠ΄). ΠΠ°ΠΈΠ±ΠΎΠ»ΡΡΠΈΠΉ Π²ΡΡ
ΠΎΠ΄ Π±ΠΈΡ-Π³Π»ΡΠΊΠΎΠ·Π°ΠΌΠΈΠ½ΠΈΠ΄ΠΎΠ² Π² ΡΡΠ»ΠΎΠ²ΠΈΡΡ
ΠΎΠΊΡΠ°Π·ΠΎΠ»ΠΈΠ½ΠΎΠ²ΠΎΠ³ΠΎ ΡΠΈΠ½ΡΠ΅Π·Π° (ΡΠ°ΡΡΠ²ΠΎΡΠΈΡΠ΅Π»Ρ Π΄ΠΈΡ
Π»ΠΎΡΡΡΠ°Π½, ΡΠ΅ΠΌΠΏΠ΅ΡΠ°ΡΡΡΠ° ΡΠ΅Π°ΠΊΡΠΈΠΎΠ½Π½ΠΎΠΉ ΡΠΌΠ΅ΡΠΈ ~100Β°Π‘, ΠΊΠ°ΡΠ°Π»ΠΈΡΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΠΊΠΎΠ»ΠΈΡΠ΅ΡΡΠ²Π° ΠΏ-ΡΠΎΠ»ΡΠΎΠ»ΡΡΠ»ΡΡΠΎΠΊΠΈΡΠ»ΠΎΡΡ) Π½Π°Π±Π»ΡΠ΄Π°Π»ΡΡ Π΄Π»Ρ ΠΎΠΊΡΠ°Π½-1,8-Π΄ΠΈΠΎΠ»Π°. ΠΠ»Ρ Π±ΡΡΠ°Π½-1,4-Π΄ΠΈΠΎΠ»Π° ΠΈ Π΄ΠΎΠ΄Π΅ΠΊΠ°Π½-1,12-Π΄ΠΈΠΎΠ»Π° ΡΠ°ΠΊΠΆΠ΅ ΠΏΠΎΠ»ΡΡΠ΅Π½Ρ ΠΏΡΠΎΠ΄ΡΠΊΡΡ ΠΌΠΎΠ½ΠΎΠ³Π»ΠΈΠΊΠΎΠ·ΠΈΠ»ΠΈΡΠΎΠ²Π°Π½ΠΈΡ. ΠΠ° ΠΌΠΎΠ΄Π΅Π»ΡΠ½ΠΎΠΉ ΡΠ΅Π°ΠΊΡΠΈΠΈ Π³Π»ΠΈΠΊΠΎΠ·ΠΈΠ»ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΎΠΊΡΠ°Π½-1,8-Π΄ΠΈΠΎΠ»Π° Ρ ΠΏΠ΅ΡΠ°ΡΠ΅ΡΠ°ΡΠΎΠΌ Ξ±-D-Π³Π»ΡΠΊΠΎΠ·Π°ΠΌΠΈΠ½ΠΈΠ»Ρ
Π»ΠΎΡΠΈΠ΄Π° Π² ΠΊΠΈΠΏΡΡΠ΅ΠΌ Π΄ΠΈΡ
Π»ΠΎΡΠΌΠ΅ΡΠ°Π½Π΅ (ΡΠΎΠΎΡΠ½ΠΎΡΠ΅Π½ΠΈΠ΅ Π³Π»ΠΈΠΊΠΎΠ·ΠΈΠ»-Π°ΠΊΡΠ΅ΠΏΡΠΎΡ : Π³Π»ΠΈΠΊΠΎΠ·ΠΈΠ»-Π΄ΠΎΠ½ΠΎΡ : Ρ
Π»ΠΎΡΠΈΠ΄ ΡΠΈΠ½ΠΊΠ° : ΡΠ΅ΡΠ²Π΅ΡΡΠΈΡΠ½Π°Ρ Π°ΠΌΠΌΠΎΠ½ΠΈΠΉΠ½Π°Ρ ΡΠΎΠ»Ρ = 1 : 2,5 : 2,5 : 2,5) Π±ΡΠ»ΠΎ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΎ Π²Π»ΠΈΡΠ½ΠΈΠ΅ ΠΏΡΠΈΡΠΎΠ΄Ρ ΡΠΎΠΏΡΠΎΠΌΠΎΡΠΎΡΠ°. ΠΡΡΡΠΈΠ΅ Π²ΡΡ
ΠΎΠ΄Ρ Π΄ΠΈΠΌΠ΅ΡΠ½ΠΎΠ³ΠΎ Π³Π»ΠΈΠΊΠΎΠ·ΠΈΠ΄Π° ΠΏΠΎΠ»ΡΡΠ΅Π½Ρ ΠΏΡΠΈ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΠΈ ΡΠ΅ΡΡΠ°Π±ΡΡΠΈΠ»Π°ΠΌΠΌΠΎΠ½ΠΈΡ Π±ΡΠΎΠΌΠΈΠ΄Π°. Π£Π²Π΅Π»ΠΈΡΠ΅Π½ΠΈΠ΅ ΠΊΠΎΠ»ΠΈΡΠ΅ΡΡΠ²Π° Ρ
Π»ΠΎΡΠΈΠ΄Π° ΡΠΈΠ½ΠΊΠ° Π΄ΠΎ 1,5 ΡΠΊΠ²ΠΈΠ²Π°Π»Π΅Π½ΡΠΎΠ² ΠΏΠΎ ΠΎΡΠ½ΠΎΡΠ΅Π½ΠΈΡ ΠΊ Π³Π»ΠΈΠΊΠΎΠ·ΠΈΠ»-Π΄ΠΎΠ½ΠΎΡΡ Π½Π΅ ΠΏΡΠΈΠ²Π΅Π»ΠΎ ΠΊ Π΄ΠΎΡΡΠΎΠ²Π΅ΡΠ½ΠΎΠΌΡ ΠΈΠ·ΠΌΠ΅Π½Π΅Π½ΠΈΡ Π²ΡΡ
ΠΎΠ΄Π° ΠΏΡΠΎΠ΄ΡΠΊΡΠ° ΡΠ΅Π°ΠΊΡΠΈΠΈ. ΠΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΠ΅ Π² ΠΊΠ°ΡΠ΅ΡΡΠ²Π΅ Π³Π»ΠΈΠΊΠΎΠ·ΠΈΠ»-Π΄ΠΎΠ½ΠΎΡΠ° ΠΏΠ΅ΡΠ°ΡΠ΅ΡΠ°ΡΠ° Ξ±-D-Π³Π»ΡΠΊΠΎΠ·Π°ΠΌΠΈΠ½ΠΈΠ»Ρ
Π»ΠΎΡΠΈΠ΄Π° ΠΏΠΎΠ·Π²ΠΎΠ»ΠΈΠ»ΠΎ ΡΠ²Π΅Π»ΠΈΡΠΈΡΡ Π²ΡΡ
ΠΎΠ΄ Π±ΠΈΡ-Π³Π»ΠΈΠΊΠΎΠ·ΠΈΠ»ΠΈΡΠΎΠ²Π°Π½ΠΈΡ Π΄Π»Ρ Π²ΡΠ΅Ρ
Π°Π³Π»ΠΈΠΊΠΎΠ½ΠΎΠ². ΠΠ»ΠΈΠΊΠΎΠ·ΠΈΠ»ΠΈΡΠΎΠ²Π°Π½ΠΈΠ΅ΠΌ 2,2β-(1,2-ΡΠ΅Π½ΠΈΠ»Π΅Π½Π΄ΠΈΠΎΠΊΡΠΈ)Π΄ΠΈΡΡΠ°Π½ΠΎΠ»Π° Π² Π΄Π°Π½Π½ΡΡ
ΡΡΠ»ΠΎΠ²ΠΈΡΡ
Π±ΡΠ»ΠΈ ΡΠΈΠ½ΡΠ΅Π·ΠΈΡΠΎΠ²Π°Π½Ρ ΡΠΎΠΎΡΠ²Π΅ΡΡΡΠ²ΡΡΡΠΈΠ΅ ΠΌΠΎΠ½ΠΎ- ΠΈ Π±ΠΈΡ-Π³Π»ΡΠΊΠΎΠ·Π°ΠΌΠΈΠ½ΠΈΠ΄Ρ. Π‘ΡΡΠΎΠ΅Π½ΠΈΠ΅ ΡΠΈΠ½ΡΠ΅Π·ΠΈΡΠΎΠ²Π°Π½Π½ΡΡ
Π³Π»ΠΈΠΊΠΎΠ·ΠΈΠ΄ΠΎΠ² Π΄ΠΎΠΊΠ°Π·Π°Π½ΠΎ 1Π-Π―ΠΠ -ΡΠΏΠ΅ΠΊΡΡΠΎΡΠΊΠΎΠΏΠΈΠ΅ΠΉ.ΠΠΎΡΠ»ΡΠ΄ΠΆΠ΅Π½ΠΎ Π³Π»ΡΠΊΠΎΠ·ΠΈΠ»ΡΠ²Π°Π½Π½Ρ Ξ±,Ο-Π΄ΡΠΎΠ»ΡΠ² Π°Π»ΡΡΠ°ΡΠΈΡΠ½ΠΎΡ Ρ Π°ΡΠΎΠΌΠ°ΡΠΈΡΠ½ΠΎΡ ΠΏΡΠΈΡΠΎΠ΄ΠΈ Π·Π° Π΄ΠΎΠΏΠΎΠΌΠΎΠ³ΠΎΡ ΠΎΠΊΡΠ°Π·ΠΎΠ»ΡΠ½ΠΎΠ²ΠΎΠ³ΠΎ ΠΌΠ΅ΡΠΎΠ΄Ρ Ρ ΠΏΠ΅ΡΠ°ΡΠ΅ΡΠ°ΡΡ Ξ±-D-Π³Π»ΡΠΊΠΎΠ·Π°ΠΌΡΠ½ΡΠ»Ρ
Π»ΠΎΡΠΈΠ΄Ρ Ρ ΠΏΡΠΈΡΡΡΠ½ΠΎΡΡΡ ΡΠΈΠ½ΠΊΡ Ρ
Π»ΠΎΡΠΈΠ΄Ρ Ρ ΡΠΎΠΏΡΠΎΠΌΠΎΡΠΎΡΡΠ² (ΡΠ΅ΡΠ²Π΅ΡΡΠΈΠ½Π½Ρ Π°ΠΌΠΎΠ½ΡΠΉΠ½Ρ ΡΠΎΠ»Ρ Π°Π±ΠΎ ΡΡΠΈΡΠΈΠ»Ρ
Π»ΠΎΡΠΈΠ΄). ΠΠ°ΠΉΠ±ΡΠ»ΡΡΠΈΠΉ Π²ΠΈΡ
ΡΠ΄ Π±ΡΡ-Π³Π»ΡΠΊΠΎΠ·Π°ΠΌΡΠ½ΡΠ΄ΡΠ² Π² ΡΠΌΠΎΠ²Π°Ρ
ΠΎΠΊΡΠ°Π·ΠΎΠ»ΡΠ½ΠΎΠ²ΠΎΠ³ΠΎ ΡΠΈΠ½ΡΠ΅Π·Ρ (ΡΠΎΠ·ΡΠΈΠ½Π½ΠΈΠΊ β Π΄ΠΈΡ
Π»ΠΎΡΠΎΠ΅ΡΠ°Π½, ΡΠ΅ΠΌΠΏΠ΅ΡΠ°ΡΡΡΠ° ΡΠ΅Π°ΠΊΡΡΠΉΠ½ΠΎΡ ΡΡΠΌΡΡΡ ~100Β°Π‘, ΠΊΠ°ΡΠ°Π»ΡΡΠΈΡΠ½Π° ΠΊΡΠ»ΡΠΊΡΡΡΡ ΠΏ-ΡΠΎΠ»ΡΠ΅Π½ΡΡΠ»ΡΡΠΎΠΊΠΈΡΠ»ΠΎΡΠΈ) ΡΠΏΠΎΡΡΠ΅ΡΡΠ³Π°Π²ΡΡ Π΄Π»Ρ ΠΎΠΊΡΠ°Π½-1,8-Π΄ΡΠΎΠ»Ρ. ΠΠ»Ρ Π±ΡΡΠ°Π½-1,4-Π΄ΡΠΎΠ»Ρ Ρ Π΄ΠΎΠ΄Π΅ΠΊΠ°Π½-1,12-Π΄ΡΠΎΠ»Ρ ΡΠ°ΠΊΠΎΠΆ ΠΎΡΡΠΈΠΌΠ°Π½Ρ ΠΏΡΠΎΠ΄ΡΠΊΡΠΈ ΠΌΠΎΠ½ΠΎΠ³Π»ΡΠΊΠΎΠ·ΠΈΠ»ΡΠ²Π°Π½Π½Ρ. ΠΠ° ΠΌΠΎΠ΄Π΅Π»ΡΠ½ΡΠΉ ΡΠ΅Π°ΠΊΡΡΡ Π³Π»ΡΠΊΠΎΠ·ΠΈΠ»ΡΠ²Π°Π½Π½Ρ ΠΎΠΊΡΠ°Π½-1,8-Π΄ΡΠΎΠ»Ρ ΠΏΠ΅ΡΠ°ΡΠ΅ΡΠ°ΡΠΎΠΌ Ξ±-D-Π³Π»ΡΠΊΠΎΠ·Π°ΠΌΡΠ½ΡΠ»Ρ
Π»ΠΎΡΠΈΠ΄Ρ Ρ ΠΊΠΈΠΏΠ»ΡΡΠΎΠΌΡ Π΄ΠΈΡ
Π»ΠΎΡΠΎΠΌΠ΅ΡΠ°Π½Ρ (ΡΠΏΡΠ²Π²ΡΠ΄Π½ΠΎΡΠ΅Π½Π½Ρ Π³Π»ΡΠΊΠΎΠ·ΠΈΠ»-Π°ΠΊΡΠ΅ΠΏΡΠΎΡ : Π³Π»ΡΠΊΠΎΠ·ΠΈΠ»-Π΄ΠΎΠ½ΠΎΡ : Ρ
Π»ΠΎΡΠΈΠ΄ ΡΠΈΠ½ΠΊΡ : ΡΠ΅ΡΠ²Π΅ΡΡΠΈΠ½Π½Π° Π°ΠΌΠΎΠ½ΡΠΉΠ½Π° ΡΡΠ»Ρ = 1 : 2,5 : 2,5 : 2,5) Π±ΡΠ»ΠΎ Π΄ΠΎΡΠ»ΡΠ΄ΠΆΠ΅Π½ΠΎ Π²ΠΏΠ»ΠΈΠ² ΠΏΡΠΈΡΠΎΠ΄ΠΈ ΡΠΎΠΏΡΠΎΠΌΠΎΡΠΎΡΡ. ΠΡΠ°ΡΡ Π²ΠΈΡ
ΠΎΠ΄ΠΈ Π΄ΠΈΠΌΠ΅ΡΠ½ΠΎΠ³ΠΎ Π³Π»ΡΠΊΠΎΠ·ΠΈΠ΄Ρ ΠΎΡΡΠΈΠΌΠ°Π½Ρ ΠΏΡΠΈ Π²ΠΈΠΊΠΎΡΠΈΡΡΠ°Π½Π½Ρ ΡΠ΅ΡΡΠ°Π±ΡΡΠΈΠ»Π°ΠΌΠΎΠ½ΡΡ Π±ΡΠΎΠΌΡΠ΄Ρ. ΠΠ±ΡΠ»ΡΡΠ΅Π½Π½Ρ ΠΊΡΠ»ΡΠΊΠΎΡΡΡ Ρ
Π»ΠΎΡΠΈΠ΄Ρ ΡΠΈΠ½ΠΊΡ Π΄ΠΎ 1,5 Π΅ΠΊΠ²ΡΠ²Π°Π»Π΅Π½ΡΡΠ² ΠΏΠΎ Π²ΡΠ΄Π½ΠΎΡΠ΅Π½Π½Ρ Π΄ΠΎ Π³Π»ΡΠΊΠΎΠ·ΠΈΠ»-Π΄ΠΎΠ½ΠΎΡΠ° Π½Π΅ ΠΏΡΠΈΠ²Π΅Π»ΠΎ Π΄ΠΎ Π΄ΠΎΡΡΠΎΠ²ΡΡΠ½ΠΎΡ Π·ΠΌΡΠ½ΠΈ Π²ΠΈΡ
ΠΎΠ΄Ρ ΠΏΡΠΎΠ΄ΡΠΊΡΡ ΡΠ΅Π°ΠΊΡΡΡ. ΠΠΈΠΊΠΎΡΠΈΡΡΠ°Π½Π½Ρ Π² ΡΠΊΠΎΡΡΡ Π³Π»ΡΠΊΠΎΠ·ΠΈΠ»-Π΄ΠΎΠ½ΠΎΡΠ° ΠΏΠ΅ΡΠ°ΡΠ΅ΡΠ°ΡΡ Ξ±-D-Π³Π»ΡΠΊΠΎΠ·Π°ΠΌΡΠ½ΡΠ»Ρ
Π»ΠΎΡΠΈΠ΄Ρ Π΄ΠΎΠ·Π²ΠΎΠ»ΠΈΠ»ΠΎ Π·Π±ΡΠ»ΡΡΠΈΡΠΈ Π²ΠΈΡ
ΡΠ΄ Π±ΡΡ-Π³Π»ΡΠΊΠΎΠ·ΠΈΠ»ΡΠ²Π°Π½Π½Ρ Π΄Π»Ρ Π²ΡΡΡ
Π°Π³Π»ΡΠΊΠΎΠ½ΡΠ². ΠΠ»ΡΠΊΠΎΠ·ΠΈΠ»ΡΠ²Π°Π½Π½ΡΠΌ 2,2β-(1,2-ΡΠ΅Π½ΡΠ»Π΅Π½Π΄ΡΠΎΠΊΡΠΈ)Π΄ΡΠ΅ΡΠ°Π½ΠΎΠ»Ρ Π² Π΄Π°Π½ΠΈΡ
ΡΠΌΠΎΠ²Π°Ρ
Π±ΡΠ»ΠΈ ΡΠΈΠ½ΡΠ΅Π·ΠΎΠ²Π°Π½Ρ Π²ΡΠ΄ΠΏΠΎΠ²ΡΠ΄Π½Ρ ΠΌΠΎΠ½ΠΎ- Ρ Π±ΡΡ-Π³Π»ΡΠΊΠΎΠ·Π°ΠΌΡΠ½ΡΠ΄ΠΈ. ΠΡΠ΄ΠΎΠ²Π° ΡΠΈΠ½ΡΠ΅Π·ΠΎΠ²Π°Π½ΠΈΡ
Π³Π»ΡΠΊΠΎΠ·ΠΈΠ΄ΡΠ² Π΄ΠΎΠ²Π΅Π΄Π΅Π½Π° 1Π-Π―ΠΠ -ΡΠΏΠ΅ΠΊΡΡΠΎΡΠΊΠΎΠΏΡΡΡ
High-Resolution Phonocardiogram Parameters
The article describes the results of studying and analyzing phonocardiograms (PCGs) obtained during a physiological experiment with Blu-ray standard equipment. It provides the findings of a spectral and spectral-time analysis for signals with a sampling frequency of 10, 44.1 and 192 kHz. It shows that the differences in the PCG spectra of identical signals are unreliable. The article specifies the onset and disappearance moments of the harmonic components of heart sounds. It also provides recommendations on the sampling frequency and bit resolution of digitized PCG signals for telemetric systems
ΠΠΠΠΠΠΠ ΠΠΠΠΠΠ ΠΠ ΠΠ¦ΠΠ‘Π‘Π Π’ΠΠΠΠΠΠΠ ΠΠΠ ΠΠΠΠ’ΠΠ ΠΠΠ’ΠΠΠ ΠΠΠΠΠΠΠ’ΠΠ«Π₯ ΠΠΠΠ‘Π’Π Π£ΠΠ¦ΠΠ
Nowadays main qualitative indices depend on concrete structure formation and curing while constructing cast-in-situ concrete and reinforced concrete structures and especially it concerns winter conditions. Therefore the regime of thermal treatment influences on concrete properties characterizing its strength, porosity, durability, frost resistance etc. In this connection selection of regimes and their corrections are reasonable to be tested while using models. Convenience in mathematical modeling is in reproduction of the operational process in time. However explicit mathematics is obtained only for relatively simple systems or at the cost of specific assumptions and suppositions. In this connection it is expedient to use physical simulation along with mathematical one. The physical simulation presupposes manufacturing, thermal treatment and testing of prototype models.Development of efficient, scientifically-substantiated technology for thermal treatment of cast-in-situ concrete is impossible without information support and working environment. The proposed mathematical model of thermal treatment for castin-situ structures determines sequence of the operations to be executed. Shapes, geometric dimensions, surface area have been determined in the paper. The required thermotechnical characteristics of formwork systems for structures under concre- ting have been used for making calculations of thermal treatment regimes. The model has taken into account three main stages of thermal treatment: temperature rising, isothermal warming and cooling. The paper provides formulae for their determination including total heat expenditure: for temperature rising of the concrete mix, for thermal treatment of 1 ΠΌ3Β concrete mix, for cement exothermic reaction per 1 ΠΌ3, for reinforcement heating per 1 ΠΌ3, for moisture evaporation, for heating of formwork system. The following heat losses have been determined: in the environment, in the process of passing through the exte- rior surface of the formwork, in case of temperature rising in one of the constructive element and per 1 ΠΌ3Β of its concrete mix. The paper reveals determination of hourly heat consumption for a concrete structure as a whole.The proposed methodology makes it possible to determine the required characteristics of heat treatment process for concrete mixes, to optimize regimes of heat treatment, promptly to make corrections in the created situation, to automatize the process and when it is necessary to make comparison of some solutions in the form of graphics and diagrams.Π Π½Π°ΡΡΠΎΡΡΠ΅Π΅ Π²ΡΠ΅ΠΌΡ ΠΏΡΠΈ Π²ΠΎΠ·Π²Π΅Π΄Π΅Π½ΠΈΠΈ ΠΌΠΎΠ½ΠΎΠ»ΠΈΡΠ½ΡΡ
Π±Π΅ΡΠΎΠ½Π½ΡΡ
ΠΈ ΠΆΠ΅Π»Π΅Π·ΠΎΠ±Π΅ΡΠΎΠ½Π½ΡΡ
ΠΊΠΎΠ½ΡΡΡΡΠΊΡΠΈΠΉ ΠΎΡΠ½ΠΎΠ²Π½ΡΠ΅ ΠΏΠΎΠΊΠ°Π·Π°ΡΠ΅Π»ΠΈ ΠΊΠ°ΡΠ΅ΡΡΠ²Π° Π·Π°Π²ΠΈΡΡΡ ΠΎΡ ΡΡΡΡΠΊΡΡΡΠΎΠΎΠ±ΡΠ°Π·ΠΎΠ²Π°Π½ΠΈΡ ΠΈ ΡΠ²Π΅ΡΠ΄Π΅Π½ΠΈΡ Π±Π΅ΡΠΎΠ½Π°, ΠΎΡΠΎΠ±Π΅Π½Π½ΠΎ Π² Π·ΠΈΠΌΠ½ΠΈΡ
ΡΡΠ»ΠΎΠ²ΠΈΡΡ
. ΠΠΎΡΡΠΎΠΌΡ ΡΠ΅ΠΆΠΈΠΌ ΡΠ΅ΠΏΠ»ΠΎΠ²ΠΎΠΉ ΠΎΠ±ΡΠ°Π±ΠΎΡΠΊΠΈ Π²Π»ΠΈΡΠ΅Ρ Π½Π° ΡΠ²ΠΎΠΉΡΡΠ²Π° Π±Π΅ΡΠΎΠ½Π°, Ρ
Π°ΡΠ°ΠΊΡΠ΅ΡΠΈΠ·ΡΡΡΠΈΠ΅ Π΅Π³ΠΎ ΠΏΡΠΎΡΠ½ΠΎΡΡΡ, ΠΏΠΎΡΠΈΡΡΠΎΡΡΡ, Π΄ΠΎΠ»Π³ΠΎΠ²Π΅ΡΠ½ΠΎΡΡΡ, ΠΌΠΎΡΠΎΠ·ΠΎΡΡΠΎΠΉΠΊΠΎΡΡΡ ΠΈ Π΄Ρ. Π ΡΡΠΎΠΉ ΡΠ²ΡΠ·ΠΈ Π²ΡΠ±ΠΎΡ ΡΠ΅ΠΆΠΈΠΌΠΎΠ² ΠΈ ΠΈΡ
ΠΊΠΎΡΡΠ΅ΠΊΡΠΈΡΠΎΠ²ΠΊΠΈ ΡΠ΅Π»Π΅ΡΠΎΠΎΠ±ΡΠ°Π·Π½ΠΎ ΠΎΡΡΠ°Π±Π°ΡΡΠ²Π°ΡΡ Π½Π° ΠΌΠΎΠ΄Π΅Π»ΡΡ
. Π£Π΄ΠΎΠ±ΡΡΠ²ΠΎ ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΠΌΠΎΠ΄Π΅Π»ΠΈΡΠΎΠ²Π°Π½ΠΈΡ Π·Π°ΠΊΠ»ΡΡΠ°Π΅ΡΡΡ Π² Π²ΠΎΡΠΏΡΠΎΠΈΠ·Π²Π΅Π΄Π΅Π½ΠΈΠΈ ΠΏΡΠΎΡΠ΅ΡΡΠ° ΡΡΠ½ΠΊΡΠΈΠΎΠ½ΠΈΡΠΎΠ²Π°Π½ΠΈΡ Π²ΠΎ Π²ΡΠ΅ΠΌΠ΅Π½ΠΈ. ΠΠ΄Π½Π°ΠΊΠΎ ΡΠ²Π½ΡΠ΅ ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΡΠΎΠΎΡΠ½ΠΎΡΠ΅Π½ΠΈΡ ΠΏΠΎΠ»ΡΡΠ°ΡΡΡΡ ΡΠΎΠ»ΡΠΊΠΎ Π΄Π»Ρ ΡΡΠ°Π²Π½ΠΈΡΠ΅Π»ΡΠ½ΠΎ ΠΏΡΠΎΡΡΡΡ
ΡΠΈΡΡΠ΅ΠΌ ΠΈΠ»ΠΈ ΡΠ΅Π½ΠΎΠΉ ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½Π½ΡΡ
ΠΏΡΠ΅Π΄ΠΏΠΎΠ»ΠΎΠΆΠ΅Π½ΠΈΠΉ ΠΈ Π΄ΠΎΠΏΡΡΠ΅Π½ΠΈΠΉ. Π ΡΠ²ΡΠ·ΠΈ Ρ ΡΡΠΈΠΌ ΡΠ΅Π»Π΅ΡΠΎΠΎΠ±ΡΠ°Π·Π½ΠΎ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°ΡΡ Π½Π°ΡΡΠ΄Ρ Ρ ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΈΠΌ ΠΈ ΡΠΈΠ·ΠΈΡΠ΅ΡΠΊΠΎΠ΅ ΠΌΠΎΠ΄Π΅Π»ΠΈΡΠΎΠ²Π°Π½ΠΈΠ΅ ΠΏΡΡΠ΅ΠΌ ΠΈΠ·Π³ΠΎΡΠΎΠ²Π»Π΅Π½ΠΈΡ, ΡΠ΅ΠΏΠ»ΠΎΠ²ΠΎΠΉ ΠΎΠ±ΡΠ°Π±ΠΎΡΠΊΠΈ ΠΈ ΠΈΡΠΏΡΡΠ°Π½ΠΈΡ ΠΎΠΏΡΡΠ½ΡΡ
ΠΎΠ±ΡΠ°Π·ΡΠΎΠ².Π‘ΠΎΠ·Π΄Π°Π½ΠΈΠ΅ ΡΡΡΠ΅ΠΊΡΠΈΠ²Π½ΠΎΠΉ, Π½Π°ΡΡΠ½ΠΎ ΠΎΠ±ΠΎΡΠ½ΠΎΠ²Π°Π½Π½ΠΎΠΉ ΡΠ΅Ρ
Π½ΠΎΠ»ΠΎΠ³ΠΈΠΈ ΡΠ΅ΠΏΠ»ΠΎΠ²ΠΎΠΉ ΠΎΠ±ΡΠ°Π±ΠΎΡΠΊΠΈ ΠΌΠΎΠ½ΠΎΠ»ΠΈΡΠ½ΠΎΠ³ΠΎ Π±Π΅ΡΠΎΠ½Π° Π½Π΅Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΠΎ Π±Π΅Π· ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΠΎΠ½Π½ΠΎΠ³ΠΎ ΠΎΠ±Π΅ΡΠΏΠ΅ΡΠ΅Π½ΠΈΡ ΠΈ ΠΏΡΠΎΠΈΠ·Π²ΠΎΠ΄ΡΡΠ²Π΅Π½Π½ΡΡ
ΡΡΠ»ΠΎΠ²ΠΈΠΉ. Π ΠΏΡΠ΅Π΄Π»Π°Π³Π°Π΅ΠΌΠΎΠΉ ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΎΠΉ ΠΌΠΎΠ΄Π΅Π»ΠΈ ΡΠ΅ΠΏΠ»ΠΎΠ²ΠΎΠΉ ΠΎΠ±ΡΠ°Π±ΠΎΡΠΊΠΈ ΠΌΠΎΠ½ΠΎΠ»ΠΈΡΠ½ΡΡ
ΠΊΠΎΠ½ΡΡΡΡΠΊΡΠΈΠΉ ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½Π° ΠΏΠΎΡΠ»Π΅Π΄ΠΎΠ²Π°ΡΠ΅Π»ΡΠ½ΠΎΡΡΡ Π²ΡΠΏΠΎΠ»Π½Π΅Π½ΠΈΡ Π½Π΅ΠΊΠΎΡΠΎΡΡΡ
ΠΎΠΏΠ΅ΡΠ°ΡΠΈΠΉ. ΠΠΏΡΠ΅Π΄Π΅Π»ΡΠ»ΠΈ ΡΠΎΡΠΌΡ, Π³Π΅ΠΎΠΌΠ΅ΡΡΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΡΠ°Π·ΠΌΠ΅ΡΡ, ΠΏΠ»ΠΎΡΠ°Π΄Ρ. ΠΠ»Ρ ΠΏΡΠΎΠ²Π΅Π΄Π΅Π½ΠΈΡ ΡΠ°ΡΡΠ΅ΡΠΎΠ² ΡΠ΅ΠΆΠΈΠΌΠΎΠ² ΡΠ΅ΠΏΠ»ΠΎΠ²ΠΎΠΉ ΠΎΠ±ΡΠ°Π±ΠΎΡΠΊΠΈ Π²Π²ΠΎΠ΄ΠΈΠ»ΠΈ Π½Π΅ΠΎΠ±Ρ
ΠΎΠ΄ΠΈΠΌΡΠ΅ ΡΠ΅ΠΏΠ»ΠΎΡΠ΅Ρ
Π½ΠΈΡΠ΅ΡΠΊΠΈΠ΅ Ρ
Π°ΡΠ°ΠΊΡΠ΅ΡΠΈΡΡΠΈΠΊΠΈ ΠΎΠΏΠ°Π»ΡΠ±ΠΎΡΠ½ΡΡ
ΡΠΈΡΡΠ΅ΠΌ Π±Π΅ΡΠΎΠ½ΠΈΡΡΠ΅ΠΌΡΡ
ΠΊΠΎΠ½ΡΡΡΡΠΊΡΠΈΠΉ. ΠΠΎΠ΄Π΅Π»Ρ ΡΡΠΈΡΡΠ²Π°Π»Π° ΡΡΠΈ ΠΎΡΠ½ΠΎΠ²Π½ΡΡ
ΡΡΠ°Π΄ΠΈΠΈ ΡΠ΅ΠΏΠ»ΠΎΠ²ΠΎΠΉ ΠΎΠ±ΡΠ°Π±ΠΎΡΠΊΠΈ: ΠΏΠΎΠ΄ΡΠ΅ΠΌ ΡΠ΅ΠΌΠΏΠ΅ΡΠ°ΡΡΡΡ, ΠΈΠ·ΠΎΡΠ΅ΡΠΌΠΈΡΠ΅ΡΠΊΠΈΠΉ ΠΏΡΠΎΠ³ΡΠ΅Π² ΠΈ ΠΎΡΡΡΠ²Π°Π½ΠΈΠ΅. ΠΡΠΈΠ²Π΅Π΄Π΅Π½Ρ ΡΠΎΡΠΌΡΠ»Ρ ΠΈΡ
ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΡ, Π² ΡΠΎΠΌ ΡΠΈΡΠ»Π΅ ΠΎΠ±ΡΠΈΠΉ ΡΠ°ΡΡ
ΠΎΠ΄ ΡΠ΅ΠΏΠ»ΠΎΡΡ: Π½Π° ΠΏΠΎΠ΄ΡΠ΅ΠΌ ΡΠ΅ΠΌΠΏΠ΅ΡΠ°ΡΡΡΡ Π±Π΅ΡΠΎΠ½Π½ΠΎΠΉ ΡΠΌΠ΅ΡΠΈ, Π΄Π»Ρ ΠΏΡΠΎΠ³ΡΠ΅Π²Π° 1Β ΠΌ3 Π±Π΅ΡΠΎΠ½Π½ΠΎΠΉ ΡΠΌΠ΅ΡΠΈ, Π² ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠ΅ ΡΠΊΠ·ΠΎΡΠ΅ΡΠΌΠΈΡΠ΅ΡΠΊΠΎΠΉ ΡΠ΅Π°ΠΊΡΠΈΠΈ ΡΠ΅ΠΌΠ΅Π½ΡΠ° Π½Π° 1 ΠΌ3, Π΄Π»Ρ Π½Π°Π³ΡΠ΅Π²Π° Π°ΡΠΌΠ°ΡΡΡΡ Π½Π° 1Β ΠΌ3, Π½Π° ΠΈΡΠΏΠ°ΡΠ΅Π½ΠΈΠ΅ Π²Π»Π°Π³ΠΈ, Π΄Π»Ρ Π½Π°Π³ΡΠ΅Π²Π° ΠΎΠΏΠ°Π»ΡΠ±ΠΎΡΠ½ΠΎΠΉ ΡΠΈΡΡΠ΅ΠΌΡ. ΠΠΏΡΠ΅Π΄Π΅Π»Π΅Π½Ρ ΠΏΠΎΡΠ΅ΡΠΈ ΡΠ΅ΠΏΠ»ΠΎΡΡ: Π² ΠΎΠΊΡΡΠΆΠ°ΡΡΡΡ ΡΡΠ΅Π΄Ρ, Π² ΠΏΡΠΎΡΠ΅ΡΡΠ΅ ΠΏΡΠΎΡ
ΠΎΠΆΠ΄Π΅Π½ΠΈΡ ΡΠ΅ΡΠ΅Π· Π½Π°ΡΡΠΆΠ½ΡΡ ΠΏΠΎΠ²Π΅ΡΡ
Π½ΠΎΡΡΡ ΠΎΠΏΠ°Π»ΡΠ±ΠΊΠΈ, ΠΏΡΠΈ ΠΏΠΎΠ΄ΡΠ΅ΠΌΠ΅ ΡΠ΅ΠΌΠΏΠ΅ΡΠ°ΡΡΡΡ ΠΎΠ΄Π½ΠΎΠ³ΠΎ ΠΊΠΎΠ½ΡΡΡΡΠΊΡΠΈΠ²Π½ΠΎΠ³ΠΎ ΡΠ»Π΅ΠΌΠ΅Π½ΡΠ° ΠΈ 1 ΠΌ3 Π΅Π³ΠΎ Π±Π΅ΡΠΎΠ½Π½ΠΎΠΉ ΡΠΌΠ΅ΡΠΈ. ΠΠΎΠΊΠ°Π·Π°Π½ΠΎ ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΠ΅ ΡΠ°ΡΠΎΠ²ΠΎΠ³ΠΎ ΡΠ°ΡΡ
ΠΎΠ΄Π° ΡΠ΅ΠΏΠ»ΠΎΡΡ Π½Π° ΠΏΠΎΠ΄ΡΠ΅ΠΌ ΡΠ΅ΠΌΠΏΠ΅ΡΠ°ΡΡΡΡ Π±Π΅ΡΠΎΠ½Π½ΠΎΠΉ ΠΊΠΎΠ½ΡΡΡΡΠΊΡΠΈΠΈ Π² ΡΠ΅Π»ΠΎΠΌ.ΠΡΠ΅Π΄Π»ΠΎΠΆΠ΅Π½Π½Π°Ρ ΠΌΠ΅ΡΠΎΠ΄ΠΈΠΊΠ° ΠΏΠΎΠ·Π²ΠΎΠ»ΡΠ΅Ρ ΠΎΠΏΡΠ΅Π΄Π΅Π»ΠΈΡΡ ΡΡΠ΅Π±ΡΠ΅ΠΌΡΠ΅ ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΡ ΠΏΡΠΎΡΠ΅ΡΡΠ° ΡΠ΅ΠΏΠ»ΠΎΠ²ΠΎΠΉ ΠΎΠ±ΡΠ°Π±ΠΎΡΠΊΠΈ Π±Π΅ΡΠΎΠ½Π½ΡΡ
ΡΠΌΠ΅ΡΠ΅ΠΉ, ΠΎΠΏΡΠΈΠΌΠΈΠ·ΠΈΡΠΎΠ²Π°ΡΡ ΡΠ΅ΠΆΠΈΠΌΡ ΡΠ΅ΠΏΠ»ΠΎΠ²ΠΎΠΉ ΠΎΠ±ΡΠ°Π±ΠΎΡΠΊΠΈ, Π±ΡΡΡΡΠΎ ΠΊΠΎΡΡΠ΅ΠΊΡΠΈΡΠΎΠ²Π°ΡΡ ΡΠΎΠ·Π΄Π°Π²ΡΡΡΡΡ ΡΠΈΡΡΠ°ΡΠΈΡ, Π°Π²ΡΠΎΠΌΠ°ΡΠΈΠ·ΠΈΡΠΎΠ²Π°ΡΡ ΠΏΡΠΎΡΠ΅ΡΡ ΠΈ, ΠΏΡΠΈ Π½Π΅ΠΎΠ±Ρ
ΠΎΠ΄ΠΈΠΌΠΎΡΡΠΈ, ΡΠΎΠΏΠΎΡΡΠ°Π²Π»ΡΡΡ ΠΎΡΠ΄Π΅Π»ΡΠ½ΡΠ΅ ΡΠ΅ΡΠ΅Π½ΠΈΡ Π² Π²ΠΈΠ΄Π΅ Π³ΡΠ°ΡΠΈΠΊΠΎΠ² ΠΈ Π΄ΠΈΠ°Π³ΡΠ°ΠΌΠΌ
Periodic orbits and semiclassical form factor in barrier billiards
Using heuristic arguments based on the trace formulas, we analytically
calculate the semiclassical two-point correlation form factor for a family of
rectangular billiards with a barrier of height irrational with respect to the
side of the billiard and located at any rational position p/q from the side. To
do this, we first obtain the asymptotic density of lengths for each family of
periodic orbits by a Siegel-Veech formula. The result K(0)=1/2+1/q obtained for
these pseudo-integrable, non-Veech billiards is different but not far from the
value of 1/2 expected for semi-Poisson statistics and from values of K(0)
obtained previously in the case of Veech billiards.Comment: 24 page
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