292 research outputs found
Reconstructing Images from Projections Using the Maximum-Entropy Method. Numerical Simulations of Low-Aspect Astrotomography
The reconstruction of images from a small number of projections using the
maximum-entropy method (MEM) with the Shannon entropy is considered. MEM
provides higher-quality image reconstruction for sources with extended
components than the Hogbom CLEAN method, which is also used in low-aspect
astrotomography. The quality of image reconstruction for sources with mixed
structure containing bright, compact features embedded in a comparatively weak,
extended base can be further improved using a difference-mapping method, which
requires a generalization of MEM for the reconstruction of sign-variable
functions.We draw conclusions based on the results of numerical simulations for
a number of model radio sources with various morphologies.Comment: 11 pages, 9 figure
High-visibility multi-photon interference of Hanbury Brown - Twiss type for classical light
Difference-phase (or Hanbury Brown - Twiss type) intensity interference of
classical light is considered in higher orders in the intensity. It is shown
that, while the visibility of sum-phase (NOON-type) interference for classical
sources drops with the order of interference, the visibility of
difference-phase interference has opposite behavior. For three-photon and
four-photon interference of two coherent sources, the visibility can be as high
as 81.8% and 94.4%, respectively. High-visibility three-photon and four-photon
interference of space-time and polarization types has been observed in
experiment, for both coherent and pseudo-thermal light.Comment: 11 pages, 9 figure
ΠΠ²Π°Π½ΡΠΎΠ²ΠΎ-Ρ ΡΠΌΡΡΠ½Π΅ Π΄ΠΎΡΠ»ΡΠ΄ΠΆΠ΅Π½Π½Ρ ΠΌΠ΅Ρ Π°Π½ΡΠ·ΠΌΡ ΡΠ΅Π°ΠΊΡΡΡ Π΅ΠΏΠΎΠΊΡΠΈΠ΄ΡΠ²Π°Π½Π½Ρ Π³Π΅ΡΠ°Π½ΡΠΎΠ»Ρ ΡΠ° Π»ΠΈΠΌΠΎΠ½Π΅Π½Ρ Π½Π°Π΄Π°ΡΠ΅ΡΠ°ΡΠ½ΠΎΡ ΡΠ° Π½Π°Π΄Π±Π΅Π½Π·ΠΎΠΉΠ½ΠΎΡ ΠΊΠΈΡΠ»ΠΎΡΠ°ΠΌΠΈ
Aim. To compare the mechanism of the epoxidation reaction of terpenes Geraniol and Limonene with peracetic acid and perbenzoic acid based on the quantum chemical study.Materials and methods. For the calculation the density functional theory (approximation UBH & HLYP/6-31G (d) Gaussian 09) method was applied. The specified density functional allows to correctly describing biradical structures; it is rather economic in terms of the computer time cost, which allows its use in the study of sufficiently complex organic compounds and reactions.Results and discussion. The quantum chemical study of mechanisms of the epoxidation reaction of such terpenes as Geraniol and Limonene with peracetic and perbenzonic acids using the density functional theory (approximation UBH & HLYP/6-31G (d) Gaussian 09 program) has been conducted. It has been shown that epoxidation of geraniol with both peroxyacids occurs preferably by the double bond C6=C7 due to stabilization of the corresponding transition state as a result of formation of hydrogen bond between the allyl hydroxyl group and the oxygen atom of the peroxy acid. Epoxidation of Limonene with perbenzoic and peracetic acids occurs via the cyclic double bond characterized by the lowest activation barrier, and it is consistent with the regioselectivity of the process generally known and experimentally proven.Conclusions. The results obtained are consistent with the experimental data, confirming the correctness of the use of this UBH & HLYP/6-31G (d) approach to study the regiochemical pecularities of the epoxidation process of alkenes containing several isolated double bonds.Π¦Π΅Π»Ρ β ΡΡΡΠ°Π½ΠΎΠ²Π»Π΅Π½ΠΈΠ΅ ΠΌΠ΅Ρ
Π°Π½ΠΈΠ·ΠΌΠ° ΡΠ΅Π°ΠΊΡΠΈΠΈ ΡΠΏΠΎΠΊΡΠΈΠ΄ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΡΠ΅ΡΠΏΠ΅Π½ΠΎΠΈΠ΄ΠΎΠ² ΠΠ΅ΡΠ°Π½ΠΈΠΎΠ»Π° ΠΈ ΠΠΈΠΌΠΎΠ½eΠ½Π° ΠΏΠ΅ΡΡΠΊΡΡΡΠ½ΠΎΠΉ ΠΈ ΠΏΠ΅ΡΠ±Π΅Π½Π·ΠΎΠΉΠ½ΠΎΠΉ ΠΊΠΈΡΠ»ΠΎΡΠ°ΠΌΠΈ Π½Π° ΠΎΡΠ½ΠΎΠ²Π°Π½ΠΈΠΈ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠΎΠ² ΠΊΠ²Π°Π½ΡΠΎΠ²ΠΎ-Ρ
ΠΈΠΌΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΡ. ΠΠ°ΡΠ΅ΡΠΈΠ°Π»Ρ ΠΈ ΠΌΠ΅ΡΠΎΠ΄Ρ. ΠΠ»Ρ ΡΠ°ΡΡΠ΅ΡΠ° ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π»ΠΈ ΠΌΠ΅ΡΠΎΠ΄ ΡΡΠ½ΠΊΡΠΈΠΎΠ½Π°Π»Π° ΠΏΠ»ΠΎΡΠ½ΠΎΡΡΠΈ (ΠΏΡΠΈΠ±Π»ΠΈΠΆΠ΅Π½ΠΈΠ΅ UBH & HLYP/6-31G (d)) ΠΏΡΠΎΠ³ΡΠ°ΠΌΠΌΡ Gaussian 09. Π£ΠΊΠ°Π·Π°Π½Π½ΡΠΉ ΡΡΠ½ΠΊΡΠΈΠΎΠ½Π°Π» ΠΏΠΎΠ·Π²ΠΎΠ»ΡΠ΅Ρ ΠΊΠΎΡΡΠ΅ΠΊΡΠ½ΠΎ ΠΎΠΏΠΈΡΡΠ²Π°ΡΡ Π±ΠΈΡΠ°Π΄ΠΈΠΊΠ°Π»ΡΠ½ΡΠ΅ ΡΡΡΡΠΊΡΡΡΡ ΠΈ ΡΠ²Π»ΡΠ΅ΡΡΡ Π΄ΠΎΡΡΠ°ΡΠΎΡΠ½ΠΎ ΡΠΊΠΎΠ½ΠΎΠΌΠΈΡΠ½ΡΠΌ Ρ ΡΠΎΡΠΊΠΈ Π·ΡΠ΅Π½ΠΈΡ Π·Π°ΡΡΠ°Ρ ΠΊΠΎΠΌΠΏΡΡΡΠ΅ΡΠ½ΠΎΠ³ΠΎ Π²ΡΠ΅ΠΌΠ΅Π½ΠΈ, ΡΡΠΎ ΠΏΠΎΠ·Π²ΠΎΠ»ΡΠ΅Ρ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°ΡΡ Π΅Π³ΠΎ Π΄Π»Ρ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΡ Π΄ΠΎΡΡΠ°ΡΠΎΡΠ½ΠΎ ΡΠ»ΠΎΠΆΠ½ΡΡ
ΠΎΡΠ³Π°Π½ΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΠΎΠ΅Π΄ΠΈΠ½Π΅Π½ΠΈΠΉ ΠΈ ΡΠ΅Π°ΠΊΡΠΈΠΉ.Π Π΅Π·ΡΠ»ΡΡΠ°ΡΡ ΠΈ ΠΈΡ
ΠΎΠ±ΡΡΠΆΠ΄Π΅Π½ΠΈΠ΅. ΠΡΠΎΠ²Π΅Π΄Π΅Π½ΠΎ ΠΊΠ²Π°Π½ΡΠΎΠ²ΠΎ-Ρ
ΠΈΠΌΠΈΡΠ΅ΡΠΊΠΎΠ΅ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΠ΅ ΠΌΠ΅Ρ
Π°Π½ΠΈΠ·ΠΌΠ° ΡΠ΅Π°ΠΊΡΠΈΠΈ ΡΠΏΠΎΠΊΡΠΈΠ΄ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΡΠ΅ΡΠΏΠ΅Π½ΠΎΠΈΠ΄ΠΎΠ² ΠΠ΅ΡΠ°Π½ΠΈΠΎΠ»Π° ΠΈ ΠΠΈΠΌΠΎΠ½eΠ½Π° ΠΏΠ΅ΡΡΠΊΡΡΡΠ½ΠΎΠΉ ΠΈ ΠΏΠ΅ΡΠ±Π΅Π½Π·ΠΎΠΉΠ½ΠΎΠΉ ΠΊΠΈΡΠ»ΠΎΡΠ°ΠΌΠΈ Ρ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΠ΅ΠΌ ΠΌΠ΅ΡΠΎΠ΄Π° ΡΡΠ½ΠΊΡΠΈΠΎΠ½Π°Π»Π° ΠΏΠ»ΠΎΡΠ½ΠΎΡΡΠΈ (ΠΏΡΠΈΠ±Π»ΠΈΠΆΠ΅Π½ΠΈΠ΅ UBH & HLYP/6-31G (d) ΠΏΡΠΎΠ³ΡΠ°ΠΌΠΌΡ Gaussian 09. ΠΠΎΠΊΠ°Π·Π°Π½ΠΎ, ΡΡΠΎ ΡΠΏΠΎΠΊΡΠΈΠ΄ΠΈΡΠΎΠ²Π°Π½ΠΈΠ΅ ΠΠ΅ΡΠ°Π½ΠΈΠΎΠ»Π° ΠΎΠ±Π΅ΠΈΠΌΠΈ ΠΏΠ΅ΡΠΎΠΊΡΠΈΠΊΠΈΡΠ»ΠΎΡΠ°ΠΌΠΈ ΠΏΡΠΎΠΈΡΡ
ΠΎΠ΄ΠΈΡ Π±ΡΡΡΡΠ΅Π΅ ΠΏΠΎ Π΄Π²ΠΎΠΉΠ½ΠΎΠΉ ΡΠ²ΡΠ·ΠΈ Π‘6=Π‘7 Π±Π»Π°Π³ΠΎΠ΄Π°ΡΡ ΡΡΠ°Π±ΠΈΠ»ΠΈΠ·Π°ΡΠΈΠΈ ΡΠΎΠΎΡΠ²Π΅ΡΡΡΠ²ΡΡΡΠ΅Π³ΠΎ ΠΏΠ΅ΡΠ΅Ρ
ΠΎΠ΄Π½ΠΎΠ³ΠΎ ΡΠΎΡΡΠΎΡΠ½ΠΈΡ Π·Π° ΡΡΠ΅Ρ Π²ΠΎΠ΄ΠΎΡΠΎΠ΄Π½ΠΎΠΉ ΡΠ²ΡΠ·ΠΈ ΠΌΠ΅ΠΆΠ΄Ρ Π²ΠΎΠ΄ΠΎΡΠΎΠ΄ΠΎΠΌ Π³ΠΈΠ΄ΡΠΎΠΊΡΠΈΠ»ΡΠ½ΠΎΠΉ Π³ΡΡΠΏΠΏΡ Π°Π»Π»ΠΈΠ»ΡΠ½ΠΎΠΉ ΡΠΈΡΡΠ΅ΠΌΡ ΠΈ Π°ΡΠΎΠΌΠΎΠΌ ΠΊΠΈΡΠ»ΠΎΡΠΎΠ΄Π° ΠΏΠ΅ΡΠΎΠΊΡΠΈΠΊΠΈΡΠ»ΠΎΡΡ. ΠΠΏΠΎΠΊΡΠΈΠ΄ΠΈΡΠΎΠ²Π°Π½ΠΈΠ΅ ΠΠΈΠΌΠΎΠ½Π΅Π½Π° ΠΏΠ΅ΡΡΠΊΡΡΡΠ½ΠΎΠΉ ΠΈ ΠΏΠ΅ΡΠ±Π΅Π½Π·ΠΎΠΉΠ½ΠΎΠΉ ΠΊΠΈΡΠ»ΠΎΡΠ°ΠΌΠΈ ΠΏΡΠΎΠΈΡΡ
ΠΎΠ΄ΠΈΡ ΠΏΠΎ ΡΠΈΠΊΠ»ΠΈΡΠ΅ΡΠΊΠΎΠΉ Π΄Π²ΠΎΠΉΠ½ΠΎΠΉ ΡΠ²ΡΠ·ΠΈ ΠΈ Ρ
Π°ΡΠ°ΠΊΡΠ΅ΡΠΈΠ·ΡΠ΅ΡΡΡ Π½Π°ΠΈΠΌΠ΅Π½ΡΡΠΈΠΌ Π°ΠΊΡΠΈΠ²Π°ΡΠΈΠΎΠ½Π½ΡΠΌ Π±Π°ΡΡΠ΅ΡΠΎΠΌ, ΡΡΠΎ ΡΠΎΠ³Π»Π°ΡΡΠ΅ΡΡΡ Ρ ΠΎΠ±ΡΠ΅ΠΈΠ·Π²Π΅ΡΡΠ½ΠΎΠΉ ΡΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠ°Π»ΡΠ½ΠΎ Π΄ΠΎΠΊΠ°Π·Π°Π½Π½ΠΎΠΉ ΡΠ΅Π³ΠΈΠΎΡΠ΅Π»Π΅ΠΊΡΠΈΠ²Π½ΠΎΡΡΡΡ ΠΏΡΠΎΡΠ΅ΡΡΠ°.ΠΡΠ²ΠΎΠ΄Ρ. ΠΠΎΠ»ΡΡΠ΅Π½Π½ΡΠ΅ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΡ ΡΠΎΠ³Π»Π°ΡΡΡΡΡΡ Ρ ΡΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠ°Π»ΡΠ½ΡΠΌΠΈ Π΄Π°Π½Π½ΡΠΌΠΈ, ΠΏΠΎΠ΄ΡΠ²Π΅ΡΠΆΠ΄Π°ΡΡ ΠΊΠΎΡΡΠ΅ΠΊΡΠ½ΠΎΡΡΡ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΡ ΠΏΡΠΈΠ±Π»ΠΈΠΆΠ΅Π½ΠΈΡ UBH & HLYP/6-31G (d) Π΄Π»Ρ ΠΈΠ·ΡΡΠ΅Π½ΠΈΡ ΡΠ΅Π³ΠΈΠΎ-Ρ
ΠΈΠΌΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΎΡΠΎΠ±Π΅Π½Π½ΠΎΡΡΠ΅ΠΉ ΡΠΏΠΎΠΊΡΠΈΠ΄ΠΈΡΠΎΠ²Π°Π½ΠΈΡ Π°Π»ΠΊΠ΅Π½ΠΎΠ² Ρ Π½Π΅ΡΠΊΠΎΠ»ΡΠΊΠΈΠΌΠΈ ΠΈΠ·ΠΎΠ»ΠΈΡΠΎΠ²Π°Π½Π½ΡΠΌΠΈ Π΄Π²ΠΎΠΉΠ½ΡΠΌΠΈ ΡΠ²ΡΠ·ΡΠΌΠΈ.ΠΠ΅ΡΠ° β Π·βΡΡΡΠ²Π°Π½Π½Ρ ΠΌΠ΅Ρ
Π°Π½ΡΠ·ΠΌΡ ΡΠ΅Π°ΠΊΡΡΡ Π΅ΠΏΠΎΠΊΡΠΈΠ΄ΡΠ²Π°Π½Π½Ρ ΡΠ΅ΡΠΏΠ΅Π½ΠΎΡΠ΄ΡΠ² ΠΠ΅ΡΠ°Π½ΡΠΎΠ»Ρ ΡΠ° ΠΠΈΠΌΠΎΠ½Π΅Π½Ρ Π½Π°Π΄Π°ΡΠ΅ΡΠ°ΡΠ½ΠΎΡ (ΠΏΠ΅ΡΠΎΠΊΡΡΠ΅ΡΠ°Π½ΠΎΠ²ΠΎΡ) ΡΠ° Π½Π°Π΄Π±Π΅Π½Π·ΠΎΠΉΠ½ΠΎΡ ΠΊΠΈΡΠ»ΠΎΡΠ°ΠΌΠΈ Π·Π° ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠ°ΠΌΠΈ ΠΊΠ²Π°Π½ΡΠΎΠ²ΠΎ-Ρ
ΡΠΌΡΡΠ½ΠΎΠ³ΠΎ Π΄ΠΎΡΠ»ΡΠ΄ΠΆΠ΅Π½Π½Ρ. ΠΠ°ΡΠ΅ΡΡΠ°Π»ΠΈ ΡΠ° ΠΌΠ΅ΡΠΎΠ΄ΠΈ. ΠΠ»Ρ ΡΠΎΠ·ΡΠ°Ρ
ΡΠ½ΠΊΡ Π²ΠΈΠΊΠΎΡΠΈΡΡΠΎΠ²ΡΠ²Π°Π»ΠΈ ΠΌΠ΅ΡΠΎΠ΄ ΡΡΠ½ΠΊΡΡΠΎΠ½Π°Π»Ρ Π³ΡΡΡΠΈΠ½ΠΈ (Π½Π°Π±Π»ΠΈΠΆΠ΅Π½Π½Ρ UBH&HLYP/6-31G(d)) ΠΏΡΠΎΠ³ΡΠ°ΠΌΠΈ Gaussian 09. ΠΠΊΠ°Π·Π°Π½ΠΈΠΉ ΡΡΠ½ΠΊΡΡΠΎΠ½Π°Π» Π΄ΠΎΠ·Π²ΠΎΠ»ΡΡ ΠΊΠΎΡΠ΅ΠΊΡΠ½ΠΎ ΠΎΠΏΠΈΡΡΠ²Π°ΡΠΈ Π±ΡΡΠ°Π΄ΠΈΠΊΠ°Π»ΡΠ½Ρ ΡΡΡΡΠΊΡΡΡΠΈ Ρ Ρ Π΄ΠΎΡΡΠ°ΡΠ½ΡΠΎ Π΅ΠΊΠΎΠ½ΠΎΠΌΡΡΠ½ΠΈΠΌ Π· ΡΠΎΡΠΊΠΈ Π·ΠΎΡΡ Π²ΠΈΡΡΠ°Ρ ΠΊΠΎΠΌΠΏβΡΡΠ΅ΡΠ½ΠΎΠ³ΠΎ ΡΠ°ΡΡ, ΡΠΎ Π΄ΠΎΠ·Π²ΠΎΠ»ΡΡ Π²ΠΈΠΊΠΎΡΠΈΡΡΠΎΠ²ΡΠ²Π°ΡΠΈ ΠΉΠΎΠ³ΠΎ Π΄Π»Ρ Π΄ΠΎΡΠ»ΡΠ΄ΠΆΠ΅Π½Π½Ρ Π΄ΠΎΡΠΈΡΡ ΡΠΊΠ»Π°Π΄Π½ΠΈΡ
ΠΎΡΠ³Π°Π½ΡΡΠ½ΠΈΡ
ΡΠΏΠΎΠ»ΡΠΊ ΡΠ° ΡΠ΅Π°ΠΊΡΡΠΉ. Π Π΅Π·ΡΠ»ΡΡΠ°ΡΠΈ ΡΠ° ΡΡ
ΠΎΠ±Π³ΠΎΠ²ΠΎΡΠ΅Π½Π½Ρ. ΠΠ΄ΡΠΉΡΠ½Π΅Π½Π΅ ΠΊΠ²Π°Π½ΡΠΎΠ²ΠΎ-Ρ
ΡΠΌΡΡΠ½Π΅ Π΄ΠΎΡΠ»ΡΠ΄ΠΆΠ΅Π½Π½Ρ ΠΌΠ΅Ρ
Π°Π½ΡΠ·ΠΌΡ ΡΠ΅Π°ΠΊΡΡΡ Π΅ΠΏΠΎΠΊΡΠΈΠ΄ΡΠ²Π°Π½Π½Ρ ΡΠ΅ΡΠΏΠ΅Π½ΠΎΡΠ΄ΡΠ² ΠΠ΅ΡΠ°Π½ΡΠΎΠ»Ρ ΡΠ° ΠΠΈΠΌΠΎΠ½eΠ½Ρ Π½Π°Π΄Π°ΡΠ΅ΡΠ°ΡΠ½ΠΎΡ ΡΠ° Π½Π°Π΄Π±Π΅Π½Π·ΠΎΠΉΠ½ΠΎΡ ΠΊΠΈΡΠ»ΠΎΡΠ°ΠΌΠΈ Π· Π²ΠΈΠΊΠΎΡΠΈΡΡΠ°Π½Π½ΡΠΌ ΠΌΠ΅ΡΠΎΠ΄Ρ ΡΡΠ½ΠΊΡΡΠΎΠ½Π°Π»Ρ Π³ΡΡΡΠΈΠ½ΠΈ (Π½Π°Π±Π»ΠΈΠΆΠ΅Π½Π½Ρ UBH&HLYP/6-31G(d) ΠΏΡΠΎΠ³ΡΠ°ΠΌΠΈ Gaussian 09. ΠΠΎΠΊΠ°Π·Π°Π½ΠΎ, ΡΠΎ Π΅ΠΏΠΎΠΊΡΠΈΠ΄ΡΠ²Π°Π½Π½Ρ ΠΠ΅ΡΠ°Π½ΡΠΎΠ»Ρ ΠΎΠ±ΠΎΠΌΠ° ΠΏΠ΅ΡΠΎΠΊΡΠΈΠΊΠΈΡΠ»ΠΎΡΠ°ΠΌΠΈ Π²ΡΠ΄Π±ΡΠ²Π°ΡΡΡΡΡ ΡΠ²ΠΈΠ΄ΡΠ΅ Π·Π° ΠΏΠΎΠ΄Π²ΡΠΉΠ½ΠΈΠΌ Π·Π²βΡΠ·ΠΊΠΎΠΌ Π‘6=Π‘7 Π·Π°Π²Π΄ΡΠΊΠΈ ΡΡΠ°Π±ΡΠ»ΡΠ·Π°ΡΡΡ Π²ΡΠ΄ΠΏΠΎΠ²ΡΠ΄Π½ΠΎΠ³ΠΎ ΠΏΠ΅ΡΠ΅Ρ
ΡΠ΄Π½ΠΎΠ³ΠΎ ΡΡΠ°Π½Ρ Π·Π° ΡΠ°Ρ
ΡΠ½ΠΎΠΊ Π²ΠΎΠ΄Π½Π΅Π²ΠΎΠ³ΠΎ Π·Π²βΡΠ·ΠΊΡ ΠΌΡΠΆ ΠΡΠ΄ΡΠΎΠ³Π΅Π½ΠΎΠΌ Π³ΡΠ΄ΡΠΎΠΊΡΠΈΠ»ΡΠ½ΠΎΡ Π³ΡΡΠΏΠΈ Π°Π»ΡΠ»ΡΠ½ΠΎΡ ΡΠΈΡΡΠ΅ΠΌΠΈ ΡΠ° Π°ΡΠΎΠΌΠΎΠΌ ΠΠΊΡΠΈΠ³Π΅Π½Ρ ΠΏΠ΅ΡΠΎΠΊΡΠΈΠΊΠΈΡΠ»ΠΎΡΠΈ. ΠΠΏΠΎΠΊΡΠΈΠ΄ΡΠ²Π°Π½Π½Ρ ΠΠΈΠΌΠΎΠ½Π΅Π½Ρ Π½Π°Π΄Π°ΡΠ΅ΡΠ°ΡΠ½ΠΎΡ ΡΠ° Π½Π°Π΄Π±Π΅Π½Π·ΠΎΠΉΠ½ΠΎΡ ΠΊΠΈΡΠ»ΠΎΡΠ°ΠΌΠΈ Π²ΡΠ΄Π±ΡΠ²Π°ΡΡΡΡΡ Π·Π° ΡΠΈΠΊΠ»ΡΡΠ½ΠΈΠΌ ΠΏΠΎΠ΄Π²ΡΠΉΠ½ΠΈΠΌ Π·Π²βΡΠ·ΠΊΠΎΠΌ Ρ Ρ
Π°ΡΠ°ΠΊΡΠ΅ΡΠΈΠ·ΡΡΡΡΡΡ Π½Π°ΠΉΠΌΠ΅Π½ΡΠΈΠΌ Π°ΠΊΡΠΈΠ²Π°ΡΡΠΉΠ½ΠΈΠΌ Π±Π°ΡβΡΡΠΎΠΌ, ΡΠΎ ΡΠ·Π³ΠΎΠ΄ΠΆΡΡΡΡΡΡ ΡΠ· Π·Π°Π³Π°Π»ΡΠ½ΠΎΠ²ΡΠ΄ΠΎΠΌΠΎΡ Π΅ΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠ°Π»ΡΠ½ΠΎ Π²ΡΡΠ°Π½ΠΎΠ²Π»Π΅Π½ΠΎΡ ΡΠ΅Π³ΡΠΎΡΠ΅Π»Π΅ΠΊΡΠΈΠ²Π½ΡΡΡΡ ΠΏΡΠΎΡΠ΅ΡΡ.ΠΠΈΡΠ½ΠΎΠ²ΠΊΠΈ. ΠΡΡΠΈΠΌΠ°Π½Ρ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠΈ ΡΠ·Π³ΠΎΠ΄ΠΆΡΡΡΡΡΡ Π· Π΅ΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠ°Π»ΡΠ½ΠΈΠΌΠΈ Π΄Π°Π½ΠΈΠΌΠΈ, ΡΠΎ ΠΏΡΠ΄ΡΠ²Π΅ΡΠ΄ΠΆΡΡ ΠΊΠΎΡΠ΅ΠΊΡΠ½ΡΡΡΡ Π²ΠΈΠΊΠΎΡΠΈΡΡΠ°Π½Π½Ρ Π½Π°Π±Π»ΠΈΠΆΠ΅Π½Π½Ρ UBH&HLYP/6-31G(d) Π΄Π»Ρ Π²ΠΈΠ²ΡΠ΅Π½Π½Ρ ΡΠ΅Π³ΡΠΎ-Ρ
ΡΠΌΡΡΠ½ΠΈΡ
ΠΎΡΠΎΠ±Π»ΠΈΠ²ΠΎΡΡΠ΅ΠΉ Π΅ΠΏΠΎΠΊΡΠΈΠ΄ΡΠ²Π°Π½Π½Ρ Π°Π»ΠΊΠ΅Π½ΡΠ² Π· Π΄Π΅ΠΊΡΠ»ΡΠΊΠΎΠΌΠ° ΡΠ·ΠΎΠ»ΡΠΎΠ²Π°Π½ΠΈΠΌΠΈ ΠΏΠΎΠ΄Π²ΡΠΉΠ½ΠΈΠΌΠΈ Π·Π²βΡΠ·ΠΊΠ°ΠΌΠΈ
ΠΠΎΡΡΠ²Π½ΡΠ»ΡΠ½Π΅ ΠΊΠ²Π°Π½ΡΠΎΠ²ΠΎ-Ρ ΡΠΌΡΡΠ½Π΅ Π΄ΠΎΡΠ»ΡΠ΄ΠΆΠ΅Π½Π½Ρ ΠΌΠ΅Ρ Π°Π½ΡΠ·ΠΌΡ ΡΠ΅Π°ΠΊΡΡΡ Π΅ΠΏΠΎΠΊΡΠΈΠ΄ΡΠ²Π°Π½Π½Ρ Π΅Π²Π³Π΅Π½ΠΎΠ»Ρ ΡΠ° ΡΠ·ΠΎΠ΅Π²Π³Π΅Π½ΠΎΠ»Ρ Π½Π°Π΄Π°ΡΠ΅ΡΠ°ΡΠ½ΠΎΡ ΡΠ° Π½Π°Π΄Π±Π΅Π½Π·ΠΎΠΉΠ½ΠΎΡ ΠΊΠΈΡΠ»ΠΎΡΠ°ΠΌΠΈ
Aim. To study the kinetics of the epoxidation reaction for eugenol and isoeugenol with perbenzoic acid, carry out the comparative quantum chemical study of the epoxidation reaction mechanism of eugenol and isoeugenol isomers (2-cis and 2-trans) with peracetic and perbenzoic acids.Results and discussion. The kinetics of the epoxidation reaction of isomeric terpenoids eugenol and isoeugenol with perbenzoic acid in the medium of methylene chloride medium at 293 K was studied using the method of iodometric titration. It was shown that the rate constant of the epoxidation reaction for eugenol was in 5.5 times higher than for isoeugenol. According to the results of quantum chemical calculations using the UBH&HLYP/6-31G (d) approximation, the structures of transition states of eugenol and isoeugenol formed during the epoxidation reactions studied were proposed, and the activation energies for the corresponding reactions were calculated. Based on the results of the studies conducted it was found that the ratio of the activation energies during the interaction of eugenol and isoeugenol with peracetic and perbenzoic acids showed the higher reactivity of isoeugenol.Experimental part. To study the kinetics of the epoxidation reaction the method of iodometric titration was used. The method of the functional density (software Gaussian 09, approximation UBH&HLYP/6-31G (d)) was applied for calculation.Conclusions. The results of the quantum chemical study of the epoxidation reaction mechanism of eugenol and isoeugenol are consistent with the kinetic data experimentally obtained; it confirms the correctness of using the UBH&HLYP/6-31G (d) approximation for studying the features of epoxidation of isomeric terpenoids with organic peracids.Π¦Π΅Π»Ρ. ΠΠ·ΡΡΠΈΡΡ ΠΊΠΈΠ½Π΅ΡΠΈΠΊΡ ΡΠ΅Π°ΠΊΡΠΈΠΈ ΡΠΏΠΎΠΊΡΠΈΠ΄ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΡΠ²Π³Π΅Π½ΠΎΠ»Π° ΠΈ ΠΈΠ·ΠΎΡΠ²Π³Π΅Π½ΠΎΠ»Π° ΠΏΠ΅ΡΠ±Π΅Π½Π·ΠΎΠΉΠ½ΠΎΠΉ ΠΊΠΈΡΠ»ΠΎΡΠΎΠΉ, ΠΏΡΠΎΠ²Π΅ΡΡΠΈ ΡΡΠ°Π²Π½ΠΈΡΠ΅Π»ΡΠ½ΠΎΠ΅ ΠΊΠ²Π°Π½ΡΠΎΠ²ΠΎ-Ρ
ΠΈΠΌΠΈΡΠ΅ΡΠΊΠΎΠ΅ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΠ΅ ΠΌΠ΅Ρ
Π°Π½ΠΈΠ·ΠΌΠ° ΡΠ΅Π°ΠΊΡΠΈΠΈ ΡΠΏΠΎΠΊΡΠΈΠ΄ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΡΠ²Π³Π΅Π½ΠΎΠ»Π° ΠΈ Π΄Π²ΡΡ
ΠΈΠ·ΠΎΠΌΠ΅ΡΠΎΠ² ΠΈΠ·ΠΎΡΠ²Π³Π΅Π½ΠΎΠ»Π° (2-ΡΠΈΡ ΠΈ 2-ΡΡΠ°Π½Ρ) ΠΏΠ΅ΡΡΠΊΡΡΡΠ½ΠΎΠΉ ΠΈ ΠΏΠ΅ΡΠ±Π΅Π½Π·ΠΎΠΉΠ½ΠΎΠΉ ΠΊΠΈΡΠ»ΠΎΡΠ°ΠΌΠΈ.Π Π΅Π·ΡΠ»ΡΡΠ°ΡΡ ΠΈ ΠΎΠ±ΡΡΠΆΠ΄Π΅Π½ΠΈΠ΅. ΠΠ΅ΡΠΎΠ΄ΠΎΠΌ ΠΉΠΎΠ΄ΠΎΠΌΠ΅ΡΡΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΡΠΈΡΡΠΎΠ²Π°Π½ΠΈΡ ΠΈΠ·ΡΡΠ΅Π½Π° ΠΊΠΈΠ½Π΅ΡΠΈΠΊΠ° ΡΠ΅Π°ΠΊΡΠΈΠΈ ΡΠΏΠΎΠΊΡΠΈΠ΄ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΈΠ·ΠΎΠΌΠ΅ΡΠ½ΡΡ
ΡΠ΅ΡΠΏΠ΅Π½ΠΎΠΈΠ΄ΠΎΠ² ΡΠ²Π³Π΅Π½ΠΎΠ»Π° ΠΈ ΠΈΠ·ΠΎΡΠ²Π³Π΅Π½ΠΎΠ»Π° ΠΏΠ΅ΡΠ±Π΅Π½Π·ΠΎΠΉΠ½ΠΎΠΉ ΠΊΠΈΡΠ»ΠΎΡΠΎΠΉ Π² ΡΡΠ΅Π΄Π΅ Ρ
Π»ΠΎΡΠΈΡΡΠΎΠ³ΠΎ ΠΌΠ΅ΡΠΈΠ»Π΅Π½Π° ΠΏΡΠΈ 298 Π ΠΈ ΠΏΠΎΠΊΠ°Π·Π°Π½ΠΎ, ΡΡΠΎ ΠΊΠΎΠ½ΡΡΠ°Π½ΡΠ° ΡΠΊΠΎΡΠΎΡΡΠΈ ΡΠ΅Π°ΠΊΡΠΈΠΈ ΡΠΏΠΎΠΊΡΠΈΠ΄ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΡΠ²Π³Π΅Π½ΠΎΠ»Π° Π² 5,5 ΡΠ°Π· Π²ΡΡΠ΅, ΡΠ΅ΠΌ ΠΈΠ·ΠΎΡΠ²Π³Π΅Π½ΠΎΠ»Π°. ΠΠΎ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠ°ΠΌ ΠΊΠ²Π°Π½ΡΠΎΠ²ΠΎ-Ρ
ΠΈΠΌΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΠ°ΡΡΠ΅ΡΠΎΠ² Ρ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΠ΅ΠΌ ΠΏΡΠΈΠ±Π»ΠΈΠΆΠ΅Π½ΠΈΡ UBH&HLYP/6-31G (d) ΠΏΡΠ΅Π΄Π»ΠΎΠΆΠ΅Π½Ρ ΡΡΡΡΠΊΡΡΡΡ ΠΏΠ΅ΡΠ΅Ρ
ΠΎΠ΄Π½ΡΡ
ΡΠΎΡΡΠΎΡΠ½ΠΈΠΉ ΡΠ²Π³Π΅Π½ΠΎΠ»Π° ΠΈ ΠΈΠ·ΠΎΡΠ²Π³Π΅Π½ΠΎΠ»Π°, ΠΎΠ±ΡΠ°Π·ΡΡΡΠΈΠ΅ΡΡ Π² Ρ
ΠΎΠ΄Π΅ ΠΈΠ·ΡΡΠ΅Π½Π½ΡΡ
ΡΠ΅Π°ΠΊΡΠΈΠΉ ΡΠΏΠΎΠΊΡΠΈΠ΄ΠΈΡΠΎΠ²Π°Π½ΠΈΡ, ΠΈ ΡΠ°ΡΡΡΠΈΡΠ°Π½Ρ Π·Π½Π°ΡΠ΅Π½ΠΈΡ ΡΠ½Π΅ΡΠ³ΠΈΠΉ Π°ΠΊΡΠΈΠ²Π°ΡΠΈΠΈ Π΄Π»Ρ ΡΠΎΠΎΡΠ²Π΅ΡΡΡΠ²ΡΡΡΠΈΡ
ΡΠ΅Π°ΠΊΡΠΈΠΉ. ΠΡΡ
ΠΎΠ΄Ρ ΠΈΠ· ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠΎΠ² ΠΏΡΠΎΠ²Π΅Π΄Π΅Π½Π½ΡΡ
ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΠΉ ΡΡΡΠ°Π½ΠΎΠ²Π»Π΅Π½ΠΎ, ΡΡΠΎ ΡΠΎΠΎΡΠ½ΠΎΡΠ΅Π½ΠΈΠ΅ ΡΠ½Π΅ΡΠ³ΠΈΠΉ Π°ΠΊΡΠΈΠ²Π°ΡΠΈΠΈ ΠΏΡΠΈ Π²Π·Π°ΠΈΠΌΠΎΠ΄Π΅ΠΉΡΡΠ²ΠΈΠΈ ΡΠ²Π³Π΅Π½ΠΎΠ»Π° ΠΈ ΠΈΠ·ΠΎΡΠ²Π³Π΅Π½ΠΎΠ»Π° Ρ ΠΏΠ΅ΡΡΠΊΡΡΡΠ½ΠΎΠΉ ΠΈ ΠΏΠ΅ΡΠ±Π΅Π½Π·ΠΎΠΉΠ½ΠΎΠΉ ΠΊΠΈΡΠ»ΠΎΡΠ°ΠΌΠΈ ΡΠ²ΠΈΠ΄Π΅ΡΠ΅Π»ΡΡΡΠ²ΡΠ΅Ρ ΠΎ Π±ΠΎΠ»Π΅Π΅ Π²ΡΡΠΎΠΊΠΎΠΉ ΡΠ΅Π°ΠΊΡΠΈΠΎΠ½Π½ΠΎΠΉ ΡΠΏΠΎΡΠΎΠ±Π½ΠΎΡΡΠΈ ΠΈΠ·ΠΎΡΠ²Π³Π΅Π½ΠΎΠ»Π°.ΠΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠ°Π»ΡΠ½Π°Ρ ΡΠ°ΡΡΡ. ΠΠ»Ρ ΠΈΠ·ΡΡΠ΅Π½ΠΈΡ ΠΊΠΈΠ½Π΅ΡΠΈΠΊΠΈ ΡΠ΅Π°ΠΊΡΠΈΠΈ ΡΠΏΠΎΠΊΡΠΈΠ΄ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π»ΠΈ ΠΌΠ΅ΡΠΎΠ΄ ΠΉΠΎΠ΄ΠΎΠΌΠ΅ΡΡΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΡΠΈΡΡΠΎΠ²Π°Π½ΠΈΡ. ΠΠ»Ρ ΡΠ°ΡΡΠ΅ΡΠ° ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π»ΠΈ ΠΌΠ΅ΡΠΎΠ΄ ΡΡΠ½ΠΊΡΠΈΠΎΠ½Π°Π»Π° ΠΏΠ»ΠΎΡΠ½ΠΎΡΡΠΈ (ΠΏΡΠΈΠ±Π»ΠΈΠΆΠ΅Π½ΠΈΠ΅ UBH&HLYP/6-31G (d)) ΠΏΡΠΎΠ³ΡΠ°ΠΌΠΌΡ Gaussian 09.ΠΡΠ²ΠΎΠ΄Ρ. Π Π΅Π·ΡΠ»ΡΡΠ°ΡΡ ΠΊΠ²Π°Π½ΡΠΎΠ²ΠΎ-Ρ
ΠΈΠΌΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΡ ΠΌΠ΅Ρ
Π°Π½ΠΈΠ·ΠΌΠ° ΡΠ΅Π°ΠΊΡΠΈΠΈ ΡΠΏΠΎΠΊΡΠΈΠ΄ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΡΠ²Π³Π΅Π½ΠΎΠ»Π° ΠΈ ΠΈΠ·ΠΎΡΠ²Π³Π΅Π½ΠΎΠ»Π° ΡΠΎΠ³Π»Π°ΡΡΡΡΡΡ Ρ ΡΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠ°Π»ΡΠ½ΠΎ ΠΏΠΎΠ»ΡΡΠ΅Π½Π½ΡΠΌΠΈ ΠΊΠΈΠ½Π΅ΡΠΈΡΠ΅ΡΠΊΠΈΠΌΠΈ Π΄Π°Π½Π½ΡΠΌΠΈ, ΡΡΠΎ ΠΏΠΎΠ΄ΡΠ²Π΅ΡΠΆΠ΄Π°Π΅Ρ ΠΊΠΎΡΡΠ΅ΠΊΡΠ½ΠΎΡΡΡ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΡ ΠΏΡΠΈΠ±Π»ΠΈΠΆΠ΅Π½ΠΈΡ UBH&HLYP/6-31G (d) Π΄Π»Ρ ΠΈΠ·ΡΡΠ΅Π½ΠΈΡ ΠΎΡΠΎΠ±Π΅Π½Π½ΠΎΡΡΠ΅ΠΉ ΡΠΏΠΎΠΊΡΠΈΠ΄ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΈΠ·ΠΎΠΌΠ΅ΡΠ½ΡΡ
ΡΠ΅ΡΠΏΠ΅Π½ΠΎΠΈΠ΄ΠΎΠ² Ρ ΠΏΠΎΠΌΠΎΡΡΡ ΠΎΡΠ³Π°Π½ΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΏΠ΅ΡΠΊΠΈΡΠ»ΠΎΡ.ΠΠ΅ΡΠ°. ΠΠΎΡΠ»ΡΠ΄ΠΈΡΠΈ ΠΊΡΠ½Π΅ΡΠΈΠΊΡ ΡΠ΅Π°ΠΊΡΡΡ Π΅ΠΏΠΎΠΊΡΠΈΠ΄ΡΠ²Π°Π½Π½Ρ Π΅Π²Π³Π΅Π½ΠΎΠ»Ρ ΡΠ° ΡΠ·ΠΎΠ΅Π²Π³Π΅Π½ΠΎΠ»Ρ Π½Π°Π΄Π±Π΅Π½Π·ΠΎΠΉΠ½ΠΎΡ ΠΊΠΈΡΠ»ΠΎΡΠΎΡ, ΠΏΡΠΎΠ²Π΅ΡΡΠΈ ΠΏΠΎΡΡΠ²Π½ΡΠ»ΡΠ½Π΅ ΠΊΠ²Π°Π½ΡΠΎΠ²ΠΎ-Ρ
ΡΠΌΡΡΠ½Π΅ Π΄ΠΎΡΠ»ΡΠ΄ΠΆΠ΅Π½Π½Ρ ΠΌΠ΅Ρ
Π°Π½ΡΠ·ΠΌΡ ΡΠ΅Π°ΠΊΡΡΡ Π΅ΠΏΠΎΠΊΡΠΈΠ΄ΡΠ²Π°Π½Π½Ρ Π΅Π²Π³Π΅Π½ΠΎΠ»Ρ ΡΠ° Π΄Π²ΠΎΡ
ΡΠ·ΠΎΠΌΠ΅ΡΡΠ² ΡΠ·ΠΎΠ΅Π²Π³Π΅Π½ΠΎΠ»Ρ (2-ΡΠΈΡ ΡΠ° 2-ΡΡΠ°Π½Ρ) Π½Π°Π΄Π°ΡΠ΅ΡΠ°ΡΠ½ΠΎΡ ΡΠ° Π½Π°Π΄Π±Π΅Π½Π·ΠΎΠΉΠ½ΠΎΡ ΠΊΠΈΡΠ»ΠΎΡΠ°ΠΌΠΈ.Π Π΅Π·ΡΠ»ΡΡΠ°ΡΠΈ ΡΠ° ΠΎΠ±Π³ΠΎΠ²ΠΎΡΠ΅Π½Π½Ρ. ΠΠ΅ΡΠΎΠ΄ΠΎΠΌ ΠΉΠΎΠ΄ΠΎΠΌΠ΅ΡΡΠΈΡΠ½ΠΎΠ³ΠΎ ΡΠΈΡΡΡΠ²Π°Π½Π½Ρ Π²ΠΈΠ²ΡΠ΅Π½ΠΎ ΠΊΡΠ½Π΅ΡΠΈΠΊΡ ΡΠ΅Π°ΠΊΡΡΡ Π΅ΠΏΠΎΠΊΡΠΈΠ΄ΡΠ²Π°Π½Π½Ρ ΡΠ·ΠΎΠΌΠ΅ΡΠ½ΠΈΡ
ΡΠ΅ΡΠΏΠ΅Π½ΠΎΡΠ΄ΡΠ² Π΅Π²Π³Π΅Π½ΠΎΠ»Ρ ΡΠ° ΡΠ·oΠ΅Π²Π³Π΅Π½ΠΎΠ»Ρ Π½Π°Π΄Π±Π΅Π½Π·ΠΎΠΉΠ½ΠΎΡ ΠΊΠΈΡΠ»ΠΎΡΠΎΡ Π² ΡΠ΅ΡΠ΅Π΄ΠΎΠ²ΠΈΡΡ ΠΌΠ΅ΡΠΈΠ»Π΅Π½Ρ
Π»ΠΎΡΠΈΠ΄Ρ ΠΏΡΠΈ 293 Π Ρ ΠΏΠΎΠΊΠ°Π·Π°Π½ΠΎ, ΡΠΎ ΠΊΠΎΠ½ΡΡΠ°Π½ΡΠ° ΡΠ²ΠΈΠ΄ΠΊΠΎΡΡΡ ΡΠ΅Π°ΠΊΡΡΡ Π΅ΠΏΠΎΠΊΡΠΈΠ΄ΡΠ²Π°Π½Π½Ρ Π΅Π²Π³Π΅Π½ΠΎΠ»Ρ Π² 5,5 ΡΠ°Π·ΡΠ² Π²ΠΈΡΠ΅, Π½ΡΠΆ Π΄Π»Ρ ΡΠ·ΠΎΠ΅Π²Π³Π΅Π½ΠΎΠ»Ρ. ΠΠ° ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠ°ΠΌΠΈ ΠΊΠ²Π°Π½ΡΠΎΠ²ΠΎ-Ρ
ΡΠΌΡΡΠ½ΠΈΡ
ΡΠΎΠ·ΡΠ°Ρ
ΡΠ½ΠΊΡΠ² Π· Π²ΠΈΠΊΠΎΡΠΈΡΡΠ°Π½Π½ΡΠΌ Π½Π°Π±Π»ΠΈΠΆΠ΅Π½Π½Ρ UBH&HLYP/6-31G (d) Π·Π°ΠΏΡΠΎΠΏΠΎΠ½ΠΎΠ²Π°Π½ΠΎ ΡΡΡΡΠΊΡΡΡΠΈ ΠΏΠ΅ΡΠ΅Ρ
ΡΠ΄Π½ΠΈΡ
ΡΡΠ°Π½ΡΠ² Π΅Π²Π³Π΅Π½ΠΎΠ»Ρ ΡΠ° ΡΠ·ΠΎΠ΅Π²Π³Π΅Π½ΠΎΠ»Ρ, ΡΠΎ ΡΡΠ²ΠΎΡΡΡΡΡΡΡ Π² Ρ
ΠΎΠ΄Ρ Π²ΠΈΠ²ΡΠ΅Π½ΠΈΡ
ΡΠ΅Π°ΠΊΡΡΠΉ Π΅ΠΏΠΎΠΊΡΠΈΠ΄ΡΠ²Π°Π½Π½Ρ, Ρ ΡΠΎΠ·ΡΠ°Ρ
ΠΎΠ²Π°Π½ΠΎ Π·Π½Π°ΡΠ΅Π½Π½Ρ Π΅Π½Π΅ΡΠ³ΡΠΉ Π°ΠΊΡΠΈΠ²Π°ΡΡΡ Π΄Π»Ρ Π²ΡΠ΄ΠΏΠΎΠ²ΡΠ΄Π½ΠΈΡ
ΡΠ΅Π°ΠΊΡΡΠΉ. ΠΠΈΡ
ΠΎΠ΄ΡΡΠΈ Π· ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΡΠ² ΠΏΡΠΎΠ²Π΅Π΄Π΅Π½ΠΈΡ
Π΄ΠΎΡΠ»ΡΠ΄ΠΆΠ΅Π½Ρ Π²ΡΡΠ°Π½ΠΎΠ²Π»Π΅Π½ΠΎ, ΡΠΎ ΡΠΏΡΠ²Π²ΡΠ΄Π½ΠΎΡΠ΅Π½Π½Ρ Π΅Π½Π΅ΡΠ³ΡΠΉ Π°ΠΊΡΠΈΠ²Π°ΡΡΡ ΠΏΡΠΈ Π²Π·Π°ΡΠΌΠΎΠ΄ΡΡ Π΅Π²Π³Π΅Π½ΠΎΠ»Ρ ΡΠ° ΡΠ·ΠΎΠ΅Π²Π³Π΅Π½ΠΎΠ»Ρ Π· Π½Π°Π΄Π°ΡΠ΅ΡΠ°ΡΠ½ΠΎΡ Ρ Π½Π°Π΄Π±Π΅Π½Π·ΠΎΠΉΠ½ΠΎΡ ΠΊΠΈΡΠ»ΠΎΡΠ°ΠΌΠΈ ΡΠ²ΡΠ΄ΡΠΈΡΡ ΠΏΡΠΎ Π±ΡΠ»ΡΡ Π²ΠΈΡΠΎΠΊΡ ΡΠ΅Π°ΠΊΡΡΠΉΠ½Ρ Π·Π΄Π°ΡΠ½ΡΡΡΡ ΡΠ·ΠΎΠ΅Π²Π³Π΅Π½ΠΎΠ»Ρ.ΠΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠ°Π»ΡΠ½Π° ΡΠ°ΡΡΠΈΠ½Π°. ΠΠ»Ρ Π²ΠΈΠ²ΡΠ΅Π½Π½Ρ ΠΊΡΠ½Π΅ΡΠΈΠΊΠΈ ΡΠ΅Π°ΠΊΡΡΡ Π΅ΠΏΠΎΠΊΡΠΈΠ΄ΡΠ²Π°Π½Π½Ρ Π²ΠΈΠΊΠΎΡΠΈΡΡΠΎΠ²ΡΠ²Π°Π»ΠΈ ΠΌΠ΅ΡΠΎΠ΄ ΠΉΠΎΠ΄ΠΎΠΌΠ΅ΡΡΠΈΡΠ½ΠΎΠ³ΠΎ ΡΠΈΡΡΡΠ²Π°Π½Π½Ρ. ΠΠ»Ρ ΡΠΎΠ·ΡΠ°Ρ
ΡΠ½ΠΊΡΠ² Π²ΠΈΠΊΠΎΡΠΈΡΡΠΎΠ²ΡΠ²Π°Π»ΠΈ ΠΌΠ΅ΡΠΎΠ΄ ΡΡΠ½ΠΊΡΡΠΎΠ½Π°Π»Ρ Π³ΡΡΡΠΈΠ½ΠΈ (Π½Π°Π±Π»ΠΈΠΆΠ΅Π½Π½Ρ UBH&HLYP/6-31G (d)) ΠΏΡΠΎΠ³ΡΠ°ΠΌΠΈ Gaussian 09.ΠΠΈΡΠ½ΠΎΠ²ΠΊΠΈ. Π Π΅Π·ΡΠ»ΡΡΠ°ΡΠΈ ΠΊΠ²Π°Π½ΡΠΎΠ²ΠΎ-Ρ
ΡΠΌΡΡΠ½ΠΎΠ³ΠΎ Π΄ΠΎΡΠ»ΡΠ΄ΠΆΠ΅Π½Π½Ρ ΠΌΠ΅Ρ
Π°Π½ΡΠ·ΠΌΡ ΡΠ΅Π°ΠΊΡΡΡ Π΅ΠΏΠΎΠΊΡΠΈΠ΄ΡΠ²Π°Π½Π½Ρ Π΅Π²Π³Π΅Π½ΠΎΠ»Ρ ΡΠ° ΡΠ·ΠΎΠ΅Π²Π³Π΅Π½ΠΎΠ»Ρ ΡΠ·Π³ΠΎΠ΄ΠΆΡΡΡΡΡΡ Π· Π΅ΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠ°Π»ΡΠ½ΠΎ ΠΎΡΡΠΈΠΌΠ°Π½ΠΈΠΌΠΈ ΠΊΡΠ½Π΅ΡΠΈΡΠ½ΠΈΠΌΠΈ Π΄Π°Π½ΠΈΠΌΠΈ, ΡΠΎ ΠΏΡΠ΄ΡΠ²Π΅ΡΠ΄ΠΆΡΡ ΠΊΠΎΡΠ΅ΠΊΡΠ½ΡΡΡΡ Π²ΠΈΠΊΠΎΡΠΈΡΡΠ°Π½Π½Ρ Π½Π°Π±Π»ΠΈΠΆΠ΅Π½Π½Ρ UBH&HLYP/6-31G (d) Π΄Π»Ρ Π²ΠΈΠ²ΡΠ΅Π½Π½Ρ ΠΎΡΠΎΠ±Π»ΠΈΠ²ΠΎΡΡΠ΅ΠΉ Π΅ΠΏΠΎΠΊΡΠΈΠ΄ΡΠ²Π°Π½Π½Ρ ΡΠ·ΠΎΠΌΠ΅ΡΠ½ΠΈΡ
ΡΠ΅ΡΠΏΠ΅Π½ΠΎΡΠ΄ΡΠ² Π·Π° Π΄ΠΎΠΏΠΎΠΌΠΎΠ³ΠΎΡ ΠΎΡΠ³Π°Π½ΡΡΠ½ΠΈΡ
Π½Π°Π΄ΠΊΠΈΡΠ»ΠΎΡ
Medical and sociological problems of cryptorchism
The problem of cryptorchidism is still of great medical and sociological
importance. Normally, at the birth of a full-term boy, the testicles should be in the
scrotum. One of the most common malformations is cryptorchidism. It occurs in 30%
of newborns, 2-4% of boys aged 1 year, and 1.8-2% - up to 15 years. In adults, the
incidence of cryptorchidism reaches 0.18-8%. Over the last 15 years, there has been a
tendency to increase the number of cases of this malformation, but the reasons for this
have not yet been established
Laplace transformations of hydrodynamic type systems in Riemann invariants: periodic sequences
The conserved densities of hydrodynamic type system in Riemann invariants
satisfy a system of linear second order partial differential equations. For
linear systems of this type Darboux introduced Laplace transformations,
generalising the classical transformations in the scalar case. It is
demonstrated that Laplace transformations can be pulled back to the
transformations of the corresponding hydrodynamic type systems. We discuss
periodic Laplace sequences of with the emphasize on the simplest nontrivial
case of period 2. For 3-component systems in Riemann invariants a complete
discription of closed quadruples is proposed. They turn to be related to a
special quadratic reduction of the (2+1)-dimensional 3-wave system which can be
reduced to a triple of pairwize commuting Monge-Ampere equations. In terms of
the Lame and rotation coefficients Laplace transformations have a natural
interpretation as the symmetries of the Dirac operator, associated with the
(2+1)-dimensional n-wave system. The 2-component Laplace transformations can be
interpreted also as the symmetries of the (2+1)-dimensional integrable
equations of Davey-Stewartson type. Laplace transformations of hydrodynamic
type systems originate from a canonical geometric correspondence between
systems of conservation laws and line congruences in projective space.Comment: 22 pages, Late
Algebraic varieties in Birkhoff strata of the Grassmannian Gr: Harrison cohomology and integrable systems
Local properties of families of algebraic subsets in Birkhoff strata
of Gr containing hyperelliptic curves of genus are
studied. It is shown that the tangent spaces for are isomorphic to
linear spaces of 2-coboundaries. Particular subsets in are described by
the intergrable dispersionless coupled KdV systems of hydrodynamical type
defining a special class of 2-cocycles and 2-coboundaries in . It is
demonstrated that the blows-ups of such 2-cocycles and 2-coboundaries and
gradient catastrophes for associated integrable systems are interrelated.Comment: 28 pages, no figures. Generally improved version, in particular the
Discussion section. Added references. Corrected typo
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