428 research outputs found
Majorana fermions in pinned vortices
Exploiting the peculiar properties of proximity-induced superconductivity on
the surface of a topological insulator, we propose a device which allows the
creation of a Majorana fermion inside the core of a pinned Abrikosov vortex.
The relevant Bogolyubov-de Gennes equations are studied analytically. We
demonstrate that in this system the zero-energy Majorana fermion state is
separated by a large energy gap, of the order of the zero-temperature
superconducting gap , from a band of single-particle non-topological
excitations. In other words, the Majorana fermion remains robust against
thermal fluctuations, as long as the temperature remains substantially lower
than the critical superconducting temperature. Experimentally, the Majorana
state may be detected by measuring the tunneling differential conductance at
the center of the Abrikosov vortex. In such an experiment, the Majorana state
manifests itself as a zero-bias anomaly separated by a gap, of the order of
, from the contributions of the nontopological excitations.Comment: 9 pages, 2 eps figures, new references are added, several typos are
correcte
Instabilities of the AA-stacked graphene bilayer
Tight-binding calculations predict that the AA-stacked graphene bilayer has
one electron and one hole conducting bands, and that the Fermi surfaces of
these bands coincide. We demonstrate that as a result of this degeneracy, the
bilayer becomes unstable with respect to a set of spontaneous symmetry
violations. Which of the symmetries is broken depends on the microscopic
details of the system. We find that antiferromagnetism is the more stable order
parameter. This order is stabilized by the strong on-site Coulomb repulsion.
For an on-site repulsion energy typical for graphene systems, the
antiferromagnetic gap can exist up to room temperatures.Comment: 4 pages, 2 eps figure, submitted to Phys. Rev. Let
Π‘ΠΈΠ½ΡΠ΅Π· Π½ΠΎΠ²ΠΈΡ ΡΠΏΡΡΠΎΡΠΈΠΊΠ»ΡΡΠ½ΠΈΡ N-Π°ΡΠΈΠ»Π·Π°ΠΌΡΡΠ΅Π½ΠΈΡ 2-ΡΡΠΎΠΏΡΡΠΈΠΌΡΠ΄ΠΈΠ½-4,6-Π΄ΡΠΎΠ½ΡΠ²
A convenient and efficient method for the synthesis of new unsaturated spiro-annulated N-aryl-4,6-dioxopyrimidine-2-thione derivatives has been developed. The resulting compounds can be potential biological active molecules or precursors for further chemical modification.Aim. To develop the methods for the synthesis of new unsaturated spiro-annulated 2-thiopyrimidine-4,6-dione derivatives, which can be used as potentially biological active molecules or precursors for their formation.Results and discussion. By condensation of N-aryl-substituted thioureas and allylmalonic acid using acetic anhydride or acetyl chloride the series of 5-allyl-substituted 2-thiopyrimidinediones has been synthesized. Their further alkylation with allyl bromide or metallyl chloride led to formation of 5,5-dialkenyl derivatives, which were converted to the corresponding unsaturated spirocyclic dioxopyrimidine-2-thiones by ring-closing metathesis.Β Experimental part. The synthesis of the starting compounds and title products was performed by preparative chemical methods, TLC and column chromatography, elemental analysis, NMR-spectroscopy.Conclusions. The efficient three-step synthetic route of new unsaturated spiro-annulated N-aryl-4,6-dioxopyrimidine-2-thione derivatives from the starting N-arylsubstituted thioureas and allylmalonic acid has been developed. The spiro-annulated products obtained can find application in biological and pharmaceutical science or as starting substrates for further chemical modification.Π Π°Π·ΡΠ°Π±ΠΎΡΠ°Π½ ΡΠ΄ΠΎΠ±Π½ΡΠΉ ΠΈ ΡΡΡΠ΅ΠΊΡΠΈΠ²Π½ΡΠΉ ΠΌΠ΅ΡΠΎΠ΄ ΡΠΈΠ½ΡΠ΅Π·Π° Π½ΠΎΠ²ΡΡ
Π½Π΅Π½Π°ΡΡΡΠ΅Π½Π½ΡΡ
ΡΠΏΠΈΡΠΎ-Π°Π½Π½Π΅Π»ΠΈΡΠΎΠ²Π°Π½Π½ΡΡ
N-Π°ΡΠΈΠ»Π·Π°ΠΌΠ΅ΡΠ΅Π½Π½ΡΡ
2-ΡΠΈΠΎΠΏΠΈΡΠΈΠΌΠΈΠ΄ΠΈΠ½-4,6-Π΄ΠΈΠΎΠ½ΠΎΠ². ΠΠΎΠ»ΡΡΠ΅Π½Π½ΡΠ΅ ΡΠΎΠ΅Π΄ΠΈΠ½Π΅Π½ΠΈΡ ΠΌΠΎΠ³ΡΡ Π±ΡΡΡ ΠΏΠΎΡΠ΅Π½ΡΠΈΠ°Π»ΡΠ½ΡΠΌΠΈ Π±ΠΈΠΎΠ°ΠΊΡΠΈΠ²Π½ΡΠΌΠΈ ΠΌΠΎΠ»Π΅ΠΊΡΠ»Π°ΠΌΠΈ ΠΈΠ»ΠΈ ΠΈΡΡ
ΠΎΠ΄Π½ΡΠΌΠΈ Π²Π΅ΡΠ΅ΡΡΠ²Π°ΠΌΠΈ Π΄Π»Ρ Π΄Π°Π»ΡΠ½Π΅ΠΉΡΠ΅ΠΉ Ρ
ΠΈΠΌΠΈΡΠ΅ΡΠΊΠΎΠΉ ΠΌΠΎΠ΄ΠΈΡΠΈΠΊΠ°ΡΠΈΠΈ.Π¦Π΅Π»Ρ ΡΠ°Π±ΠΎΡΡ β ΡΠ°Π·ΡΠ°Π±ΠΎΡΠΊΠ° ΠΌΠ΅ΡΠΎΠ΄ΠΎΠ² ΠΏΠΎΠ»ΡΡΠ΅Π½ΠΈΡ Π½ΠΎΠ²ΡΡ
Π½Π΅Π½Π°ΡΡΡΠ΅Π½Π½ΡΡ
ΡΠΏΠΈΡΠΎ-Π°Π½Π½Π΅Π»ΠΈΡΠΎΠ²Π°Π½Π½ΡΡ
ΠΏΡΠΎΠΈΠ·Π²ΠΎΠ΄Π½ΡΡ
2-ΡΠΈΠΎΠΏΠΈΡΠΈΠΌΠΈΠ΄ΠΈΠ½-4,6-Π΄ΠΈΠΎΠ½Π° ΠΊΠ°ΠΊ ΠΏΠΎΡΠ΅Π½ΡΠΈΠ°Π»ΡΠ½ΡΡ
Π±ΠΈΠΎΠ»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΈ Π°ΠΊΡΠΈΠ²Π½ΡΡ
ΡΠΎΠ΅Π΄ΠΈΠ½Π΅Π½ΠΈΠΉ ΠΈΠ»ΠΈ ΠΏΠΎΠ»ΡΠΏΡΠΎΠ΄ΡΠΊΡΠΎΠ² Π΄Π»Ρ ΠΈΡ
ΠΏΠΎΠ»ΡΡΠ΅Π½ΠΈΡ.Π Π΅Π·ΡΠ»ΡΡΠ°ΡΡ ΠΈ ΠΈΡ
ΠΎΠ±ΡΡΠΆΠ΄Π΅Π½ΠΈΠ΅. ΠΠΎΠ½Π΄Π΅Π½ΡΠ°ΡΠΈΠ΅ΠΉ N-Π°ΡΠΈΠ»Π·Π°ΠΌΠ΅ΡΠ΅Π½Π½ΡΡ
ΡΠΈΠΎΠΌΠΎΡΠ΅Π²ΠΈΠ½ ΠΈ Π°Π»Π»ΠΈΠ»ΠΌΠ°Π»ΠΎΠ½ΠΎΠ²ΠΎΠΉ ΠΊΠΈΡΠ»ΠΎΡΡ Ρ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΠ΅ΠΌ ΡΠΊΡΡΡΠ½ΠΎΠ³ΠΎ Π°Π½Π³ΠΈΠ΄ΡΠΈΠ΄Π° ΠΈΠ»ΠΈ Π°ΡΠ΅ΡΠΈΠ»Ρ
Π»ΠΎΡΠΈΠ΄Π° ΡΠΈΠ½ΡΠ΅Π·ΠΈΡΠΎΠ²Π°Π½ ΡΡΠ΄ 5-Π°Π»Π»ΠΈΠ»Π·Π°ΠΌΠ΅ΡΠ΅Π½Π½ΡΡ
2-ΡΠΈΠΎΠΏΠΈΡΠΈΠΌΠΈΠ΄ΠΈΠ½Π΄ΠΈΠΎΠ½ΠΎΠ². ΠΡΠΈ ΠΈΡ
ΠΏΠΎΡΠ»Π΅Π΄ΡΡΡΠ΅ΠΌ Π°Π»ΠΊΠΈΠ»ΠΈΡΠΎΠ²Π°Π½ΠΈΠΈ Π°Π»Π»ΠΈΠ»Π±ΡΠΎΠΌΠΈΠ΄ΠΎΠΌ ΠΈΠ»ΠΈ ΠΌΠ΅ΡΠ°Π»Π»ΠΈΠ»Ρ
Π»ΠΎΡΠΈΠ΄ΠΎΠΌ ΠΏΠΎΠ»ΡΡΠ΅Π½Ρ 5,5-Π΄ΠΈΠ°Π»ΠΊΠ΅Π½ΠΈΠ»ΡΠ½ΡΠ΅ ΠΏΡΠΎΠΈΠ·Π²ΠΎΠ΄Π½ΡΠ΅, ΠΊΠΎΡΠΎΡΡΠ΅ ΡΠ΅Π°ΠΊΡΠΈΡΠΌΠΈ ΠΌΠ΅ΡΠ°ΡΠ΅Π·ΠΈΡΠ° Ρ Π·Π°ΠΊΡΡΡΠΈΠ΅ΠΌ ΡΠΈΠΊΠ»Π° Π±ΡΠ»ΠΈ ΠΊΠΎΠ½Π²Π΅ΡΡΠΈΡΠΎΠ²Π°Π½Ρ Π² ΡΠΎΠΎΡΠ²Π΅ΡΡΡΠ²ΡΡΡΠΈΠ΅ Π½Π΅ΠΏΡΠ΅Π΄Π΅Π»ΡΠ½ΡΠ΅ ΡΠΏΠΈΡΠΎΡΠΈΠΊΠ»ΠΈΡΠ΅ΡΠΊΠΈΠ΅ Π΄ΠΈΠΎΠΊΡΠΎΠΏΠΈΡΠΈΠΌΠΈΠ΄ΠΈΠ½-2-ΡΠΈΠΎΠ½Ρ.Β Β ΠΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠ°Π»ΡΠ½Π°Ρ ΡΠ°ΡΡΡ. Π‘ΠΈΠ½ΡΠ΅Π· ΠΈΡΡ
ΠΎΠ΄Π½ΡΡ
ΡΠΎΠ΅Π΄ΠΈΠ½Π΅Π½ΠΈΠΉ ΠΈ ΡΠ΅Π»Π΅Π²ΡΡ
ΠΏΡΠΎΠ΄ΡΠΊΡΠΎΠ² ΠΊΠ»Π°ΡΡΠΈΡΠ΅ΡΠΊΠΈΠΌΠΈ ΠΌΠ΅ΡΠΎΠ΄Π°ΠΌΠΈ ΠΏΡΠ΅ΠΏΠ°ΡΠ°ΡΠΈΠ²Π½ΠΎΠΉ Ρ
ΠΈΠΌΠΈΠΈ; ΠΎΡΠΈΡΡΠΊΠ° ΠΈ ΠΈΠ΄Π΅Π½ΡΠΈΡΠΈΠΊΠ°ΡΠΈΡ ΠΏΠΎΠ»ΡΡΠ΅Π½Π½ΡΡ
ΡΠΎΠ΅Π΄ΠΈΠ½Π΅Π½ΠΈΠΉ ΠΏΡΠΎΠ²ΠΎΠ΄ΠΈΠ»ΠΈΡΡ ΠΌΠ΅ΡΠΎΠ΄Π°ΠΌΠΈ ΡΠΎΠ½ΠΊΠΎΡΠ»ΠΎΠΉΠ½ΠΎΠΉ ΠΈ ΠΊΠΎΠ»ΠΎΠ½ΠΎΡΠ½ΠΎΠΉ Ρ
ΡΠΎΠΌΠ°ΡΠΎΠ³ΡΠ°ΡΠΈΠΈ, ΠΌΠ΅ΡΠΎΠ΄ΠΎΠΌ ΡΠ»Π΅ΠΌΠ΅Π½ΡΠ½ΠΎΠ³ΠΎ Π°Π½Π°Π»ΠΈΠ·Π°, ΡΠΏΠ΅ΠΊΡΡΠΎΡΠΊΠΎΠΏΠΈΠ΅ΠΉ Π―ΠΠ .ΠΡΠ²ΠΎΠ΄Ρ. Π Π°Π·ΡΠ°Π±ΠΎΡΠ°Π½ ΡΡΡΠ΅ΠΊΡΠΈΠ²Π½ΡΠΉ ΡΡΠ΅Ρ
ΡΡΠ°Π΄ΠΈΠΉΠ½ΡΠΉ ΠΏΡΡΡ ΠΏΠΎΠ»ΡΡΠ΅Π½ΠΈΡ ΠΈΠ· ΠΈΡΡ
ΠΎΠ΄Π½ΡΡ
ΡΠΈΠΎΠΌΠΎΡΠ΅Π²ΠΈΠ½ ΠΈ Π°Π»Π»ΠΈΠ»ΠΌΠ°Π»ΠΎΠ½ΠΎΠ²ΠΎΠΉ ΠΊΠΈΡΠ»ΠΎΡΡ Π½ΠΎΠ²ΡΡ
Π½Π΅Π½Π°ΡΡΡΠ΅Π½Π½ΡΡ
ΡΠΏΠΈΡΠΎ-Π°Π½Π½Π΅Π»ΠΈΡΠΎΠ²Π°Π½Π½ΡΡ
ΠΏΡΠΎΠΈΠ·Π²ΠΎΠ΄Π½ΡΡ
N-Π°ΡΠΈΠ»-4,6-Π΄ΠΈΠΎΠΊΡΠΎΠΏΠΈΡΠΈΠΌΠΈΠ΄ΠΈΠ½-2-ΡΠΈΠΎΠ½Π°. ΠΠΎΠ»ΡΡΠ΅Π½Π½ΡΠ΅ ΡΠΏΠΈΡΠΎΡΠΈΠΊΠ»ΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΠΏΡΠΎΠ΄ΡΠΊΡΡ ΠΌΠΎΠ³ΡΡ Π½Π°ΠΉΡΠΈ ΠΏΡΠΈΠΌΠ΅Π½Π΅Π½ΠΈΠ΅ Π² Π±ΠΈΠΎΠ»ΠΎΠ³ΠΈΠΈ ΠΈ ΡΠ°ΡΠΌΠ°ΡΠ΅Π²ΡΠΈΡΠ΅ΡΠΊΠΎΠΉ Π½Π°ΡΠΊΠ΅, Π° ΡΠ°ΠΊΠΆΠ΅ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°ΡΡΡΡ ΠΊΠ°ΠΊ ΠΈΡΡ
ΠΎΠ΄Π½ΡΠ΅ ΡΠΎΠ΅Π΄ΠΈΠ½Π΅Π½ΠΈΡ Π΄Π»Ρ Π΄Π°Π»ΡΠ½Π΅ΠΉΡΠ΅ΠΉ Ρ
ΠΈΠΌΠΈΡΠ΅ΡΠΊΠΎΠΉ ΠΌΠΎΠ΄ΠΈΡΠΈΠΊΠ°ΡΠΈΠΈ.Π ΠΎΠ·ΡΠΎΠ±Π»Π΅Π½ΠΎ Π·ΡΡΡΠ½ΠΈΠΉ ΡΠ° Π΅ΡΠ΅ΠΊΡΠΈΠ²Π½ΠΈΠΉ ΠΌΠ΅ΡΠΎΠ΄ ΡΠΈΠ½ΡΠ΅Π·Ρ Π½ΠΎΠ²ΠΈΡ
Π½Π΅Π½Π°ΡΠΈΡΠ΅Π½ΠΈΡ
ΡΠΏΡΡΠΎ-Π°Π½Π΅Π»ΡΠΎΠ²Π°Π½ΠΈΡ
N-Π°ΡΠΈΠ»Π·Π°ΠΌΡΡΠ΅Π½ΠΈΡ
2-ΡΡΠΎΠΏΡΡΠΈΠΌΡΠ΄ΠΈΠ½-4,6-Π΄ΡΠΎΠ½ΡΠ². ΠΠ΄Π΅ΡΠΆΠ°Π½Ρ ΡΠΏΠΎΠ»ΡΠΊΠΈ ΠΌΠΎΠΆΡΡΡ Π±ΡΡΠΈ ΠΏΠΎΡΠ΅Π½ΡΡΠΉΠ½ΠΈΠΌΠΈ Π±ΡΠΎΠ°ΠΊΡΠΈΠ²Π½ΠΈΠΌΠΈ ΠΌΠΎΠ»Π΅ΠΊΡΠ»Π°ΠΌΠΈ Π°Π±ΠΎ ΠΏΡΠ΅ΠΊΡΡΡΠΎΡΠ°ΠΌΠΈ Π΄Π»Ρ ΠΏΠΎΠ΄Π°Π»ΡΡΠΎΡ Ρ
ΡΠΌΡΡΠ½ΠΎΡ ΠΌΠΎΠ΄ΠΈΡΡΠΊΠ°ΡΡΡ. ΠΠ΅ΡΠ° ΡΠΎΠ±ΠΎΡΠΈ β ΡΠΎΠ·ΡΠΎΠ±ΠΊΠ° ΠΌΠ΅ΡΠΎΠ΄ΡΠ² ΠΎΠ΄Π΅ΡΠΆΠ°Π½Π½Ρ Π½ΠΎΠ²ΠΈΡ
Π½Π΅Π½Π°ΡΠΈΡΠ΅Π½ΠΈΡ
ΡΠΏΡΡΠΎ-Π°Π½Π΅Π»ΡΠΎΠ²Π°Π½ΠΈΡ
ΠΏΠΎΡ
ΡΠ΄Π½ΠΈΡ
2-ΡΡΠΎΠΏΡΡΠΈΠΌΡΠ΄ΠΈΠ½-4,6-Π΄ΡΠΎΠ½Ρ ΡΠΊ ΠΏΠΎΡΠ΅Π½ΡΡΠΉΠ½ΠΈΡ
Π±ΡΠΎΠ»ΠΎΠ³ΡΡΠ½ΠΎ Π°ΠΊΡΠΈΠ²Π½ΠΈΡ
ΡΠΏΠΎΠ»ΡΠΊ Π°Π±ΠΎ Π½Π°ΠΏΡΠ²ΠΏΡΠΎΠ΄ΡΠΊΡΡΠ² Π΄Π»Ρ ΡΡ
ΠΎΡΡΠΈΠΌΠ°Π½Π½Ρ. Π Π΅Π·ΡΠ»ΡΡΠ°ΡΠΈ ΡΠ° ΡΡ
ΠΎΠ±Π³ΠΎΠ²ΠΎΡΠ΅Π½Π½Ρ. ΠΠΎΠ½Π΄Π΅Π½ΡΠ°ΡΡΡΡN-Π°ΡΠΈΠ»Π·Π°ΠΌΡΡΠ΅Π½ΠΈΡ
ΡΡΠΎΡΠ΅ΡΠΎΠ²ΠΈΠ½ ΡΠ° Π°Π»ΡΠ»ΠΌΠ°Π»ΠΎΠ½ΠΎΠ²ΠΎΡ ΠΊΠΈΡΠ»ΠΎΡΠΈ ΡΠ· Π·Π°ΡΡΠΎΡΡΠ²Π°Π½Π½ΡΠΌ ΠΎΡΡΠΎΠ²ΠΎΠ³ΠΎ Π°Π½Π³ΡΠ΄ΡΠΈΠ΄Ρ Π°Π±ΠΎ Π°ΡΠ΅ΡΠΈΠ»Ρ
Π»ΠΎΡΠΈΠ΄Ρ ΡΠΈΠ½ΡΠ΅Π·ΠΎΠ²Π°Π½ΠΎ ΡΠ΅ΡΡΡ 5-Π°Π»ΡΠ»Π·Π°ΠΌΡΡΠ΅Π½ΠΈΡ
2-ΡΡΠΎΠΏΡΡΠΈΠΌΡΠ΄ΠΈΠ½Π΄ΡΠΎΠ½ΡΠ². ΠΡΠΈ ΠΏΠΎΠ΄Π°Π»ΡΡΠΎΠΌΡ ΡΡ
Π°Π»ΠΊΡΠ»ΡΠ²Π°Π½Π½Ρ Π°Π»ΡΠ»Π±ΡΠΎΠΌΡΠ΄ΠΎΠΌ Π°Π±ΠΎ ΠΌΠ΅ΡΠ°Π»ΡΠ»Ρ
Π»ΠΎΡΠΈΠ΄ΠΎΠΌ ΠΎΠ΄Π΅ΡΠΆΠ°Π½ΠΎ 5,5-Π΄ΡΠ°Π»ΠΊΠ΅Π½ΡΠ»ΡΠ½Ρ ΠΏΠΎΡ
ΡΠ΄Π½Ρ, ΡΠΊΡ ΡΠ΅Π°ΠΊΡΡΡΠΌΠΈ ΠΌΠ΅ΡΠ°ΡΠ΅Π·ΠΈΡΡ ΡΠ· Π·Π°ΠΊΡΠΈΡΡΡΠΌ ΡΠΈΠΊΠ»Ρ Π±ΡΠ»ΠΎ ΠΏΠ΅ΡΠ΅ΡΠ²ΠΎΡΠ΅Π½ΠΎ Π½Π° Π²ΡΠ΄ΠΏΠΎΠ²ΡΠ΄Π½Ρ Π½Π΅Π½Π°ΡΠΈΡΠ΅Π½Ρ ΡΠΏΡΡΠΎΡΠΈΠΊΠ»ΡΡΠ½Ρ Π΄ΡΠΎΠΊΡΠΎΠΏΡΡΠΈΠΌΡΠ΄ΠΈΠ½-2-ΡΡΠΎΠ½ΠΈ.ΠΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠ°Π»ΡΠ½Π° ΡΠ°ΡΡΠΈΠ½Π°. Π‘ΠΈΠ½ΡΠ΅Π· Π²ΠΈΡ
ΡΠ΄Π½ΠΈΡ
ΡΠΏΠΎΠ»ΡΠΊ ΡΠ° ΡΡΠ»ΡΠΎΠ²ΠΈΡ
ΠΏΡΠΎΠ΄ΡΠΊΡΡΠ² ΠΊΠ»Π°ΡΠΈΡΠ½ΠΈΠΌΠΈ ΠΌΠ΅ΡΠΎΠ΄Π°ΠΌΠΈ ΠΏΡΠ΅ΠΏΠ°ΡΠ°ΡΠΈΠ²Π½ΠΎΡ Ρ
ΡΠΌΡΡ; ΠΎΡΠΈΡΡΠΊΡ ΡΠ° ΡΠ΄Π΅Π½ΡΠΈΡΡΠΊΠ°ΡΡΡ ΠΎΡΡΠΈΠΌΠ°Π½ΠΈΡ
ΡΠΏΠΎΠ»ΡΠΊ Π·Π΄ΡΠΉΡΠ½Π΅Π½ΠΎ ΠΌΠ΅ΡΠΎΠ΄Π°ΠΌΠΈ ΡΠΎΠ½ΠΊΠΎΡΠ°ΡΠΎΠ²ΠΎΡ ΡΠ° ΠΊΠΎΠ»ΠΎΠ½ΠΊΠΎΠ²ΠΎΡ Ρ
ΡΠΎΠΌΠ°ΡΠΎΠ³ΡΠ°ΡΡΡ, Π΅Π»Π΅ΠΌΠ΅Π½ΡΠ½ΠΈΠΌ Π°Π½Π°Π»ΡΠ·ΠΎΠΌ, Π―ΠΠ -ΡΠΏΠ΅ΠΊΡΡΠΎΡΠΊΠΎΠΏΡΡΡ.ΠΠΈΡΠ½ΠΎΠ²ΠΊΠΈ. Π ΠΎΠ·ΡΠΎΠ±Π»Π΅Π½ΠΎ Π΅ΡΠ΅ΠΊΡΠΈΠ²Π½ΠΈΠΉ ΡΡΠΈΡΡΠ°Π΄ΡΠΉΠ½ΠΈΠΉ ΡΠ»ΡΡ
ΠΎΡΡΠΈΠΌΠ°Π½Π½Ρ Π· Π²ΠΈΡ
ΡΠ΄Π½ΠΈΡ
ΡΡΠΎΡΠ΅ΡΠΎΠ²ΠΈΠ½ ΡΠ° Π°Π»ΡΠ»ΠΌΠ°Π»ΠΎΠ½ΠΎΠ²ΠΎΡ ΠΊΠΈΡΠ»ΠΎΡΠΈ Π½ΠΎΠ²ΠΈΡ
Π½Π΅Π½Π°ΡΠΈΡΠ΅Π½ΠΈΡ
ΡΠΏΡΡΠΎ-Π°Π½Π΅Π»ΡΠΎΠ²Π°Π½ΠΈΡ
ΠΏΠΎΡ
ΡΠ΄Π½ΠΈΡ
N-Π°ΡΠΈΠ»-4,6-Π΄ΡΠΎΠΊΡΠΎΠΏΡΡΠΈΠΌΡΠ΄ΠΈΠ½-2-ΡΡΠΎΠ½Ρ. ΠΠ΄Π΅ΡΠΆΠ°Π½Ρ ΡΠΏΡΡΠΎΡΠΈΠΊΠ»ΡΡΠ½Ρ ΠΏΡΠΎΠ΄ΡΠΊΡΠΈ ΠΌΠΎΠΆΡΡΡ Π·Π½Π°ΠΉΡΠΈ Π·Π°ΡΡΠΎΡΡΠ²Π°Π½Π½Ρ Π² Π±ΡΠΎΠ»ΠΎΠ³ΡΡ ΡΠ° ΡΠ°ΡΠΌΠ°ΡΠ΅Π²ΡΠΈΡΠ½ΡΠΉ Π½Π°ΡΡΡ, Π°Π±ΠΎ Π²ΠΈΠΊΠΎΡΠΈΡΡΠΎΠ²ΡΠ²Π°ΡΠΈΡΡ ΡΠΊ Π²ΠΈΡ
ΡΠ΄Π½Ρ ΡΠΏΠΎΠ»ΡΠΊΠΈ Π΄Π»Ρ ΠΏΠΎΠ΄Π°Π»ΡΡΠΎΡ Ρ
ΡΠΌΡΡΠ½ΠΎΡ ΠΌΠΎΠ΄ΠΈΡΡΠΊΠ°ΡΡΡ
Density-density propagator for one-dimensional interacting spinless fermions with non-linear dispersion and calculation of the Coulomb drag resistivity
Using bosonization-fermionization transformation we map the
Tomonaga-Luttinger model of spinless fermions with non-linear dispersion on the
model of fermionic quasiparticles whose interaction is irrelevant in the
renormalization group sense. Such mapping allows us to set up an expansion for
the density-density propagator of the original Tomonaga-Luttinger Hamiltonian
in orders of the (irrelevant) quasiparticle interaction. The lowest order term
in such an expansion is proportional to the propagator for free fermions. The
next term is also evaluated. The propagator found is used for calculation of
the Coulomb drug resistivity in a system of two capacitively coupled
one-dimensional conductors. It is shown that is proportional to for
both free and interacting fermions. The marginal repulsive in-chain interaction
acts to reduce as compared to the non-interacting result. The correction to
due to the quasiparticle interaction is found as well. It scales as
at low temperature.Comment: 5 pages, 1 eps figure; the new version of the e-print corrects an
error, which exists in the original submission; fortunately, all important
conclusions of the study remain vali
Stem-technologies: mathematics and informatics
Algorithms solutions of tasks in the field of the theory of numbers within implementation of the STEM project are proposed and realized. Calculations in a package of computer algebra on an open code in the environment of Linux DebianΠΡΠ΅Π΄Π»ΠΎΠΆΠ΅Π½Ρ ΠΈ ΡΠ΅Π°Π»ΠΈΠ·ΠΎΠ²Π°Π½Ρ Π°Π»Π³ΠΎΡΠΈΡΠΌΡ ΡΠ΅ΡΠ΅Π½ΠΈΡ Π·Π°Π΄Π°Ρ Π² ΠΎΠ±Π»Π°ΡΡΠΈ ΡΠ΅ΠΎΡΠΈΠΈ ΡΠΈΡΠ΅Π» Π² ΡΠ°ΠΌΠΊΠ°Ρ
ΡΠ΅Π°Π»ΠΈΠ·Π°ΡΠΈΠΈ ΠΏΡΠΎΠ΅ΠΊΡΠ° STEM. ΠΡΡΠΈΡΠ»Π΅Π½ΠΈΡ Π² ΠΏΠ°ΠΊΠ΅ΡΠ΅ ΠΊΠΎΠΌΠΏΡΡΡΠ΅ΡΠ½ΠΎΠΉ Π°Π»Π³Π΅Π±ΡΡ Π½Π° ΠΎΡΠΊΡΡΡΠΎΠΌ ΠΊΠΎΠ΄Π΅ Π² ΡΡΠ΅Π΄Π΅ Linux Debia
Experimental (computing) theory of numbers
Carrying out numerical experiments with Euler's function. Specification of the theorem of Mertens. Calculations in a package of computer algebra on an open code in the environment of Linux DebianΠΡΠΎΠ²Π΅Π΄Π΅Π½ΠΈΠ΅ ΡΠΈΡΠ»Π΅Π½Π½ΡΡ
ΡΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠΎΠ² Ρ ΡΡΠ½ΠΊΡΠΈΠ΅ΠΉ ΠΠΉΠ»Π΅ΡΠ°. Π£ΡΠΎΡΠ½Π΅Π½ΠΈΠ΅ ΡΠ΅ΠΎΡΠ΅ΠΌΡ ΠΠ΅ΡΡΠ΅Π½ΡΠ°. ΠΡΡΠΈΡΠ»Π΅Π½ΠΈΡ Π² ΠΏΠ°ΠΊΠ΅ΡΠ΅ ΠΊΠΎΠΌΠΏΡΡΡΠ΅ΡΠ½ΠΎΠΉ Π°Π»Π³Π΅Π±ΡΡ Π½Π° ΠΎΡΠΊΡΡΡΠΎΠΌ ΠΊΠΎΠ΄Π΅ Π² ΡΡΠ΅Π΄Π΅ Linux Debia
Assessment of forests structure and forest care efficiency
The search of the most acceptable approaches is carried out in assessment of forests care efficiency. The system from 17 indicators and the equations for result calculation of young growths care, thinning out, re-form, reconstructive cuttings, forest protection and other actions is proposed
Aggregated estimation of the basic parameters of biological production and the carbon budget of Russian terrestrial ecosytems: 2. Net primary production
The estimated net primary production (NPP) of Russian terrestrial ecosystems (annual average over the period from 1988 to 1992) is 9544 Tg of dry matter, or 4353 Tg of carbon. Of the total amount, forests account for approximately 39.2% (here and below, comparisons are made with respect to carbon content); natural grasslands and brushwoods, for 27.6%; farmlands (arable land and cultivated pastures), for 22.0%; and wetlands, for 11.2%. The average NPP density on lands covered with vegetation (1629.8 million hectares in Russia) is 267 g C/m2per year. The highest value (498 g C/m2per year) is characteristic of arable lands. Other land-use/land-cover (LULC) classes have the following NPP densities (in areas covered with vegetation): grasslands and brushwoods, 278 g C/m2; forests, 224 g C/m2; and wetlands, 219 g C/m2per year. In general, Russian terrestrial ecosystems accumulate 59.7% of the total NPP in the aboveground phytomass (47.8% in green parts and 11.9% in wood) and 40.3% in the underground phytomass. The latter parameter differs significantly in different LULC classes and bioclimatic zones. According to calculations, the uncertainty in estimating the total NPP is 11% (a priori confidential probability 0.9)
Teaching English in the higher education institution: teachers and students perspective
The purpose of the given study is to provide description of English for Specific Purposes (ESP) course implementation in Russian higher educational institutions. The authors consider the experience of ESP training at Ogarev Mordovia State University (Saransk, Russia) and outline the most typical issues faced by ESP teachers in real-life conditions of education process. The following problem aspects are pointed out: appropriate selection and use of training materials for the educational course, multilevel groups issue, necessity of due ESP course design etc. The authors also provide the results of the survey for students of some departments of Mordovia Ogarev State University listing the most relevant issues and challenges faced by them while taking an ESP course. The creators of the paper suggest several ways of solution for the issues stated and provide possible directions for the development and quality improvement of ESP courses in the higher education system of Russia
Suspensions of supracolloidal magnetic polymers: self-assembly properties from computer simulations
We study self-assembly in suspensions of supracolloidal polymer-like
structures made of crosslinked magnetic particles. Inspired by self-assembly
motifs observed for dipolar hard spheres, we focus on four different topologies
of the polymer-like structures: linear chains, rings, Y-shaped and X-shaped
polymers. We show how the presence of the crosslinkers, the number of beads in
the polymer and the magnetic interparticle interaction affect the structure of
the suspension. It turns out that for the same set of parameters, the rings are
the least active in assembling larger structures, whereas the system of Y- and
especially X-like magnetic polymers tend to form very large loose aggregates
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