49 research outputs found

    Measuring the gap in ARPES experiments

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    Angle-resolved photoemission spectroscopy (ARPES) is considered as the only experimental tool from which the momentum distribution of both the superconducting and pseudo-gap can be quantitatively derived. The binding energy of the leading edge of the photoemission spectrum, usually called the leading edge gap (LEG), is the model-independent quantity which can be measured in the modern ARPES experiments with the very high accuracy--better than 1 meV. This, however, may be useless as long as the relation between the LEG and the real gap is unknown. We present a systematic study of the LEG as a function of a number of physical and experimental parameters. The absolute gap values which have been derived from the numerical simulation prove, for example that the nodal direction in the underdoped Bi-2212 in superconducting state is really the node--the gap is zero. The other consequences of the simulations are discussed.Comment: revtex4, 9 pages, 6 figure

    Π‘Ρ€Π°Π²Π½ΠΈΡ‚Π΅Π»ΡŒΠ½ΠΎΠ΅ исслСдованиС Ρ€Π΅Π³Π΅Π½Π΅Ρ€Π°Ρ†ΠΈΠΈ Ρƒ Π³ΡƒΠ±ΠΎΠΊ (Porifera)

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    International audiencet is well known that sponges have unusually high regenerative abilities, which are often associated with their low tissue organization and high dynamics of cell differentiation. In order to identify the diversity of morphogenesis and cellular mechanisms involved in the restoration processes in Porifera, we carried out a detailed comparative study of the regeneration of a number of sponge species from phylogenetically deleted taxa that differ in their anatomical and histological organization. The objects of this project were sponges from the classes Demospongiae, Homoscleromorpha, and Calcarea, which have the leukonoid, siconoid, and asconoid types of the aquiferous system e-mines, as well as different degrees of epithelial development. The main mechanism for the regeneration of leukonoid Demospongiae is the epithelio-mesenchymal transformation involving polypotent archaeocyte cells. Epithelial morphogenesis and cell transdifferentiation are the basis for the regeneration of leukoid Homoscleromorpha and siconoid and asconoid Calcarea. Asconoid Calcarea regeneration is a rare example of β€œpure” morphallaxis. We have shown that the morphogenetic processes detected in sponges are as complex and diverse as in other higher animals. Thus, sponges can be a source of important information that will allow us to better understand the early evolution of molecular and cellular mechanisms of morphogenesis in animals.2 Π‘ΠŸΠ±Π“Π£, биологичСский Ρ„Π°ΠΊΡƒΠ»ΡŒΡ‚Π΅Ρ‚ 3 ΠœΠ“Π£ ΠΈΠΌ. Ломоносова, биологичСский Ρ„Π°ΠΊΡƒΠ»ΡŒΡ‚Π΅Ρ‚, БСломорская биологичСская станция ΠΈΠΌ. Н.А. ΠŸΠ΅Ρ€Ρ†ΠΎΠ²Π° Π₯ΠΎΡ€ΠΎΡˆΠΎ извСстно, Ρ‡Ρ‚ΠΎ Π³ΡƒΠ±ΠΊΠΈ ΠΎΠ±Π»Π°Π΄Π°ΡŽΡ‚ Π½Π΅ΠΎΠ±Ρ‹Ρ‡Π°ΠΉΠ½ΠΎ высокими Ρ€Π΅Π³Π΅Π½Π΅Ρ€Π°Ρ†ΠΈΠΎΠ½Π½Ρ‹ΠΌΠΈ сп ΠΎ-собностями Ρ‡Ρ‚ΠΎ часто ΡΠ²ΡΠ·Ρ‹Π²Π°ΡŽΡ‚ с ΠΈΡ… Π½ΠΈΠ·ΠΊΠΎΠΉ Ρ‚ΠΊΠ°Π½Π΅Π²ΠΎΠΉ ΠΎΡ€Π³Π°Π½ΠΈΠ·Π°Ρ†ΠΈΠ΅ΠΉ ΠΈ высокой Π΄ΠΈΠ½Π°ΠΌΠΈΠΊΠΎΠΉ ΠΊΠ»Π΅Ρ‚ΠΎΡ‡Π½ΠΎΠΉ Π΄ΠΈΡ„Ρ„Π΅Ρ€Π΅Π½Ρ†ΠΈΡ€ΠΎΠ²ΠΊΠΈ. Для Ρ‚ΠΎΠ³ΠΎ, Ρ‡Ρ‚ΠΎΠ±Ρ‹ Π²Ρ‹ΡΠ²ΠΈΡ‚ΡŒ Ρ€Π°Π·Π½ΠΎΠΎΠ±Ρ€Π°Π·ΠΈΠ΅ ΠΌΠΎΡ€Ρ„ΠΎΠ³Π΅Π½Π΅Π·ΠΎΠ² ΠΈ ΠΊΠ»Π΅Ρ‚ΠΎΡ‡-Π½Ρ‹Ρ… ΠΌΠ΅Ρ…Π°Π½ΠΈΠ·ΠΌΠΎΠ² Π²ΠΎΠ²Π»Π΅Ρ‡Π΅Π½Π½Ρ‹Ρ… Π² Π²ΠΎΡΡΡ‚Π°Π½ΠΎΠ²ΠΈΡ‚Π΅Π»ΡŒΠ½Ρ‹Π΅ процСссы Ρƒ Porifera, Π½Π°ΠΌΠΈ Π±Ρ‹Π»ΠΎ ΠΏΡ€Π΅Π΄ΠΏΡ€ ΠΈ-нято Π΄Π΅Ρ‚Π°Π»ΡŒΠ½ΠΎΠ΅ ΡΡ€Π°Π²Π½ΠΈΡ‚Π΅Π»ΡŒΠ½ΠΎΠ΅ исслСдованиС Ρ€Π΅Π³Π΅Π½Π΅Ρ€Π°Ρ†ΠΈΠΈ ряда Π²ΠΈΠ΄ΠΎΠ² Π³ΡƒΠ±ΠΎΠΊ ΠΈΠ· Ρ„ΠΈΠ»ΠΎΠ³Π΅Π½Π΅Ρ‚ΠΈΡ‡ Π΅-ски ΡƒΠ΄Π°Π»Π΅Π½Π½Ρ‹Ρ… таксонов, ΠΎΡ‚Π»ΠΈΡ‡Π°ΡŽΡ‰ΠΈΠ΅ΡΡ анатомичСской ΠΈ гистологичСской ΠΎΡ€Π³Π°Π½ΠΈΠ·Π°Ρ†ΠΈΠ΅ΠΉ. ΠžΠ±ΡŠΠ΅ΠΊΡ‚Π°ΠΌΠΈ Π΄Π°Π½Π½ΠΎΠ³ΠΎ ΠΏΡ€ΠΎΠ΅ΠΊΡ‚Π° послуТили Π³ΡƒΠ±ΠΊΠΈ ΠΈΠ· классов Demospongiae, Homoscleromorpha ΠΈ Calcarea, ΠΎΠ±Π»Π°Π΄Π°ΡŽΡ‰ΠΈΠ΅ Π»Π΅ΠΉΠΊΠΎΠ½ΠΎΠΈΠ΄Π½ΠΎΠΉ, сиконоидной ΠΈ асконоидной Ρ‚ΠΈΠΏΠ°ΠΌΠΈ водоносной сист Π΅-ΠΌΡ‹, Π° Ρ‚Π°ΠΊΠΆΠ΅ Ρ€Π°Π·Π½ΠΎΠΉ ΡΡ‚Π΅ΠΏΠ΅Π½ΡŒΡŽ развития эпитСлия. ΠžΡΠ½ΠΎΠ²Π½Ρ‹ΠΌ ΠΌΠ΅Ρ…Π°Π½ΠΈΠ·ΠΌΠΎΠΌ Ρ€Π΅Π³Π΅Π½Π΅Ρ€Π°Ρ†ΠΈΠΈ Π»Π΅ΠΉΠΊΠΎ-Π½ΠΎΠΈΠ΄Π½Ρ‹Ρ… Demospongiae являСтся эпитСлио-мСзСнхимная трансформация с Π²ΠΎΠ²Π»Π΅Ρ‡Π΅Π½ΠΈΠ΅ΠΌ ΠΏΠΎΠ»ΠΈ-ΠΏΠΎΡ‚Π΅Π½Ρ‚Π½Ρ‹Ρ… ΠΊΠ»Π΅Ρ‚ΠΎΠΊ-Π°Ρ€Ρ…Π΅ΠΎΡ†ΠΈΡ‚ΠΎΠ². Основой Ρ€Π΅Π³Π΅Π½Π΅Ρ€Π°Ρ†ΠΈΠΈ Π»Π΅ΠΉΠΊΠΎΠ½ΠΎΠΈΠ΄Π½Ρ‹Ρ… Homoscleromorpha ΠΈ сиконоидных ΠΈ асконоидных Calcarea слуТат ΡΠΏΠΈΡ‚Π΅Π»ΠΈΠ°Π»ΡŒΠ½Ρ‹Π΅ ΠΌΠΎΡ€Ρ„ΠΎΠ³Π΅Π½Π΅Π·Ρ‹ ΠΈ трансдиффСрСн-Ρ†ΠΈΡ€ΠΎΠ²ΠΊΠ° ΠΊΠ»Π΅Ρ‚ΠΎΠΊ. РСгСнСрация асконоидных Calcarea прСдставляСт собой Ρ€Π΅Π΄ΠΊΠΈΠΉ ΠΏΡ€ΠΈΠΌΠ΅Ρ€ Β«Ρ‡ΠΈ-стого» морфаллаксиса. ΠœΡ‹ ΠΏΠΎΠΊΠ°Π·Π°Π»ΠΈ, Ρ‡Ρ‚ΠΎ морфогСнСтичСскиС процСссы, выявлСнныС Ρƒ Π³ΡƒΠ±ΠΎΠΊ, ΡΠ²Π»ΡΡŽΡ‚ΡΡ ΡΡ‚ΠΎΠ»ΡŒ ΠΆΠ΅ слоТными ΠΈ Ρ€Π°Π·Π½ΠΎΠΎΠ±Ρ€Π°Π·Π½Ρ‹ΠΌΠΈ, ΠΊΠ°ΠΊ ΠΈ Ρƒ Π΄Ρ€ΡƒΠ³ΠΈΡ… Π²Ρ‹ΡΡˆΠΈΡ… ΠΆΠΈΠ²ΠΎΡ‚Π½Ρ‹Ρ…. Π’Π°ΠΊΠΈΠΌ ΠΎΠ±Ρ€Π°Π·ΠΎΠΌ, Π³ΡƒΠ±ΠΊΠΈ ΠΌΠΎΠ³ΡƒΡ‚ Π±Ρ‹Ρ‚ΡŒ источником Π²Π°ΠΆΠ½ΠΎΠΉ ΠΈΠ½Ρ„ΠΎΡ€ΠΌΠ°Ρ†ΠΈΠΈ, которая ΠΏΠΎΠ·Π²ΠΎΠ»ΠΈΡ‚ Π½Π°ΠΌ Π³Π»ΡƒΠ±ΠΆΠ΅ ΠΏΠΎΠ½ΡΡ‚ΡŒ Ρ€Π°Π½Π½ΡŽΡŽ ΡΠ²ΠΎΠ»ΡŽΡ†ΠΈΡŽ молСкулярных ΠΈ ΠΊΠ»Π΅Ρ‚ΠΎΡ‡Π½Ρ‹Ρ… ΠΌΠ΅Ρ…Π°Π½ΠΈΠ·ΠΌΠΎΠ² ΠΌΠΎΡ€Ρ„ΠΎΠ³Π΅Π½Π΅Π·Π° Ρƒ ΠΆΠΈΠ²ΠΎΡ‚Π½Ρ‹Ρ…. Благодарности Данная Ρ€Π°Π±ΠΎΡ‚Π° осущСствлСна ΠΏΡ€ΠΈ финансовой ΠΏΠΎΠ΄Π΄Π΅Ρ€ΠΆΠΊΠ΅ Π³Ρ€Π°Π½Ρ‚ΠΎΠ² РЀЀИ β„– 16-04-00084, ΠΈ РНЀ β„– 17-14-01089.-8

    Nanotube-based source of charges for experiments with solid helium at low temperatures

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    Methods of preparation of the field-emission sources of charges from carbon nanotubes suitable for study of injected charges in solid helium at low temperatures T < 1 K are presented. The sources have been prepared by arc discharge deposition of nanotubes onto a flat copper substrate or by mechanical rubbing of nanotubes into porous metal surface. The test study of the voltage-current characteristics of a diode cell with the nanotube source in superfluid He II have shown that at voltages above 120 V one can observe a relatively large current I β‰₯ 10⁻¹³ A of negative charges in liquid helium. The field and temperature dependences of positive and negative currents in solid ⁴He were studied in samples grown by the blocked capillary technique. Usage of the nanotube based source of injected charges had permitted us for the first time to observe motion of the positive charges in solid helium at temperatures below 0.1 К. The current-voltage dependence could be described by a power law I ~ UΞ±, with the value of the exponent Ξ± >> 2, much higher than what one would expect for the regime of space charge limited currents

    Single-photon emitters in GaSe

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    Single-photon sources are important building blocks for quantum information technology. Emitters based on solid-state systems provide a viable route to integration in photonic devices. Here, we report on single-photon emitters in the layered semiconductor GaSe. We identify the exciton and biexciton transition of the quantum emitters with power-dependent photoluminescence and photon statistics measurements. We find evidence that the localization of the excitons is related to deformations of the GaSe crystal, caused by nanoscale selenium inclusions, which are incorporated in the crystal. These deformations give rise to local strain fields, which induce confinement potentials for the excitons. This mechanism lights the way for the controlled positioning of single-photon emitters in GaSe on the nanoscale

    Photoluminescence of two-dimensional GaTe and GaSe films

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    Gallium chalcogenides are promising building blocks for novel van der Waals heterostructures. We report on the low-temperature micro-photoluminescence (PL) of GaTe and GaSe films with thicknesses ranging from 200 nm to a single unit cell. In both materials, PL shows a dramatic decrease by 10e4–10e5 when film thickness is reduced from 200 to 10 nm. Based on evidence from continuous-wave (cw) and time-resolved PL, we propose a model explaining the PL decrease as a result of non-radiative carrier escape via surface states. Our results emphasize the need for special passivation of two-dimensional films for optoelectronic applications

    ARPES Spectra of the Hubbard model

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    We discuss spectra calculated for the 2D Hubbard model in the intermediate coupling regime with the dynamical cluster approximation, which is a non-perturbative approach. We find a crossover from a normal Fermi liquid with a Fermi surface closed around the Brillouin zone center at large doping to a non-Fermi liquid for small doping. The crossover is signalled by a splitting of the Fermi surface around the XX point of the 2D Brillouin zone, which eventually leads to a hole-like Fermi surface closed around the point M. The topology of the Fermi surface at low doping indicates a violation of Luttinger's theorem. We discuss different ways of presenting the spectral data to extract information about the Fermi surface. A comparison to recent experiments will be presented.Comment: 8 pages, 7 color figures, uses RevTeX

    Effect of electron irradiation on vortex dynamics in YBa_2Cu_3O_{7-x} single crystals

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    We report on drastic change of vortex dynamics with increase of quenched disorder: for rather weak disorder we found a single vortex creep regime, which we attribute to a Bragg-glass phase, while for enhanced disorder we found an increase of both the depinning current and activation energy with magnetic field, which we attribute to entangled vortex phase. We also found that introduction of additional defects always increases the depinning current, but it increases activation energy only for elastic vortex creep, while it decreases activation energy for plastic vortex creep.Comment: 4 pages, 3 figures, submited to Phys. Rev.

    Π‘Ρ€Π°Π²Π½ΠΈΡ‚Π΅Π»ΡŒΠ½ΠΎΠ΅ исслСдованиС Ρ€Π΅Π³Π΅Π½Π΅Ρ€Π°Ρ†ΠΈΠΈ Ρƒ Π³ΡƒΠ±ΠΎΠΊ (Porifera)

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    International audiencet is well known that sponges have unusually high regenerative abilities, which are often associated with their low tissue organization and high dynamics of cell differentiation. In order to identify the diversity of morphogenesis and cellular mechanisms involved in the restoration processes in Porifera, we carried out a detailed comparative study of the regeneration of a number of sponge species from phylogenetically deleted taxa that differ in their anatomical and histological organization. The objects of this project were sponges from the classes Demospongiae, Homoscleromorpha, and Calcarea, which have the leukonoid, siconoid, and asconoid types of the aquiferous system e-mines, as well as different degrees of epithelial development. The main mechanism for the regeneration of leukonoid Demospongiae is the epithelio-mesenchymal transformation involving polypotent archaeocyte cells. Epithelial morphogenesis and cell transdifferentiation are the basis for the regeneration of leukoid Homoscleromorpha and siconoid and asconoid Calcarea. Asconoid Calcarea regeneration is a rare example of β€œpure” morphallaxis. We have shown that the morphogenetic processes detected in sponges are as complex and diverse as in other higher animals. Thus, sponges can be a source of important information that will allow us to better understand the early evolution of molecular and cellular mechanisms of morphogenesis in animals.2 Π‘ΠŸΠ±Π“Π£, биологичСский Ρ„Π°ΠΊΡƒΠ»ΡŒΡ‚Π΅Ρ‚ 3 ΠœΠ“Π£ ΠΈΠΌ. Ломоносова, биологичСский Ρ„Π°ΠΊΡƒΠ»ΡŒΡ‚Π΅Ρ‚, БСломорская биологичСская станция ΠΈΠΌ. Н.А. ΠŸΠ΅Ρ€Ρ†ΠΎΠ²Π° Π₯ΠΎΡ€ΠΎΡˆΠΎ извСстно, Ρ‡Ρ‚ΠΎ Π³ΡƒΠ±ΠΊΠΈ ΠΎΠ±Π»Π°Π΄Π°ΡŽΡ‚ Π½Π΅ΠΎΠ±Ρ‹Ρ‡Π°ΠΉΠ½ΠΎ высокими Ρ€Π΅Π³Π΅Π½Π΅Ρ€Π°Ρ†ΠΈΠΎΠ½Π½Ρ‹ΠΌΠΈ сп ΠΎ-собностями Ρ‡Ρ‚ΠΎ часто ΡΠ²ΡΠ·Ρ‹Π²Π°ΡŽΡ‚ с ΠΈΡ… Π½ΠΈΠ·ΠΊΠΎΠΉ Ρ‚ΠΊΠ°Π½Π΅Π²ΠΎΠΉ ΠΎΡ€Π³Π°Π½ΠΈΠ·Π°Ρ†ΠΈΠ΅ΠΉ ΠΈ высокой Π΄ΠΈΠ½Π°ΠΌΠΈΠΊΠΎΠΉ ΠΊΠ»Π΅Ρ‚ΠΎΡ‡Π½ΠΎΠΉ Π΄ΠΈΡ„Ρ„Π΅Ρ€Π΅Π½Ρ†ΠΈΡ€ΠΎΠ²ΠΊΠΈ. Для Ρ‚ΠΎΠ³ΠΎ, Ρ‡Ρ‚ΠΎΠ±Ρ‹ Π²Ρ‹ΡΠ²ΠΈΡ‚ΡŒ Ρ€Π°Π·Π½ΠΎΠΎΠ±Ρ€Π°Π·ΠΈΠ΅ ΠΌΠΎΡ€Ρ„ΠΎΠ³Π΅Π½Π΅Π·ΠΎΠ² ΠΈ ΠΊΠ»Π΅Ρ‚ΠΎΡ‡-Π½Ρ‹Ρ… ΠΌΠ΅Ρ…Π°Π½ΠΈΠ·ΠΌΠΎΠ² Π²ΠΎΠ²Π»Π΅Ρ‡Π΅Π½Π½Ρ‹Ρ… Π² Π²ΠΎΡΡΡ‚Π°Π½ΠΎΠ²ΠΈΡ‚Π΅Π»ΡŒΠ½Ρ‹Π΅ процСссы Ρƒ Porifera, Π½Π°ΠΌΠΈ Π±Ρ‹Π»ΠΎ ΠΏΡ€Π΅Π΄ΠΏΡ€ ΠΈ-нято Π΄Π΅Ρ‚Π°Π»ΡŒΠ½ΠΎΠ΅ ΡΡ€Π°Π²Π½ΠΈΡ‚Π΅Π»ΡŒΠ½ΠΎΠ΅ исслСдованиС Ρ€Π΅Π³Π΅Π½Π΅Ρ€Π°Ρ†ΠΈΠΈ ряда Π²ΠΈΠ΄ΠΎΠ² Π³ΡƒΠ±ΠΎΠΊ ΠΈΠ· Ρ„ΠΈΠ»ΠΎΠ³Π΅Π½Π΅Ρ‚ΠΈΡ‡ Π΅-ски ΡƒΠ΄Π°Π»Π΅Π½Π½Ρ‹Ρ… таксонов, ΠΎΡ‚Π»ΠΈΡ‡Π°ΡŽΡ‰ΠΈΠ΅ΡΡ анатомичСской ΠΈ гистологичСской ΠΎΡ€Π³Π°Π½ΠΈΠ·Π°Ρ†ΠΈΠ΅ΠΉ. ΠžΠ±ΡŠΠ΅ΠΊΡ‚Π°ΠΌΠΈ Π΄Π°Π½Π½ΠΎΠ³ΠΎ ΠΏΡ€ΠΎΠ΅ΠΊΡ‚Π° послуТили Π³ΡƒΠ±ΠΊΠΈ ΠΈΠ· классов Demospongiae, Homoscleromorpha ΠΈ Calcarea, ΠΎΠ±Π»Π°Π΄Π°ΡŽΡ‰ΠΈΠ΅ Π»Π΅ΠΉΠΊΠΎΠ½ΠΎΠΈΠ΄Π½ΠΎΠΉ, сиконоидной ΠΈ асконоидной Ρ‚ΠΈΠΏΠ°ΠΌΠΈ водоносной сист Π΅-ΠΌΡ‹, Π° Ρ‚Π°ΠΊΠΆΠ΅ Ρ€Π°Π·Π½ΠΎΠΉ ΡΡ‚Π΅ΠΏΠ΅Π½ΡŒΡŽ развития эпитСлия. ΠžΡΠ½ΠΎΠ²Π½Ρ‹ΠΌ ΠΌΠ΅Ρ…Π°Π½ΠΈΠ·ΠΌΠΎΠΌ Ρ€Π΅Π³Π΅Π½Π΅Ρ€Π°Ρ†ΠΈΠΈ Π»Π΅ΠΉΠΊΠΎ-Π½ΠΎΠΈΠ΄Π½Ρ‹Ρ… Demospongiae являСтся эпитСлио-мСзСнхимная трансформация с Π²ΠΎΠ²Π»Π΅Ρ‡Π΅Π½ΠΈΠ΅ΠΌ ΠΏΠΎΠ»ΠΈ-ΠΏΠΎΡ‚Π΅Π½Ρ‚Π½Ρ‹Ρ… ΠΊΠ»Π΅Ρ‚ΠΎΠΊ-Π°Ρ€Ρ…Π΅ΠΎΡ†ΠΈΡ‚ΠΎΠ². Основой Ρ€Π΅Π³Π΅Π½Π΅Ρ€Π°Ρ†ΠΈΠΈ Π»Π΅ΠΉΠΊΠΎΠ½ΠΎΠΈΠ΄Π½Ρ‹Ρ… Homoscleromorpha ΠΈ сиконоидных ΠΈ асконоидных Calcarea слуТат ΡΠΏΠΈΡ‚Π΅Π»ΠΈΠ°Π»ΡŒΠ½Ρ‹Π΅ ΠΌΠΎΡ€Ρ„ΠΎΠ³Π΅Π½Π΅Π·Ρ‹ ΠΈ трансдиффСрСн-Ρ†ΠΈΡ€ΠΎΠ²ΠΊΠ° ΠΊΠ»Π΅Ρ‚ΠΎΠΊ. РСгСнСрация асконоидных Calcarea прСдставляСт собой Ρ€Π΅Π΄ΠΊΠΈΠΉ ΠΏΡ€ΠΈΠΌΠ΅Ρ€ Β«Ρ‡ΠΈ-стого» морфаллаксиса. ΠœΡ‹ ΠΏΠΎΠΊΠ°Π·Π°Π»ΠΈ, Ρ‡Ρ‚ΠΎ морфогСнСтичСскиС процСссы, выявлСнныС Ρƒ Π³ΡƒΠ±ΠΎΠΊ, ΡΠ²Π»ΡΡŽΡ‚ΡΡ ΡΡ‚ΠΎΠ»ΡŒ ΠΆΠ΅ слоТными ΠΈ Ρ€Π°Π·Π½ΠΎΠΎΠ±Ρ€Π°Π·Π½Ρ‹ΠΌΠΈ, ΠΊΠ°ΠΊ ΠΈ Ρƒ Π΄Ρ€ΡƒΠ³ΠΈΡ… Π²Ρ‹ΡΡˆΠΈΡ… ΠΆΠΈΠ²ΠΎΡ‚Π½Ρ‹Ρ…. Π’Π°ΠΊΠΈΠΌ ΠΎΠ±Ρ€Π°Π·ΠΎΠΌ, Π³ΡƒΠ±ΠΊΠΈ ΠΌΠΎΠ³ΡƒΡ‚ Π±Ρ‹Ρ‚ΡŒ источником Π²Π°ΠΆΠ½ΠΎΠΉ ΠΈΠ½Ρ„ΠΎΡ€ΠΌΠ°Ρ†ΠΈΠΈ, которая ΠΏΠΎΠ·Π²ΠΎΠ»ΠΈΡ‚ Π½Π°ΠΌ Π³Π»ΡƒΠ±ΠΆΠ΅ ΠΏΠΎΠ½ΡΡ‚ΡŒ Ρ€Π°Π½Π½ΡŽΡŽ ΡΠ²ΠΎΠ»ΡŽΡ†ΠΈΡŽ молСкулярных ΠΈ ΠΊΠ»Π΅Ρ‚ΠΎΡ‡Π½Ρ‹Ρ… ΠΌΠ΅Ρ…Π°Π½ΠΈΠ·ΠΌΠΎΠ² ΠΌΠΎΡ€Ρ„ΠΎΠ³Π΅Π½Π΅Π·Π° Ρƒ ΠΆΠΈΠ²ΠΎΡ‚Π½Ρ‹Ρ…. Благодарности Данная Ρ€Π°Π±ΠΎΡ‚Π° осущСствлСна ΠΏΡ€ΠΈ финансовой ΠΏΠΎΠ΄Π΄Π΅Ρ€ΠΆΠΊΠ΅ Π³Ρ€Π°Π½Ρ‚ΠΎΠ² РЀЀИ β„– 16-04-00084, ΠΈ РНЀ β„– 17-14-01089.-8

    An Introduction to Tensors

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