On Integrability of a Special Class of Two-Component (2+1)-Dimensional Hydrodynamic-Type Systems

The particular case of the integrable two component (2+1)-dimensional hydrodynamical type systems, which generalises the so-called Hamiltonian subcase, is considered. The associated system in involution is integrated in a parametric form. A dispersionless Lax formulation is found

On generating functions in the AKNS hierarchy

It is shown that the self-induced transparency equations can be interpreted as a generating function for as positive so negative flows in the AKNS hierarchy. Mutual commutativity of these flows leads to other hierarchies of integrable equations. In particular, it is shown that stimulated Raman scattering equations generate the hierarchy of flows which include the Heisenberg model equations. This observation reveals some new relationships between known integrable equations and permits one to construct their new physically important combinations. Reductions of the AKNS hierarchy to ones with complex conjugate and real dependent variables are also discussed and the corresponding generating functions of positive and negative flows are found. Generating function of Whitham modulation equations in the AKNS hierarchy is obtained.Comment: 11 pages, no figure

A generalized hydrodynamical Gurevich-Zybin equation of Riemann type and its Lax type integrability

This paper is devoted to the study of a hydrodynamical equation of Riemann type, generalizing the remarkable Gurevich–Zybin system. This multi-component non-homogenous hydrodynamic equation is characterized by the only characteristic flow velocity. The compatible bi-Hamiltonian structures and Lax type representations of the 3-and 4-component generalized Riemann type hydrodynamical system are analyzed. For the first time the obtained results augment the theory of integrability of hydrodynamic type systems, originally developed only for distinct characteristic velocities in homogenous case.Досліджено гідродинамічне рівняння типу Рімана, що узагальнює відому систему Гуревича - Зибіна. Це багатокомпонентне гідродинамічне рівняння характеризується єдиною характеристичною швидкістю потоку. Проаналізовані сумісні бі-гамільтонові структури та представлення Лакса для три- та чотирикомпонентної узагальненої гідродинамічної системи типу Рімана. Одержані результати вперше доповнюють теорію інтегровності систем гідродинамічного типу, раніше розвиненої тільки для відмінних швидкостей в однорідному випадку

Algebro-geometric approach in the theory of integrable hydrodynamic type systems

The algebro-geometric approach for integrability of semi-Hamiltonian hydrodynamic type systems is presented. This method is significantly simplified for so-called symmetric hydrodynamic type systems. Plenty interesting and physically motivated examples are investigated

Synthesis of Gold Nanoparticles by Blue-Green Algae Spirulina Platensis

The synthesis of gold nanoparticles by one of the many popular microorganisms – blue-green algae Spirulina platensis was studied. The complex of optical and analytical methods was applied for investigation of experimental samples after exposure to chloroaurate (HAuCl4) solution at different doses and for different time intervals. To characterize formed gold nanoparticles UV-vis Spectrometry, Transmission Electron Microscopy (TEM), Scanning Electron Microscopy (SEM), Energy-dispersive analysis of X-rays (EDAX) were used. It was shown that after 1.5 – 2 days of exposure the extracellular formation of nanoparticles of spherical form and the distribution peak within the interval of 20-30 nm took place. To determine gold concentrations in the Spirulina platensis biomass neutron activation analysis (NAA) was applied. When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/3496

Electronic structure of FeSe monolayer superconductors

We review a variety of theoretical and experimental results concerning electronic band structure of superconducting materials based on FeSe monolayers. Three type of systems are analyzed: intercalated FeSe systems AxFe₂Se₂–xSx and [Li₁–xFexOH]FeSe as well as the single FeSe layer films on SrTiO₃ substrate. We present the results of detailed first principle electronic band structure calculations for these systems together with comparison with some experimental ARPES data. The electronic structure of these systems is rather different from that of typical FeAs superconductors, which is quite significant for possible microscopic mechanism of superconductivity. This is reflected in the absence of hole pockets of the Fermi surface at T-point in Brillouin zone, so that there are no “nesting” properties of different Fermi surface pockets. LDA + DMFT calculations show that correlation effects on Fe-3d states in the single FeSe layer are not that strong as in most of FeAs systems. As a result, at present there is no theoretical understanding of the formation of rather “shallow” electronic bands at M-points. LDA calculations show that the main difference in electronic structure of FeSe monolayer on SrTiO ₃ substrate from isolated FeSe layer is the presence of the band of O-2p surface states of TiO₂ layer on the Fermi level together with Fe-3d states, which may be important for understanding the enhanced Tc values in this system. We briefly discuss the implications of our results for microscopic models of superconductivity

On a nonlocal Ostrovsky–Whitham type dynamical system, its Riemann type inhomogeneous regularizations and their integrability

Short-wave perturbations in a relaxing medium, governed by a special reduction of the Ostrovsky evolution equation, and later derived by Whitham, are studied using the gradient-holonomic integrability algorithm. The bi-Hamiltonicity and complete integrability of the corresponding dynamical system is stated and an infinite hierarchy of commuting to each other conservation laws of dispersive type are found. The well defined regularization of the model is constructed and its Lax type integrability is discussed. A generalized hydrodynamical Riemann type system is considered, infinite hierarchies of conservation laws, related compatible Poisson structures and a Lax type representation for the special case N = 3 are constructed

Helium in superstrong magnetic fields

We investigate the helium atom embedded in a superstrong magnetic field gamma=100-10000 au. All effects due to the finite nuclear mass for vanishing pseudomomentum are taken into account. The influence and the magnitude of the different finite mass effects are analyzed and discussed. Within our full configuration interaction approach calculations are performed for the magnetic quantum numbers M=0,-1,-2,-3, singlet and triplet states, as well as positive and negative z parities. Up to six excited states for each symmetry are studied. With increasing field strength the number of bound states decreases rapidly and we remain with a comparatively small number of bound states for gamma=10^4 au within the symmetries investigated here.Comment: 16 pages, including 14 eps figures, submitted to Phys. Rev.

ДВУХЭТАПНОЕ РЕЭНДОПРОТЕЗИРОВАНИЕ ТАЗОБЕДРЕННОГО СУСТАВА ПРИ ОБШИРНОМ ДЕФЕКТЕ КОСТНОЙ ТКАНИ ВЕРТЛУЖНОЙ ВПАДИНЫ (СЛУЧАЙ ИЗ ПРАКТИКИ)

Favorable short-term results of arthroplasty are observed in 80–90% of cases, however, over the longer follow up period the percentage of positive outcomes is gradually reduced. Need for revision of the prosthesis or it’s components increases in proportion to time elapsed from the surgery. In addition, such revision is accompanied with a need to substitute the bone defect of the acetabulum. As a solution the authors propose to replace pelvic defects in two stages. During the first stage the defect was filled with bone allograft with platelet-rich fibrin (allografting with the use of PRF technology). After the allograft remodeling during the second stage the revision surgery is performed by implanting standard prostheses. The authors present a clinical case of a female patient with aseptic loosening of acetabular component of prosthesis in the right hip joint, with failed hip function of stage 2, right limb shortening of 2 cm. Treatment results confirm the efficiency and rationality of the proposed bone grafting option. The authors conclude bone allograft in combination with the PRF technology proves to be an alternative to the implantation of massive metal implants in the acetabulum while it reduces the risk of implant-associated infection, of metallosis in surrounding tissues and expands further revision options.Краткосрочные благоприятные результаты эндопротезирования отмечаются в 80–90% случаев, однако с увеличением сроков наблюдения процент положительных исходов постепенно снижается. Пропорционально давности операции возрастает потребность в замене эндопротеза или его компонентов. При этом нередко возникает необходимость замещения костного дефекта вертлужной впадины. Для решения этой проблемы авторы предлагают устранять дефекты костей таза в два этапа. В ходе первого оперативного вмешательства выполняют заполнение дефекта аллотрансплантатом с аутологичными тромбоцитами, обогащенными фибрином (аллопластика дефекта с применением PRF-технологии). После перестройки аллотрансплантата производят ревизионное эндопротезирование с имплантацией стандартных конструкций эндопротеза. В качестве примера в статье представлено клиническое наблюдение пациентки с асептической ацетабулярной нестабильностью эндопротеза ЭСИ правого тазобедренного сустава, несостоятельностью функции сустава (НФС) 2-й ст., укорочением правой нижней конечности на 2 см. В анамнезе пациентки в 1992 г. закрытый перелом вертлужной впадины справа в результате дорожно-транспортного происшествия, по поводу которого было выполнено эндопротезирование тазобедренного сустава. В 1992 г. пациентка перенесла первичное эндопротезирование, в 2000 и в 2005 г. по поводу асептической нестабильности эндопротеза были выполнены ревизионные операции. При поступлении по данным лучевых методов исследования у пациентки был выявлен дефект вертлужной впадины типа 3 B по классификации W.G. Paprosky. Для исключения парапротезной инфекции выполнена пункция области протеза. Результат бактериологического исследования отрицательный. Было принято решение о выполнении двухэтапного ревизионного вмешательства по предложенной авторами методике, что позволило получить положительный ближайший результат. Выполнение аллопластики костной тканью в сочетании с PRF-технологией является альтернативой установке массивных металлоконструкций в области вертлужной впадины, поскольку снижает связанный с внедрением объемного имплантата риск инфицирования и возникновения металлоза окружающих тканей и расширяет возможности дальнейшего реэндопротезирования