Spin-density-wave instability in graphene doped near the van Hove singularity

We study the instability of the metallic state towards the formation of a new ground state in graphene doped near the van Hove singularity. The system is described by the Hubbard model and a field theoretical approach is used to calculate the charge and spin susceptibility. We find that for repulsive interactions, within the random phase approximation, there is a competition between ferromagnetism and spin-density wave (SDW). It turns out that a SDW with a triangular geometry is more favorable when the Hubbard parameter is above the critical value U_c(T), which depends on the temperature T, even if there are small variations in the doping. Our results can be verified by ARPES or neutron scattering experiments in highly doped graphene.Comment: 5 pages, 5 figures, 1 tabl

Development of the algorithm for aircraft control at inaccurate measurement of the state vector and variable accuracy parameter

A parametric method of the synthesis of control in the closed circuit, taking into account explicitly generalized error of the inertial module, is presented. The law of control in the form of analytical formulas is typically assigned to the control program and does not change during flight of an unmanned aerial vehicle. This decreases the capabilities of the autonomous flight control system to overcome control errors, which occur for various reasons. To verify assumptions about a possibility of improving the accuracy of an aerial vehicle control by the data of the strapdown inertial navigation system on a certain time interval of autonomous operation, the calculation experiment was conducted with the use of the developed software complex, simulating operation of the automatic flight control system. Parametrization of the law of control is considered as the main contribution (the outcome). Introduction of the parameter made it possible to decrease a negative impact of measurement errors and other disturbing factors on accuracy of reaching by the point of flight destination. Through computer modeling, it was shown that it is possible to decrease the impact of a generalized measurement error on generation of values of control functions by changing the value of the parameter. Analytical expressions for the estimation of accuracy of automatic control at the known generalized error of the inertial module and limited disturbing influences were obtained. After analyzing the influence of these factors on accuracy of the object control, a set of recommendations on selection of a variable parameter of synthesis of control depending on precision level of the sensors, used in the inertial module of measuring sensors, was generated.Розглянуто розв’язання термінальної задачі управління та синтезований параметризований закон управління в аналітичному вигляді, який залежить від змінного параметра глибини прогнозу. Досліджено особливості впливу величини параметра управління на точність досягнення кінцевої точки, дані рекомендації з вибору параметра для нівелювання помилки інерційних вимірювань. Синтез управління здійснюється методом переслідування ведучої точки за інформацією, отриманою інтегруванням вимірювань фактичного прискорення і містить помилку, характерну для акселерометрів

Transport properties of a quantum wire: the role of extended time-dependent impurities

We study the transport properties of a quantum wire, described by the Tomonaga-Luttinger model, in the presence of a backscattering potential provided by several extended time-dependent impurities (barriers). Employing the B\" uttiker-Landauer approach, we first consider the scattering of noninteracting electrons ($g=1$) by a rectangular-like barrier and find an exact solution for the backscattering current, as well as a perturbative solution for a weak static potential with an arbitrary shape. We then include electron-electron interactions and use the Keldysh formalism combined with the bosonization technique to study oscillating extended barriers. We show that the backscattering current off time-dependent impurities can be expressed in terms of the current for the corresponding static barrier. Then we determine the backscattering current for a static extended potential, which, in the limit of noninteracting electrons ($g=1$), coincides with the result obtained using the B\" uttiker-Landauer formalism. In particular, we find that the conductance can be increased beyond its quantized value in the whole range of repulsive interactions $0<g<1$ already in the case of a single oscillating extended impurity, in contrast %contrary to the case of a point-like impurity, where this phenomenon occurs only for $0<g<1/2$.Comment: 9 pages, 5 figure

Coupled quantum wires

We study a set of crossed 1D systems, which are coupled with each other via tunnelling at the crossings. We begin with the simplest case with no electron-electron interactions and find that besides the expected level splitting, bound states can emerge. Next, we include an external potential and electron-electron interactions, which are treated within the Hartree approximation. Then, we write down a formal general solution to the problem, giving additional details for the case of a symmetric external potential. Concentrating on the case of a single crossing, we were able to explain recent experinents on crossed metallic and semiconducting nanotubes [J. W. Janssen, S. G. Lemay, L. P. Kouwenhoven, and C. Dekker, Phys. Rev. B 65, 115423 (2002)], which showed the presence of localized states in the region of crossing.Comment: 11 pages, 10 figure

Analysis of the national economy insurance market dynamics and basic clusters tools determination by economic and mathematical modeling instruments

Страховий ринок національної економіки за останні п’ять років показує швидку динаміку зростання надання послуг та виплат. За вказаний період сформувалися основні лідери надання страхових послуг, які фактично й диктують ціни на страхові послуги за основними напрямками: медичного страхування; страхові платежі зі страхування від нещасних випадків; страхові платежі КАСКО; страхові платежі ОСАГО; страхові платежі туристичні та інші види страхових послуг. Розглянуто питання діджиталізації страхових послуг, що дозволить суттєво розширити клієнтську базу, доступ клієнтів до повної інформації стосовно надання страхових послуг. Відповідно з економічної точки собівартість надання страхових послуг при діджиталізації страхових послуг зможе суттєво знизитись. Це дасть можливість частині населення з нижчим рівнем заробітної плати мати доступ до страхових послуг: медичного полісу, туристичного, страхування життя та майна від нещасних випадків і т.д. Використовуючи інструментарій на основі кореляційно-регресійного аналізу досліджено вплив макроекономічних показників, таких, як капітальні інвестиції в економіку, рівень заробітної плати населення України на фінансові показники діяльності страхових компаній. Використовуючи сучасні методики економіко-математичного моделювання, а саме кластерний аналіз, виділено основні кластерні структури провідних страхових компаній України. Кластерний аналіз страхового ринку України дозволить покращити моніторинг як за надходженням страхових внесків, так і здійсненням страхових виплат. Для цього ми пропонуємо створити державну структуру контролю та моніторингу. Застосування сучасних інформаційних систем на взірець Statistica дозволяє опрацьовувати великі масиви інформації з найточнішими результатамиOver the last five years the national economy insurance market shows the rapid dynamics of service and payment growth. Relatively, during this period, the main leaders of insurance services were formed. They actually define prices for insurance services in the following main areas: health insurance; accident insurance premiums; full comprehensive insurance premiums; Compulsory Motor Third Party Liability (CMTPL) insurance payments; travelling insurance premiums and other types of insurance services. The article deals with the problem of insurance services digitization providing significant customer base extension, customer access to total insurance services information and, relatively, in terms of economy, the cost of provided insurance services can be significantly reduced due to insurance services digitization making it possible for the population with lower wages level to access the insurance services: health insurance, travelling, accident health and property insurance, etc. The influence of macroeconomic indicators such as: capital investments in the economy, the wages level of Ukrainian population on the financial performance indicators of insurance companies is investigated in this article by means of tools based on correlation-regression analysis. Using the modern methods of economic and mathematical modeling, especially cluster analysis, the main cluster structures of the leading insurance companies of Ukraine are identified. Carried out cluster analysis of Ukrainian insurance market makes it possible to improve the monitoring of both insurance premium receipts and payments, that is why we propose to create controlling and monitoring state structure. The application of modern information systems such as Statistica enables to process large amounts of information with the most accurate results

Topological phase transitions between chiral and helical spin textures in a lattice with spin-orbit coupling and a magnetic field

We consider the combined effects of large spin-orbit couplings and a perpendicular magnetic field in a 2D honeycomb fermionic lattice. This system provides an elegant setup to generate versatile spin textures propagating along the edge of a sample. The spin-orbit coupling is shown to induce topological phase transitions between a helical quantum spin Hall phase and a chiral spin-imbalanced quantum Hall state. Besides, we find that the spin orientation of a single topological edge state can be tuned by a Rashba spin-orbit coupling, opening an interesting route towards quantum spin manipulation. We discuss the possible realization of our results using cold atoms trapped in optical lattices, where large synthetic magnetic fields and spin-orbit couplings can be engineered and finely tuned. In particular, this system would lead to the observation of a time-reversal-symmetry-broken quantum spin Hall phase.Comment: 8 pages, 3 figures, Accepted in Europhys. Lett. (Dec 2011