The effective technique of solving of reduced characteristics equations of radiation transfer theory

An integral equation of radiation transfer theory is considered. The method to solution of this equation based on its reduction to an infinity system of linear algebraic equations is presented. The solvability conditions in L2-space are given and the explicit series solution is constructed

Quantum analogue of the spin-flop transition for a spin pair

Quantum (step-like) magnetization curves are studies for a spin pair with antiferromagnetic coupling in the presence of a magnetic field parallel to the easy axis of the magnetic anisotropy. The consideration is done both analytically and numerically for a wide range of the anisotropy constants and spins up to $S \gtrsim 100$. Depending on the origin of the anisotropy (exchange or single-ion), the magnetization curve can demonstrate the jumps more than unity and the concentration of the unit jumps in a narrow range of the field. We also point the region of the problem parameters, where the behavior is quasiclassical for $S = 5$, and where system is substantially quantum in the limit $S \to \infty$.Comment: 5 pages, 5 figure

Relativistic nature of a magnetoelectric modulus of Cr_2O_3-crystals: a new 4-dimensional pseudoscalar and its measurement

Earlier, the magnetoelectric effect of chromium sesquioxide Cr_2O_3 has been determined experimentally as a function of temperature. One measures the electric field-induced magnetization on Cr_2O_3 crystals or the magnetic field-induced polarization. From the magnetoelectric moduli of Cr_2O_3 we extract a 4-dimensional relativistic invariant pseudoscalar $\widetilde{\alpha}$. It is temperature dependent and of the order of 10^{-4}/Z_0, with Z_0 as vacuum impedance. We show that the new pseudoscalar is odd under parity transformation and odd under time inversion. Moreover, $\widetilde{\alpha}$ is for Cr_2O_3 what Tellegen's gyrator is for two port theory, the axion field for axion electrodynamics, and the PEMC (perfect electromagnetic conductor) for electrical engineering.Comment: Revtex, 36 pages, 9 figures (submitted in low resolution, better quality figures are available from the authors

СПОСОБ ВОССТАНОВЛЕНИЯ ОТТОКА ЖЕЛЧИ ПРИ ОРТОТОПИЧЕСКОЙ ТРАНСПЛАНТАЦИИ ПЕЧЕНИ С ИСПОЛЬЗОВАНИЕМ ПУЗЫРНОГО ПРОТОКА

Method for restoration of bile outflow in orthotopic transplantation of liver using cystic duct may find application in anatomic version characterised by parallel location of cystic and common liver ducts in donor. After cholecystectomy, at the level of bile ducts donor segment intersection, common reservoir is formed with application of common liver and cystic ducts by dissection or wedge-shaped excision of partition segment between them. Level of bile ducts donor segment intersection is selected so that diameter of common reservoir coincides with diameter of recipient bile duct, with which biliobiliary anastomosis is formed. Biliobiliary anastomosis is formed as «end to end». If there are mucous and muscular layers in composition of partition between liver and cystic ducts, they are dissected. Edges of mucous layer are sutured. If only mucous layer is present in composition of partition, it is dissected without further suturing. Such approach supply possibility to overcome discrepancy of sutured ducts diameters and provision of bile outflow from liver in the most physiological version with «end to end» anastomosis. Описывается разработанный и клинически апробированный авторами способ восстановления оттока жел- чи при ортотопической трансплантации печени с использованием пузырного протока. Предлагаемый способ позволяет адаптировать диаметры сшиваемых желчных протоков путем создания резервуара за счет рассече- ния или клиновидного иссечения перегородки между общим печеночным и пузырным протоками и обеспе- чивает в наиболее физиологичном варианте отток желчи из печени путем формирования билиобилиарного анастомоза по типу «конец в конец».

Model theory of finite and pseudofinite groups

This is a survey, intended both for group theorists and model theorists, concerning the structure of pseudofinite groups, that is, infinite models of the first-order theory of finite groups. The focus is on concepts from stability theory and generalisations in the context of pseudofinite groups, and on the information this might provide for finite group theory

РЕТРАНСПЛАНТАЦИЯ ПЕЧЕНИ: ОПЫТ РОССИЙСКОГО НАУЧНОГО ЦЕНТРА РАДИОЛОГИИ И ХИРУРГИЧЕСКИХ ТЕХНОЛОГИЙ (РНЦРХТ)

The article gives the report about the experience in repeated liver transplantation (LT). Totally 99 LT including 6 repeated operation at five patients performed between june 1999 and june 2011. In 3 of 6 cases bile ducts necroses was the indication to repeated LT. Retransplantations were connected with difficulties, enlargement of duration and replacement therapy volume, also explained high number of complication after operation. It is demonstrated that chronic biliary infection and bad condition of patients are the main reasons of complication and poor prognosis after repeated liver transplantation. В статье представлен опыт работы РНЦРХТ. С июня 1999-го по июнь 2011 гг. было выполнено 99 ортото- пических трансплантаций печени, из них 6 повторных у 5 больных. В половине наблюдений показанием к повторной трансплантации послужил некроз желчных протоков. Вмешательства были сопряжены со значительными техническими трудностями, заключавшимися в увеличении продолжительности опера- ции, объема заместительных инфузий. Это объясняло высокую частоту осложнений в послеоперацион- ном периоде. Неблагоприятными факторами прогноза были хроническая билиарная инфекция и тяжесть состояния пациентов перед повторной трансплантацией печени (ТП).

Statistical Mechanics and the Physics of the Many-Particle Model Systems

The development of methods of quantum statistical mechanics is considered in light of their applications to quantum solid-state theory. We discuss fundamental problems of the physics of magnetic materials and the methods of the quantum theory of magnetism, including the method of two-time temperature Green's functions, which is widely used in various physical problems of many-particle systems with interaction. Quantum cooperative effects and quasiparticle dynamics in the basic microscopic models of quantum theory of magnetism: the Heisenberg model, the Hubbard model, the Anderson Model, and the spin-fermion model are considered in the framework of novel self-consistent-field approximation. We present a comparative analysis of these models; in particular, we compare their applicability for description of complex magnetic materials. The concepts of broken symmetry, quantum protectorate, and quasiaverages are analyzed in the context of quantum theory of magnetism and theory of superconductivity. The notion of broken symmetry is presented within the nonequilibrium statistical operator approach developed by D.N. Zubarev. In the framework of the latter approach we discuss the derivation of kinetic equations for a system in a thermal bath. Finally, the results of investigation of the dynamic behavior of a particle in an environment, taking into account dissipative effects, are presented.Comment: 77 pages, 1 figure, Refs.37

Teaching and Learning of Calculus

This survey focuses on the main trends in the field of calculus education. Despite their variety, the findings reveal a cornerstone issue that is strongly linked to the formalism of calculus concepts and to the difficulties it generates in the learning and teaching process. As a complement to the main text, an extended bibliography with some of the most important references on this topic is included. Since the diversity of the research in the field makes it difficult to produce an exhaustive state-of-the-art summary, the authors discuss recent developments that go beyond this survey and put forward new research questions

Multiphysics and Thermodynamic Formulations for Equilibrium and Non-equilibrium Interactions: Non-linear Finite Elements Applied to Multi-coupled Active Materials

[EN] Combining several theories this paper presents a general multiphysics framework applied to the study of coupled and active materials, considering mechanical, electric, magnetic and thermal fields. The framework is based on thermodynamic equilibrium and non-equilibrium interactions, both linked by a two-temperature model. The multi-coupled governing equations are obtained from energy, momentum and entropy balances; the total energy is the sum of thermal, mechanical and electromagnetic parts. The momentum balance considers mechanical plus electromagnetic balances; for the latter the Abraham rep- resentation using the Maxwell stress tensor is formulated. This tensor is manipulated to automatically fulfill the angular momentum balance. The entropy balance is for- mulated using the classical Gibbs equation for equilibrium interactions and non-equilibrium thermodynamics. For the non-linear finite element formulations, this equation requires the transformation of thermoelectric coupling and conductivities into tensorial form. The two-way thermoe- lastic Biot term introduces damping: thermomechanical, pyromagnetic and pyroelectric converse electromagnetic dynamic interactions. Ponderomotrix and electromagnetic forces are also considered. The governing equations are converted into a variational formulation with the resulting four-field, multi-coupled formalism implemented and val- idated with two custom-made finite elements in the research code FEAP. Standard first-order isoparametric eight-node elements with seven degrees of freedom (dof) per node (three displacements, voltage and magnetic scalar potentials plus two temperatures) are used. Non-linearities and dynamics are solved with Newton-Raphson and New- mark-b algorithms, respectively. 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