Fourier Tauberian Theorems and Applications

The main aim of the paper is to present a general version of the Fourier Tauberian theorem for monotone functions. This result, together with Berezin's inequality, allows us to obtain a refined version the Li-Yau estimate for the counting function of the Dirichlet Laplacian which implies the Li-Yau estimate itself and, at the same time, the asymptotic results obtained by the variational method.Comment: 15 page

On the comparison of the Dirichlet and Neumann counting functions

The aim of the paper is to show that L. Friedlander's results on the relation between Dirichlet and Neumann counting functions (Arch. Ration. Mech. Anal. 116, 1991) remain valid in abstract setting.Comment: To appear in "Spectral Theory of Differential Operators: M. Sh. Birman 80th Anniversary Collection" Amer. Math. Soc. Transl.(2), Vol. 225 (2008

TRANSPLANTATION OF SPLEEN (INDICATIONS, SURGICAL ASPECTS, COMPLICATIONS, PROPHYLAXIS)

No abstrac

PHAGOCYTIC ACTIVITY OF POLYMORPHONUCLEAR LEUCOCYTES AFTER EXTRACORPORAL TRANSPLANTATION OF SPLEEN (AUTOTRANSPLANTATION)

No abstrac

Families of spherical caps: spectra and ray limit

We consider a family of surfaces of revolution ranging between a disc and a hemisphere, that is spherical caps. For this family, we study the spectral density in the ray limit and arrive at a trace formula with geodesic polygons describing the spectral fluctuations. When the caps approach the hemisphere the spectrum becomes equally spaced and highly degenerate whereas the derived trace formula breaks down. We discuss its divergence and also derive a different trace formula for this hemispherical case. We next turn to perturbative corrections in the wave number where the work in the literature is done for either flat domains or curved without boundaries. In the present case, we calculate the leading correction explicitly and incorporate it into the semiclassical expression for the fluctuating part of the spectral density. To the best of our knowledge, this is the first calculation of such perturbative corrections in the case of curvature and boundary.Comment: 28 pages, 7 figure

Effects of boundary conditions on magnetization switching in kinetic Ising models of nanoscale ferromagnets

Magnetization switching in highly anisotropic single-domain ferromagnets has been previously shown to be qualitatively described by the droplet theory of metastable decay and simulations of two-dimensional kinetic Ising systems with periodic boundary conditions. In this article we consider the effects of boundary conditions on the switching phenomena. A rich range of behaviors is predicted by droplet theory: the specific mechanism by which switching occurs depends on the structure of the boundary, the particle size, the temperature, and the strength of the applied field. The theory predicts the existence of a peak in the switching field as a function of system size in both systems with periodic boundary conditions and in systems with boundaries. The size of the peak is strongly dependent on the boundary effects. It is generally reduced by open boundary conditions, and in some cases it disappears if the boundaries are too favorable towards nucleation. However, we also demonstrate conditions under which the peak remains discernible. This peak arises as a purely dynamic effect and is not related to the possible existence of multiple domains. We illustrate the predictions of droplet theory by Monte Carlo simulations of two-dimensional Ising systems with various system shapes and boundary conditions.Comment: RevTex, 48 pages, 13 figure

Spintronics: Fundamentals and applications

Spintronics, or spin electronics, involves the study of active control and manipulation of spin degrees of freedom in solid-state systems. This article reviews the current status of this subject, including both recent advances and well-established results. The primary focus is on the basic physical principles underlying the generation of carrier spin polarization, spin dynamics, and spin-polarized transport in semiconductors and metals. Spin transport differs from charge transport in that spin is a nonconserved quantity in solids due to spin-orbit and hyperfine coupling. The authors discuss in detail spin decoherence mechanisms in metals and semiconductors. Various theories of spin injection and spin-polarized transport are applied to hybrid structures relevant to spin-based devices and fundamental studies of materials properties. Experimental work is reviewed with the emphasis on projected applications, in which external electric and magnetic fields and illumination by light will be used to control spin and charge dynamics to create new functionalities not feasible or ineffective with conventional electronics.Comment: invited review, 36 figures, 900+ references; minor stylistic changes from the published versio

Фотодинамическая терапия в нейроонкологии

Literature review reflects the current status and development status of intraoperative photodynamic therapy in neurooncology and discusses the results of the most important studies on photodynamic  therapy (PDT). We searched the Pubmed, EMBASE, Cochrane Library and eLibrary data-bases for publications  published  between January 2000 and December 2022. Found 204 publications  in foreign sources and 59 publications  in domestic editions, dealing with the issues of photodynamic  therapy in neurooncology. An analysis of the literature has shown that intraoperative PDT in neurooncology is an important tool that contributes to increasing the radicality of the operation and local control. The basic rationale for the effectiveness of PDT lies in the study of the pathways leading to the complete devitalization of a malignant tumor, the study of the mechanisms of the local and systemic immune response. In addition, subcellular targets in PDT are determined by the properties of photosensitizers (PS). Second generation PSs have already been introduced into clinical practice. The effectiveness of PDT using photoditazine, 5-aminolevulinic acid has been demonstrated. The mechanisms of action and targets of these PS have been established. In Russia, a number of studies have repeatedly shown and proved the clinical effectiveness of PDT in groups of neurooncological patients with glial tumors and secondary metastatic tumors, but so far, the method has not been included in the clinical guidelines for the provision of high-tech neurosurgical care. There is certainly a need for further development of PTD techniques in neurooncology, especially in patients at high risk of recurrence and aggressive CNS tumors.Выполнен обзор литературы, отражающий современное состояние и степень разработанности  методики интраоперационной  фотодинамической терапии (ФДТ) в нейроонкологи. Представлены к обсуждению результаты наиболее значимых исследований, посвященных ФДТ в нейроонкологии. Проведен анализ научных публикаций по данной тематике в базах данных Pubmed, EMBASE, Cochrane Library и eLibrary, опубликованных в промежуток времени с января 2000 г. по декабрь 2022 г. Найдено 204 публикации в зарубежных источниках  и 59 публикаций в отечественных  изданиях, в которых рассматриваются  вопросы применения ФДТ в нейроонкологии. Анализ литературы показал, что в клинической практике интраоперационная  ФДТ в нейроонкологии  является важным инструментом, способствующим увеличению радикальности операции и локального контроля. Фундаментальное обоснование эффективности ФДТ заключается в изучении путей, ведущих к полной девитализации злокачественной  опухоли, изучении механизмов локального и системного  иммунного ответа. При этом субклеточные  мишени при ФДТ обусловлены свойствами  фотосенсибилизаторов (ФС). В многочисленных  исследованиях  показана противоопухолевая эффективность  использования  ФДТ с ФС на основе  хлорина  е6, 5-аминолевулиновой  кислоты, производных  порфиринов.  Установлены механизмы действия и мишени этих ФС. В России  в ряде исследований подтверждена клиническая эффективность  ФДТ у групп нейроонкологических пациентов с глиальным опухолями и вторичными метастатическими опухолями, однако до сих пор метод не включён в клинические рекомендации по оказанию высокотехнологичной  нейрохирургической помощи. Безусловно, необходима дальнейшая разработка методики ФДТ в нейроонкологии, особенно у пациентов с высоким риском рецидива и агрессивными опухолями ЦНС