Asymptotic formula for the moments of Minkowski question mark function in the interval [0,1]

In this paper we prove the asymptotic formula for the moments of Minkowski question mark function, which describes the distribution of rationals in the Farey tree. The main idea is to demonstrate that certain a variation of a Laplace method is applicable in this problem, hence the task reduces to a number of technical calculations.Comment: 11 pages, 1 figure (final version). Lithuanian Math. J. (to appear

A proposal for a new type of thin-film field-emission display by edge breakdown of MIS structure

A new type of field emission display(FED) based on an edge-enhance electron emission from metal-insulator-semiconductor (MIS) thin film structure is proposed. The electrons produced by an avalanche breakdown in the semiconductor near the edge of a top metal electrode are initially injected to the thin film of an insulator with a negative electron affinity (NEA), and then are injected into vacuum in proximity to the top electrode edge. The condition for the deep-depletition breakdown near the edge of the top metal electrode is analytically found in terms of ratio of the insulator thickness to the maximum (breakdown) width of the semiconductor depletition region: this ratio should be less than 2/(3 \pi - 2) = 0.27. The influence of a neighboring metal electrode and an electrode thickness on this condition are analyzed. Different practical schemes of the proposed display with a special reference to M/CaF_2/Si structure are considered.Comment: 11 pages, 5 figure

Interaction between protokimberlite melts and mantle lithosphere: evidence from mantle xenoliths from the Dalnyaya kimberlite pipe, Yakutia (Russia)

The Dalnyaya kimberlite pipe (Yakutia, Russia) contains mantle peridotite xenoliths (mostly lherzolites and harzburgites) that show both sheared porphyroclastic (deformed) and coarse granular textures, together with ilmenite and clinopyroxene megacrysts. Deformed peridotites contain high-temperature Fe-rich clinopyroxenes, sometimes associated with picroilmenites, which are products of interaction of the lithospheric mantle with protokimberlite related melts. The orthopyroxene-derived geotherm for the lithospheric mantle beneath Dalnyaya is stepped similar to that beneath the Udachnaya pipe. Coarse granular xenoliths fall on a geotherm of 35 mWm-2 whereas deformed varieties yield a 45 mWm-2 geotherm in the 2–7.5 GPa pressure interval. The chemistry of the constituent minerals including garnet, olivine and clinopyroxene shows trends of increasing Fe# (= Fe/(Fe+Mg) with decreasing pressure. This may suggest that the interaction with fractionating protokimberlite melts occurred at different levels. Two major mantle lithologies are distinguished by the trace element patterns of their constituent minerals, determined by LA-ICP-MS. Orthopyroxenes, some clinopyroxenes and rare garnets are depleted in Ba, Sr, HFSE and MREE and represent relic lithospheric mantle. Re-fertilized garnet and clinopyroxene are more enriched. The distribution of trace elements between garnet and clinopyroxene shows that the garnets dissolved primary orthopyroxene and clinopyroxene. Later high temperature clinopyroxenes related to the protokimberlite melts partially dissolved these garnets. Olivines show decreases in Ni and increases in Al, Ca and Ti from Mg-rich varieties to the more Fe-rich, deformed and refertilized ones. Minerals showing higher Fe# (0.11–0.15) are found within intergrowths of low-Cr ilmenite-clinopyroxene-garnet related to the crystallization of protokimberlite melts in feeder channels. In P-f(O2) diagrams, garnets and Cr-rich clinopyroxenes indicate reduced conditions at the base of the lithosphere at -5 log units below a FMQ buffer. However, Cr-poor clinopyroxenes, together with ilmenite and some Fe-Ca-rich garnets, demonstrate a more oxidized trend in the lower part of lithosphere at -2 to 0 log units relative to FMQ. Clinopyroxenes from xenoliths in most cases show conditions transitional between those determined for garnets and megacrystalline Cr-poor suite. The relatively low diamond grade of Dalnyaya kimberlites is explained by a high degree of interaction with the oxidized protokimberlite melts, which is greater at the base of the lithosphere

Лиганды RAGE-белков: роль в межклеточной коммуникации и патогенезе воспаления

The review contains data on the diversity of endogenous ligands of RAGE receptors (receptor for advanced glycation end products) that play an important role in the signal transduction in (patho) physiological conditions. RAGE takes part in various physiological processes like cell growth and survival, apoptosis and regeneration. They serve as regulators of inflammatory reactions due to their ability to induce secretion of cytokines and chemokines. In addition, they facilitate elimination of apoptotic cells and mediate innate immune response. We discuss mechanisms of soluble RAGE production as well as the role of membrane and soluble forms of the receptor in cell signaling. Several endogenous ligands of RAGE are well-known: advanced glycation end products (AGE), amyloid-beta (Аβ), nuclear high mobility group box 1 proteins (HMGB1), and calcium-binding proteins S100A4, S100A8/A9, S100A12 и S100B. The review is focused on the mechanisms of the ligands production, their secretion from the cells of various origin, interaction with RAGE, and associated intracellular signal transduction pathways. Special attention is paid to the role of RAGE in pathogenesis of inflammation, particularly, in brain injury and neurodegeneration.В обзоре литературы обсуждается разнообразие эндогенных лигандов RAGE-рецепторов, играющих важную роль в сигнальной трансдукции в физиологических условиях и при патологии. RAGE-рецепторы опосредуют многие физиологические функции, такие как рост клеток, апоптоз, выживание и регенерация; участвуют в воспалительных реакциях, индуцируя секрецию цитокинов и хемокинов; способствуют элиминации апоптотических клеток, являются участниками врожденного иммунного ответа. Рассмотрены механизмы образования растворимых форм RAGE, а также роль мембранной и растворимой форм рецепторов в передаче сигнальной информации при активации клеток. Признанными лигандами RAGE являются продукты неферментативного гликирования белков, бета-амилоид, ядерные белки HMGB1, кальцийсвязывающие белки S100A4, S100A8/A9, S100A12 и S100B. В статье обсуждаются механизмы продукции лигандов RAGE, секреции их из клеток различной природы, их взаимодействие с рецепторами и последствия этого взаимодействия для клеток и тканей. Особое внимание уделено анализу роли лигандов RAGE в развитии воспаления, в частности при повреждении головного мозга и нейродегенерации