Three-block exceptional collections over Del Pezzo surfaces

We study complete exceptional collections of coherent sheaves over Del Pezzo surfaces, which consist of three blocks such that inside each block all Ext groups between the sheaves are zero. We show that the ranks of all sheaves in such a block are the same and the three ranks corresponding to a complete 3-block exceptional collection satisfy a Markov-type Diophantine equation that is quadratic in each variable. For each Del Pezzo surface, there is a finite number of these equations; the complete list is given. The 3-string braid group acts by mutations on the set of complete 3-block exceptional collections. We describe this action. In particular, any orbit contains a 3-block collection with the sum of ranks that is minimal for the solutions of the corresponding Markov-type equation, and the orbits can be obtained from each other via tensoring by an invertible sheaf and with the action of the Weyl group. This allows us to compute the number of orbits up to twisting.Comment: LaTex v2.09, 32 pages with 1 figure. To appear in Izvestiya Mat

Методологические и методические основы исследования метакогнитивных детерминант организации деятельности

Modern meta-cognitivism has formulated certain key methodological and methodical problems but left them unsolved. To overcome this limitation this paper presents a new methodological approach to studying meta-cognitive determinants of activity – the principle of activity-mediated research of meta-cognitive processes and personality traits.This approach provided a basis for elaborating the complex of new research techniques for revealing the features of the meta-cognitive regulation of activity: (a) the technique of “activity probing”, (b) the technique of “style differentiation”, (c) the technique of “reflective stratification”, and (d) the technique of “factorial decompositions”. These techniques are constructive means for obtaining ecologically valid data on the specificity of the meta-cognitive regulation of activity.The paper brings forward the results of studies with the application of these techniques. By using these techniques, the explication of many new and previously undescribed features of the meta-cognitive regulation of activity becomes possible. In particular, generative synergistic effects resulting from synthesizing the key metacognitive processes and factors were revealed and interpreted. The two main types of meta-processes – meta-cognitive and meta-regulative – had facilitative (i. e. synergistic) associations in the structure of activity. This considerably expands the general cognitiveregulating potential of a subject. This finding also supports the resource approach to the interpretation of meta-cognitive factors. The results of the study determined general directions in approaching one of the most important problems of modern meta-cognitivism – overcoming its out-of-activity nature and, accordingly, its synthesis with the psychological theory of activity.Рассмотрены некоторые ключевые проблемы методологического и методического характера, сформулированные в современном метакогнитивизме, но остающиеся не решенными в нем. В целях их преодоления сформулирован и развит новый методологический подход к исследованию метакогнитивных детерминант организации и регуляции деятельности - принцип деятельностно-опосредствованного исследования метакогнитивных процессов и качеств личности. На основе данного подхода разработан комплекс новых исследовательских методик, направленных на раскрытие особенностей и закономерностей метакогнитивной регуляции деятельности: методика «деятельностного зондирования», методика «стилевой дифференциации», методика «рефлексивного расслоения» и методика «факторных декомпозиций». Посредством комплекса этих методик открываются новые - достаточно конструктивные возможности для получения экологически валидных данных о специфике метакогнитивной регуляции деятельности. Представлены также и результаты конкретных исследований, выполненных на основе этих методик. Показано, что их применение, действительно, приводит к экспликации целого ряда новых, не описанных до настоящего времени особенностей и закономерностей метакогнитивной регуляции деятельности. В частности, выявлены и проинтерпретированы генеративно-порождающие эффекты синергетического типа, возникающие в результате синтезирования ключевых метакогнитивных процессов и факторов. Так, показано, что между двумя основными типами метапроцессов - метакогнитивными и метарегулятивными – в структуре деятельности устанавливаются отношения именно взаимно фасилитирующего, т. е. синергетического характера. В результате этого существенно расширяется общий когнитивно-регулятивный потенциал субъекта. Данный вывод содействует также обоснованию развиваемого авторами ресурсного подхода к интерпретации факторов метакогнитивного плана. На основе всей совокупности представленных результатов определены общие направления и конкретные пути решения одной из наиболее важных задач современного метакогнитивизма - задачи преодоления его внедеятельностного характера и, соответственно, - его синтеза с психологической теорией деятельности

Universality in Glassy Low-Temperature Physics

We propose a microscopic translationally invariant glass model which exhibits two level tunneling systems with a broad range of asymmetries and barrier heights in its glassy phase. Their distribution is qualitatively different from what is commonly assumed in phenomenological models, in that symmetric tunneling systems are systematically suppressed. Still, the model exhibits the usual glassy low-temperature anomalies. Universality is due to the collective origin of the glassy potential energy landscape. We obtain a simple explanation also for the mysterious {\em quantitative} universality expressed in the unusually narrow universal glassy range of values for the internal friction plateau.Comment: 4 pages, 5 figures, uses RevTeX

Local Properties of the Potential Energy Landscape of a Model Glass: Understanding the Low Temperature Anomalies

Though the existence of two-level systems (TLS) is widely accepted to explain low temperature anomalies in the sound absorption, heat capacity, thermal conductivity and other quantities, an exact description of their microscopic nature is still lacking. We performed computer simulations for a binary Lennard-Jones system, using a newly developed algorithm to locate double-well potentials (DWP) and thus two-level systems on a systematic basis. We show that the intrinsic limitations of computer simulations like finite time and finite size problems do not hamper this analysis. We discuss how the DWP are embedded in the total potential energy landscape. It turns out that most DWP are connected to the dynamics of the smaller particles and that these DWP are rather localized. However, DWP related to the larger particles are more collective

Revealing the nanoparticles aspect ratio in the glass-metal nanocomposites irradiated with femtosecond laser

We studied a femtosecond laser shaping of silver nanoparticles embedded in soda-lime glass. Comparing experimental absorption spectra with the modeling based on Maxwell Garnett approximation modified for spheroidal inclusions, we obtained the mean aspect ratio of the re-shaped silver nanoparticles as a function of the laser fluence. We demonstrated that under our experimental conditions the spherical shape of silver nanoparticles changed to a prolate spheroid with the aspect ratio as high as 3.5 at the laser fluence of 0.6J/cm2. The developed approach can be employed to control the anisotropy of the glass-metal composites

Structure and diffusion processes in laminated composites of a Cu-Ti system

Characteristics of diffusion transformations in a multi-layer composite of a Cu-Ti system, which was produced by high-temperature diffusion welding followed by rolling at room temperature, are reportedye

Efficiency of true-green light emitting diodes:Non-uniformity and temperature effects

External quantum efficiency of industrial-grade green InGaN light-emitting diodes (LEDs) has been measured in a wide range of operating currents at various temperatures from 13 K to 300 K. Unlike blue LEDs, the efficiency as a function of current is found to have a multi-peak character, which could not be fitted by a simple ABC-model. This observation correlated with splitting of LED emission spectra into two peaks at certain currents. The characterization data are interpreted in terms of non-uniformity of the LED active region, which is tentatively attributed to extended defects like V-pits. We suggest a new approach to evaluation of temperature-dependent light extraction and internal quantum efficiencies taking into account the active region non-uniformity. As a result, the temperature dependence of light extraction and internal quantum efficiencies have been evaluated in the temperature range mentioned above and compared with those of blue LEDs

Fast optical variability of Naked-Eye Burst - manifestation of periodic activity of internal engine

We imaged the position of the Naked-Eye Burst, GRB080319B, before, during and after its gamma-ray activity with sub-second temporal resolution and discovered the fast variability of its prompt optical emission. Its characteristics and similarity with properties of gamma emission temporal structure suggest that it reflects the behaviour of internal engine -- supposedly, a hyperaccreting solar-mass black hole formed in the collapse of a massive stellar core.Comment: Submitted to Science; please note that this manuscript is subject to press embarg