A necessary flexibility condition of a nondegenerate suspension in Lobachevsky 3-space

We show that some combination of the lengths of all edges of the equator of a flexible suspension in Lobachevsky 3-space is equal to zero (each length is taken either positive or negative in this combination).Comment: 20 pages, 13 figure

207Pb and 17O NMR Study of the Electron Density Distribution in Metal Phase of BaPb_{1-x}Bi_xO_3

The 17O and 207Pb NMR spectra were measured in ceramic samples in the metallic phase of BaPb_{1-x}Bi_{x}O_3 oxides (0<x< 0.33). The inhomogeneous magnetic broadening which appears due to a distribution of the Knight shifts was analyzed in detail. It is shown that Bi atoms, which are randomly incorporated in BaPbO_3 parent compound give rise to an increased conduction electron spin density within an area which is delimited by its two first cation shells. According to NMR data the percolative overlap of these areas occurs in superconducting compositions and it is accompanied by a sharp growth of the average Knight shift . The decrease of with temperature revealed for x=0.33 evidences for an opening of the energy gap near E_F near the metal-semiconductor transition (x=0.35).Comment: submitted to Phys. Rev.

The diagram development for Computer Added Control and Monitoring system of drilling

The paper is concerned with the first stage of the extensive research aimed at developing design-automation system and well drilling process control. The proposed system is going to have some advantages over modern analogues, such as economic analysis at all levels, active engineering staff feedback, precedent-related principle for recommendations, etc. It will essentially reduce the risk of human errors and also optimize the well construction process from design to commissioning. The paper considers the results of the first design stage in a form of flow diagrams

The charge ordered state in half-doped Bi-based manganites studied by 17^{17}O and 209^{209}Bi NMR

We present a $^{209}$Bi and $^{17}$O NMR study of the Mn electron spin correlations developed in the charge ordered state of Bi$_{0.5}$Sr$_{0.5}$MnO$_{3}$ and Bi$_{0.5}$Ca$_{0.5}$MnO$_{3}$. The unusually large local magnetic field $^{209}H_{loc}$ indicates the dominant $6s^{2}$ character of the lone electron pair of Bi$^{3+}$-ions in both compounds. The mechanism connecting the $s$ character of the lone pairs to the high temperature of charge ordering $T_{CO}$ is still not clarified. The observed difference in $^{209}H_{loc}$ for Bi$_{0.5}$Sr$_{0.5}$MnO$_{3}$ to Bi$_{0.5}$Ca$_{0.5}$MnO$_{3}$ is probably due to a decrease in the canting of the staggered magnetic moments of Mn$^{3+}$-ions from. The modification of the $^{17}$O spectra below $T_{CO}$ demonstrates that the line due to the apical oxygens is a unique local tool to study the development of the Mn spin correlations. In the AF state the analysis of the $^{17}$O spectrum of Pr$_{0.5}$Ca$_{0.5}$MnO$_{3}$ and Bi$_{0.5}$Sr$_{0.5}$MnO$_{3}$ prompts us to try two different theoretical descriptions of the charge-ordered state, a site-centered model for the first manganite and a bond-centered model for the second one.Comment: 10 pages, 7 figure

Следящая система с бесконтактным двигателем постоянного тока и нелинейным изодромным регулятором

The paper shows that it is possible to exclude an average component of a forced tracing error in auto-oscillating systems due to switching-off an output integrator coordinate from a direct system tract within those intervals when speed signs of an input axis and engine do not coincide with each other. Investigation accuracy of such systems using a method of harmonic linearization is quite sufficient for engineering calculations

МАТЕМАТИЧЕСКИЕ ОЦЕНКИ СИНЕРГИИ, МАНЕВРЕННОСТИ, СЕРВИСА И МОБИЛЬНОСТИ В ОБРАЗОВАТЕЛЬНЫХ СИСТЕМАХ

The paper shows how applying an analogy method it is possible to describe complicated hierarchic educational systems while using such robotics notions as «synergy», «flexibility», «service» and «mobility» which are well developed and filled with mathematical content. It has been shown that the indicated notions positively supplement terminology and main principles of organizational designing, system analysis and an idea of staff management while using mathematical knowledge-activity personnel models in order to form and manage innovation projects. Предпринята попытка, применяя метод аналогий, при описании сложных иерархических образовательных систем использовать такие уже хорошо отработанные и наполненные математическим содержанием понятия из робототехники, как «синергия», «маневренность», «сервис» и «мобильность».Показано, что указанные понятия удачно дополняют терминологию и основные принципы оргпроектирования, системного анализа и идеи кадрового менеджмента с использованием математических знание-деятельностных моделей специалистов при формировании и управлении инновационными проектами

Исследование переходных процессов и скользящих движений в квазирелейных следящих системах

The paper demonstrates that it is possible significantly to simplify technical realization of sliding modes in quasi-relay follow-up systems having non-reversive direct tract supplemented by a reverse channel. Conditions for existence of sliding modes in such quasi-relay systems are obtained in the paper. The paper formulates and proves a theorem of representation point transfer on switching-over hypersurface.  Stability of sliding motions has been investigated in the paper. The paper reveals the possibility of quasi-optimum quick-action motions. The conditions for existence of such motions has been determined in the paper.В квазирелейных следящих системах, содержащих нереверсивный прямой тракт, дополненный каналом реверса, удается существенно упростить техническую реализацию скользящих режимов. В работе получены условия существования скользящих режимов в таких квазирелейных системах, сформулирована и доказана теорема о попадании изображающей точки на гиперповерхность переключения, исследована устойчивость скользящих движений, выявлена возможность квазиоптимальных по быстродействию движений и определены условия их существования