Fundamental solution of the problem of linear programming and method of its determination

The idea of a fundamental solution to a problem in linear programming is introduced. A method of determining the fundamental solution and of applying this method to the solution of a problem in linear programming is proposed. Numerical examples are cited

Решение транспортных задач ПС-методом при ограничениях на переменные

The research considers transportation problems of linear programming where restrictions (greater or less) are imposed on some variables. If the first restriction doesn’t create an additional complexity then an excessive restrictions on variables require a special approach. It has been shown that these tasks could be solved applying PC-method proposed by the author.В работе рассматриваются открытые транспортные задачи линейного программирования, в которых на некоторые переменные положено ограничение больше или меньше. Если первое ограничение не создает дополнительных трудностей при решении задачи, то ограничения сверху на переменные требуют особого подхода. Показано, что такие задачи достаточно хорошо решаются с помощью предложенного автором ПС-метода

Conversion of wooden structures into porous SiC with shape memory synthesis

Synthesis of structured silicon carbide materials can be accomplished using wooden materials as the carbon source, with various silicon impregnation techniques. We have explored the low cost synthesis of SiC by impregnation of carbon from wood with SiO gas at high temperatures, which largely retains the structure of the starting wood (shape memory synthesis). Suitably structured, porous SiC could prove to be an important type of catalyst support material. Shape memory synthesis (SMS) has earlier been tried on high surface area carbon materials. Here we have made an extensive study of SMS on carbon structures obtained from different types of wood. © 2011 Elsevier Ltd and Techna Group S.r.l

Crystal Undulator As A Novel Compact Source Of Radiation

A crystalline undulator (CU) with periodically deformed crystallographic planes is capable of deflecting charged particles with the same strength as an equivalent magnetic field of 1000 T and could provide quite a short period L in the sub-millimeter range. We present an idea for creation of a CU and report its first realization. One face of a silicon crystal was given periodic micro-scratches (grooves), with a period of 1 mm, by means of a diamond blade. The X-ray tests of the crystal deformation have shown that a sinusoidal-like shape of crystalline planes goes through the bulk of the crystal. This opens up the possibility for experiments with high-energy particles channeled in CU, a novel compact source of radiation. The first experiment on photon emission in CU has been started at LNF with 800 MeV positrons aiming to produce 50 keV undulator photons.Comment: Presented at PAC 2003 (Portland, May 12-16

Метод решения открытых транспортных задач

The article examines open transportation problems proposing to apply a modernized PC-method for their solution. Some of transportation problems could be reduced to those with bounded-variables solution for which is also given by the authors.Рассматриваются транспортные задачи линейного программирования, в которых на некоторые переменные положено ограничение больше или меньше. Если первое ограничение не создает дополнительных трудностей при решении задачи, то ограничения сверху на переменные требуют особого подхода. Показано, что такие задачи достаточно хорошо решаются с помощью предложенного автором ПС-метода

Orientation and symmetries of Alexandrov spaces with applications in positive curvature

We develop two new tools for use in Alexandrov geometry: a theory of ramified orientable double covers and a particularly useful version of the Slice Theorem for actions of compact Lie groups. These tools are applied to the classification of compact, positively curved Alexandrov spaces with maximal symmetry rank.Comment: 34 pages. Simplified proofs throughout and a new proof of the Slice Theorem, correcting omissions in the previous versio

First observation of proton reflection from bent crystals

We recently suggested using short bent crystals as primary collimators in a two stage cleaning system for hadron colliders, with the aim of providing larger impact parameters in the secondary bulk absorber, through coherent beam-halo deflection [1]. Tests with crystals a few mm long, performed with 70 GeV proton beams at IEHP in Protvino, showed a channeling efficiency exceeding 85 %. We also observed disturbing phenomena such as dechannelling at large impact angle, insufficient bending induced by volume capture inside the crystal, multiple scattering of non-channeled protons and, for the first time, a proton flux reflected by the crystalline planes. Indeed, protons with a tangent path to the curved planes somewhere inside the crystal itself are deflected in the opposite direction with respect to the channeled particles, with an angle almost twice as large as the critical angle. This effect, up to now only predicted by computer simulations [2], produces a flux of particles in the wrong direction with respect to the absorber, which may hamper the collimation efficiency if neglected

A simple proof of Perelman's collapsing theorem for 3-manifolds

We will simplify earlier proofs of Perelman's collapsing theorem for 3-manifolds given by Shioya-Yamaguchi and Morgan-Tian. Among other things, we use Perelman's critical point theory (e.g., multiple conic singularity theory and his fibration theory) for Alexandrov spaces to construct the desired local Seifert fibration structure on collapsed 3-manifolds. The verification of Perelman's collapsing theorem is the last step of Perelman's proof of Thurston's Geometrization Conjecture on the classification of 3-manifolds. Our proof of Perelman's collapsing theorem is almost self-contained, accessible to non-experts and advanced graduate students. Perelman's collapsing theorem for 3-manifolds can be viewed as an extension of implicit function theoremComment: v1: 9 Figures. In this version, we improve the exposition of our arguments in the earlier arXiv version. v2: added one more grap