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

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

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

Experimental Study For The Feasibility Of A Crystalline Undulator

We present an idea for creation of a crystalline undulator and report its first realization. One face of a silicon crystal was given periodic micro-scratches (trenches) by means of a diamond blade. The X-ray tests of the crystal deformation due to given periodic pattern of surface scratches have shown that a sinusoidal shape is observed on both the scratched surface and the opposite (unscratched) face of the crystal, that is, a periodic sinusoidal deformation goes through the bulk of the crystal. This opens up the possibility for experiments with high-energy particles channeled in crystalline undulator, a novel compact source of radiation.Comment: 12 pages, 4 figure

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

Experimental Reconstruction of Lomonosov's Discovery of Venus's Atmosphere with Antique Refractors During the 2012 Transit of Venus

In 1761, the Russian polymath Mikhail Vasilievich Lomonosov (1711-1765) discovered the atmosphere of Venus during its transit over the Sun's disc. In this paper we report on experimental reenactments of Lomonosov's discovery with antique refractors during the transit of Venus June 5-6, 2012. We conclude that Lomonosov's telescope was fully adequate to the task of detecting the arc of light around Venus off the Sun's disc during ingress or egress if proper experimental techniques as described by Lomonosov in his 1761 report are employed.Comment: 14 pages, 9 figure

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

Asymptotically Extrinsic Tamed Submanifolds

We study, from the extrinsic point of view, the structure at infinity of open submanifolds, ϕ : Mm → Mn(κ) isometrically immersed in the real space forms of constant sectional curvature κ ≤ 0.We shall use the decay of the second fundamental form of the so-called tamed immersions to obtain a description at infinity of the submanifold in the line of the structural results in Greene et al. (Int Math Res Not 1994:364–377, 1994) and Petrunin and Tuschmann (Math Ann 321:775–788, 2001) and an estimation from below of the number of its ends in terms of the volume growth of a special class of extrinsic domains, the extrinsic balls.Vicent Gimeno: Work partially supported by the Research Program of University Jaume I Project UJI-B2016-07, and DGI -MINECO Grant (FEDER) MTM2013-48371-C2-2-P. Vicente Palmer: Work partially supported by the Research Program of University Jaume I Project UJI-B2016-07, DGI -MINECO Grant (FEDER) MTM2013-48371-C2-2-P, and Generalitat Valenciana Grant PrometeoII/2014/064. G. Pacelli Bessa: Work partially supported by CNPq- Brazil grant # 301581/2013-4