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    Wyświetlanie 1-6 z 6
    Tytuł:
    More About the Height of Faces in 3-Polytopes
    Autorzy:
    Borodin, Oleg V.
    Bykov, Mikhail A.
    Ivanova, Anna O.
    Tematy:
    plane map
    planar graph
    3-polytope
    structural properties
    height of face
    Pokaż więcej
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Powiązania:
    https://bibliotekanauki.pl/articles/31342325.pdf  Link otwiera się w nowym oknie
    Opis:
    The height of a face in a 3-polytope is the maximum degree of its incident vertices, and the height of a 3-polytope, h, is the minimum height of its faces. A face is pyramidal if it is either a 4-face incident with three 3-vertices, or a 3-face incident with two vertices of degree at most 4. If pyramidal faces are allowed, then h can be arbitrarily large, so we assume the absence of pyramidal faces in what follows. In 1940, Lebesgue proved that every quadrangulated 3-polytope has h ≤ 11. In 1995, this bound was lowered by Avgustinovich and Borodin to 10. Recently, Borodin and Ivanova improved it to the sharp bound 8. For plane triangulation without 4-vertices, Borodin (1992), confirming the Kotzig conjecture of 1979, proved that h ≤ 20, which bound is sharp. Later, Borodin (1998) proved that h ≤ 20 for all triangulated 3-polytopes. In 1996, Horňák and Jendrol’ proved for arbitrarily polytopes that h ≤ 23. Recently, Borodin and Ivanova obtained the sharp bounds 10 for trianglefree polytopes and 20 for arbitrary polytopes. In this paper we prove that any polytope has a face of degree at most 10 with height at most 20, where 10 and 20 are sharp.
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Low 5-Stars at 5-Vertices in 3-Polytopes with Minimum Degree 5 and No Vertices of Degree from 7 to 9
    Autorzy:
    Borodin, Oleg V.
    Bykov, Mikhail A.
    Ivanova, Anna O.
    Tematy:
    planar map
    planar graph
    3-polytope
    structural properties
    5-star
    weight
    height
    Pokaż więcej
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Powiązania:
    https://bibliotekanauki.pl/articles/31348144.pdf  Link otwiera się w nowym oknie
    Opis:
    In 1940, Lebesgue gave an approximate description of the neighborhoods of 5-vertices in the class $P_5$ of 3-polytopes with minimum degree 5. Given a 3-polytope $P$, by $h_5(P)$ we denote the minimum of the maximum degrees (height) of the neighborhoods of 5-vertices (minor 5-stars) in $P$. Recently, Borodin, Ivanova and Jensen showed that if a polytope $P$ in $P_5$ is allowed to have a 5-vertex adjacent to two 5-vertices and two more vertices of degree at most 6, called a (5, 5, 6, 6, ∞)-vertex, then $h_5(P)$ can be arbitrarily large. Therefore, we consider the subclass \(P_5^\ast\) of 3-polytopes in $P_5$ that avoid (5, 5, 6, 6, ∞)-vertices. For each $P^\ast$ in $P_5^\ast$ without vertices of degree from 7 to 9, it follows from Lebesgue’s Theorem that $h_5(P^\ast) ≤ 17$. Recently, this bound was lowered by Borodin, Ivanova, and Kazak to the sharp bound $h_5(P^\ast) ≤ 15$ assuming the absence of vertices of degree from 7 to 11 in $P^\ast$. In this note, we extend the bound $h_5(P^\ast) ≤ 15$ to all $P^\ast$s without vertices of degree from 7 to 9.
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Size Effects in Radiospectroscopy Spectra of Ferroelectric Nanopowders
    Autorzy:
    Glinchuk, M. D.
    Kondakova, I. V.
    Laguta, V. V.
    Slipenyuk, A. M.
    Bykov, I. P.
    Ragulya, A. V.
    Klimenko, V. P.
    Tematy:
    73.22.-f
    61.72.Hh
    68.35.Rh
    Pokaż więcej
    Wydawca:
    Polska Akademia Nauk. Instytut Fizyki PAN
    Powiązania:
    https://bibliotekanauki.pl/articles/2043389.pdf  Link otwiera się w nowym oknie
    Opis:
    The theoretical and experimental investigation of ferroelectric nanopowders is performed. The manifestation in radiospectroscopy spectra of size driven ferroelectric-paraelectric phase transition at some critical particle average size R = R$\text{}_{c}$ was the main goal of the consideration. In theoretical part the size effect for the materials with ferroelectric tetragonal phase at room temperature and cubic paraelectric phase was considered allowing for the spontaneous polarization inhomogeneity inside a particle and distribution of particle sizes. In ESR the transformation of the spectra from tetragonal symmetry to cubic symmetry lines with decrease in nanoparticle sizes was calculated. The method of R$\text{}_{c}$ value extraction from the ratio of the different symmetry lines intensities in the absorption spectra was proposed. Measurements of Fe$\text{}^{3+}$ ESR spectra in nanopowder of BaTiO$\text{}_{3}$ were carried out at room temperature. The samples were prepared by rate-controlled method with different particle sizes, which depend on annealing temperature. The decrease in intensity of tetragonal symmetry ESR lines of Fe$\text{}^{3+}$ and appearance of cubic symmetry line with asymmetry of the shoulders was observed with the average sizes decrease with complete disappearance of tetragonal spectrum at R ≤ 40 nm. The comparison of the theory with experiment was carried out. The theory fits experimental data pretty good. The value of critical size R$\text{}_{c}$ ≈ 40 nm was extracted from ESR data. The asymmetry and broadening of right hand side shoulder of ESR cubic symmetry line was shown to be related to contribution of paramagnetic centers in the vicinity of the particles surface with lower than cubic symmetry. The deconvolution of the cubic line allowed to show that this region size is about 3 nm.
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Polnoe sobranìe sočinenìj
    Polnoe sobranìe sočinenìj F. I. Tûtčeva
    Autorzy:
    Bykov, Petr Vasil'evič (1843–1930). Red.
    Brûsov, Valerij Âkovlevič (1873–1924). Red.
    Tûtčev, Fëdor Ivanovič (1803–1873)
    Tovariŝestvo izdatel'skogo i pečatnogo dela A. F. Marks.
    Wydawca:
    Izdanìe T-va A. F. Marksʺ
    Opis:
    Na dole k. tyt: Priloženìe kʺ žurnalu "Niva" na 1913 g
    468 s., [1] k. tab. : il. ; 20 cm
    Dostawca treści:
    RCIN - Repozytorium Cyfrowe Instytutów Naukowych
    Książka
      Wyświetlanie 1-6 z 6

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