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  • 제목/요약/키워드: forbidden number

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Forbidden Detour Number on Virtual Knot

  • Yoshiike, Shun;Ichihara, Kazuhiro
    • Kyungpook Mathematical Journal
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    • 제61권1호
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    • pp.205-212
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    • 2021
  • We show that the forbidden detour move, essentially introduced by Kanenobu and Nelson, is an unknotting operation for virtual knots. Then we define the forbidden detour number of a virtual knot to be the minimal number of forbidden detour moves necessary to transform a diagram of the virtual knot into the trivial knot diagram. Some upper and lower bounds on the forbidden detour number are given in terms of the minimal number of real crossings or the coefficients of the affine index polynomial of the virtual knot.

The Forbidden Number of a Knot

  • CRANS, ALISSA S.;MELLOR, BLAKE;GANZELL, SANDY
    • Kyungpook Mathematical Journal
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    • 제55권2호
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    • pp.485-506
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    • 2015
  • Every classical or virtual knot is equivalent to the unknot via a sequence of extended Reidemeister moves and the so-called forbidden moves. The minimum number of forbidden moves necessary to unknot a given knot is an invariant we call the forbidden number. We relate the forbidden number to several known invariants, and calculate bounds for some classes of virtual knots.

PERMUTATIONS WITH PARTIALLY FORBIDDEN POSITIONS

  • Hwang, Suk-Geun
    • 대한수학회지
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    • 제38권4호
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    • pp.793-806
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    • 2001
  • In this paper we consider the enumeration problem of permutations with partially forbidden positions, generalizing the notion of permutations with forbidden positions. .As an alternative approach to this problem, we investigate the permanent maximization problem over some classes of (0,1)-matrices which have a given number of 1's some of which lie in prescribed positions.

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Spectroscopic Study of the Planetary Nebula NGC 6210: Velocity Structure and Permitted Lines

  • Lee, Seong-Jae;Wi, Jin-Kyung;Hyung, Siek
    • 한국지구과학회지
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    • 제30권5호
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    • pp.611-621
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    • 2009
  • Using the spectroscopic data secured with the Hamilton Echelle Spectrograph at Lick Observatory, we found the physical condition of the planetary Nebula NGC 6210. The spectral line profiles of the permitted and forbidden lines have been analyzed using IRAF and StarLink/Dipso. The hydrogen number densities (NH) are 2,000-20,000 cm3, and the electron temperatures are 8,100-10,300 K based on the forbidden lines. The expansion velocities, derived from the Full Width at Half Maximum (FWHM) and the double peak of the line profiles, are in the range of 10 to 45kms1. The expansion velocities imply a shell structure with an accelerated nebular gas. We also derived abundances from the permitted lines of CII, CIII, NII, NIII, OII, and OIII, which may have been formed through the fluorescence mechanism. NGC 6210 is likely to be evolved from a progenitor of more than 3M, which had been born near the Galactic plane.

ARC SHIFT NUMBER AND REGION ARC SHIFT NUMBER FOR VIRTUAL KNOTS

  • Gill, Amrendra;Kaur, Kirandeep;Madeti, Prabhakar
    • 대한수학회지
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    • 제56권4호
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    • pp.1063-1081
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    • 2019
  • In this paper, we formulate a new local move on virtual knot diagram, called arc shift move. Further, we extend it to another local move called region arc shift defined on a region of a virtual knot diagram. We establish that these arc shift and region arc shift moves are unknotting operations by showing that any virtual knot diagram can be turned into trivial knot using arc shift (region arc shift) moves. Based upon the arc shift move and region arc shift move, we define two virtual knot invariants, arc shift number and region arc shift number respectively.

EXPANSION VELOCITY INVESTIGATION OF THE ELLIPTICAL PLANETARY NEBULA NGC 6803

  • Choi, Youn-Su;Lee, Seong-Jae;Hyung, Siek
    • 천문학회지
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    • 제41권6호
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    • pp.163-172
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    • 2008
  • Using the spectral data in the 3700 to 10050\AA wavelength range secured with the Hamilton Echelle Spectrograph (HES) at the Lick observatory, we have investigated the expansion velocities and the physical conditions of the elliptical planetary nebula NGC 6803. Various forbidden and permitted lines, e.g. HI, HeI, HeII, [OIII], [NII], [ArIII], and [SII], indicate complicated but systematic physical conditions variation: electron temperatures Tε9000 - 11000 K and electron number densities Nε2000 - 9000cm3. The line profile analysis of these ions also indicates the systematic change or the acceleration of the expansion velocities in the range of 10 - 22kms1. We show that the velocity gradient and physical condition found in various ions are closely related to the prolate ellipsoidal structure of NGC 6803. The expansion velocity and the ionic abundance of O2+ were derived based on the OII and [OIII] lines. In spite of the discrepancy of ionic abundances derived by the two cases and their line profiles, the expansion velocities of them agree well. We find that the ratios of the red to blue line component of the HeII & OII lines are different from those of the [OIII] or other forbidden lines that indicates a possible involvement of emission of HeII & OII lines. This subtle difference and the different physical condition of the lines are likely to be caused by the elongated geometry and the latitude dependence of the emission zone.

컨볼루션 신경망 모델에 의한 악성 댓글 모자이크처리 방안 (Blurring of Swear Words in Negative Comments through Convolutional Neural Network)

  • 김유민;강효빈;한수현;정희용
    • 한국산업정보학회논문지
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    • 제27권2호
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    • pp.25-34
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    • 2022
  • 온라인 서비스의 발달로 악성 댓글의 파급력이 커져 사이버 폭력 피해가 극심해지고 있다. 이를 방지하기 위해 금칙어 기반 필터링, 신고제도 등 다양한 방법이 사용되고 있지만 악성 댓글을 완벽하게 근절하기는 어렵다. 본 연구는 딥러닝을 사용하여 악성 댓글의 분류의 정확도를 높이고 욕설에 해당하는 부분을 모자이크처리 처리하는 것을 목적으로 진행되었다. 정확도를 높이기 위해 컨볼루션의 층수, 필터 수를 다르게 설정하여 두 가지 모델링을 진행하여 비교하였고, 데이터 세트의 90%를 훈련 데이터로, 10%를 테스트 데이터로 사용한 결과 최종 88%의 정확도를 도출해 낼 수 있었다. 또한 Grad-CAM을 사용하여 모델이 댓글의 어느 부분을 결과에 반영하였는지 표시하여 욕설 위치 정보를 출력하였다. 단순 금칙어 기반으로 댓글을 분류한 정확도는 56%이지만, 컨볼루션 신경망에 의한 분류 정확도가 88%인 것과 비교하면 딥러닝 모델로 악성 댓글의 욕설을 처리하는 것이 더 효과적인 것을 확인할 수 있었다.

Second Harmonic Generation study on the transport dynamics of small molecules across liposome bilayers

  • Kim, Joon-Heon;Kim, Mahn-Won
    • 한국생물물리학회:학술대회논문집
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    • 한국생물물리학회 2003년도 정기총회 및 학술발표회
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    • pp.79-79
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    • 2003
  • SHG (Second harmonic generation) can be used to probe the surface of centrosymmetric particles suspended in bulk isotropic solution, because it is forbidden in centrosymmetric media under the dipole approximation. Using this technique, we can study the transport dynamics of small organic dye molecules across liposome bilayers. Because molecules adsorbed on the outer layer are in opposite direction with that on the inner layer by symmetry, the SH field is proportional to the difference between the number density of dye molecules on both sides of the bilayer, and the time dependence of the SH intensity is related to the time constant of the molecular transportation of dye molecules across liposome bilayers.

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FORBIDDEN THETA GRAPH, BOUNDED SPECTRAL RADIUS AND SIZE OF NON-BIPARTITE GRAPHS

  • Shuchao Li;Wanting Sun;Wei Wei
    • 대한수학회지
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    • 제60권5호
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    • pp.959-986
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    • 2023
  • Zhai and Lin recently proved that if G is an n-vertex connected 𝜃(1, 2, r + 1)-free graph, then for odd r and n ⩾ 10r, or for even r and n ⩾ 7r, one has ρ(G)n24, and equality holds if and only if G is Kn2,n2. In this paper, for large enough n, we prove a sharp upper bound for the spectral radius in an n-vertex H-free non-bipartite graph, where H is 𝜃(1, 2, 3) or 𝜃(1, 2, 4), and we characterize all the extremal graphs. Furthermore, for n ⩾ 137, we determine the maximum number of edges in an n-vertex 𝜃(1, 2, 4)-free non-bipartite graph and characterize the unique extremal graph.

PATIAL DISTRIBUTION OF STAR FORMATION ACTIVITY ON NGC 253 BY FIR AND RADIO EMISSION LINES

  • Takahashi, H.;Matsuo, H.;Nakanishi, K.
    • 천문학논총
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    • 제27권4호
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    • pp.261-262
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    • 2012
  • The aim of this research is to reveal the spatial distribution of the star formation activity of nearby galaxies by comparing CO molecular emission lines with the large area observation in far-infrared (FIR) lines. We report the imaging observations of NGC 253 by FIR forbidden lines via FIS-FTS and CO molecular lines from low to high excitation levels with ASTE, which are good tracers of star forming regions or photo-dissociation regions, especially spiral galaxies, in order to derive the information of the physical conditions of the ambient interstellar radiation fields. The combination of spatially resolved FIR and sub-mm data leads to the star formation efficiency within galaxy. The ratio between the FIR luminosity and molecular gas mass, LFIR/MH2, is expected to be proportional to the number of stars formed in the galaxy per unit molecular gas mass and time. Moreover the FIR line ux shows current star formation activity directly. Furthermore these can be systematic and statistical data for star formation history and evolution of spiral galaxies.