• 제목/요약/키워드: quotient

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PRETOPOLOGICAL CONVERGENCE QUOTIENT MAPS

  • Park, Sang-Ho
    • 한국수학교육학회지시리즈B:순수및응용수학
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    • 제3권1호
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    • pp.33-40
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    • 1996
  • A convergence structure defined by Kent [4] is a correspondence between the filters on a given set X and the subsets of X which specifies which filters converge to points of X. This concept is defined to include types of convergence which are more general than that defined by specifying a topology on X. Thus, a convergence structure may be regarded as a generalization of a topology. With a given convergence structure q on a set X, Kent [4] introduced associated convergence structures which are called a topological modification and a pretopological modification. (omitted)

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SYMPLECTIC FILLINGS OF QUOTIENT SURFACE SINGULARITIES AND MINIMAL MODEL PROGRAM

  • Choi, Hakho;Park, Heesang;Shin, Dongsoo
    • 대한수학회지
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    • 제58권2호
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    • pp.419-437
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    • 2021
  • We prove that every minimal symplectic filling of the link of a quotient surface singularity can be obtained from its minimal resolution by applying a sequence of rational blow-downs and symplectic antiflips. We present an explicit algorithm inspired by the minimal model program for complex 3-dimensional algebraic varieties.

RESOLUTION OF QUOTIENT SINGULARITIES VIA G-CONSTELLATIONS

  • Seung-Jo Jung
    • 대한수학회보
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    • 제61권2호
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    • pp.519-527
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    • 2024
  • For a finite subgroup G of GLn(ℂ), the moduli space 𝓜𝜃 of 𝜃-stable G-constellations is rarely smooth. This note shows that for a group G of type ${\frac{1}{r}}(1,a,b)$ with r = abc + a + b, there is a generic stability parameter 𝜃 ∈ Θ such that the birational component Y𝜃 of 𝜃-stable G-constellations provides a resolution of the quotient singularity X := ℂ3/G.

DEPTH AND STANLEY DEPTH OF TWO SPECIAL CLASSES OF MONOMIAL IDEALS

  • Xiaoqi Wei
    • 대한수학회보
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    • 제61권1호
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    • pp.147-160
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    • 2024
  • In this paper, we define two new classes of monomial ideals I𝑙,d and Jk,d. When d ≥ 2k + 1 and 𝑙 ≤ d - k - 1, we give the exact formulas to compute the depth and Stanley depth of quotient rings S/It𝑙,d for all t ≥ 1. When d = 2k = 2𝑙, we compute the depth and Stanley depth of quotient ring S/I𝑙,d. When d ≥ 2k, we also compute the depth and Stanley depth of quotient ring S/Jk,d.

QUOTIENT RINGS INDUCED VIA FUZZY IDEALS

  • Liu, Yong-Lin;Meng, Jie;Xin, Xiao-Long
    • Journal of applied mathematics & informatics
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    • 제8권3호
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    • pp.855-867
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    • 2001
  • This note we give a construction of a quotient ring $R/{\mu}$ induced via a fuzzy ideal ${\mu}$ in a ring R. The Fuzzy First, Second and Third Isomorphism Theorems are established. For some applications of this construction of quotient rings, we show that if ${\mu}$ is a fuzzy ideal of a commutative ring R, then $\mu$ is prime (resp. $R/{\mu}$ is a field, every zero divisor in $R/{\mu}$ is nilpotent). Moreover we give a simpler characterization of fuzzy maximal ideal of a ring.

Rayleigh Quotient와 Deflation을 이용한 대형다기(多機)전력계통의 고유치 해석 (Modal Analysis of Large Scale Multi-Machine Power System using Rayleigh Quotient and Deflation)

  • 심관식;남해곤
    • 대한전기학회:학술대회논문집
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    • 대한전기학회 1993년도 하계학술대회 논문집 A
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    • pp.76-78
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    • 1993
  • This paper describes an efficient method of computing any desired number of the most unstable eigenvalues and eigenvectors of a large scale multi-machine power system. Approximate eigenvalues obtained by Hessenberg process are refined using Rayleigh quotient iteration with cubic convergence property. If further eigenvalues and eigenvectors are needed, the procedure described above are repeated with deflation. The proposed algorithm can cover all the model types of synchronous machines, exciters, speed governing system and PSS defined in AESOPS. The proposed algorithm applied to New England test system with 10 machines and 39 buses produced the results same with AESOPS in faster computation time. Also eigenvectors computed in Rayleigh quotient iteration makes it possible to make eigen-analysis for improving unstable modes.

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THE ARTINIAN POINT STAR CONFIGURATION QUOTIENT AND THE STRONG LEFSCHETZ PROPERTY

  • Kim, Young-Rock;Shin, Yong-Su
    • 대한수학회지
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    • 제56권3호
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    • pp.645-667
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    • 2019
  • It has been little known when an Artinian point quotient has the strong Lefschetz property. In this paper, we find the Artinian point star configuration quotient having the strong Lefschetz property. We prove that if ${\mathbb{X}}$ is a star configuration in ${\mathbb{P}}^2$ of type s defined by forms (a-quadratic forms and (s - a)-linear forms) and ${\mathbb{Y}}$ is a star configuration in ${\mathbb{P}}^2$ of type t defined by forms (b-quadratic forms and (t - b)-linear forms) for $b=deg({\mathbb{X}})$ or $deg({\mathbb{X}})-1$, then the Artinian ring $R/(I{\mathbb_{X}}+I{\mathbb_{Y}})$ has the strong Lefschetz property. We also show that if ${\mathbb{X}}$ is a set of (n+ 1)-general points in ${\mathbb{P}}^n$, then the Artinian quotient A of a coordinate ring of ${\mathbb{X}}$ has the strong Lefschetz property.

IRREDUCIBILITY OF THE MODULI SPACE FOR THE QUOTIENT SINGULARITY $\frac{1}{2k+1}(k+1,1,2k)$

  • Seung-Jo, Jung
    • 대한수학회보
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    • 제59권6호
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    • pp.1409-1422
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    • 2022
  • A 3-fold quotient terminal singularity is of the type $\frac{1}{r}(b,1,-1)$ with gcd(r, b) = 1. In [6], it is proved that the economic resolution of a 3-fold terminal quotient singularity is isomorphic to a distinguished component of a moduli space 𝓜𝜃 of 𝜃-stable G-constellations for a suitable 𝜃. This paper proves that each connected component of the moduli space 𝓜𝜃 has a torus fixed point and classifies all torus fixed points on 𝓜𝜃. By product, we show that for $\frac{1}{2k+1}(k+1,1,-1)$ case the moduli space 𝓜𝜃 is irreducible.

Open Quotient와 Fundamental Frequency 정보를 이용한 성 별 분류 (Gender Classification Using Open Quotient and Fundamental Frequency)

  • 김혜진;윤영우;윤호섭;이재연
    • 한국정보처리학회:학술대회논문집
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    • 한국정보처리학회 2009년도 추계학술발표대회
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    • pp.319-320
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    • 2009
  • 본 논문은 Open Quotient 정보와 Fundamental Frequency 정보를 이용한 성별 분류에 관한 것이다. 기존의 대표적인 성별 분류 특징정보로 Fundamental Frequency가 있으나, Fundamental Frequency 정보로는 이용하여 분류하는 데에 중점을 두어왔으나 이 정보는 노인 혹은 어린이에 대해서는 성별 분류 특징이 어렵다는 단점이 있었다. 한편 본 논문에서 제안하는 방법은 Open Quotient와 Fundamental Frequency의 연령대에 따른 차별 정보를 이용하여 학습시켜 성별분류를 보다 나은 성능으로 분류할 수 있다.

ON COVERING AND QUOTIENT MAPS FOR 𝓘𝒦-CONVERGENCE IN TOPOLOGICAL SPACES

  • Debajit Hazarika;Ankur Sharmah
    • 대한수학회논문집
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    • 제38권1호
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    • pp.267-280
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    • 2023
  • In this article, we show that the family of all 𝓘𝒦-open subsets in a topological space forms a topology if 𝒦 is a maximal ideal. We introduce the notion of 𝓘𝒦-covering map and investigate some basic properties. The notion of quotient map is studied in the context of 𝓘𝒦-convergence and the relationship between 𝓘𝒦-continuity and 𝓘𝒦-quotient map is established. We show that for a maximal ideal 𝒦, the properties of continuity and preserving 𝓘𝒦-convergence of a function defined on X coincide if and only if X is an 𝓘𝒦-sequential space.