• 제목/요약/키워드: mathematical notation

검색결과 48건 처리시간 0.02초

FRIEDMAN-WEIERMANN STYLE INDEPENDENCE RESULTS BEYOND PEANO ARITHMETIC

  • Lee, Gyesik
    • 대한수학회지
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    • 제51권2호
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    • pp.383-402
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    • 2014
  • We expose a pattern for establishing Friedman-Weiermann style independence results according to which there are thresholds of provability of some parameterized variants of well-partial-ordering. For this purpose, we investigate an ordinal notation system for ${\vartheta}{\Omega}^{\omega}$, the small Veblen ordinal, which is the proof-theoretic ordinal of the theory $({\prod}{\frac{1}{2}}-BI)_0$. We also show that it sometimes suffices to prove the independence w.r.t. PA in order to obtain the same kind of independence results w.r.t. a stronger theory such as $({\prod}{\frac{1}{2}}-BI)_0$.

ON EULERIAN q-INTEGRALS FOR SINGLE AND MULTIPLE q-HYPERGEOMETRIC SERIES

  • Ernst, Thomas
    • 대한수학회논문집
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    • 제33권1호
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    • pp.179-196
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    • 2018
  • In this paper we extend the two q-additions with powers in the umbrae, define a q-multinomial-coefficient, which implies a vector version of the q-binomial theorem, and an arbitrary complex power of a JHC power series is shown to be equivalent to a special case of the first q-Lauricella function. We then present several q-analogues of hypergeometric integral formulas from the two books by Exton and the paper by Choi and Rathie. We also find multiple q-analogues of hypergeometric integral formulas from the recent paper by Kim. Finally, we prove several multiple q-hypergeometric integral formulas emanating from a paper by Koschmieder, which are special cases of more general formulas by Exton.

SELF-MAPS ON M(ℤq, n + 2) ∨ M(ℤq, n + 1) ∨ M(ℤq, n)

  • Ho Won Choi
    • 충청수학회지
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    • 제36권4호
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    • pp.289-296
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    • 2023
  • When G is an abelian group, we use the notation M(G, n) to denote the Moore space. The space X is the wedge product space of Moore spaces, given by X = M(ℤq, n+ 2) ∨ M(ℤq, n+ 1) ∨ M(ℤq, n). We determine the self-homotopy classes group [X, X] and the self-homotopy equivalence group 𝓔(X). We investigate the subgroups of [Mj , Mk] consisting of homotopy classes of maps that induce the trivial homomorphism up to (n + 2)-homotopy groups for j ≠ k. Using these results, we calculate the subgroup 𝓔dim#(X) of 𝓔(X) in which all elements induce the identity homomorphism up to (n + 2)-homotopy groups of X.

MathML을 이용한 수학교과 ICT활용 교육 개선방안 (An Improvement of Mathematics Course Using MathML in ICT Environment)

  • 홍은표;이수현
    • 정보교육학회논문지
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    • 제7권1호
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    • pp.11-26
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    • 2003
  • 웹의 장점을 활용하기 위한 수학교과 교수-학습 자료들은 이미 많이 개발되어 있으나 수학교과 자료에서 사용하는 수식이 대부분 수식 자체가 아닌 그림 형태로 표현되어 있어 수식의 계산이나 검색, 재사용 등 다양한 활용이 불가능하였다. 이를 극복하기 위하여 수식 표현을 위한 마크업 언어인 MathML이 개발되었다. 본 논문에서는 수학교과 ICT 활용 교육에서의 교재 개발, 교수-학습 도구 개발, 그리고 정보교환을 위해 MathML을 활용할 수 있는 방안을 제시한다. 교재 개발에 있어서 MathML을 이용하는 것은 수식의 수정을 편리하게 하고 재사용을 가능하게 한다. 그리고 MathML을 표준으로 사용하는 교수-학습 도구들은 수식과 수학적 개념간의 연결을 강하게 해 주고, 교사들이 이와 같은 도구들을 보다 쉽게 재구성하여 수업에 활용할 수 있도록 해 준다. MathML을 이용한 수식을 사용할 수 있는 게시판은 교사와 학생간의 정보 교환을 활발하게 하고, 이를 이용한 $\ulcorner$웹토론하기$\lrcorner$와 같은 다양한 형태의 ICT활용 수업을 가능하게 한다.

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H-FUZZY SEMITOPOGENOUS PREOFDERED SPACES

  • Chung, S.H.
    • 대한수학회논문집
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    • 제9권3호
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    • pp.687-700
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    • 1994
  • Throughout this paper we will let H denote the complete Heyting algebra ($H, \vee, \wedge, *$) with order reversing involution *. 0 and 1 denote the supermum and the infimum of $\emptyset$, respectively. Given any set X, any element of $H^X$ is called H-fuzzy set (or, simply f.set) in X and will be denoted by small Greek letters, such as $\mu, \nu, \rho, \sigma$. $H^X$ inherits a structure of H with order reversing involution in natural way, by definding $\vee, \wedge, *$ pointwise (sam notations of H are usual). If $f$ is a map from a set X to a set Y and $\mu \in H^Y$, then $f^{-1}(\mu)$ is the f.set in X defined by f^{-1}(\mu)(x) = \mu(f(x))$. Also for $\sigma \in H^X, f(\sigma)$ is the f.set in Y defined by $f(\sigma)(y) = sup{\sigma(x) : f(x) = y}$ ([4]). A preorder R on a set X is reflexive and transitive relation on X, the pair (X,R) is called preordered set. A map $f$ from a preordered set (X, R) to another one (Y,T) is said to be preorder preserving (inverting) if for $x,y \in X, xRy$ implies $f(x)T f(y) (resp. f(y)Tf(x))$. For the terminology and notation, we refer to [10, 11, 13] for category theory and [7] for H-fuzzy semitopogenous spaces.

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CHARACTERIZATIONS OF PARTITION LATTICES

  • Yoon, Young-Jin
    • 대한수학회보
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    • 제31권2호
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    • pp.237-242
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    • 1994
  • One of the most well-known geometric lattices is a partition lattice. Every upper interval of a partition lattice is a partition lattice. The whitney numbers of a partition lattices are the Stirling numbers, and the characteristic polynomial is a falling factorial. The set of partitions with a single non-trivial block containing a fixed element is a Boolean sublattice of modular elements, so the partition lattice is supersolvable in the sense of Stanley [6]. In this paper, we rephrase four results due to Heller[1] and Murty [4] in terms of matroids and give several characterizations of partition lattices. Our notation and terminology follow those in [8,9]. To clarify our terminology, let G, be a finte geometric lattice. If S is the set of points (or rank-one flats) in G, the lattice structure of G induces the structure of a (combinatorial) geometry, also denoted by G, on S. The size vertical bar G vertical bar of the geometry G is the number of points in G. Let T be subset of S. The deletion of T from G is the geometry on the point set S/T obtained by restricting G to the subset S/T. The contraction G/T of G by T is the geometry induced by the geometric lattice [cl(T), over ^1] on the set S' of all flats in G covering cl(T). (Here, cl(T) is the closure of T, and over ^ 1 is the maximum of the lattice G.) Thus, by definition, the contraction of a geometry is always a geometry. A geometry which can be obtained from G by deletions and contractions is called a minor of G.

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KD-(k0, k1)-HOMOTOPY EQUIVALENCE AND ITS APPLICATIONS

  • Han, Sang-Eon
    • 대한수학회지
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    • 제47권5호
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    • pp.1031-1054
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    • 2010
  • Let $\mathbb{Z}^n$ be the Cartesian product of the set of integers $\mathbb{Z}$ and let ($\mathbb{Z}$, T) and ($\mathbb{Z}^n$, $T^n$) be the Khalimsky line topology on $\mathbb{Z}$ and the Khalimsky product topology on $\mathbb{Z}^n$, respectively. Then for a set $X\;{\subset}\;\mathbb{Z}^n$, consider the subspace (X, $T^n_X$) induced from ($\mathbb{Z}^n$, $T^n$). Considering a k-adjacency on (X, $T^n_X$), we call it a (computer topological) space with k-adjacency and use the notation (X, k, $T^n_X$) := $X_{n,k}$. In this paper we introduce the notions of KD-($k_0$, $k_1$)-homotopy equivalence and KD-k-deformation retract and investigate a classification of (computer topological) spaces $X_{n,k}$ in terms of a KD-($k_0$, $k_1$)-homotopy equivalence.

Harriot(1560-1621) 의 대수기호와 방정식의 근 (Harriot's algebraic symbol and the roots of equation)

  • 신경희
    • 한국수학사학회지
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    • 제25권1호
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    • pp.15-27
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    • 2012
  • 16세기 후반과 17세기 전반에 활동했던 영국의 과학자이자 수학자인 Thomas Harriot은 대수기호를 독창적으로 만들어 사용하였고 일부는 오늘날에도 사용하고 있다. 또한 방정식에서 음수근 뿐만 아니라 복소수근도 받아들였는데 그의 이러한 관점은 당시로는 혁신적이었으며 나아가 방정식의 형태의 일반화에도 진일보한 모습을 보여주었다. 사후 유작 외에는 생전에 수학 저서가 한 권도 없는 탓에 Harriot 개인이나 그가 이루어 놓은 수학이 수학적 성취에 비하여 수학사나 수학교육에서 그에 대하여 소홀히 다루어진 감이 있다. 이 논문에서는 동시대 유명한 수학자였던 비에타와 데카르트의 대수기호와 방정식론을 비교함으로써 Harriot이 이루어놓은 수학을 알리고자 한다.

A GENERALIZED 4-STRING SOLUTION TANGLE OF DNA-PROTEIN COMPLEXES

  • Kim, Soo-Jeong
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • 제15권3호
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    • pp.161-175
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    • 2011
  • An n-string tangle is a three dimensional ball with n strings properly embedded in it. A tangle model of a DNA-protein complex is first introduced by C. Ernst and D. Sumners in 1980's. They assumed the protein bound DNA as strings and the protein as a three dimensional ball. By using a tangle analysis, one can predict the topology of DNA within the complex. S.Kim and I. Darcy developed the biologically reasonable 4-string tangle equations and decided a solution tangle, called R-standard tangle. The author discussed more about the simple solution tangles of the equations and found a generalized R-standard tangle solution.

연동소프트웨어의 안정성 확보를 위한 시뮬레이션 기법 (Simulation Technique for Secure Inter-locking Software)

  • 황종규;이종우;오석문;김영훈
    • 한국철도학회:학술대회논문집
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    • 한국철도학회 1999년도 춘계학술대회 논문집
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    • pp.283-290
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    • 1999
  • Recently, the ${\mu}$-processor based-controlled systems instead of conventional relays circuitry are widely used to industrial applications, and also those technology is available to railway signalings which are safety-critical systems. However, the safety and reliability of software for those systems are harder to demonstrate than in traditional relays circuitry because the faults or errors can not be analyzed and predicted to those systems. So, the safety problems are crucial more and more in ${\mu}$-processor based-controlled system. In this paper, the Grafcet language, the graphical and mathematical form, is used to obtain the high-level safety and reliability of software control logic. The general description for Grafcet notation are provided. And some partial of interlocking logic are formally modeled and simulated by Grafcet language and graphical windows.

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