• Title/Summary/Keyword: Invariants

Search Result 214, Processing Time 0.018 seconds

A Case Study on Utilizing Invariants for Mathematically Gifted Students by Exploring Algebraic Curves in Dynamic Geometry Environments (역동적 기하 환경에서 곡선 탐구를 통한 수학영재들의 불변량 활용에 관한 사례 연구)

  • Choi, Nam Kwang;Lew, Hee Chan
    • Journal of Educational Research in Mathematics
    • /
    • v.25 no.4
    • /
    • pp.473-498
    • /
    • 2015
  • The purpose of this study is to examine thinking process of the mathematically gifted students and how invariants affect the construction and discovery of curve when carry out activities that produce and reproduce the algebraic curves, mathematician explored from the ancient Greek era enduring the trouble of making handcrafted complex apparatus, not using apparatus but dynamic geometry software. Specially by trying research that collect empirical data on the role and meaning of invariants in a dynamic geometry environment and research that subdivide the process of utilizing invariants that appears during the mathematically gifted students creating a new curve, this study presents the educational application method of invariants and check the possibility of enlarging the scope of its appliance.

A NOTE ON E. CARTAN'S METHOD OF EQUIVALENCE AND LOCAL INVARIANTS FOR ISOMETRIC EMBEDDINGS OF RIEMANNIAN MANIFOLDS

  • Han, Chong-Kyu;Yoo, Jae-Nyun
    • Journal of the Korean Mathematical Society
    • /
    • v.34 no.4
    • /
    • pp.771-790
    • /
    • 1997
  • By using the method of equivalence of E. Cartan we calculate the local scalar invariants for Riemannian 2-maniolds. We define also a notion of local invariants for submanifolds in $R^{n + d}, n \geq 2, d \geq 1$, in terms of the symmetry of the local isometric embedding equations of Riemannian n-manifolds into $R^{n + d}$. We show that the local invariants obtained by the Cartan's method are the intrinsic expressions of the local invariants in our sense in the casees of surfaces in $R^3$.

  • PDF

ONE-POINTED GRAVITATIONAL GROMOV-WITTEN INVARIANTS FOR GRASSMANNIANS

  • Kim, Bum-Sig
    • Journal of the Korean Mathematical Society
    • /
    • v.38 no.5
    • /
    • pp.1061-1068
    • /
    • 2001
  • We write down explicity a recursive formula of one-pointed gravitational Gromov-Witten invariants and reduce the computation of them to a combinatoric problem which is not solved yet. The one-pointed invariants were played important role in Givental’s program in mirror symmetry. In section 3, we describe the combinatoric problem which can be read independently.

  • PDF

A FREE ℤp-ACTION AND THE SEIBERG-WITTEN INVARIANTS

  • Nakamura, Nobuhiro
    • Journal of the Korean Mathematical Society
    • /
    • v.39 no.1
    • /
    • pp.103-117
    • /
    • 2002
  • We consider the situation that ${\mathbb{Z}_p}\;=\;{\mathbb{Z}/p\mathbb{Z}}$ acts freely on a closed oriented 4-manifold X with ${b_2}^{+}\;{\geq}\;2$. In this situation, we study the relation between the Seiberg-Witten invariants of X and those of the quotient manifold $X/{\mathbb{Z}}_p$. We prove that the invariants of X are equal to those of $X/{\mathbb{Z}}_p$ modulo p.

K0-PROXIMITY INDUCED BY UNIFORMITY

  • Han, Song Ho
    • Korean Journal of Mathematics
    • /
    • v.11 no.1
    • /
    • pp.45-49
    • /
    • 2003
  • We introduce the $k_0$-proximity space as a generalization of the Efremovi$\check{c}$-proximity space. We try to show that $k_0$-proximity structure lies between topological structures and uniform structure in the sense that all topological invariants are $k_0$-proximity invariants and all $k_0$-proximity invariants are uniform invariants.

  • PDF

THE RING OF INVARIANTS OF 3 BY 3 MATRICES

  • Lee Woo
    • Journal of applied mathematics & informatics
    • /
    • v.22 no.1_2
    • /
    • pp.535-539
    • /
    • 2006
  • The ring of invariants of two 2 by 2 matrices C(2, 2) is a polynomial ring with 5 variables [1]. In this paper we find the system of parameters of C(3, 2) by Groebner bases.

CR INVARIANTS OF WEIGHT 6

  • Hirachi, Kengo
    • Journal of the Korean Mathematical Society
    • /
    • v.37 no.2
    • /
    • pp.177-191
    • /
    • 2000
  • All scalar CR invariants of weight $\leq$ 6 are explicitly given for 3-dimensional strictly pseudoconvex CR structures, as an application of Fefferman's ambient metric construction and its generalization by he author.

  • PDF