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위상수학에 관한 연구 : 리이만다양체에서의 임계사상에 관하여 On the Critical Mappings of the Riemannian Manifolds
전길웅,강명경 충남대학교 자연과학연구소 1982 忠南科學硏究誌 Vol.9 No.1
There are many defined functional on the space of smooth maps of one Riemannian manifold to another. Maps that are critical for every defined functional are called critical. This paper shows that the fibers of critical maps are minimal submanifolds. Also, it provides a characterization of hypercritical maps and shows that the inverse of the hypercritical map is hypercritical.
A NOTE ON JORDAN LEFT DERIVATIONS
Jun, Kil-Woung,Kim, Byung-Do 대한수학회 1996 대한수학회보 Vol.33 No.2
Throughout, R will represent an associative ring with center Z(R). A module X is said to be n-torsionfree, where n is an integer, if nx = 0, x ∈ X implies x = 0. An additive mapping D : R → X, where X is a left R-module, will be called a Jordan left derivation if D(α^2) = 2αD(α), α ∈ R. M. Bresar and J. Vukman [1] showed that the existence of a nonzero Jordan left derivation of R into X implies R is commutative if X is a 2-torsionfree and 3-torsionfree left R-module. They conjectured that in their results the assumption that X is 3-torsionfree can be avoided. We prove that the result holds without this requirement.
INNER DERIVATIONS MAPPING INTO THE RADICAL
Jun, Kil-Woung,Lee, Young-Whan 한국전산응용수학회 1998 Journal of applied mathematics & informatics Vol.5 No.3
In this paper we show that $\sigma$a maps into the radical if and only if for every irreducible representation $\pi$,$\pi$(a) is scalar and obtain that every inner derivation corresponding to $\sigma$-quasi central elements in some Banach algebra maps into the radical.
A Generalization of the Hyers-Ulam-Rassias Stability of the Pexiderized Quadratic Equations, II
JUN, KIL-WOUNG,LEE, YANG-HI 대한수학회 2007 Kyungpook mathematical journal Vol.47 No.1
In this paper we prove the Hyers-Ulam-Rassias stability by considering the cases that the approximate remainder ψ is defined by f(x*y)+f(x*y^(-1))-2g(x)-2g(y) = ψ(x, y), f(x*y)+g(x*y^(-1))-2h(x)-2k(y) = ψ(x, y), where (G, *) is a group, X is a real or complex Hausdorff topological vector space and f, g, h, k are functions from G into X.