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미분다양체위에서 정의된 가미분함수의 어떤 성질에 대한 소고
정완수 순천향대학교 기초과학연구소 1998 순천향자연과학연구 논문집 Vol.4 No.1
In this note we introduce the some properties of differentiable function and non-degenerated critical point
정완수 순천향대학교 1988 논문집 Vol.11 No.2
In this paper, we introduce the concepts and properties of tightness and taut immersion. Furthermor, we will show that the smooth manifold immersion f:M??→E?? is tight if and only if (a) γ=β (b) f has minimal absolute total curvature. Main theorem in this paper are as follows: 1) Let p=cosθ q+sinθ q', 0<θ<π/2, ?? is non-degenerate, then ??. 2) Suppose ??,and ?? are tight immersion of compact manifold, Then f×g is a tight immersion of M×M' into ??.
정완수 순천향대학교 기초과학연구소 2004 순천향자연과학연구 논문집 Vol.10 No.2
In this paper, we introduce the concepts of geodesic loops, closed geodesics reflexive space and quasi-reflexive spaces. In particular, generalizing the R. Bott's theorem we obtain that if M is an m(≥2) dimensional, simply connected, quasi-reflexive space, then the cohomology ring H*(M,Z) with intergral coefficients is a polynomial ring.
정완수 순천향대학교 기초과학연구소 1999 순천향자연과학연구 논문집 Vol.5 No.1
In this note we introduce the existence of critical point.
정완수 순천향대학교 기초과학연구소 1995 순천향자연과학연구 논문집 Vol.1 No.2
Boolean algebra is also important in many other branches of methematics. George Boole(1815-1864) introduced an important class of algebraic structures in connection with his research in methematical logic. These structures have been called Boolean algebras. These are a special type of lattice. It was E. Schroder, who about 1890, considered the lattice concept in today's sense. At approximately the same time, R. dedikind developed a similar concept in his work on groups and ideals. In this note, we first recall the basic structures and properties of Boolean algebra by lattice, next compare Boolean algebra with Boolean ring. There is a close connection between Boolean algebra and particular commutative rings with unit, the so-called Boolean rings. For an outline of this, we consider one more operation on Boolean algebra definable in terms of +, ·and -, symmetric deference.
鄭完秀 순천향대학교 1985 논문집 Vol.8 No.4
Riemann 多樣體에서의 閉測地線의 存在에 대한 연구는 大域微分幾何學의 性質을 究明함에 매우 重要하다. 單純連結인 Compact 多樣體에서의 閉測地線의 存在性은 Poincore, Lyustenik, Fet 等에 의하여 밝혀진바 있다. 本 論文에서는 Critical Point의 存在性을 밝힌 Morse理論[1]과 代數的 位相數學에서의 Homotopy class[3]의 槪念을 써서 Riemann測度가 주어진 Compact 多樣體에서 一般的으로 하나의 閉測地線이 存在함을 밝혔다.