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有限測度空間上의 積分可能函數列에 對한 相違한 型의 收斂性의 相互關係
吳熙駿 충남대학교 자연과학연구소 1977 學術硏究誌 Vol.4 No.1
Let a norm of integrable function f on a finite messure space be given by ∥f∥=∫_(x)F{f)}d_(μ) where the function F is continuous and bounded and nonnegative in X. In this paper ???? show the following fact. A sequence {f_(n)(χ)} of integrable functions converges in the distance which is given with the norm defined above to the integrable function f if and only if {f_(n)(χ)} converges in measure to f.
吳熙駿 충남대학교 자연과학연구소 1983 忠南科學硏究誌 Vol.10 No.2
Let a function space CBV〔a, b〕be set of bounded variation and continuous function on〔a, b〕, and let function φ be a regulated on〔a, b〕. In this paper we shall prove following theorem.〔Theorem〕. Let φ be a continuous linear functional on CBV〔a, b〕. Then there in a regulated function φ such that φ(f)=∫_a ^b fdφ. (f∈ CBV〔a, b〕)
吳熙駿 충남대학교 자연과학연구소 1982 忠南科學硏究誌 Vol.9 No.2
In this paper we shall lead to another extension of Stieltjes process for vector valued function. Let a vector valued function φ is bounded variation and continuous on [a,b] and a function f is regulated on [a,b]. Then φ and ∥φ∥are Riemann-Stielfijes integrable with respect to f and following ineguality hold. b b ∥∫φ≤∫∥φ∥│df│ a a Let g is strictly increasing continuous function that maps an interval [A,B] onto [a,b]. Define composite function Φ and F on [A,B] by Φ = φ o g and F=fog. Then B b ΦεR(F) and ∫ΦdF = ∫φdf. A a Take f(x)=x and assume g is absolutely continuous function on [A,B] and g'εR. Then b B B ∫φdx = ∫Φdg = ∫φ{g(y)} g'(y)dy a A A
이학계 및 공학계 대학의 미분방정식의 교육과정에 관한 연구
오희준,신준국 충남대학교 자연과학연구소 1984 忠南科學硏究誌 Vol.11 No.2
In this paper, The educational conditions relating to the subject of differential equations in the scientific world and the engineering world at the university were investigated and the problems concerning those conditions and suggestions for their improvement are presented as follows; 1) Differential equations (including the partial differential equations) are taught for two semesters during the sophomore year for the 6 units of credit or more. 2) The effectiveness of lectures increased with the assignment of exercises. 3) The lectures should be conducted by full-time lecturers of the Department of Mathematics for the best results, and exercise time should be assigned to teaching assistants. 4) By decreasing the lecture time of full-time lecturers they can lecture more effectively and research the subject more deeply. 5) Texts should be developed and written according to the framework of the contents of standard subjects. 6) In order to utilize the above facts,「a primary science research committee」under the Ministery of Education should be established to control the following areas in each branch of the sciences; the contents of standard subject, the development of texts, the formulation of educational policy. This will result in the qualitative improvement of the primary science education.
吳熙駿,趙炳式 충남대학교 자연과학연구소 1976 學術硏究誌 Vol.3 No.1
In this paper, with respect to the Borel function and the regulated function defined on the interval I, we have proved the following fact: The class of Borel functions contains the class of regulated functions.
吳熙駿 충남대학교 자연과학연구소 1975 學術硏究誌 Vol.2 No.2
In this paper, with respect to regulated functions defined on the closed interval Ⅰ. We have proved the following facts: 1) The regulated function space R (Ⅰ) is a Banach space inclosed in a bounded function space B(Ⅰ). 2) Tile set of discontinuous points of the regulated function is at most countable.
積分理論의 擴張에 關한 硏究Ⅱ : Regulated函數에 關한 Riemann-Stieltjes 積分의 收斂定理
吳熙駿 충남대학교 자연과학연구소 1981 忠南科學硏究誌 Vol.8 No.2
In this paper we shall derive following convergence theorems which are extended by Riemonn-Stieltjes integral with respect to regulated function. THEORM 7. Suppose function f be regulated on [a,b], and suppose {?_n} is a continuous and functions of bounded variation such that uniformly bounded on [a,b]. If ?_n→? uniformly on[a,b]. Then ?∈R(f) and ??(수식) THEORM 8. Suppose function ? be of bounded variation and continuous on [a,b], and suppose {f_n} is a sequence of regulated functions on [a,b]. If f_n→f uniformly on[a,b]. Then ?∈R(f) and ??(수식)
吳熙駿 충남대학교 자연과학연구소 1980 學術硏究誌 Vol.7 No.2
Let a function φ is of bounded variation and continuous on [a,b] and a function f is regulated on [a,b]. In this paper we shall show that an arbitrary change in the value of regulated function f at point of discontinuous does not affect the value of the Riemann - Stieltjes integral ∫_(a)^(b)φ(x)df.
On the Riemann-Stieltjes Integral with Respect to Regulated Function
Oh, Hi-Jun 충남대학교 자연과학연구소 1978 學術硏究誌 Vol.5 No.2
함수 f:I→R는 regulated 이고 Φ: I → R는 連續이고 有界變動이면 φεR(f)이다. 위 定理를 증明하여 有界變動함수에 關한 Riemann-Stieltjes 積分을 regulated function에 關한 더욱 廣括한 Riemann-Stieltjes積分으로 擴張할 수 있음을 보였다.
A Study on the Reiemann-Stieltjes Integral with rescept to Regulated Function
Oh, Hi-Jun,Kang, Myung-Kyang 충남대학교 자연과학연구소 1979 學術硏究誌 Vol.6 No.2
函 數 φ : [a, b]→lR는 regulated이고, f : [a, b]→lR가 絶對連續이면, ∫^(a)_(b)fdφ= f(b)φ(b)-f(a)φ(a)-∫^(a)_(b)φ(χ)f'(χ)dχ 이다. 위 定理를 證明하여 regulated function에 關한 Riemann-Stieltjes integral을 Riemann integral으로 나타낼 수 있음을 보였다.