Jusub Jang

Yeh obtained the conditional Wiener integral of ap{-fiV[x(u)]du} given x(t) where x is in Wiener space C[0, t] and V is a function on R 1 satisfying certain conditions. In this paper we extend Yeh's result to the conditional Yeh-Wiener integral of exp{-f$ fa V[x(u, v)] du dv} given x(s,t) where x is in Yeh-Wiener space C 2 (Q) and V is a nonnegative continuous function on R 1 satisfying the condition w 2 ) V(w) exp --} dm L (w) < oo.

매년 대학 신입생의 수학 기초실력이 현저하게 떨어지고 있어 대학의 미분적분학 강의가 점차 힘들어짐을 느낀다. 이러한 현상은 대학에 입학하는 고등학교 졸업자 수가 줄어들면서 상대적으로 수학능력이 부족한 학생들이 입학했기 때문에 일어날 수도 있고, 또는 전반적으로 학력이 저하되어 일어날 수도 있다고 본다. 통계청 자료(「장래인구추계」, 2001)에 따르면 제7차 교육과정의 시행으로 대학수학능력고사에 도입된 후 입학한 2005년도부터는 고교 졸업생수가 지금까지 계속 증가하는 것으로 나와 있다. 그러므로 전체적인 학력이 저하되었음을 추측할 수 있다. 이를 뒷받침할 전국 대학의 이공계 신입생 기초학력에 대한 객관적인 자료의 확보를 위하여, 2006년 전국자연과학대학장협의회의 요청에 따라 수학, 물리, 화학, 생물 등 자연계열 교과목 중 가장 계량화가 용이한 수학을 우선 선정하여 조사하였다. 대학의 미분적분학 강좌는 고교 과정의 ‘수학 10’, ‘수학 I’, ‘수학 II’ 그리고 ‘미분과 적

In this paper we extend Johnson and Skoug's results involving the analytic Feynman integrable functionals on Wiener space to the analytic Yeh-Feynman integrable functionals on Yeh-Wiener space. To do this we define the analytic Yeh-Feynman integral and find a Banach algebra of some Yeh-Feynman integrable functionals. Also we find formulae for the analytic Yeh-Feynman integral and extend some measurability results involving the Wiener measure to the Yeh-Wiener measure.

In this paper, we introduce the generalized conditional Yeh-Wiener integral which includes the conditional Yeh-Wiener integral and the modified conditional Yeh-Wiener integral. We also show that some of the results in the conditional Yeh-Wiener integral and the modified conditional Yeh-Wiener integral can be obtained as corollaries of our result. We also treat the generalized conditional Yeh-Wiener integral for the functional containing a generalized quasi-polyhedric function.

In this paper, we first introduce the modified Yeh- Wiener integral and then consider the modified conditional Yeh- Wiener integral. Here we use the space of continuous functions on a dierent region which was discussed before. We also evaluate some modified conditional Yeh-Wiener integral with examples using the simple formula for the modified conditional Yeh-Wiener integral.

The purpose of this paper is to treat the generalized conditional Yeh-Wiener integral for the sample path-valued conditioning function. As a special case of our results, we obtain the results in [6].

In this paper we introduce a theory of differentiation in Yeh–Wiener space We then establish the fundamental theorem of Integral calculus on C(Q). The main tools we employ here are conditional Yeh–Wiener integrals and the martingale convergence theorem

In this paper we first consider the partition of the general region made by the monotonically increasing and continuous function and then obtain the measure from the partition of the region. The results obtained here is a little bit different from the previous results in [1, 2, 3] and finally we discuss the difference.