• 대한수학회보
• /
• 제22권1호
• /
• pp.11-15
• /
• 1985

Manddelberg [9] has shown that a Clifford algebra of a free quadratic space over an arbitrary semi-local ring R in Brawer-Wall group BW(R) is determined by its rank, determinant, and Hasse invariant. In this paper, we prove a corresponding result when R is a full ring.Throughout this paper, unless otherwise specified, we assume that R is a commutative ring having 2 a unit. A quadratic space (V, B, .phi.) over R is a finitely generated projective R-module V with a symmetric bilinear mapping B: V*V.rarw.R which is non-degenerate (i.e., the natural mapping V.rarw.Ho $m_{R}$(V,R) induced by B is an isomorphism), and with a quadratic mapping .phi.: V.rarw.R such that B(x,y)=1/2(.phi.(x+y)-.phi.(x)-.phi.(y)) and .phi.(rx) = $r^{2}$.phi.(x) for all x, y in V and r in R. We denote the group of multiplicative units of R by U9R). If (V, B, .phi.) is a free rank n quadratic space over R with an orthogonal basis { $x_{1}$,.., $x_{n}$}, we will write < $a_{1}$,.., $a_{n}$> for (V, B, .phi.) where the $a_{i}$=.phi.( $x_{i}$) are in U(R), and denote the space by the table [ $a_{ij}$ ] where $a_{ij}$ =B( $x_{i}$, $x_{j}$). In the case n=2 and B( $x_{1}$, $x_{2}$)=1/2 we reserve the notation [a $a_{11}$, $a_{22}$] for the space. A commutative ring R having 2 a unit is called full [10] if for every triple $a_{1}$, $a_{2}$, $a_{3}$ of elements in R with ( $a_{1}$, $a_{2}$, $a_{3}$)=R, there is an element w in R such that $a_{1}$+ $a_{2}$w+ $a_{3}$ $w^{2}$=unit.TEX>=unit.t.t.t.

• 대한수학회지
• /
• 제50권5호
• /
• pp.1105-1127
• /
• 2013

Let C[0, $t$] denote the function space of real-valued continuous paths on [0, $t$]. Define $X_n\;:\;C[0,t]{\rightarrow}\mathbb{R}^{n+1}$ and $X_{n+1}\;:\;C[0,t]{\rightarrow}\mathbb{R}^{n+2}$ by $X_n(x)=(x(t_0),x(t_1),{\ldots},x(t_n))$ and $X_{n+1}(x)=(x(t_0),x(t_1),{\ldots},x(t_n),x(t_{n+1}))$, respectively, where $0=t_0 <; t_1 <{\ldots} < t_n < t_{n+1}=t$. In the present paper, using simple formulas for the conditional expectations with the conditioning functions $X_n$ and $X_{n+1}$, we evaluate the $L_p(1{\leq}p{\leq}{\infty})$-analytic conditional Fourier-Feynman transforms and the conditional convolution products of the functions, which have the form $fr((v_1,x),{\ldots},(v_r,x)){\int}_{L_2}_{[0,t]}\exp\{i(v,x)\}d{\sigma}(v)$ for $x{\in}C[0,t]$, where $\{v_1,{\ldots},v_r\}$ is an orthonormal subset of $L_2[0,t]$, $f_r{\in}L_p(\mathbb{R}^r)$, and ${\sigma}$ is the complex Borel measure of bounded variation on $L_2[0,t]$. We then investigate the inverse conditional Fourier-Feynman transforms of the function and prove that the analytic conditional Fourier-Feynman transforms of the conditional convolution products for the functions can be expressed by the products of the analytic conditional Fourier-Feynman transform of each function.

• 한국우주과학회:학술대회논문집(한국우주과학회보)
• /
• 한국우주과학회 1998년도 한국우주과학회보 제7권1호
• /
• pp.26.1-26
• /
• 1998

• Journal of Astronomy and Space Sciences
• /
• 제15권1호
• /
• pp.65-68
• /
• 1998

We construct the X-ray light curves of the W UMa type contact binary SS Arietis(HD12929) from the EXOSAT data in HEASARC data archive. The phase dependent X-ray light curves obtained by using the ephimeris of Kaluzny & Pojmanski of SS Ari is modulated on the orbital phase as in the case of other W UMa type binaries. Although a detailed analysis of these data is impossible because of the very low X-ray light curves in the context of the radiation in the corona region of W UMa type stars.

• 대한수학회보
• /
• 제44권2호
• /
• pp.309-313
• /
• 2007

By applying ideas from [M. S. Moslehian, et al., Norms of operators in $X_{\lambda}$ spaces, Appl. Math. Lett. (2007), doi:10.1016/j.aml.2006. 11.009], we investigate the norm of the cubic operator on the function space $X_{\lambda}$.

• 대한수학회보
• /
• 제29권2호
• /
• pp.295-300
• /
• 1992

In [5] it was shown that if T .mem. L(X) is regular on a Banach space X, with finite dimensional intersection T$^{-1}$ (0).cap.T(X) and if S .mem. L(X) is invertible, commute with T and has sufficiently small norm then T - S in upper semi-Fredholm, and hence essentially one-one, in the sense that the null space of T - S is finite dimensional ([4] Theorem 2; [5] Theorem 2). In this note we extend this result to incomplete normed space.

• 대한수학회논문집
• /
• 제25권3호
• /
• pp.477-484
• /
• 2010

In this paper, we introduce a new property (*) of a topological space and prove that if X satisfies one of the following conditions (1) and (2), then compactness, countable compactness and sequential compactness are equivalent in X; (1) Each countably compact subspace of X with (*) is a sequential or AP space. (2) X is a sequential or AP space with (*).

• 충청수학회지
• /
• 제23권4호
• /
• pp.711-720
• /
• 2010

In this note, we will establish the integration formulae for functionals such as $F(x)=\prod_{j=1}^{n}\;x(s_j)^2$ and $G(x)=\exp\{{\lambda}{\int}_{0}^{t}\;x(s)^2dm_L(s)\}$ in the analogue of Wiener measure space and using our formulae, we will derive some formulae for series.

• Journal of Astronomy and Space Sciences
• /
• 제24권4호
• /
• pp.309-314
• /
• 2007

오르트 구름을 출발하여 태양계 안쪽으로 들어오는 혜성 가운데 오르트 구름으로 되돌아가지 못하고, 태양에 매우 근접하여 태양에 충돌해 버리거나 강한 중력에 의해 쪼개져 사라지는 혜성을 sungrazing comet이라고 한다. 태양에 가까워지면서 태양열에 의해 혜성의 얼음이 승화되면서 그 존재를 확인하게 되는데, 태양풍의 고전리된 중원소이온과 충돌에 의한 전하교환의 상호 작용에 의해 혜성에서 발생하는 가스량과 X-선 방출량을 기존 모델(Mendis & Flammer 1984, Cravens 1997)을 적용하여 근사 계산한 결과, 혜성핵의 반지름이 1km 정도인 경우 태양으로부터 거리가 태양반경의 3배 이내인 거리에서 GOES 위성의 X-선 망원경으로 탐지가능한 것으로 보인다.

• 충청수학회지
• /
• 제28권3호
• /
• pp.397-408
• /
• 2015

In this paper, we solve the Hyers-Ulam stability problem for the following cubic type functional equation $$f(rx+sy)+f(rx-sy)=rs^2f(x+y)+rs^2f(x-y)+2r(r^2-s^2)f(x)$$in quasi-Banach space and non-Archimedean space, where $r={\neq}{\pm}1,0$ and s are real numbers.