• 대한수학회논문집
• /
• 제20권3호
• /
• pp.531-538
• /
• 2005

In this paper we derive the central limit theorem for ${\sum}_{i=1}^n\;a_{ni}\xi_i$, where ${a_{ni},\;1\;{\leq}\;i\;{\leq}\;n}$ is a triangular array of nonnegative numbers such that $sup_n{\sum}_{i=1}^n\;a_{ni}^2\;<\;{\infty},\;max_{1{\leq}i{\leq}n}a_{ni}{\rightarrow}0\;as\;n\;{\rightarrow}\;{\infty}\;and\;\xi'_i\;s$ are a linearly negative quadrant dependent sequence. We also apply this result to consider a central limit theorem for a partial sum of a generalized linear process $X_n\;=\;\sum_{j=-\infty}^\infty\;a_k+_j{\xi}_j$.

• 산업기술연구
• /
• 제22권B호
• /
• pp.21-26
• /
• 2002

The non-dimensional heat loss from a thermally asymmetric triangular fin is investigated as a function of a ratio of upper and lower surface Biot numbers (Bi2/Bi1), the non-dimensional fin length and tip surface Biot number using the two-dimensional separation of variables method. The effect of fin tip surface Biot number on the variation of the non-dimensional temperature along the sloped upper and lower surfaces for the thermally asymmetric condition is presented. The relationship between the non-dimensional fin length and the fin tip surface Biot number for equal amount of heat loss is also discussed as well as the relationship between upper surface Biot number and tip surface Biot number for equal amount of heat loss.

• Journal of applied mathematics & informatics
• /
• 제36권3_4호
• /
• pp.237-244
• /
• 2018

Let ${\mathcal{H}}$ be an infinite dimensional separable Hilbert space with a fixed orthonormal base $\{e_1,e_2,{\cdots}\}$. Let L be the subspace lattice generated by the subspaces $\{[e_1],[e_1,e_2],[e_1,e_2,e_3],{\cdots}\}$ and let $Alg{\mathcal{L}}$ be the algebra of bounded operators which leave invariant all projections in ${\mathcal{L}}$. Let p and q be natural numbers (p < q). Let ${\mathcal{A}}$ be a linear manifold in $Alg{\mathcal{L}}$ such that $T_{(p,q)}=0$ for all T in ${\mathcal{A}}$. If ${\mathcal{A}}$ is a Lie ideal, then $T_{(p,p)}=T_{(p+1,p+1)}={\cdots}=T_{(q,q)}$ and $T_{(i,j)}=0$, $p{\eqslantless}i{\eqslantless}q$ and i < $j{\eqslantless}q$ for all T in ${\mathcal{A}}$.

• 호남수학학술지
• /
• 제39권1호
• /
• pp.93-100
• /
• 2017

Let $\mathcal{H}$ be an infinite dimensional separable Hilbert space with a fixed orthonormal base $\{e_1,e_2,{\cdots}\}$. Let $\mathcal{L}$ be the subspace lattice generated by the subspaces $\{[e_1],[e_1,e_2],[e_1,e_2,e_3],{\cdots}\}$ and let $Alg{\mathcal{L}}$ be the algebra of bounded operators which leave invariant all projections in $\mathcal{L}$. Let p and q be natural numbers($p{\leqslant}q$). Let $\mathcal{B}_{p,q}=\{T{\in}Alg\mathcal{L}{\mid}T_{(p,q)}=0\}$. Let $\mathcal{A}$ be a linear manifold in $Alg{\mathcal{L}}$ such that $\{0\}{\varsubsetneq}{\mathcal{A}}{\subset}{\mathcal{B}}_{p,q}$. If $\mathcal{A}$ is an ideal in $Alg{\mathcal{L}}$, then $T_{(i,j)}=0$, $p{\leqslant}i{\leqslant}q$ and $i{\leqslant}j{\leqslant}q$ for all T in $\mathcal{A}$.

• 센서학회지
• /
• 제14권5호
• /
• pp.291-296
• /
• 2005

In this paper, the PDMS based micromixer having 3-dimension triangular structure has been developed for the reaction of samples in the micro volume. The mixing efficiency was measured according to the change of Reynolds number (Re: 0.08, 0.8, 8, 16) and channel height (100, 200, $300{\mu}m$). Total length of mixing region is 7.4 mm and the measured mixing efficiencies at the outlet were over 85 %. Within the mixing length 2.4 mm, the mixing efficiencies were more than 70 % at any Reynolds numbers, and this indicates the strong mixing has occurred inside the mixing channel due the triangular structures. By employing these 2 mixers, we have fabricated the microreactor to detect the glucose-catalysts reaction. The microreactor showed good reactivity of glucose and enzymes with the small amount of sample solution.

• 대한수학회지
• /
• 제43권3호
• /
• pp.529-538
• /
• 2006

In this paper we derive the central limit theorem for ${\sum}^n_{i=l}\;a_{ni}{\xi}_{i},\;where\;\{a_{ni},\;1\;{\le}\;i\;{\le}n\}$ is a triangular array of non-negative numbers such that $sup_n{\sum}^n_{i=l}\;a^2_{ni}\;<\;{\infty},\;max_{1{\le}i{\le}n\;a_{ni}{\to}\;0\;as\;n{\to}{\infty}\;and\;{\xi}'_{i}s$ are a linearly positive quadrant dependent sequence. We also apply this result to consider a central limit theorem for a partial sum of a generalized linear process of the form $X_n\;=\;{\sum}^{\infty}_{j=-{\infty}}a_{k+j}{\xi}_{j}$.

• 한국인터넷방송통신학회논문지
• /
• 제10권2호
• /
• pp.113-122
• /
• 2010

CATR(Compact Antenna Test Range)의 반사판 가장자리에서 발생되는 회절 전계는 quiet zone의 리플(ripple)을 증가시키는 원인이 되기 때문에 반사판은 서레이션(serration)을 부착하여 사용하게 된다. 본 논문에서는 삼각형을 비대칭으로 변형시킨 새로운 형태의 서레이션 구조를 제안하였고, 프레넬 회절 식을 사용하여 회절 전계를 해석하였다. 기존 삼각형 서레이션과 제안된 서레이션의 리플 특성을 확인하기 위하여 진폭 및 위상 리플을 비교하였다. 반사판의 크기, 서레이션 높이, 서레이션 개수를 변화시키며 해석한 결과, 제안된 구조의 서레이션에서 기존 삼각형 형태의 서레이션보다 리플이 감소함을 확인하였다. 따라서 본 논문에서 제안된 구조의 서레이션은 quiet zone의 리플을 감소시킬 수 있을 것으로 예상된다.

• Journal of applied mathematics & informatics
• /
• 제31권1_2호
• /
• pp.99-110
• /
• 2013

In this article, sensitivity analysis of atmospheric dispersion model RIMPUFF is considered. Uncertain parameters are taken to be triangular fuzzy numbers, and sensitivity analysis is carried out by using the Hartley-like measure. Codes for evaluating membership function using the Vertex method and the Hartley-like measure are prepared using Matlab.

• 충청수학회지
• /
• 제27권2호
• /
• pp.277-286
• /
• 2014

We define the pentagonal fuzzy sets and generalize the results of addition, subtraction, multiplication, and division based on the Zadeh's extension principle for two pentagonal fuzzy sets. In addtion, we find the condition that the result of addition or subtraction for two pentagonal fuzzy sets becomes a triangular fuzzy number and give some example.

• 한국경영과학회지
• /
• 제20권1호
• /
• pp.131-145
• /
• 1995

This paper presents a method for solving project planning problem which the opinions of experts greatly disagree in each activity processing time. Triangular fuzzy numbers (TFNs) are used to represent activity times of experts. And we introduce a pessimistic project planning with major TFNs and an optimistic project planning with minor. TFNs, and illustrate the approach using a combination of the existing composite and the comparison methods, which is used to solve the complex project planning problem.