• Communications for Statistical Applications and Methods
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• 제8권3호
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• pp.615-623
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• 2001

A functional central limit theorem is obtained for a stationary multivariate linear process of the form (no abstract. see full-text) where{ $Z_{t}$} is a sequence of strictly stationary m-dimensional negatively associated random vectors with E $Z_{t}$=O and E∥ $Z_{t}$∥$^2$<$\infty$ and { $A_{u}$} is a sequence of coefficient matrices with (no abstract. see full-text) and (no abstract. see full-text).text).).

• 대한수학회논문집
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• 제23권1호
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• pp.133-140
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• 2008

Let {${\xi}_k,\;k\;{\in}\;{\mathbb{Z}}$} be a strictly stationary associated sequence of H-valued random variables with $E{\xi}_k\;=\;0$ and $E{\parallel}{\xi}_k{\parallel}^2\;<\;{\infty}$ and {$a_k,\;k\;{\in}\;{\mathbb{Z}}$} a sequence of linear operators such that ${\sum}_{j=-{\infty}}^{\infty}\;{\parallel}a_j{\parallel}_{L(H)}\;<\;{\infty}$. For a linear process $X_k\;=\;{\sum}_{j=-{\infty}}^{\infty}\;a_j{\xi}_{k-j}$ we derive that {$X_k} fulfills the functional central limit theorem.

• 소성∙가공
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• 제3권3호
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• pp.359-374
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• 1994

Process sequence design in sheet metal forming process by the finite element method is investigated. The forming of sheet metal into a washing machine container is used to demonstrate the design of an improved process sequence which has fewer operations. The design procedure makes extensive use of the finite element method which has simulation capabilities of elastic-plastic modeling. A one-stage process to make an initial blank to the final product is simulated to obtain information on metal flow requirements. Loading simulation for a conventional method is also performed to evaluate the design criteria which are uniform thickness distribution around the finished part and maximum punch load within limit of available press capacity. The newly designed sequence has two forming operations and can achieve net-shape manufacturing, while the conventional process sequence has three forming operations. This specific case conventional process sequence has three forming operations. This specific case can be considered for application of the method and for development of the sequence design methodology in general.

• 대한수학회지
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• 제39권1호
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• pp.119-126
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• 2002

For a stationary multivariate linear process of the form X$_{t}$ = (equation omitted), where {Z$_{t}$ : t = 0$\pm$1$\pm$2ㆍㆍㆍ} is a sequence of stationary linearly positive quadrant dependent m-dimensional random vectors with E(Z$_{t}$) = O and E∥Z$_{t}$∥ $^2$< $\infty$, we prove a central limit theorem.theorem.

• Communications for Statistical Applications and Methods
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• 제2권2호
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• pp.347-349
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• 1995

In this paper a central limit theorem on $L^P(R)$ for $1{\leq}p<{\infty}$ is obtained with an example when ${X_n}$ is a sequence of independent, identically distributed random variables on $L^P(R)$.

• 대한수학회지
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• 제41권6호
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• pp.1023-1034
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• 2004

In this paper we establish limsup and liminf theorems for the increments of partial sum processes of a dependent stationary Gaussian sequence.

• 충청수학회지
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• 제12권1호
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• pp.169-177
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• 1999

In this paper, we shall define the usual fuzzy distance between two real fuzzy points, using the usual distance between two points in $\mathbb{R}$. We introduce the fuzzy sequence in the fuzzy real line and the notion of limit of fuzzy sequence in $F_p(\mathbb{R})$, and obtain uniformly fuzzy continuous in $F_p(\mathbb{R})$.

• 대한수학회지
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• 제19권1호
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• pp.19-22
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• 1982

• Journal of applied mathematics & informatics
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• 제4권1호
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• pp.147-166
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• 1997

The convergence of the power sequence of an $n{\times}n$ fuzzy matrix has been studied. Some theoretical necessary and sufficient con-ditions have been established for the power sequence to be convergent generally. Furthermore as one of our main concerns the convergence index was studied in detail especially for some special types of Boolean matrices. Also it has been established that the convergence index is bounded by $(n-1)^2+1$ from above for an arbitrary $n{\times}n$ fuzzy matrix if its power sequence converges. Our method is concentrated on the limit behavior of the power se-quence. It helped us to make our proofs be simpler and more direct that those in pure algebraic methods.

• 대한수학회지
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• 제51권1호
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• pp.1-15
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• 2014

A conditional version of the classical central limit theorem is derived rigorously by using conditional characteristic functions, and a more general version of conditional central limit theorem for the case of conditionally independent but not necessarily conditionally identically distributed random variables is established. These are done anticipating that the field of conditional limit theory will prove to be of significant applicability.