• Journal of the Korean Statistical Society
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• 제21권1호
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• pp.80-86
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• 1992

The concept of Balanced Factorial Experiment (BFE) was introduced by Shah (1958). The conditions for BFE were set up by Kurkjian and Zelen (1963) and Kshirsagar (1966). Generalized Cyclic Factorial Experiment (GCFE), which is more wide class of designs than BFE, do not satisfy the condition of BFE. So all contrasts belonging to the same interaction are not estimated with equal variance. The main purpose of this paper is to show that GCFE have orthogonal factorial structure and the scheme of the size of variances for all normalized contrasts in GCFE is similar to the original intra-block association scheme.

• Journal of the Korean Statistical Society
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• 제14권1호
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• pp.29-38
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• 1985

Cyclic Factorial Association Scheme (CFAS) for incomplete block designs in a factorial experiment is defined. It is a generalization of EGD/($2^n-1$)-PBIB designs defined by Hinkelmann (1964) or Binary Number Association Scheme (BNAS) named by Paik and Federer (1973). A property of PBIB designs having CFAS is investigated and it is shown that the structural matrix NN' of such designs has a pattern of multi-nested block circulant matrix. The generalized inverse of (rI-NN'/k) is obtained. Generalized Cyclic incomplete block designs for factorial experiments introduced by John (1973) are presented as the examples of CFAS-PBIB designs. Finally, the relationship between CFAS and BNAS in block designs is briefly discussed.

• 한국데이터정보과학회:학술대회논문집
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• 한국데이터정보과학회 2005년도 춘계학술대회
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• pp.69-82
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• 2005

Factorial experiments are studied in this paper. The Designs, thus, have factorial balance with respect to estimable main effects and interactions. John and Lewis (1983) considered generalized cyclic row-column designs for factorial experiments. A simple method of constructing confounded designs using the classical method of confounding for block designs is described in this paper.

• 대한수학회보
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• 제55권2호
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• pp.587-590
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• 2018

We shall prove certain p-indivisibility properties of so-called generalized left-factorials, where p is a prime.

• 대한수학회지
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• 제47권3호
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• pp.645-657
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• 2010

In this paper, more generalized q-factorial coefficients are examined by a natural extension of the q-factorial on a sequence of any numbers. This immediately leads to the notions of the extended q-Stirling numbers of both kinds and the extended q-Lah numbers. All results described in this paper may be reduced to well-known results when we set q = 1 or use special sequences.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제13권1호
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• pp.55-72
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• 2009

A misclassified size-biased modified power series distribution (MSBMPSD) where some of the observations corresponding to x = c + 1 are misclassified as x = c with probability $\alpha$, is defined. We obtain its recurrence relations among the raw moments, the central moments and the factorial moments. Discussion of the effect of the misclassification on the variance is considered. To illustrate the situation under consideration some of its particular cases like the size-biased generalized negative binomial (SBGNB), the size-biased generalized Poisson (SBGP) and sizebiased Borel distributions are included. Finally, an example is presented for the size-biased generalized Poisson distribution to illustrate the results.

• 대한안전경영과학회:학술대회논문집
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• 대한안전경영과학회 2009년도 춘계학술대회
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• pp.423-427
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• 2009

This study proposes the generation mechanism of various design matrix using generalized linear model for design of experiment. Design generation method of GLM analysis, factorial design(FD) with center points, ANOVA design with lack-of-fit test, and response surface design are introduced. In central composite(CC) design, orthogonal blocking and fractional factorial design(FFD) are presented. We compare the design of Box-Benhken(BB) and face-centred central compsite design.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2004년도 학술발표논문집
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• pp.313-317
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• 2004

Confounded row-column designs for factorial experiments are studied in this paper. The Designs, thus, have factorial balance with respect to estimable main effects and interactions. John and Lewis (1983) considered generalized cycle row=column designs for factorial experiments. A simple method of constructing confounded designs using the classical method of confounding for block designs is described in this paper

• Journal of applied mathematics & informatics
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• 제38권5_6호
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• pp.601-609
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• 2020

In this paper, we introduce degenerate generalized poly-Bernoulli numbers and polynomials with (p, q)-logarithm function. We find some identities that are concerned with the Stirling numbers of second kind and derive symmetric identities by using generalized falling factorial sum.

• 대한수학회지
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• 제44권4호
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• pp.863-872
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• 2007

Let D be an integral domain with quotient field K, A a nonempty set of height-one maximal t-ideals of D, F$({\Lambda})={I{\subseteq}D|I$ is an ideal of D such that $I{\subseteq}P$ for all $P{\in}A}$, and $D_F({\Lambda})={x{\in}K|xA{\subseteq}D$ for some $A{\in}F({\Lambda})}$. In this paper, we prove that if each $P{\in}A$ is the radical of a finite type v-ideal (resp., a principal ideal), then $D_{F({\Lambda})}$ is a weakly Krull domain (resp., generalized weakly factorial domain) if and only if the intersection $D_{F({\Lambda})}={\cap}_{P{\in}A}D_P$ has finite character, if and only if $F({\Lambda})$ is a t-splitting set of ideals, if and only if $F({\Lambda})$ is v-finite.