• East Asian mathematical journal
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• v.28 no.3
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• pp.333-337
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• 2012

Finiteness of regular normal binary Hermitian lattices are known in several articles. In this article, we point out that there are infinitely many imaginary quadratic fields that admit a regular subnormal binary Hermitian lattice.

• Journal of the Korean Mathematical Society
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• v.35 no.1
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• pp.207-224
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• 1998

After the review of known results on the connections between selfsimilar processes with independent increments (processes of class L) and selfdecomposable distributions and between semi-selfsimilar processes with independent increments and semi-selfdecomposable distributions, dichotomy of those processes into transient and recurrent is discussed. Due to the lack of stationarity of the increments, transience and recurrence are not expressed by finiteness and infiniteness of mean sojourn times on bound sets. Comparison in transience-recurrence of the Levy process and the process of class L associated with a common distribution of class L is made.

• Bulletin of the Korean Mathematical Society
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• v.60 no.4
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• pp.933-955
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• 2023

For any prime number p, let J(p) be the set of positive integers n such that the numerator of the n^th harmonic number in the lowest terms is divisible by this prime number p. We consider an extension of this set to the generalized harmonic numbers, which are a natural extension of the harmonic numbers. Then, we present an upper bound for the number of elements in this set. Moreover, we state an explicit condition to show the finiteness of our set, together with relations to Bernoulli and Euler numbers.

• Kyungpook Mathematical Journal
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• v.63 no.4
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• pp.571-575
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• 2023

Let D be an integral domain and let * be a star-operation on D. In this article, we give new characterizations of *_w-Noetherian domains and *_w-principal ideal domains. More precisely, we show that D is a *_w-Noetherian domain (resp., *_w-principal ideal domain) if and only if every *_w-countable type ideal of D is of *_w-finite type (resp., principal).

• Bulletin of the Korean Mathematical Society
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• v.50 no.2
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• pp.649-657
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• 2013

Let R be a commutative Noetherian ring, I an ideal of R and T be a non-zero I-cofinite R-module with dim(T) ${\leq}$ 1. In this paper, for any finitely generated R-module N with support in V(I), we show that the R-modules $Ext^i_R$(T,N) are finitely generated for all integers $i{\geq}0$. This immediately implies that if I has dimension one (i.e., dim R/I = 1), then $Ext^i_R$($H^j_I$(M), N) is finitely generated for all integers $i$, $j{\geq}0$, and all finitely generated R-modules M and N, with Supp(N) ${\subseteq}$ V(I).

• Bulletin of the Korean Mathematical Society
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• v.48 no.5
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• pp.1041-1046
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• 2011

Let {X, $X_{i};\;i{\geq}1$} be a sequence of independent and identically distributed positive random variables. Denote $S_n= \sum\array\\_{i=1}^nX_i$ and $S\array\\_n^{(k)}=S_n-X_k$ for n ${\geq}$1, $1{\leq}k{\leq}n$. Under the assumption of the finiteness of the second moments, we derive a type of the law of the iterated logarithm for $S\array\\_n^{(k)}$ and the limit point set for its certain normalization.

• Journal of the Korean Mathematical Society
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• v.41 no.4
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• pp.717-735
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• 2004

A problem raised by Selfridge and solved by Pomerance asks to find the pairs (a, b) of natural numbers for which $2^a\;-\;2^b$ divides $n^a\;-\;n^b$ for all integers n. Vajaitu and one of the authors have obtained a generalization which concerns elements ${\alpha}_1,\;{\cdots},\;{{\alpha}_{\kappa}}\;and\;{\beta}$ in the ring of integers A of a number field for which ${\Sigma{\kappa}{i=1}}{\alpha}_i{\beta}^{{\alpha}i}\;divides\;{\Sigma{\kappa}{i=1}}{\alpha}_i{z^{{\alpha}i}}\;for\;any\;z\;{\in}\;A$. Here we obtain a further generalization, proving the corresponding finiteness results in a multidimensional setting.

• Bulletin of the Korean Mathematical Society
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• v.55 no.1
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• pp.25-40
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• 2018

We focus on the structure of the set of noncentral idempotents whose role is similar to one of central idempotents. We introduce the concept of quasi-Abelian rings which unit-regular rings satisfy. We first observe that the class of quasi-Abelian rings is seated between Abelian and direct finiteness. It is proved that a regular ring is directly finite if and only if it is quasi-Abelian. It is also shown that quasi-Abelian property is not left-right symmetric, but left-right symmetric when a given ring has an involution. Quasi-Abelian property is shown to do not pass to polynomial rings, comparing with Abelian property passing to polynomial rings.

• The Korean Journal of Applied Statistics
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• v.22 no.6
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• pp.1277-1287
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• 2009

For stratifying skewed populations, the Lavall$\acute{e}$e-Hidiroglou(LH) algorithm is often considered to have a take-all stratum with the largest units and some take-some strata with the middle-size and small units. Related to its iterative nature have been reported some numerical difficulties such as the dependency of the ultimate stratum boundaries to a choice of initial boundaries and the slow convergence to locally-optimum boundaries. The geometric stratification has been recently proposed to provide initial boundaries that can avoid such numerical difficulties in implementing the LH algorithm. Since the geometric stratification does not pursuit the optimization but the equalization of the stratum CVs, the corresponding stratum boundaries may not be (near) optimal. This paper revisits these issues concerning convergence and near-optimality of optimal stratification algorithms using artificial numerical examples. We also discuss the formation of the strata and the sample allocation under the optimization process and some aspects related to discontinuity arisen from the finiteness of both population and sample as well.

• Korean Journal of Child Studies
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• v.30 no.4
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• pp.205-222
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• 2009

This study aims to understand time experiences of mothers in child counseling and to investigate the meanings of their experience of time. Phenomenological perspectives and attitudes were adopted as the basic methodology. Participants were five mothers who were interviewed in depth on their time experiences in child counseling. The data were organized by the following contents : (1) Time for compensation, (2) conscious immersion, (3) stagnation, (4) infiniteness and finiteness of time, and (5) facing the past. Based on the results, the researcher interpreted three meanings discovered in the mothers' time experiences; (1) Reconstructed time : Healing, (2) The child becomes a mirror reflecting the mother, and (3) A new beginning.