• Bulletin of the Korean Mathematical Society
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• v.54 no.5
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• pp.1851-1857
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• 2017

We study relations between two descriptions of closed orientable 3-manifolds: as branched coverings and as Heegaard splittings. An explicit relation is presented for a class of 3-manifolds which are branched cyclic coverings of connected sums of lens spaces, where the branching set is an axis of a hyperelliptic involution of a Heegaard surface.

• Bulletin of the Korean Mathematical Society
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• v.57 no.3
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• pp.607-622
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• 2020

In the paper, some probability convergence properties of series for rowwise sums of negatively superadditive dependent (NSD) random variables are discussed. We establish some sharp results on these convergence for NSD random variables under some general settings, which generalize and improve the corresponding ones of some known literatures.

• Honam Mathematical Journal
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• v.38 no.4
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• pp.819-831
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• 2016

The present paper investigates some properties of the digital homology in [1, 4, 5] and points out some unclearness of the definition of a digital homology and further, suggests a suitable form of a digital homology. Finally, we calculate a digital homology group and a relative digital homology group of some digital wedge sums. Finally, the paper corrects some errors in [6]. In the present paper all digital images (X, k) are assumed to be non-empty and k-connected.

• Journal of Applied Reliability
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• v.12 no.4
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• pp.265-274
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• 2012

We in this paper discuss the strong law of large numbers for weighted sums of arrays of rowwise LNQD random variables by using a new exponential inequality of LNQD r.v.'s under suitable conditions and we obtain one of corollary.

• Journal of the Korean Statistical Society
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• v.33 no.1
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• pp.99-106
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• 2004

Let {X, $X_{n}, n\;{\geq}\;1$} be a sequence of identically distributed, negatively associated (NA) random variables and assume that $│X│^{r}$, r > 0, has a finite moment generating function. A strong law of large numbers is established for weighted sums of these variables.

• Communications of the Korean Mathematical Society
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• v.18 no.4
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• pp.781-789
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• 2003

Formal manipulations of double series are useful in getting some other identities from given ones and evaluating certain summations, involving double series. The main object of this note is to summarize rather useful double series manipulations scattered in the literature and give their generalized formulas, for convenience and easier reference in their future use. An application of such manipulations to an evaluation for Euler sums (in itself, interesting), among other things, will also be presented to show usefulness of such manipulative techniques.

• Bulletin of the Korean Mathematical Society
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• v.58 no.6
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• pp.1463-1481
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• 2021

Divisibility properties of harmonic numbers by a prime number p have been a recurrent topic. However, finding the exact p-adic orders of them is not easy. Using class numbers of number fields and Bernoulli numbers, we compute the exact p-adic orders of harmonic type sums. Moreover, we obtain an asymptotic formula for generalized harmonic numbers whose p-adic orders are exactly one.

• Journal of the Chungcheong Mathematical Society
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• v.32 no.3
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• pp.327-336
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• 2019

In this paper, the weak laws of large numbers for sums of asymptotically almost negatively associated random vectors in Hilbert spaces are investigated. Some results in Hien and Thanh ([3]) are generalized to asymptotically almost negatively random vectors in Hilbert space.

• Journal of applied mathematics & informatics
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• v.37 no.3_4
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• pp.207-217
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• 2019

We are presented of several basic properties for negatively superadditive dependent(NSD) random variables. By using this concept we are obtained complete convergence for maximum partial sums of rowwise NSD random variables. These results obtained in this paper generalize a corresponding ones for independent random variables and negatively associated random variables.

• Honam Mathematical Journal
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• v.41 no.2
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• pp.321-328
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• 2019

We completely characterize the isomorphic class of those associative unitary rings whose elements are sums of four commuting idempotents. Our main theorem enlarges results due to Hirano-Tominaga (Bull. Austral. Math. Soc., 1988), Tang et al. (Lin. & Multilin. Algebra, 2019), Ying et al. (Can. Math. Bull., 2016) as well as results due to the author in (Alban. J. Math., 2018), (Gulf J. Math., 2018), (Bull. Iran. Math. Soc., 2018) and (Boll. Un. Mat. Ital., 2019).