• Bulletin of the Korean Mathematical Society
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• v.53 no.3
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• pp.833-842
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• 2016

For a certain kind of reciprocal polynomials $P(x),Q(x){\in}{\mathbb{Z}}[x]$, their sums are considered. We demonstrate that the Mahler measure of polynomials plays a role to prove the irreducibility of the sums over the field of rationals.

• Bulletin of the Korean Mathematical Society
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• v.48 no.5
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• pp.923-938
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• 2011

Some properties for negatively orthant dependent sequence are discussed. Some strong limit results for the weighted sums are obtained, which generalize the corresponding results for independent sequence and negatively associated sequence. At last, exponential inequalities for negatively orthant dependent sequence are presented.

• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.1841-1846
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• 2013

In this paper we establish some new results on sums of Hilbert space frames and Riesz bases. We also provide a correction to some recently established results in [2].

• Communications of the Korean Mathematical Society
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• v.13 no.2
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• pp.377-384
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• 1998

Let ${X_n,n \geq 1}$ be a sequence of stochatically dominated pairwise independent random variables. Let ${a_n, n \geq 1}$ and ${b_n, n \geq 1}$ be seqence of constants such that $a_n \neq 0$ and $0 < b_n \uparrow \infty$. A strong law large numbers of the form $\sum^{n}_{j=1}{a_j X_i//b_n \to 0$ almost surely is obtained.

• Journal of the Korean Mathematical Society
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• v.50 no.2
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• pp.379-392
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• 2013

A general result for the complete convergence of arrays of rowwise extended negatively dependent random variables is derived. As its applications eight corollaries for complete convergence of weighted sums for arrays of rowwise extended negatively dependent random variables are given, which extend the corresponding known results for independent case.

• Bulletin of the Korean Mathematical Society
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• v.50 no.5
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• pp.1539-1554
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• 2013

In this paper, we extend Donsker's invariance principle to the case of random partial sums processes based on a double sequence of row-wise i.i.d. random variables.

• Bulletin of the Korean Mathematical Society
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• v.57 no.2
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• pp.345-354
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• 2020

In this paper, we first give some representations for four new mock theta functions defined by Andrews [1] and Bringmann, Hikami and Lovejoy [5] using divisor sums. Then, some transformation and summation formulae for these functions and corresponding bilateral series are derived as special cases of ₂𝜓₂ series $${\sum\limits_{n=-{{\infty}}}^{{\infty}}}{\frac{(a,c;q)_n}{(b,d;q)_n}}z^n$$ and Ramanujan's sum $${\sum\limits_{n=-{{\infty}}}^{{\infty}}}{\frac{(a;q)_n}{(b;q)_n}}z^n$$.

• Kyungpook Mathematical Journal
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• v.45 no.1
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• pp.73-85
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• 2005

In this paper a criterion for $L^1-convergence$ of a new modified sine sums is obtained by using $Ces{\grave{a}}ro$ means of integral and non-integral orders.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2004.04a
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• pp.385-388
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• 2004

The present paper establish the improved version of central limit theorem for sums of level-continuous fuzzy random variables as a generalization of central limit theorem for sums of independent and identically distributed random sets.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.3
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• pp.491-499
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• 2013

In this paper, we prove the weak law of large numbers for weighted sums of noncommutative random variables in noncommutative Lorentz space under weaker conditions than the conditions in [7].