• Journal of the Korean Institute of Intelligent Systems
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• v.13 no.6
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• pp.754-758
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• 2003

The present paper establishes a strong law of large numbers for sums of tight fuzzy random variables as a generalization of SLLN for sums of independent and identically distributed fuzzy random variables.

• Bulletin of the Korean Mathematical Society
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• v.55 no.6
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• pp.1909-1920
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• 2018

In the paper, the authors find a common solution to three series of differential equations related to the generating function of the Bernoulli numbers of the second kind and present a recurrence relation, an explicit formula in terms of the Stirling numbers of the first kind, and a determinantal expression for the Bernoulli numbers of the second kind.

• Bulletin of the Korean Mathematical Society
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• v.57 no.5
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• pp.1231-1240
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• 2020

The asymptotic behavior of graded Betti numbers of powers of homogeneous ideals in a polynomial ring over a field has recently been reviewed. We extend quasi-polynomial behavior of graded Betti numbers of powers of homogenous ideals to ℤ-graded algebra over Noetherian local ring. Furthermore our main result treats the Betti table of filtrations which is finite or integral over the Rees algebra.

• Communications of the Korean Mathematical Society
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• v.13 no.1
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• pp.151-158
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• 1998

In this note we derive inequalities of linearly positive quadrant dependent random variables and obtain a strong law of large numbers for linealy positive quardant dependent random variables. Our results imply an extension of Birkel's strong law of large numbers for associated random variables to the linear positive quadrant dependence case.

• Bulletin of the Korean Mathematical Society
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• v.35 no.4
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• pp.709-718
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• 1998

In this paper we obtain strong laws of large numbers for 2-dimensional arrays of random variables which are either pairwise positive quadrant dependent or associated. Our results imply extensions of Etemadi`s strong laws of large numbers for nonnegative random variables to the 2-dimensional case.

• Bulletin of the Korean Mathematical Society
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• v.43 no.3
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• pp.611-617
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• 2006

In this paper we construct q-Genocchi numbers and polynomials. By using these numbers and polynomials, we investigate the q-analogue of alternating sums of powers of consecutive integers due to Euler.

• Bulletin of the Korean Mathematical Society
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• v.38 no.3
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• pp.605-610
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• 2001

It is shown that for each 1 < p < 2 there exist identically distributed uncorrelated random variables $X_n\; with\;E({$\mid$X_1$\mid$}^p)\;<\;{\infty}$, not fulfilling the weak law of large numbers (WLLN). If, however, the random variables are moreover non-negative, the weaker integrability condition $E(X_1\;log\;X_1)\;<\;{\infty}$ already guarantees the strong law of large numbers.

• Communications of the Korean Mathematical Society
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• v.13 no.2
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• pp.385-391
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• 1998

In this note, we study a weak law of large numbers for sequences of exchangeable random variables. As a special case, we have an extension of Kolmogorov's generalization of Khintchine's weak law of large numbers to i.i.d. random variables.

• Journal of Applied Reliability
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• v.14 no.2
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• pp.103-107
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• 2014

An algorithm to get network reliability, where each link has probability of fuzzy number, is proposed. Decomposition method and fuzzy numbers arithmetic are applied to the algorithm. Pivot link is chosen one by one from start node recursively at time of decomposition, and arithmetic of fuzzy complementary numbers is included at the same time. No criteria of pivot link selection and the recursive calculation make the algorithm simple.

• Honam Mathematical Journal
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• v.33 no.2
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• pp.261-270
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• 2011

The purpose of this study is to obtain some relations between q-Genocchi numbers and q-Bernstein polynomials by using fermionic p-adic q-integral on $\mathbb{Z}_p$.