• Journal of the Korean Data and Information Science Society
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• 제4권
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• pp.53-63
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• 1993

We consider various types of weak convergence for sums of sign-invariant random variables. Some results show a similarity between independence and sign-invariance. As a special case, we obtain a result which strengthens a weak law proved by Rosalsky and Teicher [6] in that some assumptions are deleted.

• 대한수학회지
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• 제45권4호
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• pp.1101-1111
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• 2008

Under the condition of h-integrability and appropriate conditions on the array of weights, we establish complete convergence and strong law of large numbers for weighted sums of an array of dependent random variables.

• 한국전기전자재료학회:학술대회논문집
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• 한국전기전자재료학회 2009년도 하계학술대회 논문집
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• pp.65-66
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• 2009

This paper describes a procedure developed to fabricate negative photo resist SUMS to a semi-insulating (SI)-GaAs-based substrate. SU-8 is attractive for micromachine multi-layer circuit fabrication, because it is photo-polymerizable resin, leading to safe, and economical processing. This work demonstrates SUMS photo resist can be used for RFIC/MMIC application.

• Journal of applied mathematics & informatics
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• 제34권1_2호
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• pp.145-156
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• 2016

It is known that certain convolution sums can be expressed as a combination of divisor functions and Bernoulli formula. In this article, we consider relationship between fifth-order combinatoric convolution sums of divisor functions and Bernoulli polynomials. As applications of these identities, we give a concrete interpretation in terms of the procedural modeling method.

• Journal of applied mathematics & informatics
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• 제38권1_2호
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• pp.145-157
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• 2020

In this article, we define a generating function of the generalized (p, q)-poly-Bernoulli polynomials with variable a by using the polylogarithm function. From the definition, we derive some properties that is concerned with other numbers and polynomials. Furthermore, we construct a special functions and give some symmetric identities involving the generalized (p, q)-poly-Bernoulli polynomials and power sums of the first integers.

• 한국지능시스템학회논문지
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• 제13권6호
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• pp.754-758
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• 2003

이 논문에서는 서로 독립이고 동일한 분포를 갖는 퍼지 랜덤변수의 합에 대하여 잘 알려진 강한 대수의 법칙을 tight인 퍼지 랜덤변수의 합에 대한 경우로 일반화 하였다.

• 대한수학회논문집
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• 제29권2호
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• pp.351-358
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• 2014

In this paper, under some suitable integrability and smoothness conditions on f, we establish the central limit theorems for $$\sum_{k{\leq}N}k^{-1}f(S_k/{\sigma}\sqrt{k})$$, where $S_k$ is the partial sums of strictly stationary mixing random variables with $EX_1=0$ and ${\sigma}^2=EX^2_1+2\sum_{k=1}^{\infty}EX_1X_{1+k}$. We also establish an almost sure limit behaviors of the above sums.

• Journal of applied mathematics & informatics
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• 제26권3_4호
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• pp.643-652
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• 2008

We construct the sets of Boolean matrix pairs, which are naturally occurred at the extreme cases for the Boolean rank inequalities relative to the sums and difference of two Boolean matrices or compared between their Boolean ranks and their real ranks. For these sets, we consider the linear operators that preserve them. We characterize those linear operators as T(X) = PXQ or $T(X)\;=\;PX^tQ$ with appropriate invertible Boolean matrices P and Q.

• 대한수학회보
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• 제53권3호
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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.

• 대한수학회보
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• 제48권5호
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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.