• 한국수학사학회지
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• 제33권1호
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• pp.1-19
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• 2020

Under 2009 Revised Mathematics Curriculum and 2015 Revised Mathematics Curriculum, mathematics teachers can help students inductively express real life problems related to sequences but have difficulties in dealing with problems asking the general terms of the sequences defined inductively due to 'Guidelines for Teaching and Learning'. Because most of textbooks mainly deal with the simple calculation for the sums of sequences, students tend to follow them rather than developing their inductive and deductive reasoning through finding patterns in the sequences. In this study, we reconstruct 8 problems to find the sums of sequences in MukSaJipSanBup which is known as one of the oldest mathematics book of Chosun Dynasty, using the terminology and symbols of the current curriculum. Such kind of problems can be given in textbooks and used for teaching and learning. Using problems in mathematical books of Chosun Dynasty with suitable modifications for teaching and learning is a good method which not only help students feel the usefulness of mathematics but also learn the cultural value of our traditional mathematics and have the pride for it.

• 한국수학사학회지
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• 제20권3호
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• pp.1-16
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• 2007

이상혁(李尙爀)(익산(翼算))의 퇴타술중 삼각타, 사각타 계열에 관한 부분을 조사하고, 익산(翼算)의 결과를 부분합 복수열의 성질로 재해석한다. 유한생성 부분합 복수열의 개념을 도입하고 삼각타, 사각타 계열에 의한 부분합 복수열이 유한생성 부분합 복수열임을 보인다. 단위 부분합 복수열이 부분합 복수열의 연구에 핵심적 역할을 함을 보인다. 또한, 부분합 복수열이 유한생성이 되기 위한 필요충분조건을 구한다. 그리고, 교초적에 대한 곱셈법칙에 대응하는 삼각타적, 삼각낙일적(三角落一積)에 대한 곱셈법칙을 구한다.

• 충청수학회지
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• 제21권2호
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• pp.223-230
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• 2008

In this paper, we present an upper bound of the reciprocal sums of generalized subset-sum-distinct sequences with respect to the first terms of the sequences. And we show the suggested upper bound is best possible. This is a kind of generalization of [1] which contains similar result for classical subset-sum-distinct sequences.

• Kyungpook Mathematical Journal
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• 제50권3호
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• pp.433-445
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• 2010

Although, interesting properties on the partial sums of analytic univalent functions have been investigated extensively by several researchers, yet analogous results on partial sums of harmonic univalent functions have not been so far explored. The main purpose of the present paper is to establish some new and interesting results on the ratio of starlike harmonic univalent function to its sequences of partial sums.

• Communications for Statistical Applications and Methods
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• 제19권2호
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• pp.247-256
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• 2012

In this paper we prove the complete convergence for weighted sums of pairwise negatively quadrant dependent random variables. Some results on identically distributed and negatively associated setting of Liang and Su (1999) are generalized and extended to the pairwise negative quadrant dependence case.

• East Asian mathematical journal
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• 제30권1호
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• pp.31-50
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• 2014

In this paper we establish limsup results and a generalized uniform law of the iterated logarithm (LIL) for the increments of partial sums of strictly stationary and linearly positive quadrant dependent (LPQD) or linearly negative quadrant dependent (LNQD) random sequences.

• 충청수학회지
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• 제36권2호
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• pp.65-76
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• 2023

With the Stirling matrix S of the second kind and the Pascal matrix T, we study recurrence rules and sequences of certain sums over the matrix ST^k. We find a matrix E satisfying ST = ES and interrelations of S and the Stirling matrix of the first kind.

• 대한수학회논문집
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• 제16권2호
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• pp.291-296
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• 2001

For randomly indexed sums of the form (Equation. See Full-text), where {X(sub)ni, i$\geq$1, n$\geq$1} are random variables, {N(sub)n, n$\geq$1} are suitable conditional expectations and {b(sub)n, n$\geq$1} are positive constants, we establish a general weak law of large numbers. Our result improves that of Hong [3].

• 대한수학회논문집
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• 제33권2호
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• pp.535-547
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• 2018

In the present investigation our main aim is to give lower bounds for the ratio of some normalized q-Bessel functions and their sequences of partial sums. Especially, we consider Jackson's second and third q-Bessel functions and we apply one normalization for each of them.

• Korean Journal of Mathematics
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• 제30권3호
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• pp.433-442
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• 2022

Let N^(q) be an arithmetic table of a negative exponent polynomial with q-commuting variables. We study sequential properties of diagonal sums of N^(q). We first device a q-coefficient table $\hat{N}$ of N^(q), find sequences of diagonal sums over $\hat{N}$, and then retrieve the findings of $\hat{N}$ to N^(q). We also explore recurrence rules of s-slope diagonal sums of N^(q) with various s and q.