• 대한수학회지
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• 제49권3호
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• pp.537-547
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• 2012

In this paper, we define a $p$, $q$-difference operator and obtain an explicit formula which is used to express the $p$, $q$-analogue of the unified generalization of Stirling numbers and its exponential generating function in terms of the $p$, $q$-difference operator. Explicit formulas for the non-central $q$-Stirling numbers of the second kind and non-central $q$-Lah numbers are derived using the new $q$-analogue of Newton's interpolation formula. Moreover, a $p$, $q$-analogue of Newton's interpolation formula is established.

• 한국수학사학회지
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• 제27권2호
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• pp.127-138
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• 2014

In this paper we investigate how Newton discovered the generalized binomial theorem. Newton's binomial theorem, or binomial series can be found in Calculus text books as a special case of Taylor series. It can also be understood as a formal power series which was first conceived by Euler if convergence does not matter much. Discovered before Taylor or Euler, Newton's binomial theorem must have a good explanation of its birth and validity. Newton learned the interpolation method from Wallis' famous book ${\ll}$Arithmetica Infinitorum${\gg}$ and employed it to get the theorem. The interpolation method, which Wallis devised to find the areas under a family of curves, was by nature arithmetrical but not geometrical. Newton himself used the method as a way of finding areas under curves. He noticed certain patterns hidden in the integer binomial sequence appeared in relation with curves and then applied them to rationals, finally obtained the generalized binomial sequence and the generalized binomial theorem.

• Kyungpook Mathematical Journal
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• 제34권2호
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• pp.207-216
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• 1994

• Journal of the Korean Data and Information Science Society
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• 제16권1호
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• pp.127-136
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• 2005

We will derive some results on the perturbation of roots using Newton's interpolation formula. And we also compare our results with those obtained by Ostrowski by giving some numerical experiments with Wilkinson's polynomials.

• 대한수학회지
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• 제32권1호
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• pp.61-76
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• 1995

Much research has been done to estimate the magnitudes of the changes of the roots from the perturbed polynomials. For more information and references on such work, see [2, 4, 5, 10, 17].

• 대한수학회논문집
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• 제17권3호
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• pp.423-430
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• 2002

The object of this Paper is to Present a q-analogue of the Newton's forward-difference interpolation formula. We relate the q-beta function and the q-gamma function by the q-difference operators.

• 한국통신학회논문지
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• 제19권6호
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• pp.1016-1026
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• 1994

본 논문에서 분산 시스템의 각 노드들은 노드들간에 주기적으로 교환되는 시스템 상태 정보를 히스토리에 저장하고, 그 히스토리 정보에 Newton의 후향 보간법의 5차 보간 다항식을 사용하여 다음 주기의 예측 부하 지수(ELI)를 계산한다. 계산되어진 ELI를 동적 부하 균등화 시스템의 로케이션 정책에 이용하였다. 그 결과 ELI 기반 동적 부하 균등화 시스템은 기존의 부하 균등화 알고리즘에 비해 성능이 우수함을 시뮬레이션을 통하여 알 수 있었다.