• East Asian mathematical journal
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• 제15권2호
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• pp.201-210
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• 1999

Morley provided an interesting identity about 20 years earlier before its more generalized form was given by Dixon. In this note some of its generalized forms and an application of Morley's formula are considered.

• 대한수학회보
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• 제58권2호
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• pp.315-326
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• 2021

Korobov type polynomials are introduced and extensively investigated many mathematicians ([1, 8-10, 12-14]). In this work, we define unified Apostol Korobov type polynomials and give some recurrences relations for these polynomials. Further, we consider the q-poly Korobov polynomials and the q-poly-Korobov type Changhee polynomials. We give some explicit relations and identities above mentioned functions.

• 대한수학회보
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• 제31권2호
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• pp.237-242
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• 1994

One of the most well-known geometric lattices is a partition lattice. Every upper interval of a partition lattice is a partition lattice. The whitney numbers of a partition lattices are the Stirling numbers, and the characteristic polynomial is a falling factorial. The set of partitions with a single non-trivial block containing a fixed element is a Boolean sublattice of modular elements, so the partition lattice is supersolvable in the sense of Stanley [6]. In this paper, we rephrase four results due to Heller[1] and Murty [4] in terms of matroids and give several characterizations of partition lattices. Our notation and terminology follow those in [8,9]. To clarify our terminology, let G, be a finte geometric lattice. If S is the set of points (or rank-one flats) in G, the lattice structure of G induces the structure of a (combinatorial) geometry, also denoted by G, on S. The size vertical bar G vertical bar of the geometry G is the number of points in G. Let T be subset of S. The deletion of T from G is the geometry on the point set S/T obtained by restricting G to the subset S/T. The contraction G/T of G by T is the geometry induced by the geometric lattice [cl(T), over ^1] on the set S' of all flats in G covering cl(T). (Here, cl(T) is the closure of T, and over ^ 1 is the maximum of the lattice G.) Thus, by definition, the contraction of a geometry is always a geometry. A geometry which can be obtained from G by deletions and contractions is called a minor of G.

• 대한수학회논문집
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• 제16권2호
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• pp.319-332
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• 2001

The main object of this paper is first to give tow contiguous analogues of a well-known hypergeometric summation formula for $_2$F$_1$(1/2). We then apply each of these analogues with a view to evaluating the sums of several classes of series in terms of Psi(or Digamma) and the Zeta functions. Relevant connections of the series identities presented here with those given elsewhere are also pointed out.

• Korean Journal of Mathematics
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• 제32권2호
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• pp.285-295
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• 2024

In this work, we consider the function $${\Psi}(z)=\frac{z}{\ln(1+z)}=1+\sum\limits_{n=1}^{\infty}\,G_nz^n$$ whose coefficients G_n are the Gregory coefficients related to Stirling numbers of the first kind and introduce a new subclass ${\mathcal{G}}^{{\lambda},{\mu}}_{\Sigma}(\Psi)$ of analytic bi-univalent functions subordinate to the function Ψ. For functions belong to this class, we investigate the estimates for the general Taylor-Maclaurin coefficients by using the Faber polynomial expansions. In certain cases, our estimates improve some of those existing coefficient bounds.

• 한국어류학회지
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• 제11권2호
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• pp.134-138
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• 1999

피부흡충인 Entobdella hippoglossi가 숙주인 Atlantic halibut의 피부에 기생할 때 기생 부위별 밀도와 숙주의 피부 점액세포 밀도를 조사하여 E. hippoglossi의 기생이 피부점액 세포의 밀도와 관계가 있는가를 조사하였다. 숙주인 Atlantic halibut 복측과 배측에 기생하는 E. hippoglossi의 밀도는 비슷하였으나 기생충의 크기는 복측이 배측보다 더 컸으며, 배측내에서는 배측의 머리부분에 기생하는 E. hippoglossi의 밀도가 배측의 중앙부나 꼬리부분에서보다 높았다. 숙주의 점액세포 크기, 밀도 그리고 표피 점액층의 두께는 대체로 기생충의 밀도와 비례하였고, 숙주내에서 기생충의 선택적 기생은 점액세포의 밀도와 관계가 있었다.