• 충청수학회지
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• 제3권1호
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• pp.49-56
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• 1990

We do an attempt to solve the Zeeman's tolerance stability conjecture and Takens' conjecture using the concepts of chains.

• 대한수학회보
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• 제59권2호
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• pp.345-350
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• 2022

In this work, we confirm a weak version of a conjecture proposed by Hong Wang. The ideal of the work comes from the tree packing conjecture made by Gyárfás and Lehel. Bollobás confirms the tree packing conjecture for many small tree, who showed that one can pack T₁, T₂, …, $T_{n/\sqrt{2}}$ into Kn and that a better bound would follow from a famous conjecture of Erdős. In a similar direction, Hobbs, Bourgeois and Kasiraj made the following conjecture: Any sequence of trees T₁, T₂, …, T_n, with T_i having order i, can be packed into K_n-1,[n/2]. Further Hobbs, Bourgeois and Kasiraj [3] proved that any two trees can be packed into a complete bipartite graph K_n-1,[n/2]. Motivated by the result, Hong Wang propose the conjecture: For each k-partite tree T(𝕏) of order n, there is a restrained packing of two copies of T(𝕏) into a complete k-partite graph B_n+m(𝕐), where $m={\lfloor}{\frac{k}{2}}{\rfloor}$. Hong Wong [4] confirmed this conjecture for k = 2. In this paper, we prove a weak version of this conjecture.

• 대한수학회지
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• 제54권6호
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• pp.1841-1851
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• 2017

Motivated by the Bloch-Beilinson conjectures, Voisin has made a conjecture concerning zero-cycles on self-products of Calabi-Yau varieties. We reformulate Voisin's conjecture in the setting of $hyperk{\ddot{a}}hler$ varieties, and we prove this reformulated conjecture for one family of $hyperk{\ddot{a}}hler$ fourfolds.

• 충청수학회지
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• 제20권1호
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• pp.31-35
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• 2007

In dealing with transformation group, topological approach is very natural. But, it is not sufficient to investigate geometric properties of transformation group and we need geometric method. Frankel-McDuff Conjecture is very interesting in the point that it shows struggling between topological method and geometric method. In this paper, the author suggest generalized Frankel-McDuff conjecture as a topological version of the conjecture and construct a counterexample for the generalized version, and from this we assert that topological method does not work for Frankel-McDuff Conjecture.

• Kyungpook Mathematical Journal
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• 제49권2호
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• pp.355-387
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• 2009

Functoriality conjecture is one of the central and influential subjects of the present day mathematics. Functoriality is the profound lifting problem formulated by Robert Langlands in the late 1960s in order to establish nonabelian class field theory. In this expository article, I describe the Langlands-Shahidi method, the local and global Langlands conjectures and the converse theorems which are powerful tools for the establishment of functoriality of some important cases, and survey the interesting results related to functoriality conjecture.

• Kyungpook Mathematical Journal
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• 제60권4호
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• pp.797-803
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• 2020

The Brück conjecture is still open for an entire function f with hyper order of no less than 1/2, which is not an integer. In this paper, it is proved that the hyper order of solutions of a linear complex differential equation that is related to the Brüuck Conjecture is infinite. The results show that the conjecture holds in a special case when the hyper order of f is 1/2.

• 한국수학사학회지
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• 제17권3호
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• pp.13-22
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• 2004

이 논문에서는 두 추측, 사실로 판명된 비버바흐 추측과 올지 않다고 판명된 루퀴켕 추측을 다루었다. 두 추측을 역사적으로 고찰하고 흥미로운 결과를 소개한다. 이들로부터 수학의 심오한 이론은 연속되는 추측의 결과임을 발견한다.

• 대한수학회보
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• 제55권3호
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• pp.699-715
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• 2018

In this paper, we show a proof of Gordon's Conjecture by using Qiu's labels and two new labels.

• Korean Journal of Mathematics
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• 제27권3호
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• pp.657-660
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• 2019

We give necessary and sufficient condition for the Greenberg's generalized conjecture conjecture on certain imaginary quadratic fields.

• 대한수학회보
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• 제48권5호
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• pp.951-957
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• 2011

In 1996, Br$\ddot{u}$ck studied the relation between f and f' if an entire function f shares one value a CM with its first derivative f' and posed the famous Br$\ddot{u}$ck conjecture. In this work, we generalize the value a in the Br$\ddot{u}$ck conjecture to a small function ${\alpha}$. Meanwhile, we prove that the Br$\ddot{u}$ck conjecture holds for a class of meromorphic functions.