• 대한수학회지
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• 제43권5호
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• pp.951-965
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• 2006

In this paper, we study a topological mirror symmetry on noncommutative complex tori. We show that deformation quantization of an elliptic curve is mirror symmetric to an irrational rotation algebra. From this, we conclude that a mirror reflection of a noncommutative complex torus is an elliptic curve equipped with a Kronecker foliation.

• 대한수학회지
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• 제57권5호
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• pp.1135-1165
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• 2020

Polishchuk-Zaslow explained the homological mirror symmetry between Fukaya category of symplectic torus and the derived category of coherent sheaves of elliptic curves via Lagrangian torus fibration. Recently, Cho-Hong-Lau found another proof of homological mirror symmetry using localized mirror functor, whose target category is given by graded matrix factorizations. We find an explicit relation between these two approaches.

• 대한수학회보
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• 제49권6호
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• pp.1199-1211
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• 2012

In this paper we give an introduction to the theory of universal central extensions of perfect Lie algebras. In particular, we will provide a model for the universal coverings of Lie tori and we show that automorphisms and derivations lift to the universal coverings. We also prove that the universal covering of a Lie ${\Lambda}$-torus of type ${\Delta}$ is again a Lie ${\Lambda}$-torus of type ${\Delta}$.

• Kyungpook Mathematical Journal
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• 제57권2호
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• pp.331-360
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• 2017

Unknotting numbers for torus knots and links are well known. In this paper, we present a new approach to determine the position of unknotting number crossing changes in a toric braid such that the closure of the resultant braid is equivalent to the trivial knot or link. Further we give unknotting numbers of more than 600 knots.

• 호남수학학술지
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• 제7권1호
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• pp.119-127
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• 1985

A study is made of a special type of $C^{\ast}$ -dynamical systems, consisting of a class $n^{\infty}$ uniformly hyperfinite $C^{\ast}$-algebra A, the torus group $G=T^{d}$ ($$1{\leq_-}d{\leq_-}n-1$$) and a natural product action of G on A by $^{*}-automorphisms$. We give some conditions for product states on the fixed point algebra $A^{G}$ of A by G to be factorial.

• Journal of applied mathematics & informatics
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• 제19권1_2호
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• pp.57-75
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• 2005

Quasigroups are algebraic structures closely related to Latin squares which have many different applications. There are several classifications of quasigroups based on their algebraic properties. In this paper we propose another classification based on the properties of strings obtained by specific quasigroup transformations. More precisely, in our research we identified some quasigroup transformations which can be applied to arbitrary strings to produce pseudo random sequences. We performed tests for randomness of the obtained pseudo-random sequences by random walks on torus. The randomness tests provided an empirical classification of quasigroups.

• 대한수학회보
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• 제54권5호
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• pp.1719-1724
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• 2017

In this note, companion to the paper [10], we describe an alternative method for finding Laurent polynomials mirror-dual to complete intersections in Grassmannians of planes, in the sense discussed in [10]. This calculation follows a general method for finding torus charts on Hori-Vafa mirrors to complete intersections in toric varieties, detailed in [5] generalising the method of [8].

• 대한수학회보
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• 제37권2호
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• pp.249-254
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• 2000

We give an easy proof of the fact that every noncommutative torus $A_{\omega}$ is stably isomorphic to the noncommutative torus $C(\widehat{S\omega}){\;}\bigotimes{\;}A_p$ which hasa trivial bundle structure. It is well known that stable isomorphism of two separable $C^{*}-algebras$ is equibalent to the existence of eqivalence bimodule between the two stably isomorphic $C^{*}-algebras{\;}A_{\omega}$ and $C(\widehat{S\omega}){\;}\bigotimes{\;}A_p$.

• Journal of applied mathematics & informatics
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• 제23권1_2호
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• pp.329-335
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• 2007

A map is bisingular if each edge is either a loop or an isthmus (i.e., on the boundary of the same face). In this paper we study the number of rooted bisingular maps on the sphere and the torus, and we also present formula for such maps with four parameters: the root-valency, the number of isthmus, the number of planar loops and the number of essential loops.

• 한국정보과학회:학술대회논문집
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• 한국정보과학회 2000년도 가을 학술발표논문집 Vol.27 No.2 (2)
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• pp.9-11
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• 2000

전형적인 단순 유전자 알고리즘은 한 개의 모집단으로 구성되며, 진화 과정이 거듭되면 모집단의 개체들은 한 개의 전역해로 수렴하게 된다. 그러나, 많은 문제들은 여러 개의 최적해를 가질 수 있으며, 그것들 모두를 찾는 것이 중요한 경우가 많다. 이 논문에서는 모집단을 원환체(Torus)로 구성하고 개체에 이웃의 개념을 부여하여 모집단이 최적해 집단으로 수렴하는 유전자 알고리즘의 변형을 연구한다. 제안한 방법은 개체사이에 이웃이라는 개념을 부여함으로써 다수의 해를 동시에 찾는다는 생각을 넘어서 다양한 변형 유전자 알고리즘에 대한 새로운 모델이 될 것으로 기대된다.