• 한국수학교육학회지시리즈D:수학교육연구
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• 제8권2호
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• pp.107-114
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• 2004

University teachers of linear algebra often feel annoyed and disarmed when faced with the inability of their students to cope with concepts that they consider to be very simple. Usually, they lay the blame on the impossibility for the students to use geometrical intuition or the lack of practice in basic logic and set theory. J.-L. Dorier [(2002): Teaching Linear Algebra at University. In: T. Li (Ed.), Proceedings of the International Congress of Mathematicians (Beijing: August 20-28, 2002), Vol. III: Invited Lectures (pp. 875-884). Beijing: Higher Education Press] mentioned that the situation could not be improved substantially with the teaching of Cartesian geometry or/and logic and set theory prior to the linear algebra. In East Asian countries, science-orientated mathematics curricula of the high schools consist of calculus with many other materials. To understand differential and integral calculus efficiently or for other reasons, students have to learn a lot of content (and concepts) in linear algebra, such as ordered pairs, n-tuple numbers, planar and spatial coordinates, vectors, polynomials, matrices, etc., from an early age. The content of linear algebra is spread out from grades 7 to 12. When the high school teachers teach the content of linear algebra, however, they do not concern much about the concepts of content. With small effort, teachers can help the students to build concepts of vocabularies and languages of linear algebra.

• 충청수학회지
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• 제29권4호
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• pp.613-629
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• 2016

In this paper, we introduced the notion of multiplier of Boolean algebras and discuss related properties between multipliers and special mappings, like dual closures, homomorphisms on B. We introduce the notions of xed set $Fix_f(X)$ and normal ideal and obtain interconnection between multipliers and $Fix_f(B)$. Also, we introduce the special multiplier ${\alpha}_p$a nd study some properties. Finally, we show that if B is a Boolean algebra, then the set of all multipliers of B is also a Boolean algebra.

• 대한수학회논문집
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• 제18권1호
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• pp.59-63
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• 2003

Let A be a $C^*$-algebra and $K_{A}$ its Pedersen's ideal. A is called a PCS-algebra if the multiplier $\Gamma(K_{A})\;of\;K_{A}$ is the multiplier M(A) of A. J. Mack [5]characterized PCS-algebras by weak compactness on the spectrum of A. We give a new simple proof of this Mack's result using the concept of semicontinuity and N. C. Phillips' description of $\Gamma(K_{A})$.

• 대한수학회지
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• 제42권6호
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• pp.1111-1120
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• 2005

Hong and Nel in [8] obtained a number of spectral dualities between a cartesian closed topological category X and a category of algebras of suitable type in X in accordance with the original formalism of Porst and Wischnewsky[12]. In this paper, there arises a dual adjointness S $\vdash$ C between the category X = Lim of limit spaces and that A of MV-algebras in X. We firstly show that the spectral duality: $S(A)^{op}{\simeq}C(X^{op})$ holds for the dualizing object K = I = [0,1] or K = 2 = {0, 1}. Secondly, we study a duality between the category of Tychonoff spaces and the category of semi-simple MV-algebras. Furthermore, it is shown that for any $X\;\in\;Lim\;(X\;{\neq}\;{\emptyset})\;C(X,\;I)$ is densely embedded into a cube $I^/H/$, where H is a set.

• 대한전자공학회논문지
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• 제13권6호
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• pp.20-23
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• 1976

본논문에서는 통신회로망의 신뢰도를 계산하는데 부울대수를 이용하는 방법을 제시하였다. 한 회로의 두 접합점사이의 모든 단순통로가 주어지면 병렬연산이라고 명명되는 부울대수산법에 의하여 두 단점사이의 신뢰도가 기호적으로 계산된다. 이 방법은 회로가 방향성이거나 비방향성이거나 다 효과적이다. A boolean algebra method for computing the reliability in a communication network is prosented. Given the set of all simple paths between two nodes in a network, the terminal reliability can be symbolically computed by the Boolean operation which is named parallel operation. The method seems to be promising for both oriented and nonoriented network.

• 대한수학회지
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• 제51권2호
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• pp.427-442
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• 2014

A previous work gave a combinatorial description of the crystal B(${\infty}$), in terms of certain simple Young tableaux referred to as the marginally large tableaux, for finite dimensional simple Lie algebras. Using this result, we present an explicit description of the crystal B(${\lambda}$), in terms of the marginally large tableaux, for the $G_2$ Lie algebra type. We also provide a new description of B(${\lambda}$), in terms of Nakajima monomials, that is in natural correspondence with our tableau description.

• 충청수학회지
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• 제30권4호
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• pp.357-367
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• 2017

In this paper, we introduce the notion of multiplier of AC-algebra and consider the properties of multipliers in AC-algebras. Also, we characterized the fixed set $Fix_d(X)$ by multipliers. Moreover, we prove that M(X), the collection of all multipliers of AC-algebras, form a semigroup under certain binary operation.

• Kyungpook Mathematical Journal
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• 제48권2호
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• pp.223-232
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• 2008

We estimate the real rank of CCR C*-algebras under some assumptions. A applications we determine the real rank of the reduced group C*-algebras of non-compac connected, semi-simple and reductive Lie groups and that of the group C*-algebras of connected nilpotent Lie groups.

• 호남수학학술지
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• 제28권2호
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• pp.197-204
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• 2006

For the evaluation algebra $F[e^{{\pm}{\chi}}]_M$, if M={$\partial$}, the automorphism group $Aut_{non}$($F[e^{{\pm}{\chi}}]_M$) and $Der_{non}$($F[e^{{\pm}{\chi}}]_M$) of the evaluation algebra $F[e^{{\pm}{\chi}}]_M$ are found in the paper [12]. For M={${\partial}^n$}, we find $Aut_{non}$($F[e^{{\pm}{\chi}}]_M$) and $Der_{non}$($F[e^{{\pm}{\chi}}]_M$) of the evaluation algebra $F[e^{{\pm}{\chi}}]_M$ in this paper. We show that a derivation of some non-associative algebra is not inner.

• 호남수학학술지
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• 제41권2호
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• pp.421-433
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• 2019

Let n denote an integer greater than 2 and let c denote a nonzero complex number. In this paper, we introduce a family of elements of the rational Cherednik algebra $H^{sl_n}(c)$ of type $sl_n$, which are analogous to the Dunkl-Cherednik elements of the rational Cherednik algebra $H^{gl_n}(c)$ of type $gl_n$. We also introduce the raising and lowering element of $H^{sl_n}(c)$ which are useful in the representation theory of the algebra $H^{sl_n}(c)$, and provide simple results related to these elements.