• 한국수학교육학회지시리즈D:수학교육연구
• /
• 제9권2호
• /
• pp.153-173
• /
• 2005

Recently Bianshi problems, math isomorphic problems by changing the conditions, conclusions or deduction process of the three components of the example problem, are consistently identified as an important element in Chinese math education, characteristics in Chinese math education culture and form a hot point in China, 5 main factors related to reasons why is regarded as CULTURE characteristics in Chinese math education are discussed: (a) Exam goal (b) the curriculum objectives (c) traditional mode and conception, (d) Chinese situation, (e) Chinese math tradition.

• Kyungpook Mathematical Journal
• /
• 제45권4호
• /
• pp.481-489
• /
• 2005

We first show that any complete MV-algebra whose Boolean subalgebra of idempotent elements is atomic, called a complete MV-algebra with atomic center, is isomorphic to a product of unit interval MV-algebra 1's and finite linearly ordered MV-algebras of A(m)-type $(m{\in}{\mathbb{Z}}^+)$. Secondly, for a semi-simple MV-algebra A, we introduce a completion ${\delta}(A)$ of A which is a complete, MV-algebra with atomic center. Under their intrinsic topologies $(see\;{\S}3)$ A is densely embedded into ${\delta}(A)$. Moreover, ${\delta}(A)$ has the extension universal property so that complete MV-algebras with atomic centers are epireflective in semi-simple MV-algebras

• Kyungpook Mathematical Journal
• /
• 제45권4호
• /
• pp.561-570
• /
• 2005

Weak Crossed Product Algebras correspond to certain graphs called lower subtractive graphs. The properties of such algebras can be obtained by studying this kind of graphs ([4], [5]). In [1], the author showed that a weak crossed product is Frobenius and its restricted subalgebra is symmetric if and only if its associated graph has a unique maximal vertex. A special construction of these graphs came naturally and was known as standard lower subtractive graph. It was a deep question that when such a special graph possesses unique maximal vertex? This work is to answer the question partially and to give a particular characterization for such graphs at which the corresponding algebras are isomorphic. A graph that follows the mentioned characterization is called flexible. Flexibility is to some extend a generalization of the so-called Coxeter groups and its weak Bruhat ordering.

• 한국수학사학회지
• /
• 제18권4호
• /
• pp.113-124
• /
• 2005

티코노프공간 X에 대하여 C(X)와 $C^*(X)$는 Riesz-공간이다 C(X)가 순서-코시완비일 필요충분한조건은 X가 quasi-F 공간이고, X가 컴팩트공간이며 QF(X)가 X의 극소 quasi-F cover일 때, C(X)의 순서-코시완비화와 C(QF(X))는 동형이다. 본 논문에서는 quasi-F 공간의 정의와 극소 quasi-F cover의 구성에 관한 동기 및 역사적 배경을 살펴본다.

• 대한수학회보
• /
• 제37권1호
• /
• pp.181-189
• /
• 2000

Let (X, J) be a closed, connected almost complex four-manifold. Let $X_1$ be the complement of an open disc in X and let ${\varepsilon}_1$be the contact structure on the boundary ${\varepsilon}X_1$ which is compatible with a symplectic structure on $X_1$, Then we show that (X, J) is symplectic if and only if the contact structure ${\varepsilon}_1$ on ${\varepsilon}X_1$ is isomorphic to the standard contact structure on the 3-sphere $S^3$ and ${\varepsilon}X_1$is J-concave. Also we show that there is a contact structure ${\varepsilon}_0\ on\ S^2\times\ S^1$which is not strongly symplectically fillable but symplectically fillable, and that $(S^2{\times}S^1,\;{\varepsilon})$ has infinitely many non-diffeomorphic minimal fillings whose restrictions on$\S^2\times\ S^1$are ${\sigma}$ where ${\sigma}$ is the restriction of the standard symplectic structure on $S^2{\times}D^2$.

• 대한수학회논문집
• /
• 제19권4호
• /
• pp.715-720
• /
• 2004

Suppose X is a closed subspace of Z = ${({{\Sigma}^{\infty}}_{n=1}Z_{n})}_{p}$ (1 < p < ${\infty}$, dim $Z_{n}$ < ${\infty}$). We investigate an isometrically isomorphic embedding of L(X)/K(X) into L(X, Z)/K(X, Z), where L(X, Z) (resp. L(X)) is the space of the bounded linear operators from X to Z (resp. from X to X) and K(X, Z) (resp. K(X)) is the space of the compact linear operators from X to Z (resp. from X to X).

• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 2001년도 ICCAS
• /
• pp.29.1-29
• /
• 2001

Neuro-fuzzy systems are multi-layered connectionist networks that realize the elements and functions of traditional fuzzy logic control/decision systems. A trained neuro-fuzzy system is isomorphic to a fuzzy logic system, and fuzzy IF-THEN rule knowledge can be explicitly extracted from the network. This talk presents a brief introduction to self-adaptive neuro-fuzzy systems and addresses some recent research results and applications. Most of the existing neuro-fuzzy systems exhibit several major drawbacks that lead to performance degradation. These drawbacks are the curse of dimensionality (i.e., fuzzy rule explosion), inability to re-structure their internal nodes in a changing environment, and their lack of ability to extract knowledge from a given set of training data. This talk focuses on our investigation of network architectures, self-adaptation algorithms, and efficient learning algorithms that will enable existing neuro-fuzzy systems to self-adapt themselves in an unstructured and uncertain environment.

• 충청수학회지
• /
• 제32권1호
• /
• pp.15-21
• /
• 2019

Let X be a reduced closed subscheme in ${\mathbb{P}}^n$ and $${\pi}_q:X{\rightarrow}Y={\pi}_q(X){\subset}{\mathbb{P}}^{n-1}$$ be an isomorphic projection from the center $q{\in}{\mathbb{P}}^n{\backslash}X$. Suppose that the minimal free presentation of $I_X$ is of the following form $$R(-3)^{{\beta}2,1}{\oplus}R(-4){\rightarrow}R(-2)^{{\beta}1,1}{\rightarrow}I_X{\rightarrow}0$$. In this paper, we prove that $H^1(I_X(k))=H^1(I_Y(k))$ for all $k{\geq}3$. This implies that Y is k-normal if and only if X is k-normal for $k{\geq}3$. Moreover, we also prove that reg(Y) ${\leq}$ max{reg(X), 4} and that $I_Y$ is generated by homogeneous polynomials of degree ${\leq}4$.

• 대한수학회지
• /
• 제56권5호
• /
• pp.1285-1307
• /
• 2019

For a multiplication R-module M we consider the Zariski topology in the set Spec (M) of prime submodules of M. We investigate the relationship between the algebraic properties of the submodules of M and the topological properties of some subspaces of Spec (M). We also consider some topological aspects of certain frames. We prove that if R is a commutative ring and M is a multiplication R-module, then the lattice Semp (M/N) of semiprime submodules of M/N is a spatial frame for every submodule N of M. When M is a quasi projective module, we obtain that the interval ${\uparrow}(N)^{Semp}(M)=\{P{\in}Semp(M){\mid}N{\subseteq}P\}$ and the lattice Semp (M/N) are isomorphic as frames. Finally, we obtain results about quantales and the classical Krull dimension of M.

• Korean Journal of Mathematics
• /
• 제27권2호
• /
• pp.465-474
• /
• 2019

Let ${\mathbb{Z}}$ be the ring of integers and ${\mathbb{Z}}[X]$ (resp., $h({\mathbb{Z}})$) be the ring of polynomials (resp., Hurwitz polynomials) over ${\mathbb{Z}}$. In this paper, we study the irreducibility of Hurwitz polynomials in $h({\mathbb{Z}})$. We give a sufficient condition for Hurwitz polynomials in $h({\mathbb{Z}})$ to be irreducible, and we then show that $h({\mathbb{Z}})$ is not isomorphic to ${\mathbb{Z}}[X]$. By using a relation between usual polynomials in ${\mathbb{Z}}[X]$ and Hurwitz polynomials in $h({\mathbb{Z}})$, we give a necessary and sufficient condition for Hurwitz polynomials over ${\mathbb{Z}}$ to be irreducible under additional conditions on the coefficients of Hurwitz polynomials.