• 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.

• 호남수학학술지
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• 제30권4호
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• pp.589-602
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• 2008

As a survey-type article, the paper reviews various digital topological utilities from digital covering theory. Digital covering theory has strongly contributed to the calculation of the digital k-fundamental group of both a digital space(a set with k-adjacency or digital k-graph) and a digital product. Furthermore, it has been used in classifying digital spaces, establishing almost Van Kampen theory which is the digital version of van Kampen theorem in algebrate topology, developing the generalized universal covering property, and so forth. Finally, we remark on the digital k-surface structure of a Cartesian product of two simple closed $k_i$-curves in ${\mathbf{Z}}^n$, $i{\in}{1,2}$.

• 대한수학회보
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• 제59권6호
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• pp.1387-1408
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• 2022

Let R be a commutative ring with a non-zero identity, S be a multiplicatively closed subset of R and M be a unital R-module. In this paper, we define a submodule N of M with (N :_R M)∩S = ∅ to be weakly S-prime if there exists s ∈ S such that whenever a ∈ R and m ∈ M with 0 ≠ am ∈ N, then either sa ∈ (N :_R M) or sm ∈ N. Many properties, examples and characterizations of weakly S-prime submodules are introduced, especially in multiplication modules. Moreover, we investigate the behavior of this structure under module homomorphisms, localizations, quotient modules, cartesian product and idealizations. Finally, we define two kinds of submodules of the amalgamation module along an ideal and investigate conditions under which they are weakly S-prime.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 2003년도 춘계 학술대회 학술발표 논문집
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• pp.33-36
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• 2003

We introduce the subcategory IRel$\_$R/ (H) of IRel (H) consisting of intuitionistic H-fuzzy reflexive relational spaces on sets and we study structures of IRel$\_$R/ (H) in a viewpoint of the topological universe introduce by L.D.Nel. We show that IRel$\_$R/ (H) is a topological universe over Set. Moreover, we show that exponential objects in IRel$\_$R/ (H) are quite different from those in IRel (H) constructed in [7].

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 2003년도 춘계 학술대회 학술발표 논문집
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• pp.29-32
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• 2003

We introduce the subcategories IRe $l_{PR}$ (H), IRe $l_{PO}$ (H) and IRe $l_{E}$(H) of IRe $l_{R}$(H) and study their structures in a viewpoint of the topological universe introduced by L.D.Nel. In particular, the category IRe $l_{R}$(H)(resp. IRe $l_{P}$(H) and IRe $l_{E}$(H)) is a topological universe eve, Set. Moreover, we show that IRe $l_{E}$(H) has exponential objects.ial objects.

• 호남수학학술지
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• 제37권1호
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• pp.135-147
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• 2015

Owing to the notion of a normal adjacency for a digital product in [8], the study of product properties of digital topological properties has been substantially done. To explain a normal adjacency of a digital product more efficiently, the recent paper [22] proposed an S-compatible adjacency of a digital product. Using an S-compatible adjacency of a digital product, we also study product properties of digital topological properties, which improves the presentations of a normal adjacency of a digital product in [8]. Besides, the paper [16] studied the product property of two digital covering maps in terms of the $L_S$- and the $L_C$-property of a digital product which plays an important role in studying digital covering and digital homotopy theory. Further, by using HS- and HC-properties of digital products, the paper [18] studied multiplicative properties of a digital fundamental group. The present paper compares among several kinds of adjacency relations for digital products and proposes their own merits and further, deals with the problem: consider a Cartesian product of two simple closed $k_i$-curves with $l_i$ elements in $Z^{n_i}$, $i{\in}\{1,2\}$ denoted by $SC^{n_1,l_1}_{k_1}{\times}SC^{n_2,l_2}_{k_2}$. Since a normal adjacency for this product and the $L_C$-property are different from each other, the present paper address the problem: for the digital product does it have both a normal k-adjacency of $Z^{n_1+n_2}$ and another adjacency satisfying the $L_C$-property? This research plays an important role in studying product properties of digital topological properties.

• 대한기계학회논문집A
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• 제29권4호
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• pp.534-539
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• 2005

Nodal displacements are referred to the initial configuration in the total Lagrangian formulation and to the last converged configuration in the updated Lagrangian furmulation. This research proposes a relative nodal displacement method to represent the position and orientation for a node in truss structures. Since the proposed method measures the relative nodal displacements relative to its adjacent nodal reference frame, they are still small for a truss structure undergoing large deformations for the small size elements. As a consequence, element formulations developed under the small deformation assumption are still valid for structures undergoing large deformations, which significantly simplifies the equations of equilibrium. A structural system is represented by a graph to systematically develop the governing equations of equilibrium for general systems. A node and an element are represented by a node and an edge in graph representation, respectively. Closed loops are opened to form a spanning tree by cutting edges. Two computational sequences are defined in the graph representation. One is the forward path sequence that is used to recover the Cartesian nodal displacements from relative nodal displacement sand traverses a graph from the base node towards the terminal nodes. The other is the backward path sequence that is used to recover the nodal forces in the relative coordinate system from the known nodal forces in the absolute coordinate system and traverses from the terminal nodes towards the base node. One open loop and one closed loop structure undergoing large deformations are analyzed to demonstrate the efficiency and validity of the proposed method.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2005년도 추계학술대회논문집
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• pp.788-791
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• 2005

Nodal displacements are referred to the Initial configuration in the total Lagrangian formulation and to the last converged configuration in the updated Lagrangian formulation. This research proposes a relative nodal displacement method to represent the position and orientation for a node in truss structures. Since the proposed method measures the relative nodal displacements relative to its adjacent nodal reference frame, they are still small for a truss structure undergoing large deformations for the small size elements. As a consequence, element formulations developed under the small deformation assumption are still valid fer structures undergoing large deformations, which significantly simplifies the equations of equilibrium. A structural system is represented by a graph to systematically develop the governing equations of equilibrium for general systems. A node and an element are represented by a node and an edge in graph representation, respectively. Closed loops are opened to form a spanning tree by cutting edges. Two computational sequences are defined in the graph representation. One is the forward path sequence that is used to recover the Cartesian nodal displacements from relative nodal displacements and traverses a graph from the base node towards the terminal nodes. The other is the backward path sequence that is used to recover the nodal forces in the relative coordinate system from the known nodal forces in the absolute coordinate system and traverses from the terminal nodes towards the base node. One closed loop structure undergoing large deformations is analyzed to demonstrate the efficiency and validity of the proposed method.

• 지구물리와물리탐사
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• 제25권1호
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• pp.38-43
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• 2022

화산의 화도나 불발탄과 같이 축 대칭을 갖지만 단면의 반지름이 변하는 경우 대칭축에 수직인 얇은 원판들의 반응을 더하여 모델링하는 것이 효율적이다. 이런 모양의 이상체에 대한 자력 및 자력 변화율 텐서 모델링을 위해서는 얇은 원판에 대한 해석해가 필수적이다. 따라서 이 논문에서는 원판형 이상체에 대한 벡터 자력과 자력 변화율 텐서 반응식을 유도하였다. 벡터 자력은 중력 변화율 텐서를 자력으로 변환하는 포아송 관계식을 이용하여 원판형 이상체의 기존 중력 변화율 텐서로부터 유도하였다. 자력 변화율 텐서는 직교 좌표계의 미분 관계식을 원통 좌표계로 미분 관계식으로 변환한 후 벡터 자력을 미분하여 유도하였다. 벡터 자력과 자력 변화율 텐서는 원판형 이상체의 축 대칭성을 이용한 립쉬츠-한켈(Lipschitz-Hankel) 적분을 기반으로 구하였다.

• 지구물리와물리탐사
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• 제25권2호
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• pp.85-92
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• 2022

한쪽 방향으로 연장된 이상체를 멀리 떨어져서 관측하면 선형 이상체로 근사가 가능하다. 이런 경우 자력 및 자력 변화율 텐서를 적용하기 위해서는 선형 이상체에 대한 해석해가 필요하다. 따라서 이 논문에서는 선형 이상체에 대한 자력과 자력 변화율 텐서 반응식을 유도하였다. 벡터 자력은 기존에 유도한 선형 이상체에 대한 중력 변화율 텐서를 포아송 관계식을 이용하여 벡터 자력으로 변환하여 유도하였다. 자력 변화율 텐서는 벡터 자력를 기준 직교 좌표계의 성분으로 한번 더 미분하여 유도하였다. 시추공에서 얻은 총자력 탐사 자료를 가정하고, 선형 이상체의 길이, 방향, 자력 모멘트를 비선형 역산 방법으로 추정하는 사례를 보여주었다.