• The Journal of Korean Institute of Communications and Information Sciences
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• v.28 no.6B
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• pp.523-532
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• 2003

GENMET(GEneralized Multihop Network) which is based on Wavelength-Division Multiplexsing(WDM) and can be used in order to construct the next generation lightwave network is a logical(virtual), packet-switched and multihop topology network. GENMET is a regular multihop network which is a generalization of Shuffle network and do Bruijn network As such, it has the advantage of simple routing which is critical in a high speed network Given a physical topology, different logical topologies can be derived for assigning wavelengths to the UserNodes. By appropriately assigning wavelengths, performance of the network, such as mean hop count, maximum throughput and mean packet delay can be improved. In this paper, we propose heuristic algorithms for effectively assigning a limited number of wavelengths to the given UserNodes. The Performance of proposed algorithm is compared with the random assignment and the lower bounds.

• The Pure and Applied Mathematics
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• v.28 no.3
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• pp.199-215
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• 2021

The purpose of this paper is to define and study some new classes of sets by using nano operation namely, ζ-nano regular open, ζ-nano open, ζ-nano α-open, ζ-nano pre-open, ζ-nano semi-open, ζ-nano b-open and ζ-nano β-open in nano topology. Some properties and the relationships between these sets and the related concepts are investigated. Also, we found the deciding factors for the most common disease fever.

• Communications of the Korean Mathematical Society
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• v.37 no.3
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• pp.905-913
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• 2022

We characterize metrizability and submetrizability for point-open, open-point and bi-point-open topologies on C(X, Y), where C(X, Y) denotes the set of all continuous functions from space X to Y ; X is a completely regular space and Y is a locally convex space.

• Proceedings of the IEEK Conference
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• 2002.07c
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• pp.1371-1374
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• 2002

This paper compares four network con-figurations for using as the logical topology in multi- hop wavelength division multiplexing (WDM) networks. The regular network configurations studied in this paper axe ShuffleNet, de Bruijn graph, hypercube, and Man-hattan street network. Instead of using the weight mean hop distance of node placement problem for comparing optimum logical topology, we introduce a new objective function that includes h and the network cost. It can be seen that the network cost strongly depends on the logical topology selected for the implementation of the network. The objective of this paper is to find an optimum logical topology for WDM networks that gives low as well as low network cost.

• Communications of the Korean Mathematical Society
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• v.25 no.3
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• pp.457-475
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• 2010

In this paper, we have use a fuzzy bitopological space (X, $\tau_1$, $\tau_2$) to create a family $\tau_{ij}^s$ which is a supra fuzzy topology on X. Also, we introduce and study the concepts of r-($\tau_i$, $\tau_j$)-generalized fuzzy regular closed, r-($\tau_i$, $\tau_j$)-generalized fuzzy strongly semi-closed and r-($\tau_i$, $\tau_j$)-generalized fuzzy regular strongly semi-closed sets in fuzzy bitopological space in the sense of $\check{S}$ostak. Also, these classes of fuzzy subsets are applied for constructing several type of fuzzy closed mapping and some type of fuzzy separation axioms called fuzzy binormal, fuzzy mildly binormal and fuzzy almost pairwise normal.

• The Pure and Applied Mathematics
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• v.29 no.1
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• pp.93-102
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• 2022

The impact of programming languages in the research sector has helped lot of researchers to broaden their view and extend their work without any limitation. More importantly, even the complex problems can be solved in no matter of time while converting them into a programming language. This convenience provides upper hand for the researchers as it places them in a comfort zone where they can work without much stress. With this context, we have converted the research problems in Topology into programming language with the help of Python. In this paper, we have developed a Python program to find the weaker form of closed sets namely alpha closed set, semi closed set, pre closed set, beta closed set and regular closed set.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.39 no.6
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• pp.19-25
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• 2002

A regular virtual topology requires little processing time for routing purposes which may be a desirable property for high-speed networks. Asymmetric bilayered ShuffleNet, proposed by us as a virtual topology, can be more efficient to be used to design a wide-area optical network compared to ShuffleNet. In this paper, asymmetric bilayered ShuffleNet is imbedded on a given physical topology with the objective of minimizing the total message delay.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.47 no.2
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• pp.1-10
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• 2010

Mapping virtual process topology to physical processor topology is one of the most important design issues in parallel programming. However, the mapping problem is complicated due to the topology irregularity and routing complexity. This paper proposes a new process mapping scheme called adjacency-based mapping (AM) for irregular cluster systems assuming that the two-dimensional mesh process topology is specified as an interprocess communication pattern. The cluster systems have been studied and developed for many years since they provide high interconnection flexibility, scalability, and expandability which are not attainable in traditional regular networks. The proposed AM tries to map neighboring processes in virtual process topology to adjacent processors in physical processor topology. Simulation study shows that the proposed AM results in better mapping quality and shorter interprocess latency compared to the conventional approaches.

• The Mathematical Education
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• v.12 no.2
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• pp.5-12
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• 1974

단위원을 가지는 하환환에 있어서의 Prime Spectrum에 관하여 다음 세가지 사실을 증명하였다. 1. X를 환 R의 prime spectrum, C(X)를 X에서 정의되는 실연적함수의 환, X를 C(X)의 maximal spectrum이라 하면 X는 C(X)의 prime spectrum의 부분공간으로서의 한 T-space로 된다. N을 환 R의 nilradical이라 하면, R/N이 regula 이면 X와 X는 위상동형이다. 2. f: R$\longrightarrow$R'을 ring homomorphism, P를 R의 한 Prime ideal, $R_{p}$, R'$_{p}$를 각각 S=R-P 및 f(S)에 관한 분수환(ring of fraction)이라 하고, k(P)를 local ring $R_{p}$의 residue' field라 할 때, R'의 prime spectrum의 부분공간인 $f^{*-1}$(P)는 k(P)(equation omitted)$_{R}$R'의 prime spectrum과 위상동형이다. 단 f*는 f*(Q)=$f^{-1}$(Q)로서 정의되는 함수 s*:Spec(R')$\longrightarrow$Spec(R)이다. 3. X를 환 S의 prime spectrum, N을 R의 nilradical이라 할 때, 다음 네가지 사실은 동치이다. (1) R/N 은 regular 이다. (2) X는 Zarski topology에 관하여 Hausdorff 공간이다. (3) X에서의 Zarski topology와 constructible topology와는 일치한다. (4) R의 임의의 원소 f에 대하여 f를 포함하지 않는 R의 prime ideal 전체의 집합 $X_{f}$는 Zarski topology에 관하여 개집합인 동시에 폐집합이다.폐집합이다....

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.41 no.5
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• pp.1-7
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• 2004

A regular logical topology requires little processing time for routing purposes which may be a desirable property for high-speed networks. Asymmetric bilayered ShuffleNet, proposed by us as a logical topology, can be used to a wavelength division multiplexing ring network to increase the network capacity compared to ShuffleNet. In this paper, asymmetric bilayered ShuffleNet is imbedded on a wavelength division multiplexing ring with the objective of minimizing the total number of wavelengths assigned.