• East Asian mathematical journal
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• 제26권5호
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• pp.655-670
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• 2010

The complete multipartite graph $K_{n(m)}$ with n $ {\geq}$ 4 partite sets of size m is shown to have a decomposition into 4-cycles in such a way that vertices of each cycle belong to distinct partite sets of $K_{n(m)}$, if 4 divides the number of edges. Such cycles are called gregarious, and were introduced by Billington and Hoffman ([2]) and redefined in [3]. We independently came up with the result of [3] by using a difference set method, and improved the result so that the composition is circulant, in the sense that it is invariant under the cyclic permutation of partite sets. The composition is then used to construct gregarious 4-cycle decompositions when one partite set of the graph has different cardinality than that of others. Some results on joins of decomposable complete multipartite graphs are also presented.

• Journal of applied mathematics & informatics
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• 제39권5_6호
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• pp.689-701
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• 2021

The purpose of this paper is to optimize the number of source places required for the unique representation of the destination using the tools of graph theory. A subset S of vertices of a graph G is called a rational resolving set of G if for each pair u, v ∈ V - S, there is a vertex s ∈ S such that d(u/s) ≠ d(v/s), where d(x/s) denotes the mean of the distances from the vertex s to all those y ∈ N[x]. A rational resolving set is called minimal rational resolving set if no proper subset of it is a rational resolving set. In this paper we study varieties of minimal rational resolving sets defined on the basis of its complements and compute the minimum and maximum cardinality of such sets, respectively called as lower and upper rational metric dimensions for power of a path P_n analysing various possibilities.

• 한국문헌정보학회지
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• 제6권
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• pp.87-103
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• 1979

Information storage and retrieval is a part of general communication process. In the Shannon's information theory, information contained in a message is a measure of -uncertainty about information source and the amount of information is measured by entropy. Indexing is a process of reducing entropy of information source since document collection is divided into many smaller groups according to the subjects documents deal with. Significant concepts contained in every document are mapped into the set of all sets of index terms. Thus index itself is formed by paired sets of index terms and documents. Without indexing the entropy of document collection consisting of N documents is $log_2\;N$, whereas the average entropy of smaller groups $(W_1,\;W_2,...W_m)$ is as small $(as\;(\sum\limits^m_{i=1}\;H(W_i))/m$. Retrieval efficiency is a measure of information system's performance, which is largely affected by goodness of index. If all and only documents evaluated relevant to user's query can be retrieved, the information system is said $100\%$ efficient. Document file W may be potentially classified into two sets of relevant documents and non-relevant documents to a specific query. After retrieval, the document file W' is reclassified into four sets of relevant-retrieved, relevant-not retrieved, non-relevant-retrieved and non-relevant-not retrieved. It is shown in the paper that the difference in two entropies of document file Wand document file W' is a proper measure of retrieval efficiency.

• 수산해양기술연구
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• 제35권3호
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• pp.215-226
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• 1999

The experimented rangefinder consist of sets of V/A-Code GPS and sets of L1 C/A-code & carrier phase receivers connected by two spread spectrum radio modems in order to measure relative range and bearing between two ship antennas by real time, comparing and analyzing accuracy of both GPS receivers at the fix point on the land by means of executing zero baseline test by C/A code and by carrier phase as well as measuring distance range 5m, 10m, 15m between each other receivers. The results from the measurement of relative range and bearing are as follows as ;1. According to the results from zero baseline test, the average error by C/A-code receiver is less than 0.1m, which proves theories from published books but when each GPS receivers track different satellites, the range accuracy error becomes up to 100m by means of S/A. Because of this sudden wide range error, rangefinder is not appropriate at relative range measurement without additional modification of the algorism of the GPS receiver itself.2. According to relative range measurement by Carrier Phase and zero baseline test at static condition, the range error is less than 3.5cm in case that it passes more than 5 minutes after GPS sets can track simultaneously more than 6 satellites. Its main reason is understood that the phase center of antenna is bigger than geodetic antenna.3. When range measurement of two receivers from 5m, to 10m to 15m, the each range error is 0.340m, 0.190m, 0.011m and each standard variation is 0.0973m, 0.0884m, 0.0790m. The range error and standard variation are in inverse proportion to distance between two receivers. 4. L1 Carrier Phase GPS generally needs 5 minutes to fix and during this ambiguity search, the relative range and bearing angle is shown to be various.

• Journal of applied mathematics & informatics
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• 제41권2호
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• pp.265-272
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• 2023

This article presents a novel notion of hesitant fuzzy cleanly covered in hesitant fuzzy topological spaces;moreover two strong hesitant fuzzy separation axioms are investigated. Based on fuzzy maximal open sets few properties of hesitant fuzzy cleanly covered are obtained. By dint of hesitant fuzzy minimal open and fuzzy maximal closed sets two strong hesitant fuzzy separation axioms are extended.

• Kyungpook Mathematical Journal
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• 제59권3호
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• pp.363-375
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• 2019

Let G = (V, E) be a simple graph with p vertices and q edges. A subset S of V (G) is called a strong (weak) efficient dominating set of G if for every $v{\in}V(G)$ we have ${\mid}N_s[v]{\cap}S{\mid}=1$ (resp. ${\mid}N_w[v]{\cap}S{\mid}=1$), where $N_s(v)=\{u{\in}V(G):uv{\in}E(G),\;deg(u){\geq}deg(v)\}$. The minimum cardinality of a strong (weak) efficient dominating set of G is called the strong (weak) efficient domination number of G and is denoted by ${\gamma}_{se}(G)$ (${\gamma}_{we}(G)$). A graph G is strong efficient if there exists a strong efficient dominating set of G. In this paper, some cycle and star related Nordhaus-Gaddum type relations on strong efficient dominating sets and the number of strong efficient dominating sets are studied.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제6권3호
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• pp.255-263
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• 2006

In this paper, we introduce the concepts of ${\gamma}$-fuzzy feebly open and ${\gamma}$-fuzzy feebly closed sets in Sostak's fuzzy topological spaces and by using them, we explain the notions of ${\gamma}$-fuzzy F-closed spaces. Also, we give some characterization of ${\gamma}$-fuzzy F-closedness in terms of fuzzy filterbasis and ${\gamma}$-fuzzy feebly-${\theta}$-cluster points.

• Journal of applied mathematics & informatics
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• 제5권1호
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• pp.13-22
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• 1998

Fractals which represent many of the sets in various scien-tific fields as well as in nature is geometrically too complicate. Then we usually use Hausdorff dimension to estimate their geometrical proper-ties. But to explain the fractals from the hausdorff dimension induced by the Euclidan metric are not too sufficient. For example in digi-tal communication while encoding or decoding the fractal images we must consider not only their geometric sizes but also many other fac-tors such as colours densities and energies etc. So in this paper we define the dimension matrix of the sets by redefining the new metric.

• 한국정보처리학회:학술대회논문집
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• 한국정보처리학회 2014년도 추계학술발표대회
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• pp.783-786
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• 2014

맵리듀스(MapReduce)는 대용량의 데이터를 여러 컴퓨터에서 분산, 병렬 처리하는 프레임워크이다. Grouping sets 질의는 사용자가 지정한 여러 개의 group-by들을 모두 구하는 질의로서, 롤업(rollup)과 큐브(cube)가 너무 많은 결과를 반환하는 단점을 보완하여 원하는 group-by들에 대한 결과만 얻을 수 있도록 한다. 본 논문은 맵리듀스 환경에서 grouping sets 질의를 효율적으로 계산하는 방법을 제안한다. 제안 방법은 grouping sets 질의를 2개의 맵리듀스 잡(job)을 통해 단계적으로 계산한다. 첫 번째 맵리듀스 잡은 grouping sets 질의에 포함된 group-by들이 모두 계산될 수 있는 '부모' group-by를 먼저 계산한다. 두 번째 맵리듀스 잡은 부모 group-by를 입력으로 하여 grouping sets 질의에 포함된 group-by들을 각각 계산한다. 부모 group-by의 크기가 입력 데이터의 크기에 비해 매우 작은 경우, 제안 방법은 입력 데이터로부터 각 group-by를 독립적으로 구하는 단순 방법보다 좋은 성능을 보인다. 실험을 통해 제안 방법이 각 group-by를 독립적으로 구하는 단순 방법보다 좋은 성능을 가짐을 보인다.

• 대한수학회지
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• 제50권6호
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• pp.1271-1290
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• 2013

Let M be a fixed left R-module. For a left R-module X, we introduce the notion of M-prime (resp. M-semiprime) submodule of X such that in the case M=R, it coincides with prime (resp. semiprime) submodule of X. Other concepts encountered in the general theory are M-$m$-system sets, M-$n$-system sets, M-prime radical and M-Baer's lower nilradical of modules. Relationships between these concepts and basic properties are established. In particular, we identify certain submodules of M, called "primeM-ideals", that play a role analogous to that of prime (two-sided) ideals in the ring R. Using this definition, we show that if M satisfies condition H (defined later) and $Hom_R(M,X){\neq}0$ for all modules X in the category ${\sigma}[M]$, then there is a one-to-one correspondence between isomorphism classes of indecomposable M-injective modules in ${\sigma}[M]$ and prime M-ideals of M. Also, we investigate the prime M-ideals, M-prime submodules and M-prime radical of Artinian modules.