• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.2001-2011
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• 2013

Cho and Kim [4] have introduced the concept of the competition index of a digraph. Similarly, the competition index of an $n{\times}n$ Boolean matrix A is the smallest positive integer q such that $A^{q+i}(A^T)^{q+i}=A^{q+r+i}(A^T)^{q+r+i}$ for some positive integer r and every nonnegative integer i, where $A^T$ denotes the transpose of A. In this paper, we study the upper bound of the competition index of a Boolean matrix. Using the concept of Boolean rank, we determine the upper bound of the competition index of a nearly reducible Boolean matrix.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.569-573
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• 2006

Nagata and Higman proved that any nil-algebra of finite nilindex is nilpotent of finite index. The Nagata-Higman Theorem can be formulated in terms of T-ideals. TheT-ideal generated by $a^n$ for all $a{\in}A$ is also generated by the symmetric polynomials. The symmetric polynomials play an importmant role in analyzing nil-algebra. We construct the incidence matrix with the symmetric polynomials. Using this incidence matrix, we determine the nilpotency index of nil-algebra of nil-index 3.

• Bulletin of the Korean Chemical Society
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• v.35 no.5
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• pp.1413-1416
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• 2014

A novel topological index (TG Index) has been introduced. The graphical matrix representation of the TG index includes the use of directed subgraphs for the first time in graph theory literature. The application of the TG index on certain properties of polyenes yielded very well correlation data.

• The Korean Journal of Applied Statistics
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• v.27 no.1
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• pp.103-114
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• 2014

Significant research has been devoted to the consistency index of the Analytic Hierarchy Process(AHP) from several perspectives. Critics of the consistency index in AHP state that the critical value of consistency index depends on an average of the random index based simulation study using a 9 scale comparison matrix. We found that the distribution of the consistency index followed the skew distribution according to the dimension of the comparison matrix based on a simulation study with a 9 scale comparison matrix. From the simulation study, we suggest a consistency index quantile table to assist the decision-making process in AHP; in addition, we can approximate the distribution of the consistency index to the gamma distribution under the limited assumptions.

• Proceedings of the KIEE Conference
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• 1987.11a
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• pp.133-136
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• 1987

This paper presents a new algorithm of optimal measurement system by using band matrix characteristic respectively for state estimation. A performance index of measurement system is established to reflect relation among measurement sets, probability of measurement failure and cost of individual meter installation. Selection ranking in the candidates of measurement sets is composed to guarantee the observability for any any single meter outage. Performance index sensitivity is introduced and recursive formula which based on the matrix inversion lemma used for selection. The proposed algorithm is composed of successive addition algorithm, successive elimination algorithm and combinatorial algorithm. The band matrix characteristic could save in memory requirements and calculate the performance index faster than earlier.

• Structural Engineering and Mechanics
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• v.67 no.4
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• pp.327-336
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• 2018

In this study, an efficient damage index is proposed to identify multiple damage cases in structural systems using the concepts of frequency response function (FRF) matrix and strain energy of a structure. The index is defined based on the change of strain energy of an element due to damage. For obtaining the strain energy stored in elements, the columnar coefficients of the FRF matrix is used. The new indicator is named here as frequency response function strain energy based index (FRFSEBI). In order to assess the performance of the proposed index for structural damage detection, some benchmark structures having a number of damage scenarios are considered. Numerical results demonstrate that the proposed index even with considering noise can accurately identify the actual location and approximate severity of the damage. In order to demonstrate the high efficiency of the proposed damage index, its performance is also compared with that of the flexibility strain energy based index (FSEBI) provided in the literature.

• Journal of Environmental Impact Assessment
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• v.8 no.3
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• pp.49-59
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• 1999

In this study, we individualize the clauses to sort out the troubled ones, draw up a interrelation model in order to visually organize the relations, and finally, suggest the desirable application idea. The interrelation model suggested in this study has been made based on the matrix method. On this matrix, we arranged the environmental factors on horizontal and vertical axis, and when we describe the relation of each factors, we set the horizontal axis as the base and divided the content into three grades : Fine, Medium, and Poor. In addition to that, we expressed those three grades into numerical value like 3 points for Level Fine, 2 points for Level Medium, and 1 point for Level Poor and then, we converted this numerical values into index numbers. We could classify the index numbers such as AS, PS, Q-index, P-index. AS is an index numerically shows the degree of giving environmental effect, PS is an index numerically shows the degree of receiving environmental effect, Q-index is an index shows the aggravate degree, and P-index shows the relation degree. The Q/P-index with large numbers has considerable effect on the environmental system, while the small numbered Q/P-index barely effect on the environmental system. Moreover, we classified the environmental factors into 5 levels(I~V) according to the relations between the Q-index and P-index. Level I is less affected by the environment and has more giving effect, while Level V is more sensitively affected by the environment and has more receiving effect, which we considered important. Therefore, we could come up with the result that if we consider the each level of factors when we evaluate the EIA, the result would be far more accurate and reliable since it contains mutual relation aspect of EIA. The suggested interrelation model in this thesis is presentable as one of those scoping system. We highly believe the need of scoping system in EIA and suggest the interrelation model as the alternative idea for scoping system.

• Journal of the Korean Society for information Management
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• v.24 no.4
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• pp.173-189
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• 2007

By measuring satisfaction index of the users of Information System, it is possible not only to estimate ROI(Return on Investment) but also to draw the device for the efficiency and improvement of the System. This study tries to give User Satisfaction Index Model for the System, and present operators and managers of the system with the method for improving satisfaction and efficiency by measuring the User Satisfaction Index of representative information systems. For this, the survey was carried out for the representative information systems. On the basis of the analysis, Satisfaction Index was drawn and through Matrix Analysis, the strategy for system improvement was derived.

• Communications of the Korean Mathematical Society
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• v.17 no.4
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• pp.577-581
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• 2002

The incidence matrices corresponding to a nil-algebra of finite index % can be used to determine the nilpotency. We find the smallest positive integer n such that the sum of the incidence matrices Σ$\_$p/$\^$p/ is invertible. In this paper, we give a different proof of the case that the nil-algebra of index 2 has nilpotency less than or equal to 4.

• Earthquakes and Structures
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• v.22 no.6
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• pp.609-623
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• 2022

To study the empirical seismic fragility of a reinforced concrete girder bridge, based on the theory of numerical analysis and probability modelling, a regression fragility method of a rapid fragility prediction model (Gaussian first-order regression probability model) considering empirical seismic damage is proposed. A total of 1,069 reinforced concrete girder bridges of 22 highways were used to verify the model, and the vulnerability function, plane, surface and curve model of reinforced concrete girder bridges (simple supported girder bridges and continuous girder bridges) considering the number of samples in multiple intensity regions were established. The new empirical seismic damage probability matrix and curve models of observation frequency and damage exceeding probability are developed in multiple intensity regions. A comparative vulnerability analysis between simple supported girder bridges and continuous girder bridges is provided. Depending on the theory of the regional mean seismic damage index matrix model, the empirical seismic damage prediction probability matrix is embedded in the multidimensional mean seismic damage index matrix model, and the regional rapid prediction matrix and curve of reinforced concrete girder bridges, simple supported girder bridges and continuous girder bridges in multiple intensity regions based on mean seismic damage index parameters are developed. The established multidimensional group bridge vulnerability model can be used to quantify and predict the fragility of bridges in multiple intensity regions and the fragility assessment of regional group reinforced concrete girder bridges in the future.