• Journal of applied mathematics & informatics
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• v.39 no.5_6
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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.

• Imaging Science in Dentistry
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• v.46 no.2
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• pp.117-125
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• 2016

Purpose: This study evaluated and compared interradicular distances and cortical bone thickness in Thai patients with Class I and Class II skeletal patterns, using cone-beam computed tomography (CBCT). Materials and Methods: Pretreatment CBCT images of 24 Thai orthodontic patients with Class I and Class II skeletal patterns were included in the study. Three measurements were chosen for investigation: the mesiodistal distance between the roots, the width of the buccolingual alveolar process, and buccal cortical bone thickness. All distances were recorded at five different levels from the cementoenamel junction (CEJ). Descriptive statistical analysis and t-tests were performed, with the significance level for all tests set at p<0.05. Results: Patients with a Class II skeletal pattern showed significantly greater maxillary mesiodistal distances (between the first and second premolars) and widths of the buccolingual alveolar process (between the first and second molars) than Class I skeletal pattern patients at 10 mm above the CEJ. The maxillary buccal cortical bone thicknesses between the second premolar and first molar at 8 mm above the CEJ in Class II patients were likewise significantly greater than in Class I patients. Patients with a Class I skeletal pattern showed significantly wider mandibular buccolingual alveolar processes than did Class II patients (between the first and second molars) at 4, 6, and 8 mm below the CEJ. Conclusion: In both the maxilla and mandible, the mesiodistal distances, the width of the buccolingual alveolar process, and buccal cortical bone thickness tended to increase from the CEJ to the apex in both Class I and Class II skeletal patterns.

• Journal of the Korean Society of Clothing and Textiles
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• v.44 no.4
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• pp.626-638
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• 2020

In this study, protective masks were designed in varying internal volume and analyzed in regards to wearing effect. Masks were measured by surface temperature and subjective wear evaluation. Four experimental masks were created with an increasing distance between the mask center line and nose in increments. The distances were set at 0.0 cm (M0), 2.0 cm (M2), 4.0 cm (M4), and 6.0 cm (M6). The area and volume of each experimental mask was measured and both measurements had a positive correlation with the set distances. Among the experimental masks, M2 was the most breathable. The heat between the face and the mask created by exhalation was able to escape from the mask and provided the highest comfort sensation when worn. Conversely, an internal volume that is too large would decrease its comfort because repetitive breathing deforms the appearance of the mask and adversely affects its fit. Therefore, creating and maintaining the optimal internal volume of the M2 mask is important to achieve maximum thermal sensation and ease of wear.

• International Journal of Advanced Culture Technology
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• v.7 no.3
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• pp.134-142
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• 2019

As the 4th industry has been widely distributed, there is a need for a process of real-time image recognition in various fields such as identification of company employees, security maintenance, and development of military weapons. Therefore, in this paper, we will propose an algorithm that effectively recognizes a test object by comparing it with the DB model. The proposed object recognition system first expresses the outline of the test object as a set of vertices with the distances of predefined length or more. Then, the degree of matching of the structures of the two objects is calculated by examining the distances to the outline of the DB model from the vertices constituting the test object. Because the proposed recognition algorithm uses the outline of the object, the recognition process is easy to understand, simple to implement, and a satisfactory recognition result is obtained.

• The Pure and Applied Mathematics
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• v.11 no.1
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• pp.37-49
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• 2004

We are interested in the problem of fitting a sphere to a set of data points in the three dimensional Euclidean space. In Spath [6] a descent algorithm already have been given to find the sphere of best fit in least squares sense of minimizing the orthogonal distances to the given data points. In this paper we present another new algorithm which computes a parametric represented sphere in order to minimize the sum of the squares of the distances to the given points. For any choice of initial approximations our algorithm has the advantage of ensuring convergence to a local minimum. Numerical examples are given.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2007.04a
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• pp.175-178
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• 2007

We give a geometrical interpretation of the interval-valued fuzzy set. So, based on the geometrical background, we propose new distance measures between interval-valued fuzzy sets and compare these measures with distance measures proposed by Burillo and Bustince and Grzegorzewski, respectively. Furthermore, we extend three methods for measuring distances between interval-valued fuzzy sets to interval-valued intuitionistic fuzzy sets.

• Communications of the Korean Mathematical Society
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• v.37 no.3
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• pp.915-938
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• 2022

We are interested in the problem of fitting a parabola to a set of data points in ℝ³. It can be usually solved by minimizing the geometric distances from the fitted parabola to the given data points. In this paper, a parabola fitting algorithm will be proposed in such a way that the sum of the squares of the geometric distances is minimized in ℝ³. Our algorithm is mainly based on the steepest descent technique which determines an adequate number λ such that h(λ) = Q(u - λ𝛁Q(u)) < Q(u). Some numerical examples are given to test our algorithm.

• Communications for Statistical Applications and Methods
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• v.18 no.5
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• pp.637-644
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• 2011

Partially ranked data refers to the situation in which there are p distinct objects; however each judge specifies only first s (s < p) choices. The group theoretic formulation for partially ranked data analysis was set up by Critchlow (1985). We propose a graphical method for partially ranked data by quantifying objects and judges. In a plot for judges, the interpoint distances can be interpreted as Spearman or Kendall distances between two rankings given by respective judges. Similarly, we also construct a plot for objects with a sensible relationship to the previous plot for judges. This study extends the Han and Huh (1995) quantification method of fully ranked data using Gabriel's (1971) biplot technique for multivariate data matrix.

• Proceedings of the Korean Society of Near Infrared Spectroscopy Conference
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• 2001.06a
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• pp.1154-1154
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• 2001

Near infra-red (NIR) spectroscopy has been used for the non-invasive assessment of intact fruit for eating quality attributes such as total soluble solids (TSS) content. However, little information is available in the literature with respect to the robustness of such calibration models validated against independent populations (however, see Peiris et al. 1998 and Guthrie et al. 1998). Many studies report ‘prediction’ statistics in which the calibration and prediction sets are subsets of the same population (e. g. a three year calibration validated against a set from the same population, Peiris et al. 1998; calibration and validation subsets of the same initial population, Guthrie and Walsh 1997 and McGlone and Kawano 1998). In this study, a calibration was developed across 84 melon fruit (R$^2$= 0.86$^{\circ}$Brix, SECV = 0.38$^{\circ}$Brix), which predicted well on fruit excluded from the calibration set but taken from the same population (n = 24, SEP = 0.38$^{\circ}$Brix with 0.1$^{\circ}$Brix bias), relative to an independent group (same variety and farm but different harvest date) (n = 24, SEP= 0.66$^{\circ}$ Brix with 0.1$^{\circ}$Brix bias). Prediction on a different variety, different growing district and time was worse (n = 24, SEP = 1.2$^{\circ}$Brix with 0.9$^{\circ}$Brix bias). Using an ‘in-line’ unit based on a silicon diode array spectrometer, as described in Walsh et al. (2000), we collected spectra from fruit populations covering different varieties, growing districts and time. The calibration procedure was optimized in terms of spectral window, derivative function and scatter correction. Performance of a calibration across new populations of fruit (different varieties, growing districts and harvest date) is reported. Various calibration sample selection techniques (primarily based on Mahalanobis distances), were trialled to structure the calibration population to improve robustness of prediction on independent sets. Optimization of calibration population structure (using the ISI protocols of neighbourhood and global distances) resulted in the elimination of over 50% of the initial data set. The use of the ISI Local Calibration routine was also investigated.

• Phonetics and Speech Sciences
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• v.5 no.4
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• pp.99-107
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• 2013

The purpose of this study is to examine the relative distances among English front vowels in a message produced by 47 Korean and American speakers in order to better instruct pronunciation skills of English vowels for Korean English learners. A Praat script was developed to collect the first and second formant values(F1 and F2) of eight words in each sound file which was recorded from an internet speech archive. Then, the Euclidean distances were measured between the three vowel pairs: [i-ɛ], [i-ɪ], and [ɛ-æ]. The first vowel pair [i-ɛ] was set as the reference from which the relative distances of the other two vowel pairs were measured in percent in order to compare the vowel sounds among speakers of different vocal tract lengths. Results show that F1 values of the front vowels produced by the Korean and American speakers increased from the high front vowel to the low front vowel wih differences among the groups. The Korean speakers generally produced the front vowels with smaller jaw openings than the American speakers did. Secondly, the relative distance of the high front vowel pair [i-ɪ] showed a significant difference between the Korean and American speakers while that of the low front vowel pair [ɛ-æ] showed a non-significant difference. Finally, the Korean speakers in the higher proficiency level produced front vowels with higher F1 values than those in the lower proficiency level. The author concluded that Korean speakers should produce the front high vowels distinctively by securing sufficient relative distance of the formant values. Further studies would be desirable to examine how strong the Korean speakers' English proficiency correlate with the relative distance of target words of comparable productions.