• Journal of the Chungcheong Mathematical Society
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• v.34 no.3
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• pp.259-269
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• 2021

We shall study the following. Let 𝜙 be an expansive flow on a compact TVS-cone metric space (X, d). First, we give some equivalent ways of defining expansiveness. Second, we show that expansiveness is conjugate invariance. Finally, we prove that lim sup ${\frac{1}{t}}$ log v(t) ≤ h(𝜙), where v(t) denotes the number of closed orbits of 𝜙 with a period 𝜏 ∈ [0, t] and h(𝜙) denotes the topological entropy. Remark that in 1972, R. Bowen and P. Walters had proved this three statements for an expansive flow on a compact metric space [?].

• Journal of the Korean Mathematical Society
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• v.32 no.3
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• pp.573-582
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• 1995

J.Milnor[Mi2] has introduced the notion of directional entropy in his study of Cellular Automata. Cellular Automaton map can be considered as a continuous map from a space $K^Z^n$ to itself which commute with the translation of the lattice $Z^n$. Since the space $K^Z^n$ is compact, map S is uniformly continuous. Hence S is a block map(a finite code)[He]. (S is said to have a finite memory.) In the case of n = 1, we have a shift map, T on $K^Z$, and a block map S and they together generate a $Z^2$ action.

• Imaging Science in Dentistry
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• v.53 no.1
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• pp.43-51
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• 2023

Purpose: This study aimed to assess texture analysis(TA) of cone-beam computed tomography (CBCT) images as a quantitative tool for the differential diagnosis of odontogenic and non-odontogenic maxillary sinusitis(OS and NOS, respectively). Materials and Methods: CBCT images of 40 patients diagnosed with OS (N=20) and NOS (N=20) were evaluated. The gray level co-occurrence (GLCM) matrix parameters, and gray level run length matrix texture (GLRLM) parameters were extracted using manually placed regions of interest on lesion images. Seven texture parameters were calculated using GLCM and 4 parameters using GLRLM. The Mann-Whitney test was used for comparisons between the groups, and the Levene test was performed to confirm the homogeneity of variance (α=5%). Results: The results showed statistically significant differences(P<0.05) between the OS and NOS patients regarding 3 TA parameters. NOS patients presented higher values for contrast, while OS patients presented higher values for correlation and inverse difference moment. Greater textural homogeneity was observed in the OS patients than in the NOS patients, with statistically significant differences in standard deviations between the groups for correlation, sum of squares, sum of entropy, and entropy. Conclusion: TA enabled quantitative differentiation between OS and NOS on CBCT images by using the parameters of contrast, correlation, and inverse difference moment.

• Imaging Science in Dentistry
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• v.53 no.2
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• pp.109-115
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• 2023

Purpose: The aim of this study was to evaluate changes in the trabecular bone through texture analysis and compare the texture analysis characteristics of different areas in patients with medication-related osteonecrosis of the jaw (MRONJ). Materials and Methods: Cone-beam computed tomographic images of 16 patients diagnosed with MRONJ were used. In sagittal images, 3 regions were chosen: active osteonecrosis(AO); intermediate tissue (IT), which presented a zone of apparently healthy tissue adjacent to the AO area; and healthy bone tissue (HT) (control area). Texture analysis was performed evaluating 7 parameters: secondary angular momentum, contrast, correlation, sum of squares, inverse moment of difference, sum of entropies, and entropy. Data were analyzed using the Kruskal-Wallis test with a significance level of 5%. Results: Comparing the areas of AO, IT, and HT, significant differences (P<0.05) were observed. The IT and AO area images showed higher values for parameters such as contrast, entropy, and secondary angular momentum than the HT area, indicating greater disorder in these tissues. Conclusion: Through texture analysis, changes in the bone pattern could be observed in areas of osteonecrosis. The texture analysis demonstrated that areas visually identified and classified as IT still had necrotic tissue, thereby increasing the accuracy of delimiting the real extension of MRONJ.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.55 no.3
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• pp.131-137
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• 2006

The secondary system of nuclear power plants consists of sophisticated piping systems operating in very aggressive erosion and corrosion environments, which make a piping system vulnerable to the wear and degradation due to the several chemical components and high flow rate (~10 m/sec) of the coolant. To monitor the wear and degradation on a pipe, the vibration signals are measured from the pipe with an accelerometer For analyzing the vibration signal the time-frequency analysis (TFA) is used, which is known to be effective for the analysis of time-varying or transient signals. To reduce the inteferences (cross-terms) due to the bilinear structure of the time-frequency distribution, an adaptive cone-kernel distribution (ACKD) is proposed. The cone length of ACKD to determine the characteristics of distribution is optimally selected through an adaptive algorithm using the normalized Shannon's entropy And the ACKD's are compared with the results of other analyses based on the Fourier Transform (FT) and other TFA's. The ACKD shows a better signature for the wear/degradation within a pipe and provides the additional information in relation to the time that any analysis based on the conventional FT can not provide.