• Proceedings of the IEEK Conference
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• 2006.06a
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• pp.825-826
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• 2006

In this paper, we propose an algorithm that applies Rolle's theorem to automatically detect and label peak III and V of the normal, suprathreshold auditory brainstem response (ABR). ABR waveform were recorded from 55 normal-hearing ears at screening levels varying from 30 to 60 dBnHL. For each ABR waveform, the peak-finding algorithm proceeded in fourth steps: (1) Select maximum and minimum values of the target ABR waveform, (2) divide this range into n equal parts, (3) effective candidate peaks in the ABR waveform are identified using Rolle's theorem (4) peak III and V are identified from these candidate peaks based on their latency and morphology. As a result, proposed auto dectection method showed high correlation and accuracy with manual detection method performed by clinician. By using proposed algorithm, clinician can detect and label peak III and V faster and more efficient than manual detection method.

• Communications of the Korean Mathematical Society
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• v.37 no.2
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• pp.503-520
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• 2022

We introduce a new type of fractional derivative, which we call as the right local general truncated M-fractional derivative for α-differentiable functions that generalizes the fractional derivative type introduced by Anastassiou. This newly defined operator generalizes the standard properties and results of the integer order calculus viz. the Rolle's theorem, the mean value theorem and its extension, inverse property, the fundamental theorem of calculus and the theorem of integration by parts. Then we represent a relation of the newly defined fractional derivative with known fractional derivative and in context with this derivative a physical problem, Kirchoff's voltage law, is generalized. Also, the importance of this newly defined operator with respect to the flexibility in the parametric values is described via the comparison of the solutions in the graphs using MATLAB software.

• Bulletin of the Korean Mathematical Society
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• v.33 no.3
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• pp.329-334
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• 1996

The notion of approximate derivative was introduced by Denjoy in 1916 [3]. Khintchine [5] proved that Rolle's theorem holds for approximate derivatives and Tolstoff [8] proved that every approximate derivative is of Baire class 1 and has Darboux property. Goffman and Neugebauer [4] proved the above results of Tolstoff [8] in a different and simplified method. Also they [4] proved indirectly (via Darboux property) that approximate derivatives possess mean value property.

• Journal of Industrial Technology
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• v.18
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• pp.61-67
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• 1998

이 논문에서는 Diruchlet 경계 조건을 갖는 비선형 타원형 방정식 $-{\Delta}u+g(u)=f(x)$의 해의 존재에 대한 연구를 하였다. 존재하는 해의 다중성을 증명하기 위하여 임계점 이론과 롤의 정리를 사용하였으며, 대응되는 범함수에 따라서 방정식의 해와 임계점이 동시에 나타난다는 정리를 이용하였다. 이 때 $g(u)=bu^+-au^-$으로 나타날 때 외력항 (방정식의 우변)의 상수로 주어지는 경우 적어도 두 개의 해가 존재한다는 것을 증명하였다. 만약 우변(외력항)의 상수가 음수이거나 0인 경우이 방정식의 해가 존재하지 않거나 자명한 해만 존재하기 때문에 상수는 양수인 것으로 가정하였다.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.44 no.1
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• pp.100-107
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• 2007

AABR(automated auditory brainstem response) test is used for the screening purpose of hearing ability of neonates. In this paper, algorithm using Rolle's theorem is suggested for automatic detection of the ensemble averaged ABR waveform. The ABR waveforms were recorded from 55 normal-hearing ears of neonates at screening levels varying from 30 to 60 dBnHL. Recorded signals were analyzed by expert audiologist and by the proposed algorithm. The results showed that the proposed algorithm correctly identified latencies of the major ABR waves (III, V) with latent difference below 0.2 ms. No significant differences were found between the two methods. We also analyzed the ABR signals using derivative algorithm and compared the results with proposed algorithm. The number of detected candidate waves using the proposed algorithm was 47 % less than that of the existing one. The proposed method had lower relative errors (0.01 % error at 60dBnHL) compared to the existing one. By using proposed algorithm, clinicians can detect and label waves III and V more objectively and quantitatively than the manual detection method.