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Exponentially Convex Functions Depending on the Norm
A. S. Okb El-Bab ...et al KYUNGPOOK UNIVERSITY 2000 Kyungpook mathematical journal Vol.40 No.1
A number of results concerning exponentially convex functions defined on infinite dimensional spaces and depends on the norm are considered. First, we show that if F(x) = f(||x||²) is a continuous exponentially convex function on an in?nite dimensional space then f must be completely monotone and hence the integral representation of F can be obtained. The case of the Hilbert space is also considered. The necessary and sufficient condition for the function exp(-t^(α)) to be completely monotone is obtained and the integral representation of a f(·)-dependent exponentially convex function is also obtained. As a special case, the lpspaces, 0 < p ≤ 2, are considered.
Frank Efe Erukainure,Victor Parque,Mohsen A. Hassan,Ahmed M. R. Fath El-Bab 대한기계학회 2022 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.36 No.10
The measurement of viscoelastic properties of soft tissues has become a research interest with applications in the stiffness estimation of soft tissues, sorting and quality control of postharvest fruit, and fruit ripeness estimation. This paper presents a tactile sensor configuration to estimate the stiffness properties of soft tissues, using fruit as case study. Previous stiffness-measuring tactile sensor models suffer from unstable and infinite sensor outputs due to irregularities and inclination angles of soft tissue surfaces. The proposed configuration introduces two low stiffness springs at the extreme ends of the sensor with one high stiffness spring in-between. This study also presents a closed form mathematical model that considers the maximum inclination angle of the tissue’s (fruit) surface, and a finite element analysis to verify the mathematical model, which yielded stable sensor outputs. A prototype of the proposed configuration was fabricated and tested on kiwifruit samples. The experimental tests revealed that the sensor’s output remained stable, finite, and independent on both the inclination angle of the fruit surface and applied displacement of the sensor. The sensor distinguished between kiwifruit at various stiffness and ripeness levels with an output error ranging between 0.18 % and 3.50 %, and a maximum accuracy of 99.81 %, which is reasonable and competitive compared to previous design concepts.
Gamal A. Nasser,Ahmed L. Abdel-Mawgood,A. A. Abouelsoud,Hisham Mohamed,Shinjiro Umezu,Ahmed M. R. Fath El-Bab 대한기계학회 2021 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.35 No.7
Temperature control is a critical factor in PCR for efficient DNA amplification. The main aim is to achieve tight control and high rate of heating and cooling for a portable, cost-effective PCR device. This speed depends on reduction of the thermal mass of the PCR heating part. The common methods used to decrease the device's thermal mass or heating/ cooling time are to improve desirable device structural design and to choose a better heating and cooling mechanism with robust controller. Increasing the thermal mass provides a good temperature distribution on the heater surface, but it delays the heat transfer. Therefore, removing thermal mass makes the controller struggle to provide a high temperature uniformity distribution on Peltier surface. In this paper, we provide a cost-effective PCR heating/cooling system using Peltier element. This system is controlled using adaptive FLC with bang-bang as a hybrid controller to provide good accuracy with maximum available temperature changing rate. The results show that in cooling, the adaptive FLC with bang-bang controller is faster by 20 % than the normal PD-like FLC, however in heating it is faster by 5 to 10 %. The adaptive FLC provided steady state error 3 % and 1.5 % less than the normal FLC at denaturation and annealing steps, respectively. Temperature distribution is tested using thermal camera. The device is validated by performing conventional PCR. The amplification product was analyzed by electrophoresis on a 1.5 % agarose gel then stained with ethidium bromide and the products show successfully amplified.