Search results for: Wen Liang Chang

Authors: Po-Yun Chen, Jui-Liang Yen, Chang-Ping Chang, Wen-Hua Hu, Yu-Liang Chen, Yih-Ming Liu, Chin-Yi Chou, Ming-Der Ger

Abstract:

The stab resistance performance of newly developed fabric composites composed of hexagonal paper honeycombs, filled with shear thickening fluid (STF), and woven Kevlar® fabric or UHMPE was investigated in this study. The STF was prepared by dispersing submicron SiO2 particles into polyethylene glycol (PEG). Our results indicate that the STF-Kevlar composite possessed lower penetration depth than that of neat Kevlar. In other words, the STF-Kevlar composite can attain the same energy level in stab-resistance test with fewer layers of Kevlar fabrics than that of the neat Kevlar fabrics. It also indicates that STF can be used for the fabrication of flexible body armors and can provide improved protection against stab threats. We found that the stab resistance of the STF-Kevlar composite increases with the increase of SiO2 concentration in STF. Moreover, the silica particles functionalized with silane coupling agent can further improve the stab resistance.

Keywords: shear thickening fluid, SiO2, Kevlar, stab

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Authors: Hae-Soon Ahn, Eun-Jun Yoon

Abstract:

With the rapid development of wireless mobile communication, applications for mobile devices must focus on network security. In 2008, Chang-Chang proposed security improvements on the Lu et al.-s elliptic curve authentication key agreement protocol for wireless mobile networks. However, this paper shows that Chang- Chang-s improved protocol is still vulnerable to off-line password guessing attacks unlike their claims.

Keywords: Authentication, key agreement, wireless mobile networks, elliptic curve, password guessing attacks.

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Authors: Z. C. Chang, S. C. Liang

Abstract:

RF magnetron sputtering is used on the ceramic targets, each of which contains zinc oxide (ZnO), zinc oxide doped with aluminum (AZO) and zinc oxide doped with gallium (GZO). The electric conduction mechanism of the AZO and GZO films came mainly from the Al and Ga, the oxygen vacancies, Zn interstitial atoms, and Al and/or Ga interstitial atoms. AZO and GZO films achieved higher conduction than did ZnO film, it being ion vacant and nonstoichiometric. The XRD analysis showed a preferred orientation along the (002) plane for ZnO, AZO, and GZO films.

Keywords: ZnO, AZO, GZO, Doped, Sputtering

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Authors: Jheng-Long Wu, Pei-Chann Chang, Shih-Ling Chang, Liang-Chih Yu, Jui-Feng Yeh, Chin-Sheng Yang

Abstract:

The Major Depressive Disorder has been a burden of medical expense in Taiwan as well as the situation around the world. Major Depressive Disorder can be defined into different categories by previous human activities. According to machine learning, we can classify emotion in correct textual language in advance. It can help medical diagnosis to recognize the variance in Major Depressive Disorder automatically. Association language incremental is the characteristic and relationship that can discovery words in sentence. There is an overlapping-category problem for classification. In this paper, we would like to improve the performance in classification in principle of no overlapping-category problems. We present an approach that to discovery words in sentence and it can find in high frequency in the same time and can-t overlap in each category, called Association Language Features by its Category (ALFC). Experimental results show that ALFC distinguish well in Major Depressive Disorder and have better performance. We also compare the approach with baseline and mutual information that use single words alone or correlation measure.

Keywords: Association language features, Emotion Classification, Overlap-Category Feature, Nature Language Processing.

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Authors: Chih-Hsiang Chang, Liang-Chien Lee, Shu-Ling Wu

Abstract:

This study investigates the investors- behavioral reaction to the investment rating change announcements from the views of behavioral finance. The empirical results indicate that self-interest does affect the intention of securities firms to release investment ratings for individual stocks. In addition, behavioral pitfalls are also found in the response of retail investors to investment rating change announcements.

Keywords: Investment ratings, Behavioral finance, Self-interest, Behavioral pitfalls

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Authors: Liang-Chien Lee, Chih-Hsiang Chang, Ying-Shu Tseng

Abstract:

Comparing with prior studies mainly focused on the effect of a certain event (it may be the initial announcement of bad news or the repeated announcements of identical bad news) on stock price, the aim of this study is to explore how investors react to subsequent bad news with identical content. Empirical results show that as a result of behavioral pitfalls, investors underreact to the initial announcement of the bad news (i.e., unknown bad news) and overreact to the repeated announcements of the identical bad news (i.e., known bad news).

Keywords: Subsequent bad news, Behavioral finance, Investors’ misreaction, Behavioral pitfalls.

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Authors: Onuma Ruangwong, Wen-Jinn Liang, S.Y. Zhang, Chi-I Chang

Abstract:

The effect of antifungal compound from Bacillus subtilis strain LB5 was tested against conidial germination of Colletotrichum gloeosporioides and Pestalotiopsis eugeniae, causal agent of anthracnose and fruit rot of wax apple, respectively. Observation under scanning electron microscope and light compound microscope revealed that conidial germination was completely inhibited when treated with culture broth, culture filtrate, or crude extract from strain LB5. Identification of purified antifungal compound produced by strain LB5 in cell-free supernatant by nuclear magnetic resonance and fast atom bombardment showed that the active compound was iturin A-2.

Keywords: Iturin A-2, Bacillus subtilis LB5, Colleteotrichum gloeospporioides, Pestalotiopsis eugeniae, wax apple

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Authors: Cheng-En Tsai, Chung-Chun Hsiao, Fu-Yuan Chang, Liang-Lun Lan, Jia-Ying Tu

Abstract:

New design of three dimensional (3D) flywheel system based on gimbal and gyro mechanics is proposed. The 3D flywheel device utilizes the rotational motion of three spherical shells and the conservation of angular momentum to achieve planar locomotion. Actuators mounted to the ring-shape frames are installed within the system to drive the spherical shells to rotate, for the purpose of steering and stabilization. Similar to the design of 2D flywheel system, it is expected that the spherical shells may function like a “flyball” to store and supply mechanical energy; additionally, in comparison with typical single-wheel and spherical robots, the 3D flywheel can be used for developing omnidirectional robotic systems with better mobility. The Lagrangian method is applied to derive the equation of motion of the 3D flywheel system, and simulation studies are presented to verify the proposed design.

Keywords: Gimbal, spherical robot, gyroscope, Lagrangian formulation, flyball.

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Authors: Cheng-En Tsai, Chung-Chun Hsiao, Fu-Yuan Chang, Liang-Lun Lan, Jia-Ying Tu

Abstract:

New design of three dimensional (3D) flywheel system based on gimbal and gyro mechanics is proposed. The 3D flywheel device utilizes the rotational motion of three spherical shells and the conservation of angular momentum to achieve planar locomotion. Actuators mounted to the ring-shape frames are installed within the system to drive the spherical shells to rotate, for the purpose of steering and stabilization. Similar to the design of 2D flywheel system, it is expected that the spherical shells may function like a “flyball” to store and supply mechanical energy; additionally, in comparison with typical single-wheel and spherical robots, the 3D flywheel can be used for developing omnidirectional robotic systems with better mobility. The Lagrangian method is applied to derive the equation of motion of the 3D flywheel system, and simulation studies are presented to verify the proposed design.

Keywords: Gimbal, spherical robot, gyroscope, Lagrangian formulation, flyball.

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Authors: Hsiao-Ming Chang, Jui-Liang Hsu

Abstract:

The purpose of this study is to analyze the cognitive and travel experience the situation of the tourist attraction of the sport tourism in Penghu. This study used a questionnaires, the main island of Taiwan to Penghu in the way of marine sports tourists adopted the designated convenience sampling method, a total of 1447 valid questionnaires. After statistical analysis, this study found that: 1. Tourists to Penghu sports tourism attraction cognitive as “good air quality, suitable for water activities". 2. Tourists in Penghu's tourism experience, “Let me taste the delicious specialties and snacks". 3. The attraction of the sport tourism, travel experience and perceived value are correlated, and both the perceived value with a high degree of predictive ability. Based on the findings of this study not only for Penghu's tourism industry with the unit in charge of the proposed operating and suggestions for future research to other researchers.

Keywords: Sport tourism, travel experience, perceived value, sport attraction.

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Authors: Liang-Hsuan Chen, Chia-Jung Chang

Abstract:

Fuzzy random variables have been introduced as an imprecise concept of numeric values for characterizing the imprecise knowledge. The descriptive parameters can be used to describe the primary features of a set of fuzzy random observations. In fuzzy environments, the expected values are usually represented as fuzzy-valued, interval-valued or numeric-valued descriptive parameters using various metrics. Instead of the concept of area metric that is usually adopted in the relevant studies, the numeric expected value is proposed by the concept of distance metric in this study based on two characters (fuzziness and randomness) of FRVs. Comparing with the existing measures, although the results show that the proposed numeric expected value is same with those using the different metric, if only triangular membership functions are used. However, the proposed approach has the advantages of intuitiveness and computational efficiency, when the membership functions are not triangular types. An example with three datasets is provided for verifying the proposed approach.

Keywords: Fuzzy random variables, Distance measure, Expected value.

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Authors: Wen Liang Chang

Abstract:

This paper provides a replacement policy for warranty products with different failure rate from the consumer-s viewpoint. Assume that the product is replaced once within a finite planning horizon, and the failure rate of the second product is lower than the failure rate of the first product. Within warranty period (WP), the failed product is corrected by minimal repair without any cost to the consumers. After WP, the failed product is repaired with a fixed repair cost to the consumers. However, each failure incurs a fixed downtime cost to the consumers over a finite planning horizon. In this paper, we derive the model of the expected total disbursement cost within a finite planning horizon and some properties of the optimal replacement policy under some reasonable conditions are obtained. Finally, numerical examples are given to illustrate the features of the optimal replacement policy under various maintenance costs.

Keywords: Planning horizon, Free-repair warranty, Minimal repair, Replacement.

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Authors: Liu Ji-Wei, Pei Yu-Liang, Liu Qian, Han Xiang, Zeng De-Liang

Abstract:

The economic and stable operation was affected seriously by coal quality disturbance for power plants. Based on model analysis, influence of the disturbance can be considered as gain change of control system. Power capability coefficient of coal was constructed to inhibit it. Accuracy of the coefficient was verified by operating data. Then coal quality disturbance free system based on gain scheduling was designed for coordinated control system. Simulation showed that, the strategy improved control quality obviously, and inhibited the coal quality disturbance.

Keywords: coordinate control system, coal quality disturbance, energy coefficient of coal quality, gain scheduling

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Authors: Eileen Chih-Ying Yang, Liang-Han Wu, Chieh-Min Chang

Abstract:

The design of an active leg orthosis for tumble protection is proposed in this paper. The orthosis would be applied to assist elders or invalids in rebalancing while they fall unexpectedly. We observe the regain balance motion of healthy and youthful people, and find the difference to elders or invalids. First, the physical model of leg would be established, and we consider the leg motions are achieve through four joints (phalanx stem, ankle, knee, and hip joint) and five links (phalanges, talus, tibia, femur, and hip bone). To formulate the dynamic equations, the coordinates which can clearly describe the position in 3D space are first defined accordance with the human movement of leg, and the kinematics and dynamics of the leg movement can be formulated based on the robotics. For the purpose, assisting elders and invalids in avoiding tumble, the posture variation of unbalance and regaining balance motion are recorded by the motion-capture image system, and the trajectory is taken as the desire one. Then we calculate the force and moment of each joint based on the leg motion model through programming MATLAB code. The results would be primary information of the active leg orthosis design for tumble protection.

Keywords: Active leg orthosis, Tumble protection

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Authors: Yuchih Lin, Chung-Liang Chang, Hong-Yi Cao, Sheng-Hsuan Hsiao

Abstract:

Cu-mesoporous TiO2 is developed for removal acid odor cooperated with ozone assistance and online- regeneration system with/without UV irradiation (all weather) in study. The results showed that Cu-mesoporous TiO2 present the desirable adsorption efficiency of acid odor without UV irradiation, due to the larger surface area, pore sizeand the additional absorption ability provided by Cu. In the photocatalysis process, the material structure also benefits Cu-mesoporous TiO2 to perform the more outstanding efficiency on degrading acid odor. Cu also postponed the recombination of electron-hole pairs excited from TiO2 to enhance photodegradation ability. Cu-mesoporous TiO2 could gain the conspicuous increase on photocatalysis ability from ozone assistance, but without any benefit on adsorption. In addition, the online regeneration procedure could process the used Cu-mesoporous TiO2 to reinstate the adsorption ability and maintain the photodegradtion performance, depended on scrubbing, desorping acid odor and reducing Cu to metal state.

Keywords: mesoporous material, photocatalyst, adsorption, regeneration usage, photocatalytic ozonation

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Authors: Yeong-Hwa Chang, Chia-Wen Chang, Hung-Wei Lin, C.W. Tao

Abstract:

In this paper, an improved ant colony optimization (ACO) algorithm is proposed to enhance the performance of global optimum search. The strategy of the proposed algorithm has the capability of fuzzy pheromone updating, adaptive parameter tuning, and mechanism resetting. The proposed method is utilized to tune the parameters of the fuzzy controller for a real beam and ball system. Simulation and experimental results indicate that better performance can be achieved compared to the conventional ACO algorithms in the aspect of convergence speed and accuracy.

Keywords: Ant colony algorithm, Fuzzy control, ball and beamsystem

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Authors: Shun-Chang Chang

Abstract:

In this paper, different nonlinear dynamics analysis techniques are employed to unveil the rich nonlinear phenomena of the electromagnetic system. In particular, bifurcation diagrams, time responses, phase portraits, Poincare maps, power spectrum analysis, and the construction of basins of attraction are all powerful and effective tools for nonlinear dynamics problems. We also employ the method of Lyapunov exponents to show the occurrence of chaotic motion and to verify those numerical simulation results. Finally, two cases of a chaotic electromagnetic system being effectively controlled by a reference signal or being synchronized to another nonlinear electromagnetic system are presented.

Keywords: bifurcation, Poincare map, Lyapunov exponent, chaotic motion.

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Authors: Yeong-Hwa Chang, Chang-Hung Hsu, Huei-Lung Chu, Chia-Wen Chang, Wei-Shou Chan, Chun-Yao Lee; Chia-Shiang Yao, Yan-Lou He

Abstract:

This study reports the preparation of soft magnetic ribbons of Fe-based amorphous alloys using the single-roller melt-spinning technique. Ribbon width varied from 142 mm to 213 mm and, with a thickness of approximately 22 μm 2 μm. The microstructure and magnetic properties of the ribbons were characterized by differential scanning calorimeter (DSC), X-ray diffraction (XRD), vibrating sample magnetometer (VSM), and electrical resistivity measurements (ERM). The amorphous material properties dependence of the cooling rate and nozzle pressure have uneven surface in ribbon thicknesses are investigated. Magnetic measurement results indicate that some region of the ribbon exhibits good magnetic properties, higher saturation induction and lower coercivity. However, due to the uneven surface of 213 mm wide ribbon, the magnetic responses are not uniformly distributed. To understand the transformer magnetic performances, this study analyzes the measurements of a three-phase 2 MVA amorphous-cored transformer. Experimental results confirm that the transformer with a ribbon width of 142 mm has better magnetic properties in terms of lower core loss, exciting power, and audible noise. 

Keywords: Amorphous ribbon, uneven surface, magnetic properties, and rapid solidification

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Authors: Jong-Jy Shyu, Soo-Chang Pei, Min-Han Chang

Abstract:

In this paper, the least-squares design of variable fractional-delay (VFD) finite impulse response (FIR) digital differentiators is proposed. The used transfer function is formulated so that Farrow structure can be applied to realize the designed system. Also, the symmetric characteristics of filter coefficients are derived, which leads to the complexity reduction by saving almost a half of the number of coefficients. Moreover, all the elements of related vectors or matrices for the optimal process can be represented in closed forms, which make the design easier. Design example is also presented to illustrate the effectiveness of the proposed method.

Keywords: Differentiator, variable fractional-delay filter, FIR filter, least-squares method, Farrow structure.

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Authors: Wei-Der Chang, Dai-Ming Chang, Eri-Wei Chiang, Chia-Hung Lin, Jian-Liung Chen

Abstract:

In this paper, a fractional-order FIR differentiator design method using the differential evolution (DE) algorithm is presented. In the proposed method, the FIR digital filter is designed to meet the frequency response of a desired fractal-order differentiator, which is evaluated in the frequency domain. To verify the design performance, another design method considered in the time-domain is also provided. Simulation results reveal the efficiency of the proposed method.

Keywords: Fractional-order differentiator, FIR digital filter, Differential evolution algorithm.

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Authors: Chang-Hung Hsu, Yeong-Hwa Chang, Chun-Yao Lee, Chia-Shiang Yao, Yan-Lou He, Huei-Lung Chu, Chia-Wen Chang, Wei-Shou Chan

Abstract:

This study reports the preparation of soft magnetic ribbons of Fe-based amorphous alloys using the single-roller melt-spinning technique. Ribbon width varied from 142 mm to 213 mm and, with a thickness of approximately 22 μm ± 2 μm. The microstructure and magnetic properties of the ribbons were characterized by differential scanning calorimeter (DSC), X-ray diffraction (XRD), vibrating sample magnetometer (VSM), and electrical resistivity measurements (ERM). The amorphous material properties dependence of the cooling rate and nozzle pressure have uneven surface in ribbon thicknesses are investigated. Magnetic measurement results indicate that some region of the ribbon exhibits good magnetic properties, higher saturation induction and lower coercivity. However, due to the uneven surface of 213 mm wide ribbon, the magnetic responses are not uniformly distributed. To understand the transformer magnetic performances, this study analyzes the measurements of a three-phase 2 MVA amorphous-cored transformer. Experimental results confirm that the transformer with a ribbon width of 142 mm has better magnetic properties in terms of lower core loss, exciting power, and audible noise.

Keywords: Amorphous ribbon, uneven surface, magnetic properties, and rapid solidification

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Authors: Yu-Wei Chang, Hsuan-Yu Ku, Jo-Shan Chiu, Shao-Fu Chang, Chien-Chon Chen

Abstract:

This paper aims to discuss the hydrophilicity about the anodic aluminum oxide (AAO) template with titania nanotubes (NTs). The AAO templates with pore size diameters of 20-250 nm were generated by anodizing 6061 aluminum alloy substrates in acid solution of sulfuric acid (H₂SO₄), oxalic acid (COOH)₂, and phosphoric acid (H₃PO₄), respectively. TiO₂-NTs were grown on AAO templates by the sol-gel deposition process successfully. The water contact angle on AAO/TiO₂-NTs surface was lower compared to the water contact angle on AAO surface. So, the characteristic of hydrophilicity was significantly associated with the AAO pore size and what kinds of materials were immersed variables.

Keywords: Anodic aluminum oxide, nanotube, anodization, Sol-Gel, hydrophilicity.

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Authors: Kettawa Boonprakarn, Jedsarid Sangkaphan, Bejapornd Deekhuntod, Nuntharat Suriyo

Abstract:

This study aimed to investigate the existence of field corn networks on the Thailand-Burma border under the patron-client contract farming system. The data of this qualitative study were collected through in-depth interviews with nine key informants.

The results of the study revealed that the existence of the field corn networks was associated with the relationship where farmers had to share their crops with protectors in the areas under the influence of the KNU (Karen National Union) and the DKBA (Democratic Karen Buddhist Army) or Burmese soldiers. A Mae Liang, the person who starts a network has a connection with a Thaokae, Luk Rai Hua Chai or the head of a group of farmers, and farmers. They are under the patron-client system with trust and loyalty that enable the head of the group and the farmers in the Burma border side to remain under the same Mae Liang even though the business has been passed down to later generations.

Keywords: Existence, field-corn networks, patron-client system, contract farming.

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Authors: Young-Jin Baik, Minsung Kim, Junhyun Cho, Ho-Sang Ra, Young-Soo Lee, Ki-Chang Chang

Abstract:

Surplus electricity can be converted into potential energy via pumped hydroelectric storage for future usage. Similarly, thermo-electric energy storage (TEES) uses heat pumps equipped with thermal storage to convert electrical energy into thermal energy; the stored energy is then converted back into electrical energy when necessary using a heat engine. The greatest advantage of this method is that, unlike pumped hydroelectric storage and compressed air energy storage, TEES is not restricted by geographical constraints. In this study, performance variation of the TEES according to the changes in cold-side storage temperature was investigated by simulation method.

Keywords: Energy Storage System, Heat Pump.

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Authors: Chang-Hsing Lee, Cheng-Chang Lien, Chin-Chuan Han

Abstract:

In this paper, an edge-strength guided multiscale retinex (EGMSR) approach will be proposed for color image contrast enhancement. In EGMSR, the pixel-dependent weight associated with each pixel in the single scale retinex output image is computed according to the edge strength around this pixel in order to prevent from over-enhancing the noises contained in the smooth dark/bright regions. Further, by fusing together the enhanced results of EGMSR and adaptive multiscale retinex (AMSR), we can get a natural fused image having high contrast and proper tonal rendition. Experimental results on several low-contrast images have shown that our proposed approach can produce natural and appealing enhanced images.

Keywords: Image Enhancement, Multiscale Retinex, Image Fusion.

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Authors: Yi-Chang Chen, Shan-Lin Chang, Chia-Chun Wu

Abstract:

Unlike this study focused extensively on trading behavior of option market, those researches were just taken their attention to model-driven option pricing. For example, Black-Scholes (B-S) model is one of the most famous option pricing models. However, the arguments of B-S model are previously mentioned by some pricing models reviewing. This paper following suggests the importance of the dynamic character for option pricing, which is also the reason why using the genetic algorithm (GA). Because of its natural selection and species evolution, this study proposed a hybrid model, the Genetic-BS model which combining GA and B-S to estimate the price more accurate. As for the final experiments, the result shows that the output estimated price with lower MAE value than the calculated price by either B-S model or its enhanced one, Gram-Charlier garch (G-C garch) model. Finally, this work would conclude that the Genetic-BS pricing model is exactly practical.

Keywords: genetic algorithm, Genetic-BS, option pricing model.

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Authors: Zhiqing Zhang, Xiangong Zhou, Zihan Zhou

Abstract:

Ground fissures can be seen in some cities all over the world. As a special urban geological disaster, ground fissures in Xi'an have caused great harm to infrastructure. Chang'an Road Interchange in Xi'an City is a bridge across ground fissures. The damage to Chang'an Road interchange is the most serious and typical. To study the influence of ground fissures on the bridge, we established a bridge monitoring system. The main monitoring items include elevation monitoring, structural displacement monitoring, etc. The monitoring results show that the typical failure is mainly reflected in the bridge deck damage caused by horizontal tension and vertical dislocation. For the construction of urban interchange spanning ground fissures, the interchange should be divided reasonably, a simple support structure with less restriction should be adopted, and the monitoring of supports should be strengthened to prevent the occurrence of beam falling.

Keywords: Bridge monitoring, ground fissures, typical disease, structural displacement.

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Authors: Chuen-Ching Wang, Yao-Tang Chang, Yu-Chang Hsu

Abstract:

A simple but effective digital watermarking scheme utilizing a context adaptive variable length coding (CAVLC) method is presented for wireless communication system. In the proposed approach, the watermark bits are embedded in the final non-zero quantized coefficient of each DCT block, thereby yielding a potential reduction in the length of the coded block. As a result, the watermarking scheme not only provides the means to check the authenticity and integrity of the video stream, but also improves the compression ratio and therefore reduces both the transmission time and the storage space requirements of the coded video sequence. The results confirm that the proposed scheme enables the detection of malicious tampering attacks and reduces the size of the coded H.264 file. Therefore, the current study is feasible to apply in the video applications of wireless communication such as 3G system

Keywords: 3G, wireless communication, CAVLC, digitalwatermarking, motion compensation

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Authors: Cheng-Hsien Chang, Jyi-Tsong Lin, Po-Hsieh Lin, Hung-Pei Hsu, Chan-Hsiang Chang, Ming-Tsung Shih, Shih-Chuan Tseng, Min-Yan Lin

Abstract:

In this paper, we have proposed a novel FinFET with extended body under the poly gate, which is called EB-FinFET, and its characteristic is demonstrated by using three-dimensional (3-D) numerical simulation. We have analyzed and compared it with conventional FinFET. The extended body height dependence on the drain induced barrier lowering (DIBL) and subthreshold swing (S.S) have been also investigated. According to the 3-D numerical simulation, the proposed structure has a firm structure, an acceptable short channel effect (SCE), a reduced series resistance, an increased on state drain current (I on) and a large normalized I DS. Furthermore, the structure can also improve corner effect and reduce self-heating effect due to the extended body. Our results show that the EBFinFET is excellent for nanoscale device.

Keywords: SOI, FinFET, tri-gate, self-heating effect.

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Authors: Kemal Efe, Gui-Liang Feng

Abstract:

The optimal bisection width of r-dimensional N× · · ·× N grid is known to be Nr-1 when N is even, but when N is odd, only approximate values are available. This paper shows that the exact bisection width of grid is Nr -1 N-1 when N is odd.

Keywords: Grids, Parallel Architectures, Graph Bisection, VLSI Layouts.

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