Search results for: color difference histogram

Authors: K. Sontaya, B. Pitiyont, V. Punsuvon

Abstract:

The objective of this study is to investigate the performance of the electrocoagulation process for color and COD removal in palm oil wastewater using a 10 L batch reactor. Iron was used as electrodes and the distance between electrodes was 2 cm. The effects of operating parameters: current voltage (6, 12 and 18 volt), reaction time (5, 15, 30, 45 and 60 min) and initial pH (4 and 9) of treatment efficiency were examine. The result showed that decolorization and COD removal efficiency increased with the increase in current voltage and reaction time. The proper condition for decolorization achieved at initial pH 4 and 9 were current voltage of 12 volt, reaction time 30 min. The decolorization efficiency reached 90.4% and 88.9%, respectively. COD removal was achiveved at current voltage 12 volt, reaction time 15 min. COD removal efficiency was 89.2 % and 83.0%, respectively. From the results, to show electrocoagulation process can treat palm oil mill wastewater in both acidic and basic condition at high efficiency for color and COD removal. Consequently, electrocoagulation process can be used or applied as a post-treatment step to improve the quality of the final discharge in term of color and residual COD removal.

Keywords: COD removal, decolorizaton, electrocoagulation, iron electrode, palm oil mill wastewater.

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Authors: Chia-Hung Lin, Mei-Sung Kang, Cong-Hui Huang, Chao-Lin Kuo

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This paper proposes fractal patterns for power quality (PQ) detection using color relational analysis (CRA) based classifier. Iterated function system (IFS) uses the non-linear interpolation in the map and uses similarity maps to construct various fractal patterns of power quality disturbances, including harmonics, voltage sag, voltage swell, voltage sag involving harmonics, voltage swell involving harmonics, and voltage interruption. The non-linear interpolation functions (NIFs) with fractal dimension (FD) make fractal patterns more distinguishing between normal and abnormal voltage signals. The classifier based on CRA discriminates the disturbance events in a power system. Compared with the wavelet neural networks, the test results will show accurate discrimination, good robustness, and faster processing time for detecting disturbing events.

Keywords: Power Quality (PQ), Color Relational Analysis(CRA), Iterated Function System (IFS), Non-linear InterpolationFunction (NIF), Fractal Dimension (FD).

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Authors: M. Ghasemi-Varnamkhasti, S. H. Yoosefian. A. Mohammad- Razdari

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The effect of 1.0 kJ/m² Ultraviolet-C (UV-C) light on pH, weight loss, color, and firmness of button mushroom (Agaricus bisporus) tissues during 21-days storage at 4 ºC was studied. UV-C irradiation enhanced pH, weight, color parameters, and firmness of mushroom during storage compared to control treatment. However, application of 1.0 kJ/m² UV-C treatment could effectively induce the increase of weight loss, firmness, and pH to 14.53%, 49.82%, and 10.39%, respectively. These results suggest that the application of UV-C irradiation could be an effective method to maintain the postharvest quality of mushrooms.

Keywords: Mushroom, polyethylene film, quality, UV-C irradiation.

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Authors: Jiming Yang

Abstract:

An upwind difference approximation is used for a singularly perturbed problem in material science. Based on the discrete Green-s function theory, the error estimate in maximum norm is achieved, which is first-order uniformly convergent with respect to the perturbation parameter. The numerical experimental result is verified the valid of the theoretical analysis.

Keywords: Singularly perturbed, upwind difference, uniform convergence.

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Authors: Youngsuck Ji, Youngjoon Han, Hernsoo Hahn

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In this paper, we proposed the robust mobile object detection method for light effect in the night street image block based updating reference background model using block state analysis. Experiment image is acquired sequence color video from steady camera. When suddenly appeared artificial illumination, reference background model update this information such as street light, sign light. Generally natural illumination is change by temporal, but artificial illumination is suddenly appearance. So in this paper for exactly detect artificial illumination have 2 state process. First process is compare difference between current image and reference background by block based, it can know changed blocks. Second process is difference between current image-s edge map and reference background image-s edge map, it possible to estimate illumination at any block. This information is possible to exactly detect object, artificial illumination and it was generating reference background more clearly. Block is classified by block-state analysis. Block-state has a 4 state (i.e. transient, stationary, background, artificial illumination). Fig. 1 is show characteristic of block-state respectively [1]. Experimental results show that the presented approach works well in the presence of illumination variance.

Keywords: Block-state, Edge component, Reference backgroundi, Artificial illumination.

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Authors: Hu-Hsiao Hsu, Po-Ren Chung, Ming-Chin Ho, Chieh-Feng Tsai, Che-Ming Chiang, Shin-Ku Lee

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Lighting upgrades involve relatively lower costs which allow the benefits to be spread more widely than is possible with any other energy efficiency measure. In order to popularize the adoption of CFL in Taiwan, the authority proposes to implement a new energy efficient lamp comparative label system. The current study was accordingly undertaken to investigate the factors affecting the performance and the deviation of actual and labeled performance of commercially available integrated CFLs. In this paper, standard test methods to determine the electrical and photometric performances of CFL were developed based on CIE 84-1989 and CIE 60901-1987, then 55 selected CFLs from market were tested. The results show that with higher color temperature of CFLs lower efficacy are achieved. It was noticed that the most packaging of CFL often lack the information of Color Rendering Index. Also, there was no correlation between price and performance of the CFLs was indicated in this work. The results of this paper might help consumers to make more informed CFL-purchasing decisions.

Keywords: Compact fluorescent lamp (CFL), Efficacy, Color Rendering Index (CRI), Energy saving.

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Authors: J. Hardeberg, J. Hernandez-Andrès, J. L. Nieves, M. Hauta-Kasari, J. Parkkinen, A. Trémeau

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The main objective of this paper is to identify and disseminate good practice in quality assurance and enhancement as well as in teaching and learning at master level. This paper focuses on the experience of the Erasmus Mundus Master program CIMET (Color in Informatics and Media Technology). Amongst topics covered, we discuss the adjustments necessary to a curriculum designed for excellent international students and their preparation for a global labor market.

Keywords: Good practice, internal quality systems, innovationsin curriculum design, challenges of internationalization

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Authors: Takashi Kaburagi, Takamasa Komura, Yosuke Kurihara

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Absolute pitch is the ability to identify a musical note without a reference tone. Training for absolute pitch often occurs in preschool education. It is necessary to clarify how well the trainee can make use of synesthesia in order to evaluate the effect of the training. To the best of our knowledge, there are no existing methods for objectively confirming whether the subject is using synesthesia. Therefore, in this study, we present a method to distinguish the use of color-auditory synesthesia from the separate use of color and audition during absolute pitch training. This method measures blood volume in the prefrontal cortex using functional Near-infrared spectroscopy (fNIRS) and assumes that the cognitive step has two parts, a non-linear step and a linear step. For the linear step, we assume a second order ordinary differential equation. For the non-linear part, it is extremely difficult, if not impossible, to create an inverse filter of such a complex system as the brain. Therefore, we apply a method based on a self-organizing map (SOM) and are guided by the available data. The presented method was tested using 15 subjects, and the estimation accuracy is reported.

Keywords: Absolute pitch, functional near-infrared spectroscopy, prefrontal cortex, synesthesia.

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Authors: Şehri Çınar, Aydın Akın

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This study was conducted Razakı grape variety (Vitis vinifera L.) and its vine which was aged 19 was grown on 5 BB rootstock in a vegetation period of 2014 in Afyon province in Turkey. In this research, it was investigated whether the applications of Control (C), 1/3 Cluster Tip Reduction (1/3 CTR), Shoot Tip Reduction (STR), 1/3 CTR + STR, Boric Acid (BA), 1/3 CTR + BA, STR + BA, 1/3 CTR + STR + BA on yield and yield components of Razakı grape variety. The results were obtained as the highest fresh grape yield (7.74 kg/vine) with C application; as the highest cluster weight (244.62 g) with STR application; as the highest 100 berry weight (504.08 g) with C application; as the highest maturity index (36.89) with BA application; as the highest must yield (695.00 ml) with BA and (695.00 ml) with 1/3 CTR + STR + BA applications; as the highest intensity of L* color (46.93) with STR and (46.10) with 1/3 CTR + STR + BA applications; as the highest intensity of a* color (-5.37) with 1/3 CTR + STR and (-5.01) with STR, as the highest intensity of b* color (12.59) with STR application. The shoot tip reduction to increase cluster weight and boric acid application to increase maturity index of Razakı grape variety can be recommended.

Keywords: Razakı, 1/3 cluster tip reduction, shoot tip reduction, boric acid, yield and yield components.

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Authors: Mahkameh S. Mostafavi

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In this paper an algorithm is used to detect the color defects of ceramic tiles. First the image of a normal tile is clustered using GCMA; Genetic C-means Clustering Algorithm; those results in best cluster centers. C-means is a common clustering algorithm which optimizes an objective function, based on a measure between data points and the cluster centers in the data space. Here the objective function describes the mean square error. After finding the best centers, each pixel of the image is assigned to the cluster with closest cluster center. Then, the maximum errors of clusters are computed. For each cluster, max error is the maximum distance between its center and all the pixels which belong to it. After computing errors all the pixels of defected tile image are clustered based on the centers obtained from normal tile image in previous stage. Pixels which their distance from their cluster center is more than the maximum error of that cluster are considered as defected pixels.

Keywords: C-Means algorithm, color spaces, Genetic Algorithm, image clustering.

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Authors: Qianhong Zhang, Lihui Yang, Daixi Liao,

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In this paper, we study the existence, the boundedness and the asymptotic behavior of the positive solutions of a fuzzy nonlinear difference equations xn+1 = A + k i=0 Bi xn-i , n= 0, 1, · · · . where (xn) is a sequence of positive fuzzy numbers, A,Bi and the initial values x-k, x-k+1, · · · , x0 are positive fuzzy numbers. k ∈ {0, 1, 2, · · ·}.

Keywords: Fuzzy difference equation, boundedness, persistence, equilibrium point, asymptotic behaviour.

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Authors: Raghad Jawad Ahmed

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Segmentation of a color image composed of different kinds of regions can be a hard problem, namely to compute for an exact texture fields. The decision of the optimum number of segmentation areas in an image when it contains similar and/or un stationary texture fields. A novel neighborhood-based segmentation approach is proposed. A genetic algorithm is used in the proposed segment-pass optimization process. In this pass, an energy function, which is defined based on Markov Random Fields, is minimized. In this paper we use an adaptive threshold estimation method for image thresholding in the wavelet domain based on the generalized Gaussian distribution (GGD) modeling of sub band coefficients. This method called Normal Shrink is computationally more efficient and adaptive because the parameters required for estimating the threshold depend on sub band data energy that used in the pre-stage of segmentation. A quad tree is employed to implement the multi resolution framework, which enables the use of different strategies at different resolution levels, and hence, the computation can be accelerated. The experimental results using the proposed segmentation approach are very encouraging.

Keywords: Color image segmentation, Genetic algorithm, Markov random field, Scale space filter.

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Authors: S. Zith Dey Babu, S. Kour, S. Verma, C. Verma, V. Pathania, A. Agrawal, V. Chaudhary, A. Manoj Puthur, R. Goyal, A. Pal, T. Danti Dey, A. Kumar, K. Wadhwa, O. Ved

Abstract:

Background: Skin cancer is now is the buzzing button in the field of medical science. The cyst's pandemic is drastically calibrating the body and well-being of the global village. Methods: The extracted image of the skin tumor cannot be used in one way for diagnosis. The stored image contains anarchies like the center. This approach will locate the forepart of an extracted appearance of skin. Partitioning image models has been presented to sort out the disturbance in the picture. Results: After completing partitioning, feature extraction has been formed by using genetic algorithm and finally, classification can be performed between the trained and test data to evaluate a large scale of an image that helps the doctors for the right prediction. To bring the improvisation of the existing system, we have set our objectives with an analysis. The efficiency of the natural selection process and the enriching histogram is essential in that respect. To reduce the false-positive rate or output, GA is performed with its accuracy. Conclusions: The objective of this task is to bring improvisation of effectiveness. GA is accomplishing its task with perfection to bring down the invalid-positive rate or outcome. The paper's mergeable portion conflicts with the composition of deep learning and medical image processing, which provides superior accuracy. Proportional types of handling create the reusability without any errors.

Keywords: Computer-aided system, detection, image segmentation, morphology.

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Authors: Nopparat Pochai, Rujira Deepana

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Water pollution assessment problems arise frequently in environmental science. In this research, a finite difference method for solving the one-dimensional steady convection-diffusion equation with variable coefficients is proposed; it is then used to optimize water treatment costs.

Keywords: Finite difference, One-dimensional, Steady state, Waterpollution control, Optimization, Convection-diffusion equation.

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Authors: Farhad H. Mustafa, Mohamad S. Jaafar , Asaad H. Ismail, Ahamad F. Omar, Zahra A. Timimi, Hend A. A. Houssein

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The process of laser absorption in the skin during laser irradiation was a critical point in medical application treatments. Delivery the correct amount of laser light is a critical element in photodynamic therapy (PDT). More amounts of laser light able to affect tissues in the skin and small amount not able to enhance PDT procedure in skin. The knowledge of the skin tone laser dependent distribution of 635 nm radiation and its penetration depth in skin is a very important precondition for the investigation of advantage laser induced effect in (PDT) in epidermis diseases (psoriasis). The aim of this work was to estimate an optimum effect of diode laser (635 nm) on the treatment of epidermis diseases in different color skin. Furthermore, it is to improve safety of laser in PDT in epidermis diseases treatment. Advanced system analytical program (ASAP) which is a new approach in investigating the PDT, dependent on optical properties of different skin color was used in present work. A two layered Realistic Skin Model (RSM); stratum corneum and epidermal with red laser (635 nm, 10 mW) were used for irradiative transfer to study fluence and absorbance in different penetration for various human skin colors. Several skin tones very fair, fair, light, medium and dark are used to irradiative transfer. This investigation involved the principles of laser tissue interaction when the skin optically injected by a red laser diode. The results demonstrated that the power characteristic of a laser diode (635 nm) can affect the treatment of epidermal disease in various color skins. Power absorption of the various human skins were recorded and analyzed in order to find the influence of the melanin in PDT treatment in epidermal disease. A two layered RSM show that the change in penetration depth in epidermal layer of the color skin has a larger effect on the distribution of absorbed laser in the skin; this is due to the variation of the melanin concentration for each color.

Keywords: Photodynamic therapy, Realistic skin model, Laser, Light penetration, simulation, Optical properties of skin, Melanin.

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Authors: P. Bountris, E. Farantatos, N. Apostolou

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Autofluorescence (AF) bronchoscopy is an established method to detect dysplasia and carcinoma in situ (CIS). For this reason the “Sotiria" Hospital uses the Karl Storz D-light system. However, in early tumor stages the visualization is not that obvious. With the help of a PC, we analyzed the color images we captured by developing certain tools in Matlab®. We used statistical methods based on texture analysis, signal processing methods based on Gabor models and conversion algorithms between devicedependent color spaces. Our belief is that we reduced the error made by the naked eye. The tools we implemented improve the quality of patients' life.

Keywords: Bronchoscopy, digital image processing, lung cancer, texture analysis.

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Authors: Hassan Saberi-Nik, Mahin Golchaman

Abstract:

This paper applies the homotopy analysis method method to a nonlinear differential-difference equation arising in nanotechnology. Continuum hypothesis on nanoscales is invalid, and a differential-difference model is considered as an alternative approach to describing discontinued problems. Comparison of the approximate solution with the exact one reveals that the method is very effective.

Keywords: Homotopy analysis method, differential-difference, nanotechnology.

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Authors: Gholam Hossein Naseri, Manucher Tamizi

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Light is one of the most important qualitative and symbolic factors and has a special position in architecture and urban development in regard to practical function. The main function of light, either natural or artificial, is lighting up the environment and the constructional forms which is called lighting. However, light is used to redefine the urban spaces by architectural genius with regard to three aesthetic, conceptual and symbolic factors. In architecture and urban development, light has a function beyond lighting up the environment, and the designers consider it as one of the basic components. The present research aims at studying the function of light and color in architectural view and their effects in buildings.

Keywords: Architectural View , Color , Light

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Authors: Syong-Yang Chung, Xin-An Chen

Abstract:

This study aims to explore the less well-known animation “Final Flight of the Osiris”, consisting of an initial exploration of the film color, storyline, and the simulacrum meanings of the roles, which leads to a further exploration of the light-shadow contrast and the psychological images presented by the screen colors and the characters. The research is based on literature review, and all data was compiled for the analysis of the visual vocabulary evolution of the characters. In terms of the structure, the relational study of the animation and the historical background of that time came first, including The Wachowskis’ and Andy Jones’ impact towards the cinematographic version and the animation version of “The Matrix”. Through literature review, the film color, the meaning and the relevant points were clarified. It was found in this research that “Final Flight of the Osiris” separates the realistic and virtual spaces by the changing the color tones; the "self" of the audience gradually dissolves into the "virtual" in the simulacra world, and the "Animatrix" has become a virtual field for the audience to understand itself about "existence" and "self".

Keywords: The Matrix, The Final Flight of Osiris, Wachowski sisters, simulacrum.

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Authors: Michela Lecca

Abstract:

System MEMORI automatically detects and recognizes rotated and/or rescaled versions of the objects of a database within digital color images with cluttered background. This task is accomplished by means of a region grouping algorithm guided by heuristic rules, whose parameters concern some geometrical properties and the recognition score of the database objects. This paper focuses on the strategies implemented in MEMORI for the estimation of the heuristic rule parameters. This estimation, being automatic, makes the system a highly user-friendly tool.

Keywords: Automatic object recognition, clustering, content based image retrieval system, image segmentation, region adjacency graph, region grouping.

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Authors: Supatchalee Sirichokworrakit, Pannin Intasen, Chansuda Angkawut

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Hom Nin rice (Oryza Sativa L.) was processed into flour and used to substitute wheat flour in donuts. The donuts were prepared with 0, 20, 40, 60, and 80% Hom Nin rice flour (HNF). The donuts were subjected to proximate, texture, color and sensory evaluations. The results of the study revealed that the ash, moisture, crude fiber contents increased while crude fat and protein contents decreased as the level of HNF increased. The hardness and chewiness of donut increased as the HNF increased but the cohesiveness, springiness, and specific volume decreased. Color of donut (L*, a*, and b* values) decreased with the addition of HNF. Overall acceptability for the 20-40% HNF additions did not differ significantly from the score of the 100% wheat flour.

Keywords: Hom Nin rice, donut, texture evaluation, sensory evaluation.

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Authors: Jer-Huan Jang, Han-Chieh Chiu, Wei-Chung Yeih, Jia-Jui Yang, Chien-Sheng Huang

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In this paper, numerical simulation is used to investigate the thermal performance of liquid cooling heatsink with microchannels due to geometric arrangement. Commercial software ICEPAK is utilized for the analysis. The considered parameters include aspect ratio, porosity and the length and height of microchannel. The aspect ratio varies from 3 to 16 and the length of microchannel is 10mm, 14mm, and 18mm. The height of microchannel is 2mm, 3mm and 4mm. It is found short channel have better thermal efficiency than long channel at 490Pa. No matter the length of channel the best aspect ratio is 4. It is also noted that pressure difference at 2940Pa the best aspect ratio from 4 to 8, it means pressure difference affect aspect ratio, effective thermal resistance at low pressure difference but lower effective thermal resistance at high pressure difference.

Keywords: thermal resistance, liquid cooling, microchannels, numerical analysis, pressure difference

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Authors: R. C. Joshi, Shashikala Tapaswi

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The paper proposes an approach using genetic algorithm for computing the region based image similarity. The image is denoted using a set of segmented regions reflecting color and texture properties of an image. An image is associated with a family of image features corresponding to the regions. The resemblance of two images is then defined as the overall similarity between two families of image features, and quantified by a similarity measure, which integrates properties of all the regions in the images. A genetic algorithm is applied to decide the most plausible matching. The performance of the proposed method is illustrated using examples from an image database of general-purpose images, and is shown to produce good results.

Keywords: Image Features, color descriptor, segmented classes, texture descriptors, genetic algorithm.

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Authors: Michela Lecca

Abstract:

System MEMORI automatically detects and recognizes rotated and/or rescaled versions of the objects of a database within digital color images with cluttered background. This task is accomplished by means of a region grouping algorithm guided by heuristic rules, whose parameters concern some geometrical properties and the recognition score of the database objects. This paper focuses on the strategies implemented in MEMORI for the estimation of the heuristic rule parameters. This estimation, being automatic, makes the system a self configuring and highly user-friendly tool.

Keywords: Automatic Object Recognition, Clustering, Contentbased Image Retrieval System, Image Segmentation, Region Adjacency Graph, Region Grouping.

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Authors: Zainab Almukhtar, Adel Merabet

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In this paper, a method for maximum power point tracking of a photovoltaic energy conversion system is presented. This method is based on using the difference between the power from the solar panel and an estimated power value to control the DC-DC converter of the photovoltaic system. The difference is continuously compared with a preset error permitted value. If the power difference is more than the error, the estimated power is multiplied by a factor and the operation is repeated until the difference is less or equal to the threshold error. The difference in power will be used to trigger a DC-DC boost converter in order to raise the voltage to where the maximum power point is achieved. The proposed method was experimentally verified through a PV energy conversion system driven by the OPAL-RT real time controller. The method was tested on varying radiation conditions and load requirements, and the Photovoltaic Panel was operated at its maximum power in different conditions of irradiation.

Keywords: Control system, power error, solar panel, MPPT.

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Authors: P. Chaijak, M. Lertworapreecha, C. Sukkasem

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A huge of dark color palm oil mill effluent (POME) cannot pass the discharge standard. It has been identified as the major contributor to the pollution load into ground water. Here, lignin-degrading yeast isolated from a termite nest was tested to treat the POME. Its lignin-degrading and decolorizing ability was determined. The result illustrated that Galactomyces sp. was successfully grown in POME. The decolorizing test demonstrated that 40% of Galactomyces sp. could reduce the color of POME (50% v/v) about 74-75% in 5 days without nutrient supplement. The result suggested that G. reessii has a potential to apply for decolorizing the dark wastewater like POME and other industrial wastewaters.

Keywords: Decolorization, palm oil mill effluent, ligninolytic enzyme, yeast, termite.

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Authors: M. Dehghan, R. Al-Mahaidi, I. Sbarski

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An industrial epoxy adhesive used in Carbon Fiber Reinforced Polymer (CFRP) strengthening systems was modified by dispersing multi-walled carbon nanotubes (MWCNTs). Nanocomposites were fabricated using the solvent-assisted dispersion method and ultrasonic mixing. Thermogravimetric analysis (TGA), dynamic mechanical analysis (DMA) and tensile tests were conducted to study the effect of nanotubes dispersion on the thermal and mechanical properties of the epoxy composite. Experimental results showed a substantial enhancement in the decomposition temperature and tensile properties of epoxy composite, while, the glass transition temperature (T_g) was slightly reduced due to the solvent effect. The morphology of the epoxy nanocomposites was investigated by SEM. It was proved that using solvent improves the nanotubes dispersion. However, at contents higher than 2 wt. %, nanotubes started to re-bundle in the epoxy matrix which negatively affected the final properties of epoxy composite.

Keywords: Carbon Fiber Reinforced Polymer, Epoxy, Multi-Walled Carbon Nanotube, Glass Transition Temperature.

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Authors: Krishnamurthy G N, V Ramaswamy

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This paper demonstrates the results when either Shiftrows stage or Mixcolumns stage and when both the stages are omitted in the well known block cipher Advanced Encryption Standard(AES) and its modified version AES with Key Dependent S-box(AES-KDS), using avalanche criterion and other tests namely encryption quality, correlation coefficient, histogram analysis and key sensitivity tests.

Keywords: Encryption, Decryption, Avalanche, keysensitivity.

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Authors: Piercarlo Dondi, Luca Lombardi, Marco Porta

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In the last years numerous applications of Human- Computer Interaction have exploited the capabilities of Time-of- Flight cameras for achieving more and more comfortable and precise interactions. In particular, gesture recognition is one of the most active fields. This work presents a new method for interacting with a virtual object in a 3D space. Our approach is based on the fusion of depth data, supplied by a ToF camera, with color information, supplied by a HD webcam. The hand detection procedure does not require any learning phase and is able to concurrently manage gestures of two hands. The system is robust to the presence in the scene of other objects or people, thanks to the use of the Kalman filter for maintaining the tracking of the hands.

Keywords: Gesture recognition, human-computer interaction, Time-of-Flight camera.

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Authors: Aiman Elragig, Hanan Dreiwi, Dung Ly, Idriss Elmabrook

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This paper highlights a new approach to look at online principle components analysis (OPCA). Given a data matrix X ∈ R,^m x n we characterise the online updates of its covariance as a matrix perturbation problem. Up to the principle components, it turns out that online updates of the batch PCA can be captured by symmetric matrix perturbation of the batch covariance matrix. We have shown that as n→ n0 >> 1, the batch covariance and its update become almost similar. Finally, utilize our new setup of online updates to find a bound on the angle distance of the principle components of X and its update.

Keywords: Online data updates, covariance matrix, online principle component analysis (OPCA), matrix perturbation.

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