Search results for: Color Distance map

Authors: M. Nashriyah, M. Y. Nur Athiqah, H. Syahril Amin, N. Norhayati, A. W. Mohamad Azhar, M. Khairil

Abstract:

An ethnobotanical study was conducted to document local knowledge and potentials of wild edible tubers that has been reported and sighted and to investigate and record their distribution in Pulau Redang and nearby islands of Terengganu, Malaysia. Information was gathered from 42 villagers by using semi-structured questionnaire. These respondents were selected randomly and no appointment was made prior to the visits. For distribution, the locations of wild edible tubers were recorded by using the Global Positioning System (GPS). The wild edible tubers recorded were ubi gadung, ubi toyo, ubi kasu, ubi jaga, ubi seratus and ubi kertas. Dioscorea or commonly known as yam is reported to be one of the major food sources worldwide. The majority of villagers used Dioscorea hispida Dennst. or ubi gadung in many ways in their life such as for food, medicinal purposes and fish poison. The villagers have identified this ubi gadung by looking at the morphological characteristics; that include leaf shape, stem and the color of the tuber-s flesh.

Keywords: Ethnobotany, distribution, wild edible tubers, Dioscorea hispida Dennst., ubi gadung

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Authors: Sameer Kumar, Jariah Mohd. Jan

Abstract:

Earlier studies in kinship networks have primarily focused on observing the social relationships existing between family relatives. In this study, we pre-identified hubs in the network to investigate if they could play a catalyst role in the transfer of physical information. We conducted a case study of a ceremony performed in one of the families of a small Hindu community – the Uttar Rarhi Kayasthas. Individuals (n = 168) who resided in 11 geographically dispersed regions were contacted through our hub-based representation. We found that using this representation, over 98% of the individuals were successfully contacted within the stipulated period. The network also demonstrated a small-world property, with an average geodesic distance of 3.56.

Keywords: Social Networks, Kinship Networks, Social Network Analysis, Geospatial Communication, Hubs

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Authors: Youngseok Kim, Chul Park, Jonghwa Yi, Sangsik Choi

Abstract:

The 2-MHz Side Scan SONAR (SSS) attached to the boat for inspection of underwater structures is affected by shaking. It is difficult to determine the exact scale of damage of structure. In this study, a motion sensor is attached to the inside of the 2-MHz SSS to get roll, pitch, and yaw direction data, and developed the image stabilization tool to correct the sonar image. We checked that reliable data can be obtained with an average error rate of 1.99% between the measured value and the actual distance through experiment. It is possible to get the accurate sonar data to inspect damage in underwater structure.

Keywords: Image stabilization, motion sensor, safety inspection, sonar image, underwater structure.

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Authors: Hector D. Cortes, Jesus A. del Rio, Esther O. Garcia, Miguel Robles

Abstract:

Recently the use of data mining to scientific bibliographic data bases has been implemented to analyze the pathways of the knowledge or the core scientific relevances of a laureated novel or a country. This specific case of data mining has been named citation mining, and it is the integration of citation bibliometrics and text mining. In this paper we present an improved WEB implementation of statistical physics algorithms to perform the text mining component of citation mining. In particular we use an entropic like distance between the compression of text as an indicator of the similarity between them. Finally, we have included the recently proposed index h to characterize the scientific production. We have used this web implementation to identify users, applications and impact of the Mexican scientific institutions located in the State of Morelos.

Keywords: Citation Mining, Text Mining, Science Impact

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Authors: Hossein Riazoshams, Midi Habshah, Jr., Mohamad Bakri Adam

Abstract:

The detection of outliers is very essential because of their responsibility for producing huge interpretative problem in linear as well as in nonlinear regression analysis. Much work has been accomplished on the identification of outlier in linear regression, but not in nonlinear regression. In this article we propose several outlier detection techniques for nonlinear regression. The main idea is to use the linear approximation of a nonlinear model and consider the gradient as the design matrix. Subsequently, the detection techniques are formulated. Six detection measures are developed that combined with three estimation techniques such as the Least-Squares, M and MM-estimators. The study shows that among the six measures, only the studentized residual and Cook Distance which combined with the MM estimator, consistently capable of identifying the correct outliers.

Keywords: Nonlinear Regression, outliers, Gradient, LeastSquare, M-estimate, MM-estimate.

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Authors: Sallehan Ismail, Mahyuddin Ramli

Abstract:

This study examined the properties of fresh and hardened concretes as influenced by the moisture state of the coarse recycled concrete aggregates (RCA) after surface treatment. Surface treatment was performed by immersing the coarse RCA in a calcium metasilicate (CM) solution. The treated coarse RCA was maintained in three controlled moisture states, namely, air-dried, oven-dried, and saturated surface-dried (SSD), prior to its use in a concrete mix. The physical properties of coarse RCA were evaluated after surface treatment during the first phase of the experiment to determine the density and the water absorption characteristics of the RCA. The second phase involved the evaluation of the slump, slump loss, density, and compressive strength of the concretes that were prepared with different proportions of natural and treated coarse RCA. Controlling the moisture state of the coarse RCA after surface treatment was found to significantly influence the properties of the fresh and hardened concretes. 

Keywords: Moisture state, recycled concrete aggregate, surface treatment.

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Authors: Abdelrasoul, Khalid Ahmed Elrabie

Abstract:

The study was conducted on Sahiwal cattle bulls maintained at the Artificial Breeding Complex, NDRI, Karnal, Hayana, India, to determine the effect of exercise on the sexual behavior and semen quality. Fourteen Sahiwal bulls were classified into two groups of seven each. Group-1, bulls were exercised by walking in a bull exerciser once a week one hour before semen collection, whereas bulls in group-2 were exercised daily. Sexual behavior and semen quality traits studied were: Reaction time (RT), Dismounting time (DMT), Total time taken in mounts (TTTM), Flehmen response (FR), Erection Score (ES), Protrusion Score (PS), Intensity of thrust (ITS), Temperament Score (TS), Libido Score (LS), Semen volume, Physical appearance, Mass activity, Initial progressive motility, Non-eosinophilic spermatozoa count (NESC) and post thaw motility percent. Data were analyzed by least squares technique. Group-2 showed significantly (p < 0.01) higher value in RT (sec), DMT (sec), TTTM (sec), ES, PS, ITS, LS, semen volume, semen color density and mass activity.

Keywords: Exercise, Sahiwal bulls, semen quality, sexual behavior.

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Authors: Ahmad Puad Mat Som, Mohammad Bader Badarneh

Abstract:

Tourism researchers have recently focused on repeat visitation as a part of destination loyalty. Different models have also considered satisfaction as the main determinant of revisit intention, while findings in many studies show it as a continuous issue. This conceptual paper attempts at evaluating recent empirical studies on satisfaction and revisit intention. Based on limitations and gaps in recent studies, the current paper suggests a new model that would be more comprehensive than those in previous studies. The new model offers new relationships between antecedents (destination image, perceived value, specific novelty seeking, and distance to destination) and both of satisfaction and revisit intention. Revisit intention in turn is suggested to be measured in a temporal approach.

Keywords: Satisfaction, revisit intention, a new model.

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Authors: Rujijan Vichivanives, Kittiya Poonsilp, Canasanan Wanavijit

Abstract:

This research aims to create mobile tools to analyze rice disease quickly and easily. The principle of object-oriented software engineering and objective-C language were used for software development methodology and the principle of decision tree technique was used for analysis method. Application users can select the features of rice disease or the color appears on the rice leaves for recognition analysis results on iOS mobile screen. After completing the software development, unit testing and integrating testing method were used to check for program validity. In addition, three plant experts and forty farmers have been assessed for usability and benefit of this system. The overall of users’ satisfaction was found in a good level, 57%. The plant experts give a comment on the addition of various disease symptoms in the database for more precise results of the analysis. For further research, it is suggested that image processing system should be developed as a tool that allows users search and analyze for rice diseases more convenient with great accuracy.

Keywords: Rice disease, analysis system, mobile application, iOS operating system.

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Authors: H. Çimen, İ. Yabanova, M. Nartkaya, S. M. Çinar

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This paper presents a web based remote access microcontroller laboratory. Because of accelerated development in electronics and computer technologies, microcontroller-based devices and appliances are found in all aspects of our daily life. Before the implementation of remote access microcontroller laboratory an experiment set is developed by teaching staff for training microcontrollers. Requirement of technical teaching and industrial applications are considered when experiment set is designed. Students can make the experiments by connecting to the experiment set which is connected to the computer that set as the web server. The students can program the microcontroller, can control digital and analog inputs and can observe experiment. Laboratory experiment web page can be accessed via www.elab.aku.edu.tr address.

Keywords: Embedded systems education, distance learning, internet-based control, remote microcontroller laboratory.

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Authors: Jawad H AlKhateeb, Jianmin Jiang, Jinchang Ren, Stan S Ipson

Abstract:

Efficient preprocessing is very essential for automatic recognition of handwritten documents. In this paper, techniques on segmenting words in handwritten Arabic text are presented. Firstly, connected components (ccs) are extracted, and distances among different components are analyzed. The statistical distribution of this distance is then obtained to determine an optimal threshold for words segmentation. Meanwhile, an improved projection based method is also employed for baseline detection. The proposed method has been successfully tested on IFN/ENIT database consisting of 26459 Arabic words handwritten by 411 different writers, and the results were promising and very encouraging in more accurate detection of the baseline and segmentation of words for further recognition.

Keywords: Arabic OCR, off-line recognition, Baseline estimation, Word segmentation.

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Authors: Bit-Na Kwon, Dong-Hyun Ha, Hyoung-Kyu Song

Abstract:

In wireless communication, space-time block code (STBC), cyclic delay diversity (CDD) and space-time cyclic delay diversity (STCDD)are used as the spatial diversity schemes and have been widely studied for the reliablecommunication. If these schemes are used, the communication system can obtain the improved performance. However,the quality of the system is degraded when the distance between a source and a destination is distant in wireless communication system. In this paper, the cooperative transmission scheme using two sources is proposed and improves the performance of the wireless communication system.

Keywords: OFDM, Cooperative communication, CDD, STBC, STCDD.

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Authors: W. Wiyaratn, A. Watanapa

Abstract:

The objective of this research is to study plant layout of iron manufacturing based on the systematic layout planning pattern theory (SLP) for increased productivity. In this case study, amount of equipments and tools in iron production are studied. The detailed study of the plant layout such as operation process chart, flow of material and activity relationship chart has been investigated. The new plant layout has been designed and compared with the present plant layout. The SLP method showed that new plant layout significantly decrease the distance of material flow from billet cutting process until keeping in ware house.

Keywords: Plant layout, Systematic Layout Planning, Flowanalysis, Activity relationship chart

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Authors: Anuar Ishak

Abstract:

The mixed convection stagnation point flow toward a vertical plate is investigated. The external flow impinges normal to the heated plate and the surface temperature is assumed to vary linearly with the distance from the stagnation point. The governing partial differential equations are transformed into a set of ordinary differential equations, which are then solved numerically using MATLAB routine boundary value problem solver bvp4c. Numerical results show that dual solutions are possible for a certain range of the mixed convection parameter. A stability analysis is performed to determine which solution is linearly stable and physically realizable.

Keywords: Dual solutions, heat transfer, mixed convection, stability analysis.

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Authors: H. Aissa, L. Mouzai, M. Bouhadef

Abstract:

The effects of down slope steepness on soil splash distribution under a water drop impact have been investigated in this study. The equipment used are the burette to simulate a water drop, a splash cup filled with sandy soil which forms the source area and a splash board to collect the ejected particles. The results found in this study have shown that the apparent mass increased with increasing downslope angle following a linear regression equation with high coefficient of determination. In the same way, the radial soil splash distribution over the distance has been analyzed statistically, and an exponential function was the best fit of the relationship for the different slope angles. The curves and the regressions equations validate the well known FSDF and extend the theory of Van Dijk.

Keywords: Splash distribution, water drop, slope steepness, soil detachment.

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Authors: E. E. Mantilla, C. R. Reyes, B. G. Ramos

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This paper describes the development of a WLAN propagation model, using Spectral Analyzer measurements. The signal is generated by two Access Points (APs) on the base floor at the administrative Communication School of ESPOL building. In general, users do not have a Q&S reference about a wireless network; however, this depends on the level signal as a function of frequency, distance and other path conditions between receiver and transmitter. Then, power density of the signal decrease as it propagates through space and data transfer rate is affected. This document evaluates and implements empirical mathematical formulation for the characterization of WLAN radio wave propagation on two aisles of the building base floor.

Keywords: frequency, Spectral Analyzer, transmitter, WLAN.

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Authors: Md. Zahangir Alom, Mei-Lan Piao, Md. Ashraful Alam, Nam Kim, Jae-Hyeung Park

Abstract:

A new approach for facial expressions recognition based on face context and adaptively weighted sub-pattern PCA (Aw-SpPCA) has been presented in this paper. The facial region and others part of the body have been segmented from the complex environment based on skin color model. An algorithm has been proposed to accurate detection of face region from the segmented image based on constant ratio of height and width of face (δ= 1.618). The paper also discusses on new concept to detect the eye and mouth position. The desired part of the face has been cropped to analysis the expression of a person. Unlike PCA based on a whole image pattern, Aw-SpPCA operates directly on its sub patterns partitioned from an original whole pattern and separately extracts features from them. Aw-SpPCA can adaptively compute the contributions of each part and a classification task in order to enhance the robustness to both expression and illumination variations. Experiments on single standard face with five types of facial expression database shows that the proposed method is competitive.

Keywords: Aw-SpPC, Expressoin Recognition, Face context, Face Detection, PCA

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Authors: Mahmoud Elmezain, Ayoub Al-Hamadi, Jörg Appenrodt, Bernd Michaelis

Abstract:

Gesture recognition is a challenging task for extracting meaningful gesture from continuous hand motion. In this paper, we propose an automatic system that recognizes isolated gesture, in addition meaningful gesture from continuous hand motion for Arabic numbers from 0 to 9 in real-time based on Hidden Markov Models (HMM). In order to handle isolated gesture, HMM using Ergodic, Left-Right (LR) and Left-Right Banded (LRB) topologies is applied over the discrete vector feature that is extracted from stereo color image sequences. These topologies are considered to different number of states ranging from 3 to 10. A new system is developed to recognize the meaningful gesture based on zero-codeword detection with static velocity motion for continuous gesture. Therefore, the LRB topology in conjunction with Baum-Welch (BW) algorithm for training and forward algorithm with Viterbi path for testing presents the best performance. Experimental results show that the proposed system can successfully recognize isolated and meaningful gesture and achieve average rate recognition 98.6% and 94.29% respectively.

Keywords: Computer Vision & Image Processing, Gesture Recognition, Pattern Recognition, Application

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Authors: Imran Ahmed, Muhammad Islam, Syed Inayat Ali Shah, Awais Adnan

Abstract:

The identification and classification of weeds are of major technical and economical importance in the agricultural industry. To automate these activities, like in shape, color and texture, weed control system is feasible. The goal of this paper is to build a real-time, machine vision weed control system that can detect weed locations. In order to accomplish this objective, a real-time robotic system is developed to identify and locate outdoor plants using machine vision technology and pattern recognition. The algorithm is developed to classify images into broad and narrow class for real-time selective herbicide application. The developed algorithm has been tested on weeds at various locations, which have shown that the algorithm to be very effectiveness in weed identification. Further the results show a very reliable performance on weeds under varying field conditions. The analysis of the results shows over 90 percent classification accuracy over 140 sample images (broad and narrow) with 70 samples from each category of weeds.

Keywords: Weed detection, Image Processing, real-timerecognition, Standard Deviation.

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Authors: Susana Cortez, Pilar Teixeira, Rosário Oliveira, Manuel Mota

Abstract:

Mature landfill leachates contain some macromolecular organic substances that are resistant to biological degradation. Recently, Fenton-s oxidation has been investigated for chemical treatment or pre-treatment of mature landfill leachates. The aim of this study was to reduce the recalcitrant organic load still remaining after the complete treatment of a mature landfill leachate by Fenton-s oxidation post-treatment. The effect of various parameters such as H2O2 to Fe2+ molar ratio, dosage of Fe2+ reagent, initial pH, reaction time and initial chemical oxygen demand (COD) strength, that have an important role on the oxidation, was analysed. A molar ratio H2O2/Fe2+ = 3, a Fe2+ dosage of 4 mmol·L-1, pH 3, and a reaction time of 40 min were found to achieve better oxidation performances. At these favorable conditions, COD removal efficiency was 60.9% and 31.1% for initial COD of 93 and 743 mg·L-1 respectively (diluted and non diluted leachate). Fenton-s oxidation also presented good results for color removal. In spite of being extremely difficult to treat this leachate, the above results seem rather encouraging on the application of Fenton-s oxidation.

Keywords: Fenton's oxidation, mature landfill leachate, recalcitrant organic matter.

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Authors: B. Munro, D. Lim, A. Anvar

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This paper describes a feasibility study that is included with the research, development and testing of a micro communications sonobuoy deployable by Maritime Fixed wing Unmanned Aerial Vehicles (M-UAV) and rotor wing Quad Copters which are both currently being developed by the University of Adelaide. The micro communications sonobuoy is developed to act as a seamless communication relay between an Autonomous Underwater Vehicle (AUV) and an above water human operator some distance away. Development of such a device would eliminate the requirement of physical communication tethers attached to submersible vehicles for control and data retrieval.

Keywords: Autonomous Underwater Vehicle, AUV, Maritime, Unmanned Aerial Vehicle, UAV, Micro Sonobuoy, Communication.

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Authors: K. Sheehy, R. Ferguson, G. Clough

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This paper examines ethical and social issues which have proved important when initiating and creating educational spaces within a virtual environment. It focuses on one project, identifying the key decisions made, the barriers to new practice encountered and the impact these had on the project. It demonstrates the importance of the 'backstage' ethical and social issues involved in the creation of a virtual education community and offers conclusions, and questions, which will inform future research and practice in this area. These ethical issues are considered using Knobel-s framework of front-end, in-process and back-end concerns, and include establishing social practices for the islands, allocating access rights, considering personal safety and supporting researchers appropriately within this context.

Keywords: distance education, ethics, virtual environments.

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Authors: Ishtiaq A. Chaudhry, Zia R. Tahir

Abstract:

Experimental investigation has been carried out towards understanding the complex fluid dynamics involved in the interaction of vortical structures with zero pressure gradient boundary layer. A laminar boundary layer is produced on the flat plate placed in the water flume and the synthetic jet actuator is deployed on top of the plate at a definite distance from the leading edge. The synthetic jet actuator has been designed in such a way that the to and fro motion of the diaphragm is maneuvered at will by varying the operating parameters to produce the typical streamwise vortical structures namely hairpin and tilted vortices. PIV measurements are made on the streamwise plane normal to the plate to evaluate their interaction with the near wall fluid.

Keywords: Boundary layer, synthetic jet actuator, flow separation control, vortical structures.

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Authors: Emil G. Ioanid, Viorica Frunză, Dorina Rusu, Ana Maria Vlad, Catalin Tanase, Simona Dunca

Abstract:

The application of cold Radio-Frequency (RF) plasma in the conservation of cultural heritage became important in the last decades due to the positive results obtained in decontamination treatments. This paper presents an equipment especially designed for cold RF plasma application on paper documents, developed within a research project. The equipment consists in two modules: the first one is designed for decontamination and cleaning treatments of any type of paper supports, while the second one can be used for coating friable papers with adequate polymers, for protection purposes. All these operations are carried out in cold radio-frequency plasma, working in gaseous nitrogen, at low pressure. In order to optimize the equipment parameters ancient paper samples infested with microorganisms have been treated in nitrogen plasma and the decontamination effects, as well as changes in surface properties (color, pH) were assessed. The microbiological analysis revealed complete decontamination at 6 minutes treatment duration; only minor modifications of the surface pH were found and the colorimetric analysis showed a slight yellowing of the support.

Keywords: Cultural heritage, nitrogen plasma, paper support.

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Authors: Ayhan Aydoğdu, Ercan Ceyhan, Ali Kahraman, Nursel Çöl

Abstract:

This research was conducted to determine effects of plant densities on seed yield and some agricultural characteristics of pea variety- Jofs in Konya ecological conditions during 2012 vegetation period. The trial was set up according to “Randomized Blocks Design” with three replications. The material “Jofs” pea variety was subjected to 3-row spaces (30, 40 and 50 cm) and 3-row distances (5, 10 and 15 cm). According to the results, difference was shown statistically for the effects of row spaces and row distances on seed yield. The highest seed yield was 2582.1 kg ha-1 on 30 cm of row spaces while 2562.2 kg ha-1 on 15 cm of distances. Consequently, the optimum planting density was determined as 30 x 15 cm for Jofs pea variety growing in Konya.

Keywords: Pea, row space, row distance, seed yield.

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Authors: K. Raghuwaiya, B. Sharma, J. Vanualailai

Abstract:

This paper presents a set of artificial potential field functions that improves upon, in general, the motion planning and posture control, with theoretically guaranteed point and posture stabilities, convergence and collision avoidance properties of the general3-trailer system in a priori known environment. We basically design and inject two new concepts; ghost walls and the distance optimization technique (DOT) to strengthen point and posture stabilities, in the sense of Lyapunov, of our dynamical model. This new combination of techniques emerges as a convenient mechanism for obtaining feasible orientations at the target positions with an overall reduction in the complexity of the navigation laws. Simulations are provided to demonstrate the effectiveness of the controls laws.

Keywords: Artificial potential fields, 3-trailer systems, motion planning, posture.

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Authors: E. Ahvar, M. Fathy

Abstract:

Ad hoc networks are characterized by multihop wireless connectivity, frequently changing network topology and the need for efficient dynamic routing protocols. We compare the performance of three routing protocols for mobile ad hoc networks: Dynamic Source Routing (DSR), Ad Hoc On-Demand Distance Vector Routing (AODV), location-aided routing (LAR1).Our evaluation is based on energy consumption in mobile ad hoc networks. The performance differentials are analyzed using varying network load, mobility, and network size. We simulate protocols with GLOMOSIM simulator. Based on the observations, we make recommendations about when the performance of either protocol can be best.

Keywords: Ad hoc Network, energy consumption, Glomosim, routing protocols.

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Authors: Feifei Lee, Qiu Chen, Koji Kotani, Tadahiro Ohmi

Abstract:

In this paper, we present an improved fast and robust search algorithm for copy detection using histogram-based features for short MPEG video clips from large video database. There are two types of histogram features used to generate more robust features. The first one is based on the adjacent pixel intensity difference quantization (APIDQ) algorithm, which had been reliably applied to human face recognition previously. An APIDQ histogram is utilized as the feature vector of the frame image. Another one is ordinal histogram feature which is robust to color distortion. Furthermore, by Combining with a temporal division method, the spatial and temporal features of the video sequence are integrated to realize fast and robust video search for copy detection. Experimental results show the proposed algorithm can detect the similar video clip more accurately and robust than conventional fast video search algorithm.

Keywords: Fast search, Copy detection, Adjacent pixel intensity difference quantization (APIDQ), DC image, Histogram feature.

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Authors: Gopalu Karunakaran, Matheswaran Jagathambal, Nguyen Van Minh, Evgeny Kolesnikov, Denis Kuznetsov

Abstract:

This work investigated the use of Beijerinckia indica extracellular extract for the synthesis of silver nanoparticles using AgNO₃. The formation of nanoparticles was confirmed by different methods, such as UV-Vis absorption spectroscopy, XRD, FTIR, EDX, and TEM analysis. The formation of silver nanoparticles (AgNPs) was confirmed by the change in color from light yellow to dark brown. The absorbance peak obtained at 430 nm confirmed the presence of silver nanoparticles. The XRD analysis showed the cubic crystalline phase of the synthesized nanoparticles. FTIR revealed the presence of groups that acts as stabilizing and reducing agents for silver nanoparticles formation. The synthesized silver nanoparticles were generally found to be spherical in shape with size ranging from 5 to 20 nm, as evident by TEM analysis. These nanoparticles were found to inhibit pathogenic bacterial strains. This work proved that the bacterial extract is a potential eco-friendly candidate for the synthesis of silver nanoparticles with promising antibacterial and antioxidant properties. 

Keywords: Antioxidant activity, antimicrobial activity, Beijerinckia indica, characterisation, extracellular extracts, silver nanoparticles.

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Authors: P. K. Rahul Krishna, S. Sandeep Kumar, Jayanthi Sunder Raj

Abstract:

The article explores one of the important relations between numbers-the Pythagorean triples (triplets) which finds its application in distance measurement, construction of roads, towers, buildings and wherever Pythagoras theorem finds its application. The Pythagorean triples are numbers, that satisfy the condition “In a given set of three natural numbers, the sum of squares of two natural numbers is equal to the square of the other natural number”. There are numerous methods and equations to obtain the triplets, which have their own merits and demerits. Here, quadratic approach for generating triples uses the hypotenuse leg difference method. The advantage is that variables are few and finally only three independent variables are present.

Keywords: Arithmetic progression, hypotenuse leg difference method, natural numbers, Pythagorean triplets, quadratic equation.

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