Search results for: Central Difference Method

Authors: Bharathi P. T, P. Subashini

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Ice cover County has a significant impact on rivers as it affects with the ice melting capacity which results in flooding, restrict navigation, modify the ecosystem and microclimate. River ices are made up of different ice types with varying ice thickness, so surveillance of river ice plays an important role. River ice types are captured using infrared imaging camera which captures the images even during the night times. In this paper the river ice infrared texture images are analysed using first-order statistical methods and secondorder statistical methods. The second order statistical methods considered are spatial gray level dependence method, gray level run length method and gray level difference method. The performance of the feature extraction methods are evaluated by using Probabilistic Neural Network classifier and it is found that the first-order statistical method and second-order statistical method yields low accuracy. So the features extracted from the first-order statistical method and second-order statistical method are combined and it is observed that the result of these combined features (First order statistical method + gray level run length method) provides higher accuracy when compared with the features from the first-order statistical method and second-order statistical method alone.

Keywords: Gray Level Difference Method, Gray Level Run Length Method, Kurtosis, Probabilistic Neural Network, Skewness, Spatial Gray Level Dependence Method.

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Authors: Kokiat Aodsup, Thanatchai Kulworawanichpong

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This paper describes a finite-difference time-domainFDTD) method to analyze lightning surge propagation in electric transmission lines. Numerical computation of solving the Telegraphist-s equations is determined and investigated its effectiveness. A source of lightning surge wave on power transmission lines is modeled by using Heidler-s surge model. The proposed method was tested against medium-voltage power transmission lines in comparison with the solution obtained by using lattice diagram. As a result, the calculation showed that the method is one of accurate methods to analyze transient lightning wave in power transmission lines.

Keywords: Traveling wave, Lightning surge, Bewley lattice diagram, Telegraphist's equations, Finite-difference time-domain (FDTD) method,

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Authors: Handan Ertaş

Abstract:

The aim of the study is to determine the relationship between organizational trust level and organizational justice of Municipality officials. Correlational method has been used via descriptive survey model and Organizational Justice Perception Scale, Organizational Trust Inventory and Interpersonal Trust Scale have been applied to 353 participants who work in Konya Metropolitan Municipality and central district municipalities in the study. Frequency as statistical method, Independent Samples t test for binary groups, One Way-ANOVA analyses for multi-groups and Pearson Correlation analysis have been used to determine the relation in the data analysis process.It has been determined in the outcomes of the study that participants have high level of organizational trust, “Interpersonal Trust” is in the first place and there is a significant difference in the favor of male officials in terms of Trust on the Organization Itself and Interpersonal Trust. It has also been understood that officials in district municipalities have higher perception level in all dimensions, there is a significant difference in Trust on the Organization sub-dimension and work status is an important factor on organizational trust perception. Moreover, the study has shown that organizational justice implementations are important in raising trust of official on the organization, administrator and colleagues, and there is a parallel relation between Organizational Trust components and Organizational Trust dimensions.

Keywords: Konya, Organizational Justice, Organizational.

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Authors: Abdenour Bourabaa, Malika Fekih, Mohamed Saighi

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A numerical investigation of the fin efficiency and temperature distribution of an annular fin under dehumidification has been presented in this paper. The non-homogeneous second order differential equation that describes the temperature distribution from the fin base to the fin tip has been solved using the central finite difference method. The effects of variations in parameters including relative humidity, air temperature, air face velocity on temperature distribution and fin efficiency are investigated and compared with those under fully dry fin conditions. Also, the effect of fin pitch on the dimensionless temperature has been studied.

Keywords: Annular fin, Dehumidification, Fin efficiency, Heat and mass transfer, Wet fin.

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Authors: Norhashidah Hj. Mohd Ali, Teng Wai Ping

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In this paper, we present a high order group explicit method in solving the two dimensional Helmholtz equation. The presented method is derived from a nine-point fourth order finite difference approximation formula obtained from a 45-degree rotation of the standard grid which makes it possible for the construction of iterative procedure with reduced complexity. The developed method will be compared with the existing group iterative schemes available in literature in terms of computational time, iteration counts, and computational complexity. The comparative performances of the methods will be discussed and reported.

Keywords: Explicit group method, finite difference, Helmholtz equation, rotated grid, standard grid.

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Authors: P. Thepnarintra, S. Nikorn

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Agricultural machinery industry plays an important role in the industrial development especially the production industry of the country. There has been continuing development responding to the higher demand of the production. However, the problem in agricultural machinery production still exists. Thus, the purpose of this research is to investigate problems on fundamental factors of industry based on the entrepreneurs’ point of view. The focus was on the small and medium size industry receiving factory license type number 0660 from the Department of Industrial Works. The investigation was on the comparison between the management of the small and medium size agricultural industry in 3 provinces in the central region of Thailand. Population in this study consisted of 189 company managers or managing directors, of which 101 were from the small size and 88 were from the medium size industry. The data were analyzed to find percentage, arithmetic mean, and standard deviation with independent sample T-test at the statistical significance .05. The results showed that the small and medium size agricultural machinery manufacturers in the central region of Thailand reported high problems in every aspect. When compared the problems on basic factors in running the business, it was found that there was no statistically difference at .05 in managing of the small and medium size agricultural machinery manufacturers. However, there was a statistically significant difference between the small and medium size agricultural machinery manufacturers on the aspect of policy and services of the government. The problems reported by the small and medium size agricultural machinery manufacturers were the services on public tap water and the problem on politic and stability of the country.

Keywords: Agricultural machinery, manufacturers, problems, on running the business.

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Authors: Guyue Zhu, Liangping Hong

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Chinese overall urban design faces a large number of problems such as the neglect of urban characteristics, generalization of content, and difficulty in implementation. Focusing on these issues, this paper proposes the main points of shaping urban characteristics in overall urban design: focuses on core problems in city function and scale, landscape pattern, historical culture, social resources and modern city style and digs the urban characteristic genes. Then, we put forward “core problem location and characteristic gene enhancement” as a kind of overall urban design technical method. Firstly, based on the main problems in urban space as a whole, for the operability goal, the method extracts the key genes and integrates into the multi-dimension system in a targeted manner. Secondly, hierarchical management and guidance system is established which may be in line with administrative management. Finally, by converting the results, action plan is drawn up that can be dynamically implemented. Based on the above idea and method, a practical exploration has been performed in the case of Xiangyang central city.

Keywords: City characteristics, overall urban design, planning implementation, Xiangyang central city.

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Authors: Seung-Hun Kim, Kye-Hoon Jeon, Byoung-Doo Kang, I1-Kyun Jung

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Intelligent traffic surveillance technology is an issue in the field of traffic data analysis. Therefore, we need the technology to detect moving objects in real-time while there are variations in background and natural light. In this paper, we proposed a Weighted-Center Surround Difference method for object detection in outdoor environments. The proposed system detects objects using the saliency map that is obtained by analyzing the weight of each layers of Gaussian pyramid. In order to validate the effectiveness of our system, we implemented the proposed method using a digital signal processor, TMS320DM6437. Experimental results show that blurred noisy around objects was effectively eliminated and the object detection accuracy is improved.

Keywords: Saliency Map, Center Surround Difference, Object Detection, Surveillance System

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Authors: Kelemewerk Destalem, Jungjae Cho, Jaeseong Lee, Ju H. Park, Joonhyuk Yoo

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Background subtraction and temporal difference are often used for moving object detection in video. Both approaches are computationally simple and easy to be deployed in real-time image processing. However, while the background subtraction is highly sensitive to dynamic background and illumination changes, the temporal difference approach is poor at extracting relevant pixels of the moving object and at detecting the stopped or slowly moving objects in the scene. In this paper, we propose a simple moving object detection scheme based on adaptive background subtraction and temporal difference exploiting dynamic background updates. The proposed technique consists of histogram equalization, a linear combination of background and temporal difference, followed by the novel frame-based and pixel-based background updating techniques. Finally, morphological operations are applied to the output images. Experimental results show that the proposed algorithm can solve the drawbacks of both background subtraction and temporal difference methods and can provide better performance than that of each method.

Keywords: Background subtraction, background updating, real time and lightweight algorithm, temporal difference.

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Authors: M.Rajasimman, S.Subathra

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The process parameters, temperature, pH and substrate concentration, were optimized for the production of gentamicin using Micromonouspora echinospora. Experiments were carried out according to central composite design in response surface method. The optimum conditions for the maximum production of gentamicin were found to be: temperature – 31.7oC, pH – 6.8 and substrate concentration – 3%. At these optimized conditions the production of gentamicin was found to be – 1040 mg/L. The R2 value of 0.9465 indicates a good fitness of the model.

Keywords: Gentamicin, Micromonouspora echinospora, response surface method, optimization, central composite design.

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Authors: Shazalina Mat Zin, Ahmad Abd. Majid, Ahmad Izani Md. Ismail, Muhammad Abbas

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The generalized wave equation models various problems in sciences and engineering. In this paper, a new three-time level implicit approach based on cubic trigonometric B-spline for the approximate solution of wave equation is developed. The usual finite difference approach is used to discretize the time derivative while cubic trigonometric B-spline is applied as an interpolating function in the space dimension. Von Neumann stability analysis is used to analyze the proposed method. Two problems are discussed to exhibit the feasibility and capability of the method. The absolute errors and maximum error are computed to assess the performance of the proposed method. The results were found to be in good agreement with known solutions and with existing schemes in literature.

Keywords: Collocation method, Cubic trigonometric B-spline, Finite difference, Wave equation.

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Authors: Vijay Kumar Kukreja, Ravneet Kaur

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In this paper, one dimensional advection diffusion model is analyzed using finite difference method based on Crank-Nicolson scheme. A practical problem of filter cake washing of chemical engineering is analyzed. The model is converted into dimensionless form. For the grid Ω × ω = [0, 1] × [0, T], the Crank-Nicolson spatial derivative scheme is used in space domain and forward difference scheme is used in time domain. The scheme is found to be unconditionally convergent, stable, first order accurate in time and second order accurate in space domain. For a test problem, numerical results are compared with the analytical ones for different values of parameter.

Keywords: Consistency, Crank-Nicolson scheme, Gerschgorin circle, Lax-Richtmyer theorem, Peclet number, stability.

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Authors: Carla E. O. de Moraes, Gladson O. Antunes, Mauro A. Rincon

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The aim of this paper is to study the internal stabilization of the Bernoulli-Euler equation numerically. For this, we consider a square plate subjected to a feedback/damping force distributed only in a subdomain. An algorithm for obtaining an approximate solution to this problem was proposed and implemented. The numerical method used was the Finite Difference Method. Numerical simulations were performed and showed the behavior of the solution, confirming the theoretical results that have already been proved in the literature. In addition, we studied the validation of the numerical scheme proposed, followed by an analysis of the numerical error; and we conducted a study on the decay of the energy associated.

Keywords: Bernoulli-Euler Plate Equation, Numerical Simulations, Stability, Energy Decay, Finite Difference Method.

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Authors: Suparat Niwitpong

Abstract:

Motivated by the recent work of Herbert, Hayen, Macaskill and Walter [Interval estimation for the difference of two independent variances. Communications in Statistics, Simulation and Computation, 40: 744-758, 2011.], we investigate, in this paper, new confidence intervals for the difference between two normal population variances based on the generalized confidence interval of Weerahandi [Generalized Confidence Intervals. Journal of the American Statistical Association, 88(423): 899-905, 1993.] and the closed form method of variance estimation of Zou, Huo and Taleban [Simple confidence intervals for lognormal means and their differences with environmental applications. Environmetrics 20: 172-180, 2009]. Monte Carlo simulation results indicate that our proposed confidence intervals give a better coverage probability than that of the existing confidence interval. Also two new confidence intervals perform similarly based on their coverage probabilities and their average length widths.

Keywords: Confidence interval, generalized confidence interval, the closed form method of variance estimation, variance.

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Authors: Jeong Hye Moon, Byung Hoon Kang, PooGyeon Park

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In this paper, we proposed the direct method for converting Finite-Impulse Response (FIR) filter with low nonzero tap into Infinite-Impulse Response (IIR) filter using the pre-determined table. The prony method is used by ghost cancellator which is IIR approximation to FIR filter which is better performance than IIR and have much larger calculation difference. The direct method for many ghost combination with low nonzero tap of NTSC(National Television System Committee) TV signal in Korea is described. The proposed method is illustrated with an example.

Keywords: NTSC, Ghost cancellation, FIR, IIR, Prony method.

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Authors: Ekesa B. Nakhauka, De Lange M., Macharia I., Garming H., Ouma E., Birachi E., Van Asten P., Van-Lauwe B., Blomme G.

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Impact of adopting products promoted by the Consortium for Improving Agriculture-based livelihoods in Central Africa (CIALCA) on food and nutrition security was tested. Multi-stage sampling was used to select 7 project mandate areas, 5 villages/mandate area (stratified into action, satellite and control sites) and 913 households. Structured questionnaires were administered; analysis of impact based on comparison between stratums, differences in means tested by ANOVA and significance of difference obtained by Tukey's HSD multiple rank tests. Perception of adequate food sufficiency received a higher rating in action and satellite sites compared to control sites reason being improved agricultural technologies. For >60% of households, worsened food security was due to climatic conditions. Although a higher proportion of households in action and satellite was meeting calorie RDIs in DRC and Burundi the difference was insignificant from control sites. 53% of respondents in control sites indicated a decrease in intake of protein rich foods, this was significantly higher than the proportion in the action (46%) and satellite (41%) sites.

Keywords: Food security, Farmer-households, Nutrition security

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Authors: Davod Khojasteh Salkuyeh

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An important task in solving second order linear ordinary differential equations by the finite difference is to choose a suitable stepsize h. In this paper, by using the stochastic arithmetic, the CESTAC method and the CADNA library we present a procedure to estimate the optimal stepsize hopt, the stepsize which minimizes the global error consisting of truncation and round-off error.

Keywords: Ordinary differential equations, optimal stepsize, error, stochastic arithmetic, CESTAC, CADNA.

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Authors: Valeri A. Makarov, Ezequiel Del Rio, Manuel G. Bedia, Manuel G. Velarde, Werner Ebeling

Abstract:

We proposed the use of a Toda-Rayleigh ring as a central pattern generator (CPG) for controlling hexapodal robots. We show that the ring composed of six Toda-Rayleigh units coupled to the limb actuators reproduces the most common hexapodal gaits. We provide an electrical circuit implementation of the CPG and test our theoretical results obtaining fixed gaits. Then we propose a method of incorporation of the actuator (motor) dynamics in the CPG. With this approach we close the loop CPG – environment – CPG, thus obtaining a decentralized model for the leg control that does not require higher level intervention to the CPG during locomotion in a nonhomogeneous environments. The gaits generated by the novel CPG are not fixed, but adapt to the current robot bahvior.

Keywords: Central pattern generator, electrical circuit, hexapod robot

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Authors: Zhanar Aldubasheva, Mukhtar Senggirbay, Elnura Assyltayeva

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The modern world is experiencing fundamental and dynamic changes. The transformation of international relations; the end of confrontation and successive overcoming of the Cold War consequences have expanded possible international cooperation. The global nuclear conflict threat has been minimized, while a tendency to establish a unipolar world structure with the U.S. economic and power domination is growing. The current world system of international relations, apparently is secular. However, the religious beliefs of one or another nations play a certain (sometimes a key) role, both in the domestic affairs of the individual countries and in the development of bilateral ties. Political situation in Central Asia has been characterized by new factors such as international terrorism; religious extremism and radicalism; narcotrafficking and illicit arms trade of a global character immediately threaten to peace and political stability in Central Asia. The role and influence of Islamic fundamentalism is increasing; political ethnocentrism and the associated aggravation of inter-ethnic relations, the ambiguity of national interests and objectives of major geo-political groups in the Central Asian region regarding the division the political influence, emerge. This article approaches the following issues: the role of Islam in Central Asia; destabilizing factors in Central Asia; Islamic movements in Central Asia, Western Europe and the United States; the United States, Western Europe and Central Asia: religion, politics, ideology, and the US-Central Asia antiterrorism and religious extremism cooperation.

Keywords: USA, Central Asia, religious conflict, terrorism, regional security.

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Authors: S. Mehran, S. Rouhi, F.Rouzbahani, E. Haghgoo

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In this paper, growth and collapse of a vapour bubble generated due to a local energy input inside a rigid cylinder and in the absence of buoyancy forces is investigated using Boundary Integral Equation Method and Finite Difference Method .The fluid is treated as potential flow and Boundary Integral Equation Method is used to solve Laplace-s equation for velocity potential. Different ratios of the diameter of the rigid cylinder to the maximum radius of the bubble are considered. Results show that during the collapse phase of the bubble inside a vertical rigid cylinder, two liquid micro jets are developed on the top and bottom sides of the vapour bubble and are directed inward. It is found that by increasing the ratio of the cylinder diameter to the maximum radius of the bubble, the rate of the growth and collapse phases of the bubble increases and the life time of the bubble decreases.

Keywords: Vapour bubble, Vertical rigid cylinder, Boundaryelement method, Finite difference method, Buoyancy forces.

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Authors: Hui-Yu Huang, Shih-Hsu Chang

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In this paper, we propose a high capacity image hiding technology based on pixel prediction and the difference of modified histogram. This approach is used the pixel prediction and the difference of modified histogram to calculate the best embedding point. This approach can improve the predictive accuracy and increase the pixel difference to advance the hiding capacity. We also use the histogram modification to prevent the overflow and underflow. Experimental results demonstrate that our proposed method within the same average hiding capacity can still keep high quality of image and low distortion

Keywords: data hiding, predictor

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Authors: Kazuko Sakamoto

Abstract:

Recently, the design is becoming important in product development. The technology which is a strong point of Japan is immediately caught up by the foreign countries, and the price competition begins. Therefore companies tend to plan differentiation of products by the design or a color. The purpose of my work was to consider the optimal color for using by product development. We needed to clarify the thing leading to color preference for this purpose. Two kinds of investigations were made. By the first investigation, we found out that a geographical factor difference existed in color preference. Then, investigation which regarded the difference as latitude was conducted. However, the result expected from the difference in latitude was not obtained. It seems that it is necessary to set up difference of latitude a little more greatly, or to reexamine by other geographical factors.

Keywords: Color preference, product color, difference of latitude, design marketing, international comparison.

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Authors: Anirut Luadsong, Nitima Aschariyaphotha

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The spectral action balance equation is an equation that used to simulate short-crested wind-generated waves in shallow water areas such as coastal regions and inland waters. This equation consists of two spatial dimensions, wave direction, and wave frequency which can be solved by finite difference method. When this equation with dominating convection term are discretized using central differences, stability problems occur when the grid spacing is chosen too coarse. In this paper, we introduce the splitting upwind schemes for avoiding stability problems and prove that it is consistent to the upwind scheme with same accuracy. The splitting upwind schemes was adopted to split the wave spectral action balance equation into four onedimensional problems, which for each small problem obtains the independently tridiagonal linear systems. For each smaller system can be solved by direct or iterative methods at the same time which is very fast when performed by a multi-processor computer.

Keywords: upwind scheme, parallel algorithm, spectral action balance equation, splitting method.

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Authors: S. Aghainajafi Zadeh, M.R. Hemami., F. Heydari

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Knowledge of food resource of the houbara which an endangered species would be a important step toward the preservation of this bird. Adequate study has not been done in this field and therefore the food sources of the houbara during the brooding season was studied in the central steppe of Iran. In order to determine the density of insect in plant communities the pitfall trap was used , positioned in five linear transects divided between plant communities and in two repetitions. The results showed that the among communities there was a significant difference in term of the number beetles and ants ( p= 0.01, F2, 29= 4.66) collectively. Also bush steppe habitat had a higher arthropoda density in comparison with the shrub steppe habitat. Considering that most houbara nests were found in the bush steppe habitat .It seems this habitat provides the most available food supply for the houbara chicks.

Keywords: Asiatic houbara bustard, Brooding season, Food resource

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Authors: Heroe Wijanto, Sugihartono, Suhartono Tjondronegoro, Kuspriyanto

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The use of High Order Statistics (HOS) analysis is expected to provide so many candidates of features that can be selected for pattern recognition. More candidates of the feature can be extracted using simple manipulation through a specific mathematical function prior to the HOS analysis. Feature extraction method using HOS analysis combined with Difference to the Nth-Power manipulation has been examined in application for Automatic Modulation Recognition (AMR) to perform scheme recognition of three digital modulation signal, i.e. QPSK-16QAM-64QAM in the AWGN transmission channel. The simulation results is reported when the analysis of HOS up to order-12 and the manipulation of Difference to the Nth-Power up to N = 4. The obtained accuracy rate of AMR using the method of Simple Decision obtained 90% in SNR > 10 dB in its classifier, while using the method of Voted Decision is 96% in SNR > 2 dB.

Keywords: modulation, automatic modulation recognition, feature analysis, feature manipulation.

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Authors: Hamed Qazanfari, Hamid Hassanpour, Kazem Qazanfari

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In this paper, a method is provided for content-based image retrieval. Content-based image retrieval system searches query an image based on its visual content in an image database to retrieve similar images. In this paper, with the aim of simulating the human visual system sensitivity to image's edges and color features, the concept of color difference histogram (CDH) is used. CDH includes the perceptually color difference between two neighboring pixels with regard to colors and edge orientations. Since the HSV color space is close to the human visual system, the CDH is calculated in this color space. In addition, to improve the color features, the color histogram in HSV color space is also used as a feature. Among the extracted features, efficient features are selected using entropy and correlation criteria. The final features extract the content of images most efficiently. The proposed method has been evaluated on three standard databases Corel 5k, Corel 10k and UKBench. Experimental results show that the accuracy of the proposed image retrieval method is significantly improved compared to the recently developed methods.

Keywords: Content-based image retrieval, color difference histogram, efficient features selection, entropy, correlation.

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Authors: Nareelux Suwannobol, JintanaTapin, Khuanchanok Narachan

Abstract:

The objective of this study was to determine the accuracy to estimation fetal weight by Johnson-s method and compares it with actual birth weight. The sample group was 126 infants delivered in Dan KhunThot hospital from January March 2012. Fetal weight was estimated by measuring fundal height according to Johnson-s method. The information was collected by studying historical delivery records and then analyzed by using the statistics of frequency, percentage, mean, and standard deviation. Finally, the difference was analyzed by a paired t-test.The results showed had an average birth weight was 3093.57 ± 391.03 g (mean ± SD) and 3,455 ± 454.55 g average estimated fetal weight by Johnson-s method higher than average actual birth weight was 384.09 grams. When classifying the infants according to birth weight found that low birth weight (<2500 g) and the appropriate birth weight (2500-3999g) actual birth weight less than estimate fetal weight . But the high birth weight (> 4000 g) actual birth weight was more than estimated fetal weight. The difference was found between actual birth weight and estimation fetal weight of the minimum weight in high birth weight ( > 4000 g) , the appropriate birth weight (2500-3999g) and low birth weight (<2500 g) respectively. The rate of estimates fetal weight within 10% of actual birth weight was 35.7%. Actual birth weight were compared with the found that the difference is statistically significant (p <.000). Employing Johnson-s method to estimate fetal weight can estimate initial fetal weight before passing to special examinations, which may require excessive high cost. A variety of methods should be employed to estimate fetal weight more precisely, which will help plan care for mother-s and infant-s safety.

Keywords: Johnson's method, Fetal weight estimate, Delivery Room, Student nurse.

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Authors: Sansanee Sansiribhan, Orrawan Rewthong, Anusorn Rattanathanaophat, Sarun Saensiriphan

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The objective of this work was to study potential of rice straw for power plant in the Central region of Thailand. Provincial power plant capacity was studied. The results showed that provinces central region had potential for small power plants with a capacity of over 10 MW in 13 provinces, 1-10 MW in 6 provinces and less than 1 MW in 3 provinces.

Keywords: Rice straw, Power plant, Central region, Thailand.

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Authors: Appanah Rao Appadu, Muhammad Zaid Dauhoo

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In this paper, we have combined some spatial derivatives with the optimised time derivative proposed by Tam and Webb in order to approximate the linear advection equation which is given by = 0. Ôêé Ôêé + Ôêé Ôêé x f t u These spatial derivatives are as follows: a standard 7-point 6 th -order central difference scheme (ST7), a standard 9-point 8 th -order central difference scheme (ST9) and optimised schemes designed by Tam and Webb, Lockard et al., Zingg et al., Zhuang and Chen, Bogey and Bailly. Thus, these seven different spatial derivatives have been coupled with the optimised time derivative to obtain seven different finite-difference schemes to approximate the linear advection equation. We have analysed the variation of the modified wavenumber and group velocity, both with respect to the exact wavenumber for each spatial derivative. The problems considered are the 1-D propagation of a Boxcar function, propagation of an initial disturbance consisting of a sine and Gaussian function and the propagation of a Gaussian profile. It is known that the choice of the cfl number affects the quality of results in terms of dissipation and dispersion characteristics. Based on the numerical experiments solved and numerical methods used to approximate the linear advection equation, it is observed in this work, that the quality of results is dependent on the choice of the cfl number, even for optimised numerical methods. The errors from the numerical results have been quantified into dispersion and dissipation using a technique devised by Takacs. Also, the quantity, Exponential Error for Low Dispersion and Low Dissipation, eeldld has been computed from the numerical results. Moreover, based on this work, it has been found that when the quantity, eeldld can be used as a measure of the total error. In particular, the total error is a minimum when the eeldld is a minimum.

Keywords: Optimised time derivative, dissipation, dispersion, cfl number, Nomenclature: k : time step, h : spatial step, β :advection velocity, r: cfl/Courant number, hkrβ= , w =θ, h : exact wave number, n :time level, RPE : Relative phase error per unit time step, AFM :modulus of amplification factor

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Authors: M. Zarebnia, R. Parvaz

Abstract:

In this paper the Kuramoto-Sivashinsky equation is solved numerically by collocation method. The solution is approximated as a linear combination of septic B-spline functions. Applying the Von-Neumann stability analysis technique, we show that the method is unconditionally stable. The method is applied on some test examples, and the numerical results have been compared with the exact solutions. The global relative error and L∞ in the solutions show the efficiency of the method computationally.

Keywords: Kuramoto-Sivashinsky equation, Septic B-spline, Collocation method, Finite difference.

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