Search results for: collector efficiency factor

Authors: Chuen Tse Kuah, Kuan Yew Wong, Farzad Behrouzi

Abstract:

This paper is aimed to give an illustration on the application of Data Envelopment Analysis (DEA) as a tool to assess Quality Management (QM) efficiency. A variant of DEA, slack based measure (SBM) is used for this purpose. From this study, it is found that DEA is suitable to measure QM efficiency and give improvement suggestions to the inefficient QM.

Keywords: Quality Management, Data Envelopment Analysis, Slack Based Measure, Efficiency Measurement.

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Authors: Sang Won Han, Won Joo Lee, Sang Jun Lee

Abstract:

A new multi inner stage (MIS) cyclone was designed to remove the acidic gas and fine particles produced from electronic industry. To characterize gas flow in MIS cyclone, pressure and velocity distribution were calculated by means of CFD program. Also, the flow locus of fine particles and particle removal efficiency were analyzed by Lagrangian method. When outlet pressure condition was –100mmAq, the efficiency was the best in this study.

Keywords: Cyclone, SiO2 particle, Particle removal efficiency, CFD simulation

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Authors: Yi He, Nutdechatorn Puangngernmak, Suramate Chalermwisutkul

Abstract:

Microwave heating process has been developed about sixty years while measurement system has also progressed. Because of irradiation of high frequency of microwave, researchers have been utilized many costly technical instrument measuring parameters to evaluate the performance of microwave heating system. Therefore, this paper is intended to present an easier and feasible efficiency measurement method. It can help inspecting efficiency of microwave heating system with good accuracy, while the method can also give reference to optimizing procedure for microwave heating system for various load material

Keywords: measurement, microwave heating system, systemic power efficiency

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Authors: S. P. Singh

Abstract:

This paper measures technical and scale efficiencies of 40 Indian sugar companies for the period from 2004-05 to 2013-14. The efficiencies are estimated through input-oriented DEA models using one output variable—value of output (VOP) and five input variables—capital cost (CA), employee cost (EMP), raw material (RW), energy & fuel (E&F) and other manufacturing expenses (OME). The sugar companies are classified into integrated and non-integrated categories to know which one achieves higher level of efficiency. Sources of inefficiency in the industry are identified through decomposing the overall technical efficiency (TE) into pure technical efficiency (PTE) and scale efficiency (SE). The paper also estimates input-reduction targets for relatively inefficient companies and suggests measures to improve their efficiency level. The findings reveal that the TE does not evince any trend rather it shows fluctuations across years, largely due to erratic and cyclical pattern of sugar production. Further, technical inefficiency in the industry seems to be driven more by the managerial inefficiency than the scale inefficiency, which implies that TE can be improved through better conversion of inputs into output.

Keywords: Sugar industry, companies, technical efficiency, data envelopment analysis, targets.

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Authors: P. Ram Mohan, M. Vijaya Kumar, O. V. Raghava Reddy

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This paper deals with the simulation of a Boost Power Factor Correction (PFC) Converter with Electro Magnetic Interference (EMI) Filter. The diode rectifier with output capacitor gives poor power factor. The Boost Converter of PFC Circuit is analyzed and then simulated with diode rectifier. The Boost PFC Converter with EMI Filter is simulated for resistive load. The power factor is improved using the proposed converter.

Keywords: Boost Converter, Power Factor Correction, Electro Magnetic Interference, Diode Rectifier

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Authors: A. M. Hasna

Abstract:

Today global warming, climate change and energy supply are of greater concern as it is widely realized that the planet earth does not provide an infinite capacity for absorbing human industrialization in the 21st century. The aim of this paper is to analyze upstream and downstream electricity production in selected case studies: a coal power plant, a pump system and a microwave oven covering and consumption to explore the position of energy efficiency in engineering sustainability. Collectively, the analysis presents energy efficiency as a major pathway towards sustainability that requires an inclusive and a holistic supply chain response in the engineering design process.

Keywords: Sustainability, technology, efficiency, engineering, energy.

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Authors: Natalya G. Filimonova, Mariya G. Ozerova, Irina N. Ermakova

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The long-term strategy of the economic development of Russia up to 2030 is based on the concept of sustainable growth. The determining factor of such development is complex changes in the economic system which may be achieved by making progressive changes in its structure. The structural changes determine the character and the direction of economic development, as well as they include all elements of this system without exception, and their regulated character ensures the most rapid aim achievement. This article has discussed the industrial structure of the agriculture in Russia. With the use of the system of indexes, the article has determined the directions, intensity, and speed of structural shifts. The influence of structural changes on agricultural production development has been found out. It is noticed that the changes in the industrial structure are synchronized with the changes in the organisation and economic structure. Efficiency assessment of structural changes allowed to trace the efficiency of structural changes and elaborate the main directions for agricultural policy improvement.

Keywords: Russian agriculture system, sectoral structure, organizational and economic structure, structural changes.

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Authors: T. Tanitteerapan, E.Thanpo

Abstract:

This paper, a simple continuous conduction mode (CCM) pulse-width-modulated (PWM) controller for high power factor boost converters is introduced. The duty ratios were obtained by the comparison of a sensed signal from inductor current or switch current and a negative slope ramp carrier waveform in each switching period. Due to the proposed control requires only the inductor current or switch current sensor and the output voltage sensor, its circuit implementation was very simple. To verify the proposed control, the circuit experimentation of a 350 W boost converter with the proposed control was applied. From the results, the input current waveform was shaped to be closely sinusoidal, implying high power factor and low harmonics.

Keywords: High power factor converters, boost converters, low harmonic rectifiers, power factor correction, and current control.

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Authors: Saima Ayaz, Zakir Hussain, Maqbool Hussain Sial

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The study identified the sources of production inefficiency of the farming sector in district Faisalabad in the Punjab province of Pakistan. Data Envelopment Analysis (DEA) technique was utilized at farm level survey data of 300 farmers for the year 2009. The overall mean efficiency score was 0.78 indicating 22 percent inefficiency of the sample farmers. Computed efficiency scores were then regressed on farm specific variables using Tobit regression analysis. Farming experience, education, access to farming credit, herd size and number of cultivation practices showed constructive and significant effect on the farmer-s technical efficiency.

Keywords: Agricultural credit, DEA, Technical efficiency, Tobit analysis

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Authors: Fang Yao, Minglei Chen

Abstract:

City shrinkage is one of the thorny problems that many European cities have to face with nowadays. It is mainly expressed as the decrease of population in these cities. Eastern Germany is one of the pioneers of European shrinking cities with long shrinking history. The paper selects one representative shrinking city Halle (Saale) in eastern Germany as research objective, collecting and investigating nearly 20 years (1993-2010) municipal data after the reunification of Germany. These data based on five dimensions, which are demographic, economic, social, spatial and environmental and total 16 eligible variables. Factor Analysis is used to deal with these variables in order to assess the most important factors affecting shrinking Halle. The results show that there are three main factors determine the shrinkage of Halle, respectively named “demographical and economical factor”, “social stability factor”, and “city vitality factor”. The three factors act at different time period of Halle’s shrinkage: from 1993 to 1997 the demographical and economical factor played an important role; from 1997 to 2004 the social stability factor is significant to city shrinkage; since 2005 city vitality factor determines the shrinkage of Halle. In recent years, the shrinkage in Halle mitigates that shows the sign of growing population. Thus the city Halle should focus on attaching more importance on the city vitality factor to prevent the city from shrinkage. Meanwhile, the city should possess a positive perspective to shift the growth-oriented development to tap the potential of shrinking cities. This method is expected to apply to further research and other shrinking cities

Keywords: Demography, Factor analysis, Halle, Shrinking cities.

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Authors: Dongheon Shin, Kyungnam Ko, Jongchul Huh

Abstract:

The investigation on wind turbine degradation was carried out using the nacelle wind data. The three Vestas V80-2MW wind turbines of Sungsan wind farm in Jeju Island, South Korea were selected for this work. The SCADA data of the wind farm for five years were analyzed to draw power curve of the turbines. It is assumed that the wind distribution is the Rayleigh distribution to calculate the normalized capacity factor based on the drawn power curve of the three wind turbines for each year. The result showed that the reduction of power output from the three wind turbines occurred every year and the normalized capacity factor decreased to 0.12%/year on average.

Keywords: Wind energy, Power curve, Capacity factor, Annual energy production.

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Authors: Shin-Hyung Cho, Dong-Kyu Kim, Seung-Young Kho

Abstract:

Truck-involved crashes have higher crash severity than non-truck-involved crashes. There have been many studies about the frequency of crashes and the development of severity models, but those studies only analyzed the relationship between observed variables. To identify why more people are injured or killed when trucks are involved in the crash, we must examine to quantify the complex causal relationship between severity of the crash and risk factors by adopting the latent factors of crashes. The aim of this study was to develop a structural equation or model based on truck-involved and non-truck-involved crashes, including five latent variables, i.e. a crash factor, environmental factor, road factor, driver’s factor, and severity factor. To clarify the unique characteristics of truck-involved crashes compared to non-truck-involved crashes, a confirmatory analysis method was used. To develop the model, we extracted crash data from 10,083 crashes on Korean freeways from 2008 through 2014. The results showed that the most significant variable affecting the severity of a crash is the crash factor, which can be expressed by the location, cause, and type of the crash. For non-truck-involved crashes, the crash and environment factors increase severity of the crash; conversely, the road and driver factors tend to reduce severity of the crash. For truck-involved crashes, the driver factor has a significant effect on severity of the crash although its effect is slightly less than the crash factor. The multiple group analysis employed to analyze the differences between the heterogeneous groups of drivers.

Keywords: Crash severity, structural equation modeling, truck-involved crashes, multiple group analysis, crash on freeway.

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Authors: Alexey V. Klyuev, Arkady V. Yakimov, Mikhail I. Ryzhkin, Andrey V. Klyuev

Abstract:

Fluctuations of Schottky diode parameters in a structure of the mixer are investigated. These fluctuations are manifested in two ways. At the first, they lead to fluctuations in the transfer factor that is lead to the amplitude fluctuations in the signal of intermediate frequency. On the basis of the measurement data of 1/f noise of the diode at forward current, the estimation of a spectrum of relative fluctuations in transfer factor of the mixer is executed. Current dependence of the spectrum of relative fluctuations in transfer factor of the mixer and dependence of the spectrum of relative fluctuations in transfer factor of the mixer on the amplitude of the heterodyne signal are investigated. At the second, fluctuations in parameters of the diode lead to occurrence of 1/f noise in the output signal of the mixer. This noise limits the sensitivity of the mixer to the value of received signal.

Keywords: Current-voltage characteristic, fluctuations, mixer, Schottky diode, 1/f noise.

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Authors: Aigerim Uyzbayeva, Valeriya Tyo, Nurlan Ibrayev

Abstract:

Kazakhstan is currently one of the dynamically developing states in its region. The stable growth in all sectors of the economy leads to a corresponding increase in energy consumption. Thus country consumes significant amount of energy due to the high level of industrialisation and the presence of energy-intensive manufacturing such as mining and metallurgy which in turn leads to low energy efficiency. With allowance for this the Government has set several priorities to adopt a transition of Republic of Kazakhstan to a “green economy”. This article provides an overview of Kazakhstan’s energy efficiency situation in for the period of 1991- 2014. First, the dynamics of production and consumption of conventional energy resources are given. Second, the potential of renewable energy sources is summarised followed by the description of GHG emissions trends in the country. Third, Kazakhstan’ national initiatives, policies and locally implemented projects in the field of energy efficiency are described.

Keywords: Energy efficiency in Kazakhstan, greenhouse gases, renewable energy, sustainable development.

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Authors: Tomislav Stambolic, Anton Causevski

Abstract:

The deficit of power supply in Macedonia is almost 30% or reached up to 3000 GWh in a year. The existing thermal and hydro power plants are not enough to cover the power and energy, so the import increases every year. Therefore, in order to have more domestic energy supply, the new trends in renewable and energy efficiency should be implemented in power sector. The paper gives some perspectives for development of the power system in Macedonia, taking into account the growth of electricity demand and in the same time with implementation of renewable and energy efficiency. The development of power system is made for the period up to 2030 with the period of every 5 years.

Keywords: Energy, Power System, Renewable, Efficiency

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Authors: Long Van Hoang, Mitsuyasu Yabe

Abstract:

Environmental factors affect agriculture production productivity and efficiency resulted in changing of profit efficiency. This paper attempts to estimate the impacts of environmental factors to profitability of rice farmers in the Red River Delta of Vietnam. The dataset was extracted from 349 rice farmers using personal interviews. Both OLS and MLE trans-log profit functions were used in this study. Five production inputs and four environmental factors were included in these functions. The estimation of the stochastic profit frontier with a two-stage approach was used to measure profitability. The results showed that the profit efficiency was about 75% on the average and environmental factors change profit efficiency significantly beside farm specific characteristics. Plant disease, soil fertility, irrigation apply and water pollution were the four environmental factors cause profit loss in rice production. The result indicated that farmers should reduce household size, farm plots, apply row seeding technique and improve environmental factors to obtain high profit efficiency with special consideration is given for irrigation water quality improvement.

Keywords: Profit efficiency; Profit function; Environmental factors; OLS and MLE estimations; Rice Production; Vietnam

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Authors: Ahmed Elsebaay, Maged A. Abu Adma, Mahmoud Ramadan

Abstract:

This study presents a technique clarifying the effect of ambient air temperature and loads power factor changing from standard values on electric generator power rating. The study introduces an optimized technique for selecting the correct electric generator power rating for certain application and operating site ambient temperature. The de-rating factors due to the previous effects will be calculated to be applied on a generator to select its power rating accurately to avoid unsafe operation and save its lifetime. The information in this paper provides a simple, accurate, and general method for synchronous generator selection and eliminates common errors.

Keywords: Ambient temperature, de-rating factor, electric generator, power factor.

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Authors: Sizhong Zhou, Hongxia Liu

Abstract:

Let G be a graph of order n, and let k  2 and m  0 be two integers. Let h : E(G)  [0, 1] be a function. If e∋x h(e) = k holds for each x  V (G), then we call G[Fh] a fractional k-factor of G with indicator function h where Fh = {e  E(G) : h(e) > 0}. A graph G is called a fractional (k,m)-deleted graph if there exists a fractional k-factor G[Fh] of G with indicator function h such that h(e) = 0 for any e  E(H), where H is any subgraph of G with m edges. In this paper, it is proved that G is a fractional (k,m)-deleted graph if (G)  k + m + m k+1 , n  4k2 + 2k − 6 + (4k 2 +6k−2)m−2 k−1 and max{dG(x), dG(y)}  n 2 for any vertices x and y of G with dG(x, y) = 2. Furthermore, it is shown that the result in this paper is best possible in some sense.

Keywords: Graph, degree condition, fractional k-factor, fractional (k, m)-deleted graph.

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Authors: R. Geetha, T. Padmavathy

Abstract:

Security audit is an important aspect or feature to be considered in cloud service customer. It is basically a certification process to audit the controls that deliver the security requirements. Security audits are conducted by trained and qualified staffs that belong to an independent auditing organization. Security audits must be carried as a standard of security controls. Proper check to be made that the cloud user has a proper reporting and logging facilities with the customer's system and hence ensuring appropriate business and operational flow of data through cloud service. We propose a cloud-based secure auditing framework, which enables confided in power to safely store their mystery information on the semi-believed cloud specialist co-ops, and specifically share their mystery information with a wide scope of information recipient, to diminish the key administration intricacy for power proprietors and information collectors. Unique in relation to past cloud-based information framework, data proprietors transfer their mystery information into cloud utilizing static and dynamic evaluating plan. Another propelled determination is, if any information beneficiary needs individual record to download, the information collector will send the solicitation to the expert. The specialist proprietor has the Access Control. At the off probability, the businessman must impart the primary record to the knowledge collector, acknowledge statistics beneficiary solicitation. Once the acknowledgement for the records is over, the recipient downloads the first record and this record shifting time with date and downloading time with date are monitored by the inspector. In addition to deduplication concept, diminished cloud memory area using dynamic document distribution has been proposed.

Keywords: Cloud computing, cloud storage auditing, data integrity, key exposure.

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Authors: Abdulrahman M. Homadi

Abstract:

As a great source of renewable energy, solar energy is considered to be one of the most important in the world, since it will be one of solutions cover the energy shortage in the future. Photovoltaic (PV) is the most popular and widely used among solar energy technologies. However, PV efficiency is fairly low and remains somewhat expensive. High temperature has a negative effect on PV efficiency and cooling system for these panels is vital, especially in warm weather conditions. This paper presents the results of a simulation study carried out on silicon solar cells to assess the effects of elevation on enhancing the efficiency of solar panels. The study included four different terrains. The study also took into account the direction of the wind hitting the solar panels. To ensure the simulation mimics reality, six silicon solar panels are designed in two columns and three rows, facing to the south at an angle of 30 ^o. The elevations are assumed to change from 10 meters to 200 meters. The results show that maximum increase in efficiency occurs when the wind comes from the north, hitting the back of the panels.

Keywords: Solar panels, elevation, wind direction, efficiency.

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Authors: Wojciech B. Cieśliński, Igor Perechuda

Abstract:

The paper identifies the features of Polish sports clubs in the particular organizational forms: profit and nonprofit. Identification and description of these features is carried out in terms of financial efficiency of the given organizational form. Under the terms of the efficiency the research allows you to specify the advantages of particular organizational sports club form and the following limitations. Paper considers features of sports clubs in range of Polish conditions as legal regulations. The sources of the functioning efficiency of sports clubs may lie in the organizational forms in which they operate. Each of the available forms can be considered either a for-profit or nonprofit enterprise. Depending on this classification there are different capabilities of increasing organizational and financial efficiency of a given sports club. Authors start with general classification and difference between for-profit and non-profit sport clubs. Next identifies specific financial and organizational conditions of both organizational form and then show examples of mixed activity forms and their efficiency effect.

Keywords: Financial efficiency, for-profit, non-profit, sports club.

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Authors: Unnop Panpuang

Abstract:

The objectives of this project are to study on the work efficiency of the employees, sorted by their profiles, and to study on the relation between job attributes and work efficiency of employees of Suan Sunandha Rajabhat University. The samples used for this study are 292 employees. The statistics used in this study are frequencies, standard deviations, One-way ANOVA and Pearson’s correlation coefficient. Majority of respondent were male with an undergraduate degree, married and lives together. The average age of respondents was between 31-41 years old, married and the educational background are higher than bachelor’s degree. The job attribute is correlated to the work efficiency with the statistical significance level of.o1. This concurs with the predetermined hypothesis. The correlation between the two main factors is in the moderate level. All the categories of job attributes such as the variety of skills, job clarity, job importance, freedom to do work are considered separately.

Keywords: Employees, Job Attributes, Work Efficiency.

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Authors: S. Mbatha, A. Mastamet-Mason

Abstract:

This paper applied factor conditions from Porter’s Diamond Model (1990) to understand the various challenges facing the AMISA. Factor conditions highlighted in Porter’s model are grouped into two groups namely, basic and advance factors. Two AMISA associations representing over 10 000 employees were interviewed. The largest Clothing, Textiles and Leather (CTL) apparel retail group was also interviewed with a government department implementing the industrialization policy were interviewed. The paper points out that AMISA have basic factor conditions necessary for competitive advantage in the apparel industries. However advance factor creation has proven to be a challenge for AMISA, Higher Education Institutions (HEIs) and government. Poor infrastructural maintenance has contributed to high manufacturing costs and poor quick response technologies. The use of Porter’s Factor Conditions as a tool to analyze the sector’s competitive advantage challenges and opportunities has increased knowledge regarding factors that limit the AMISA’s competitiveness. It is therefore argued that other studies on Porter’s Diamond model factors like Demand conditions, Firm strategy, structure and rivalry and Related and supporting industries can be used to analyze the situation of the AMISA for the purposes of improving competitive advantage.

Keywords: Compliance rule, apparel manufacturing industry, factor conditions, advance skills.

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Authors: Iveta Řepková

Abstract:

The aim of this paper is to estimate the efficiency of the Slovak commercial banks employing the Data Envelopment Analysis (DEA) window analysis approach during the period 2003-2012. The research is based on unbalanced panel data of the Slovak commercial banks. Undesirable output was included into analysis of banking efficiency. It was found that most efficient banks were Postovabanka, UniCredit Bank and Istrobanka in CCR model and the most efficient banks were Slovenskasporitelna, Istrobanka and UniCredit Bank in BCC model. On contrary, the lowest efficient banks were found Privatbanka and CitiBank. We found that the largest banks in the Slovak banking market were lower efficient than medium-size and small banks. Results of the paper is that during the period 2003-2008 the average efficiency was increasing and then during the period 2010-2011 the average efficiency decreased as a result of financial crisis.

Keywords: Data Envelopment Analysis, efficiency, Slovak banking sector, window analysis.

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Authors: Peng Li, Chuanri Li, Tao Li

Abstract:

Reliability allocation is quite important during early design and development stages for a system to apportion its specified reliability goal to subsystems. This paper improves the reliability fuzzy allocation method, and gives concrete processes on determining the factor and sub-factor sets, weight sets, judgment set, and multi-stage fuzzy evaluation. To determine the weight of factor and sub-factor sets, the modified trapezoidal numbers are proposed to reduce errors caused by subjective factors. To decrease the fuzziness in fuzzy division, an approximation method based on linear programming is employed. To compute the explicit values of fuzzy numbers, centroid method of defuzzification is considered. An example is provided to illustrate the application of the proposed reliability allocation method based on fuzzy arithmetic.

Keywords: Reliability allocation, fuzzy arithmetic, allocation weight.

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Authors: Mojca Ciglaric, Andrej Krevl, Matjaž Pancur, Tone Vidmar

Abstract:

P2P Networks are highly dynamic structures since their nodes – peer users keep joining and leaving continuously. In the paper, we study the effects of network change rates on query routing efficiency. First we describe some background and an abstract system model. The chosen routing technique makes use of cached metadata from previous answer messages and also employs a mechanism for broken path detection and metadata maintenance. Several metrics are used to show that the protocol behaves quite well even with high rate of node departures, but above a certain threshold it literally breaks down and exhibits considerable efficiency degradation.

Keywords: Network dynamics, overlay network, P2P system, routing efficiency.

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Authors: Saisundar. S., I Made Darmayuda, Zhou Jun, Krishna Mainali, Simon Ng Sheung Yan, Eran Ofek

Abstract:

This paper compares the recent transformerless ACDC power converter architectures and provides an assessment of each. A prototype of one of the transformerless AC-DC converter architecture is also presented depicting the feasibility of a small form factor, power supply design. In this paper component selection guidelines to achieve high efficiency AC-DC power conversion are also discussed.

Keywords: AC-DC converter, digitally controlled, switched mode power supply, transformerless.

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Authors: Chuan-Kun Liu, Chi-Wang Li

Abstract:

Simultaneous recovery of copper and DCA from simulated MEUF concentrated stream was investigated. Effects of surfactant (DCA) and metal (copper) concentrations, surfactant to metal molar ratio (S/M ratio), electroplating voltage, EDTA concentration, solution pH, and salt concentration on metal recovery and current efficiency were studied. Electric voltage of -0.5 V was shown to be optimum operation condition in terms of Cu recovery, current efficiency, and surfactant recovery. Increasing Cu recovery and current efficiency were observed with increases of Cu concentration while keeping concentration of DCA constant. However, increasing both Cu and DCA concentration while keeping S/M ratio constant at 2.5 showed detrimental effect on Cu recovery at DCA concentration higher than 15 mM. Cu recovery decreases with increasing pH while current efficiency showed an opposite trend. It is believed that conductivity is the main cause for discrepancy of Cu recovery and current efficiency observed at different pH. Finally, it was shown that EDTA had adverse effect on both Cu recovery and current efficiency while addition of NaCl salt had negative impact on current efficiency at concentration higher than 8000 mg/L.

Keywords: metal recovery, MEUF waste, surfactant, electroplating.

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Authors: Sanjay L. Kurkute, Pradeep M. Patil, Kakasaheb C. Mohite

Abstract:

An optimal control strategy based on simple model, a single phase unity power factor boost converter is presented with an evaluation of first order differential equations. This paper presents an evaluation of single phase boost converter having power factor correction. The simple discrete model of boost converter is formed and optimal control is obtained, digital PI is adopted to adjust control error. The method of instantaneous current control is proposed in this paper for its good tracking performance of dynamic response. The simulation and experimental results verified our design.

Keywords: Single phase, boost converter, Power factor correction (PFC), Pulse Width Modulation (PWM).

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Authors: A. Tavangari, N. Salehzadeh

Abstract:

In the crack growth analysis, the Stress Intensity Factor (SIF) is a fundamental prerequisite. In the present study, the mode I stress intensity factor (SIF) of three-dimensional penny- Shaped crack is obtained in an isotropic elastic cylindrical medium with arbitrary dimensions under arbitrary loading at the top of the cylinder, by the semi-analytical method based on the Rayleigh-Ritz method. This method that is based on minimizing the potential energy amount of the whole of the system, gives a very close results to the previous studies. Defining the displacements (elastic fields) by hypothetical functions in a defined coordinate system is the base of this research. So for creating the singularity conditions at the tip of the crack the appropriate terms should be found.

Keywords: Penny-shaped crack, Stress intensity factor, Fracture mechanics, Ritz method.

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