Search results for: residue to weighted converter

Authors: Nazli Yildiz İkikardes, Gokhan Soydan, Musa Demirci, Ismail Naci Cangul

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In this work, we first give in what fields Fp, the cubic root of unity lies in F*p, in Qp and in K*p where Qp and K*p denote the sets of quadratic and non-zero cubic residues modulo p. Then we use these to obtain some results on the classification of the Bachet elliptic curves y2 ≡ x3 +a3 modulo p, for p ≡ 1 (mod 6) is prime.

Keywords: Elliptic curves over finite fields, quadratic residue, cubic residue.

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Authors: Cheewaphongphan P., Garivait S., Pongpullponsak A., Patumsawad S.

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Thailand is one of the world-s leaders of rice producers and exporters. Farmers have to increase the rice cultivation frequency for serving the national increasing of export-s demand. It leads to an elimination of rice residues by open burning which is the quickest and costless management method. The open burning of rice residue is one of the major causes of air pollutants and greenhouse gas (GHG) emission. Under ASEAN agreement on trans-boundary haze, Thailand set the master plan to mitigate air pollutant emission from open burning of agricultural residues. In this master plan, residues incorporation is promoted as alternative management method to open burning. However, the assessment of both options in term of GHG emission in order to investigate their contribution to long-term global warming is still scarce or inexistent. In this study, a method on rice residues assessment was first developed in order to estimate and compare GHG emissions from rice cultivation under rice residues open burning and the case with incorporation of the same amount of rice residues, using 2006 IPCC guidelines for emission estimation and Life Cycle Analysis technique. The emission from rice cultivation in different preparing area practice was also discussed.

Keywords: Greenhouse gases, Incorporation, Rice cultivation, Rice field residue, Rice residue management

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Authors: Jae-Chang Kwak, Yong-Seo Koo

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The high efficiency power management IC (PMIC) with switching device is presented in this paper. PMIC is controlled with PFM control method in order to have high power efficiency at high current level. Dynamic Threshold voltage CMOS (DT-CMOS) with low on-resistance is designed to decrease conduction loss. The threshold voltage of DT-CMOS drops as the gate voltage increase, resulting in a much higher current handling capability than standard MOSFET. PFM control circuits consist of a generator, AND gate and comparator. The generator is made to have 1.2MHz oscillation voltage. The DC-DC converter based on PFM control circuit and low on-resistance switching device is presented in this paper.

Keywords: DT-CMOS, PMIC, PFM, DC-DC converter.

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Authors: Y. K. Lin, H. T. Hsieh, F. Y. Hsieh

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Total weighted tardiness is a measure of customer satisfaction. Minimizing it represents satisfying the general requirement of on-time delivery. In this research, we consider an ant colony optimization (ACO) algorithm to solve the problem of scheduling unrelated parallel machines to minimize total weighted tardiness. The problem is NP-hard in the strong sense. Computational results show that the proposed ACO algorithm is giving promising results compared to other existing algorithms.

Keywords: ant colony optimization, total weighted tardiness, unrelated parallel machines.

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Authors: O. Farobie, S S. Achmadi, L K. Darusman

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Biodiesel production results in glycerol production as the main by-product in biodiesel industry.One of the utilizations of glycerol obtained from biodiesel production is as a cement grinding aid (CGA). Results showed that crude glycerol content was 40.19% whereas pure glycerol content was 82.15%. BSS value of the cement with CGA supplementation was higher than that of nonsupplemented cement (blank) indicating that CGA-supplemented cement had higher fineness than the non-supplemented one. It was also found that pure glycerol 95% and TEA 5% at 80ºC was the optimum CGA used to result in finest cement with BSS value of 4.836 cm2/g. Residue test showed that the smallest percent residue value (0.11%) was obtained in cement with supplementation of pure glycerol 95% and TEA 5%. Results of residue test confirmed those of BSS test showing that cement with supplementation of pure glycerol 95% and TEA 5% had the finest particle size.

Keywords: biodiesel, cement grinding aid, glycerol, Jatropha curcas

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Authors: Young-Seok Choi

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This paper presents a normalized subband adaptive filtering (NSAF) algorithm to cope with the sparsity condition of an underlying system in the context of compressive sensing. By regularizing a weighted l1-norm of the filter taps estimate onto the cost function of the NSAF and utilizing a subgradient analysis, the update recursion of the l1-norm constraint NSAF is derived. Considering two distinct weighted l1-norm regularization cases, two versions of the l1-norm constraint NSAF are presented. Simulation results clearly indicate the superior performance of the proposed l1-norm constraint NSAFs comparing with the classical NSAF.

Keywords: Subband adaptive filtering, sparsity constraint, weighted l1-norm.

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Authors: Jenica Ileana Corcau, Liviu Dinca

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The electrical power systems of aircrafts have made serious progress in recent years because the aircrafts depend more and more on the electricity. There is a trend in the aircraft industry to replace hydraulic and pneumatic systems with electrical systems, achieving more comfort and monitoring features and enlarging the energetic efficiency. Thus, was born the concept More Electric Aircraft. In this paper is analyzed the integration of a fuel cell into the existing electrical generation and distribution systems of an aircraft. The dynamic characteristics of fuel cell systems necessitate an adaptation of the electrical power system. The architecture studied in this paper consists of a 50kW fuel cell, a dc to dc converter and several loads. The dc to dc converter is used to step down the fuel cell voltage from about 625Vdc to 28Vdc.

Keywords: Electrical power system, More Electric Aircraft, Fuel Cell, dc to dc converter

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Authors: Panos Kotsas, Tony Dodd

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This paper presents the application of a signal intensity independent similarity criterion for rigid and non-rigid body registration of binary objects. The criterion is defined as the weighted ratio image of two images. The ratio is computed on a voxel per voxel basis and weighting is performed by setting the raios between signal and background voxels to a standard high value. The mean squared value of the weighted ratio is computed over the union of the signal areas of the two images and it is minimized using the Chebyshev polynomial approximation.

Keywords: rigid and non-rigid body registration, binary objects

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Authors: Jin-Hong Kim, Joon Sung Park, Jun-Hyuk Choi, In-Soung Jung

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With a development of Hybrid Electric Vehicle(HEV), A photovoltaic(PV) generation system is used for charging batteries in many cases. A dc/dc converter using PV power for a battery charger requires a high efficiency. In this paper, A ZVS boost converter using the renewable energies for HEV charger is proposed. Through the theoretical analysis and experimental result, operation modes and characteristics of the proposed topology are verified.

Keywords: HEV, EV, charger, resonant

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Authors: Jingjing Lan, Jun Zhou, Xin Liu

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In this paper, a low-power digital controller for DC-DC power conversion was presented. The controller generates the pulse-width modulated (PWM) signal from digital inputs provided by analog-to-digital converter (ADC). An efficient and simple design scheme to develop the control unit was discussed. This method allows minimization of the consumed resources of the chip and it is based on direct digital design approach. In this application, with the proposed scheme, nearly half area and two-third of the power consumption was saved compared to the conventional schemes. This work illustrates the possibility of implementing low-power and area-efficient power management circuit using direct digital design based approach. 

Keywords: Buck converter, DC-DC power conversion, digital control, proportional-integral (PI) controller.

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Authors: Halil Ibrahim Demir, Abdullah Hulusi Kokcam, Fuat Simsir, Özer Uygun

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Traditionally, three important manufacturing functions which are process planning, scheduling and due-date assignment are performed sequentially and separately. Although there are numerous works on the integration of process planning and scheduling and plenty of works focusing on scheduling with due date assignment, there are only a few works on integrated process planning, scheduling and due-date assignment. Although due-dates are determined without taking into account of weights of the customers in the literature, here weighted due-date assignment is employed to get better performance. Jobs are scheduled according to weighted earliest due date dispatching rule and due dates are determined according to some popular due date assignment methods by taking into account of the weights of each job. Simulated Annealing, Evolutionary Strategies, Random Search, hybrid of Random Search and Simulated Annealing, and hybrid of Random Search and Evolutionary Strategies, are applied as solution techniques. Three important manufacturing functions are integrated step-by-step and higher integration levels are found better. Search meta-heuristics are found to be very useful while improving performance measure.

Keywords: Evolutionary strategies, hybrid searches, process planning, simulated annealing, weighted due-date assignment, weighted scheduling.

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Authors: Abdelaziz Sahbani, Kamel Ben Saad, Mohamed Benrejeb

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This paper deals with the comparison between two proposed control strategies for a DC-DC boost converter. The first control is a classical Sliding Mode Control (SMC) and the second one is a distance based Fuzzy Sliding Mode Control (FSMC). The SMC is an analytical control approach based on the boost mathematical model. However, the FSMC is a non-conventional control approach which does not need the controlled system mathematical model. It needs only the measures of the output voltage to perform the control signal. The obtained simulation results show that the two proposed control methods are robust for the case of load resistance and the input voltage variations. However, the proposed FSMC gives a better step voltage response than the one obtained by the SMC.

Keywords: Boost DC-DC converter, Sliding Mode Control (SMC), Fuzzy Sliding Mode Control (FSMC), Robustness.

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Authors: Chungkuk Jin, Moo-Hyun Kim, HeonYong Kang

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A surface riding (SR) wave energy converter (WEC) is designed and its feasibility and performance are numerically simulated by the author-developed floater-mooring-magnet-electromagnetics fully-coupled dynamic analysis computer program. The biggest advantage of the SR-WEC is that the performance is equally effective even in low sea states and its structural robustness is greatly improved by simply riding along the wave surface compared to other existing WECs. By the numerical simulations and actuator testing, it is clearly demonstrated that the concept works and through the optimization process, its efficiency can be improved.

Keywords: Computer simulation, electromagnetics fully-coupled dynamics, floater-mooring-magnet, optimization, performance evaluation, surface riding, wave energy converter.

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Authors: P. Subha Karuvelam, M. Rajaram

Abstract:

Brushless DC motors (BLDC) are widely used in industrial areas. The BLDC motors are driven either by indirect ACAC converters or by direct AC-AC converters. Direct AC-AC converters i.e. matrix converters are used in this paper to drive the three phase BLDC motor and it eliminates the bulky DC link energy storage element. A matrix converter converts the AC power supply to an AC voltage of variable amplitude and variable frequency. A control technique is designed to generate the switching pulses for the three phase matrix converter. For the control of speed of the BLDC motor a separate PI controller and Fuzzy Logic Controller (FLC) are designed and a hysteresis current controller is also designed for the control of motor torque. The control schemes are designed and tested separately. The simulation results of both the schemes are compared and contrasted in this paper. The results show that the fuzzy logic control scheme outperforms the PI control scheme in terms of dynamic performance of the BLDC motor. Simulation results are validated with the experimental results.

Keywords: Fuzzy logic controller, matrix converter, permanent magnet brushless DC motor, PI controller.

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Authors: S. Phanyaem

Abstract:

Exponentially weighted moving average control chart (EWMA) is a popular chart used for detecting shift in the mean of parameter of distributions in quality control. The objective of this paper is to compare the efficiency of control chart to detect an increases in the mean of a process. In particular, we compared the Maximum Exponentially Weighted Moving Average (MaxEWMA) and Maximum Generally Weighted Moving Average (MaxGWMA) control charts when the observations are Exponential distribution. The criteria for evaluate the performance of control chart is called, the Average Run Length (ARL). The result of comparison show that in the case of process is small sample size, the MaxEWMA control chart is more efficiency to detect shift in the process mean than MaxGWMA control chart. For the case of large sample size, the MaxEWMA control chart is more sensitive to detect small shift in the process mean than MaxGWMA control chart, and when the process is a large shift in mean, the MaxGWMA control chart is more sensitive to detect mean shift than MaxEWMA control chart.

Keywords: Maximum Exponentially Weighted Moving Average, Maximum General Weighted Moving Average, Average Run Length.

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Authors: Chih-Chiang Hua, Yi-Hsiung Fang, Yuan-Jhen Siao

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A bridgeless boost (BLB) power factor correction (PFC) rectifier with hold-up time extension circuit is proposed in this paper. A full bridge rectifier is widely used in the front end of the ac/dc converter. Since the shortcomings of the full bridge rectifier, the bridgeless rectifier is developed. A BLB rectifier topology is utilized with the hold-up time extension circuit. Unlike the traditional hold-up time extension circuit, the proposed extension scheme uses fewer active switches to achieve a longer hold-up time. Simulation results are presented to verify the converter performance.

Keywords: Bridgeless boost, boost converter, power factor correction, hold-up time.

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Authors: Samee Ullah Khan, C.Ardil

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With data centers, end-users can realize the pervasiveness of services that will be one day the cornerstone of our lives. However, data centers are often classified as computing systems that consume the most amounts of power. To circumvent such a problem, we propose a self-adaptive weighted sum methodology that jointly optimizes the performance and power consumption of any given data center. Compared to traditional methodologies for multi-objective optimization problems, the proposed self-adaptive weighted sum technique does not rely on a systematical change of weights during the optimization procedure. The proposed technique is compared with the greedy and LR heuristics for large-scale problems, and the optimal solution for small-scale problems implemented in LINDO. the experimental results revealed that the proposed selfadaptive weighted sum technique outperforms both of the heuristics and projects a competitive performance compared to the optimal solution.

Keywords: Meta-heuristics, distributed systems, adaptive methods, resource allocation.

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Authors: H. Meradi, S. Bouhouche, M. Lahreche

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In this work, we consider an application of neural networks in LD converter. Application of this approach assumes a reliable prediction of steel temperature and reduces a reblow ratio in steel work. It has been applied a conventional model to charge calculation, the obtained results by this technique are not always good, this is due to the process complexity. Difficulties are mainly generated by the noisy measurement and the process non linearities. Artificial Neural Networks (ANNs) have become a powerful tool for these complex applications. It is used a backpropagation algorithm to learn the neural nets. (ANNs) is used to predict the steel bath temperature in oxygen converter process for the end condition. This model has 11 inputs process variables and one output. The model was tested in steel work, the obtained results by neural approach are better than the conventional model.

Keywords: LD converter, bath temperature, neural networks.

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Authors: C. Lanzerstorfer

Abstract:

The off-gas from the basic oxygen furnace (BOF), where pig iron is converted into steel, is treated in the primary ventilation system. This system is in full operation only during oxygen-blowing when the BOF converter vessel is in a vertical position. When pig iron and scrap are charged into the BOF and when slag or steel are tapped, the vessel is tilted. The generated emissions during charging and tapping cannot be captured by the primary off-gas system. To capture these emissions, a secondary ventilation system is usually installed. The emissions are captured by a canopy hood installed just above the converter mouth in tilted position. The aim of this study was to investigate the dependence of Zn and other components on the particle size of BOF secondary ventilation dust. Because of the high temperature of the BOF process it can be expected that Zn will be enriched in the fine dust fractions. If Zn is enriched in the fine fractions, classification could be applied to split the dust into two size fractions with a different content of Zn. For this air classification experiments with dust from the secondary ventilation system of a BOF were performed. The results show that Zn and Pb are highly enriched in the finest dust fraction. For Cd, Cu and Sb the enrichment is less. In contrast, the non-volatile metals Al, Fe, Mn and Ti were depleted in the fine fractions. Thus, air classification could be considered for the treatment of dust from secondary BOF off-gas cleaning.

Keywords: Air classification, converter dust, recycling, zinc.

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Authors: Nesapriya. P., S. Rajalaxmi

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This paper is based on the bridgeless single-phase Ac–Dc Power Factor Correction (PFC) converters with Fuzzy Logic Controller. High frequency isolated Cuk converters are used as a modular dc-dc converter in Discontinuous Conduction Mode (DCM) of operation of Power Factor Correction. The aim of this paper is to simplify the program complexity of the controller by reducing the number of fuzzy sets of the Membership Functions (MFs) and to improve the efficiency and to eliminate the power quality problems. The output of Fuzzy controller is compared with High frequency triangular wave to generate PWM gating signals of Cuk converter. The proposed topologies are designed to work in Discontinuous Conduction Mode (DCM) to achieve a unity power factor and low total harmonic distortion of the input current. The Fuzzy Logic Controller gives additional advantages such as accurate result, uncertainty and imprecision and automatic control circuitry. Performance comparisons between the proposed and conventional controllers and circuits are performed based on circuit simulations.

Keywords: Fuzzy Logic Controller (FLC), Bridgeless rectifier, Cuk converter, Pulse Width Modulation (PWM), Power Factor Correction, Total Harmonic Distortion (THD).

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Authors: Rizwan Ullah, Abdar Ali, Zahid Ullah

Abstract:

This paper illustrates the study of three isolated zero voltage switched (ZVS) PWM full bridge (FB) converters to charge the high voltage battery in the charger of electric vehicle (EV). EV battery chargers have several challenges such as high efficiency, high reliability, low cost, isolation, and high power density. The cost of magnetic and filter components in the battery charger is reduced when switching frequency is increased. The increase in the switching frequency increases switching losses. ZVS is used to reduce switching losses and to operate the converter in the battery charger at high frequency. The performance of each of the three converters is evaluated on the basis of ZVS range, dead times of the switches, conduction losses of switches, circulating current stress, circulating energy, duty cycle loss, and efficiency. The limitations and merits of each PWM FB converter are reviewed. The converter with broader ZVS range, high efficiency and low switch stresses is selected for battery charger applications in EV.

Keywords: Electric vehicle, PWM FB converter, zero voltage switching, circulating energy, duty cycle loss, battery charger.

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Authors: Shang-En Yu

Abstract:

Human society, there are many uncertainties, such as economic growth rate forecast of the financial crisis, many scholars have, since the the Song Chissom two scholars in 1993 the concept of the so-called fuzzy time series (Fuzzy Time Series)different mode to deal with these problems, a previous study, however, usually does not consider the relevant variables selected and fuzzy process based solely on subjective opinions the fuzzy semantic discrete, so can not objectively reflect the characteristics of the data set, in addition to carrying outforecasts are often fuzzy rules as equally important, failed to consider the importance of each fuzzy rule. For these reasons, the variable selection (Factor Selection) through self-organizing map (Self-Organizing Map, SOM) and proposed high-end weighted multivariate fuzzy time series model based on fuzzy neural network (Fuzzy-BPN), and using the the sequential weighted average operator (Ordered Weighted Averaging operator, OWA) weighted prediction. Therefore, in order to verify the proposed method, the Taiwan stock exchange (Taiwan Stock Exchange Corporation) Taiwan Weighted Stock Index (Taiwan Stock Exchange Capitalization Weighted Stock Index, TAIEX) as experimental forecast target, in order to filter the appropriate variables in the experiment Finally, included in other studies in recent years mode in conjunction with this study, the results showed that the predictive ability of this study further improve.

Keywords: Heterogeneity, residential mortgage loans, foreclosure.

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Authors: Fekkak Bouazza, Menaa Mohamed, Loukriz Abdelhamid, Krim Mohamed L.

Abstract:

This paper presents modeling and control strategy for the grid connected wind turbine system based on Permanent Magnet Synchronous Generator (PMSG). The considered system is based on back-to-back converter topology. The Grid Side Converter (GSC) achieves the DC bus voltage control and unity power factor. The Machine Side Converter (MSC) assures the PMSG speed control. The PMSG is used as a variable speed generator and connected directly to the turbine without gearbox. The pitch angle control is not either considered in this study. Further, Optimal Tip Speed Ratio (OTSR) based MPPT control strategy is used to ensure the most energy efficiency whatever the wind speed variations. A filter (L) is put between the GSC and the grid to reduce current ripple and to improve the injected power quality. The proposed grid connected wind system is built under MATLAB/Simulink environment. The simulation results show the feasibility of the proposed topology and performance of its control strategies.

Keywords: Wind, grid, PMSG, MPPT, OTSR.

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Authors: Sorawit Stapornchaisit, Sidshchadhaa Aumted, Hiroshi Takami

Abstract:

In this paper, we propose a novel adaptive voltage control strategy for boost converter via Inverse LQ Servo-Control. Our presented strategy is based on an analytical formula of Inverse Linear Quadratic (ILQ) design method, which is not necessary to solve Riccati’s equation directly. The optimal and adaptive controller of the voltage control system is designed. The stability and the robust control are analyzed. Whereas, we can get the analytical solution for the optimal and robust voltage control is achieved through the natural angular velocity within a single parameter and we can change the responses easily via the ILQ control theory. Our method provides effective results as the stable responses and the response times are not drifted even if the condition is changed widely.

Keywords: Boost converter, optimal voltage control, inverse LQ design method, type-1 servo-system, adaptive control.

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Authors: Xiaoji Liu, Yonghui Qin

Abstract:

In this note, we consider a family of iterative formula for computing the weighted Minskowski inverses AM,N in Minskowski space, and give two kinds of iterations and the necessary and sufficient conditions of the convergence of iterations.

Keywords: iterative method, the Minskowski inverse, A

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Authors: Derya Ören Duran, Şeyma Akalin Benderli

Abstract:

Cold press technique is a traditional method to obtain oil. The cold-pressing procedure involves neither heat nor chemical treatments; therefore, cold press technique has low oil yield. The cold pressed herbal material residue still contains some oil after cold press. In this study, the oil that is remained in the cold pressed aniseed was extracted with hexane; and it was analyzed to determine physicochemical properties and quality parameters. It was found that the aniseed after cold press process still contained 10% oil. The values of other analysis parameters were 2.1 mgKOH/g for free fatty acid (FFA) and 7.6 meq0₂/kg for peroxide. Cold pressed aniseed oil values were determined as 2.1 mgKOH/g for FFA and 4.5 meq0₂/kg for peroxide, respectively. In addition, fatty acid composition was analyzed, and it was found that both types of oil had same fatty acid compositions. The main fatty acids were oleic, linoleic and palmitic acids.

Keywords: Aniseed oil, cold press, extraction, residue.

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Authors: Yasunori Sugita, Toshinori Yoshikawa, Naoyuki Aikawa

Abstract:

Variable digital filters are useful for various signal processing and communication applications where the frequency characteristics, such as fractional delays and cutoff frequencies, can be varied. In this paper, we propose a design method of variable FIR digital filters with an approximate linear phase characteristic in the passband. The proposed variable FIR filters have some large attenuation in stopband and their large attenuation can be varied by spectrum parameters. In the proposed design method, a quasi-equiripple characteristic can be obtained by using an iterative weighted least square method. The usefulness of the proposed design method is verified through some examples.

Keywords: Weighted Least Squares Approximation, Variable FIR Filters, Low-Delay, Quasi-Equiripple

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Authors: Halil Ibrahim Demir, Tarık Cakar, Ibrahim Cil, Muharrem Dugenci, Caner Erden

Abstract:

Conventionally, process planning, scheduling, and due-date assignment functions are performed separately and sequentially. The interdependence of these functions requires integration. Although integrated process planning and scheduling, and scheduling with due date assignment problems are popular research topics, only a few works address the integration of these three functions. This work focuses on the integration of process planning, WMS scheduling, and WPPW due date assignment. Another novelty of this work is the use of a weighted due date assignment. In the literature, due dates are generally assigned without considering the importance of customers. However, in this study, more important customers get closer due dates. Typically, only tardiness is punished, but the JIT philosophy punishes both earliness and tardiness. In this study, all weighted earliness, tardiness, and due date related costs are penalized. As no customer desires distant due dates, such distant due dates should be penalized. In this study, various levels of integration of these three functions are tested and genetic search and random search are compared both with each other and with ordinary solutions. Higher integration levels are superior, while search is always useful. Genetic searches outperformed random searches.

Keywords: Process planning, weighted scheduling, weighted due-date assignment, genetic algorithm, random search.

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Authors: Srinivasa Reddy Mallampati, Chi-Hyeon Lee, Nguyen Thi Thanh Truc, Byeong-Kyu Lee

Abstract:

In the present study, feasibility of the selective surface hydrophilization of polyvinyl chloride (PVC) by microwave treatment was evaluated to facilitate the separation from automotive shredder residue (ASR), by the froth flotation. The combination of 60 sec microwave treatment with PAC, a sharp and significant decrease about 16.5° contact angle of PVC was observed in ASR plastic compared with other plastics. The microwave treatment with the addition of PAC resulted in a synergetic effect for the froth flotation, which may be a result of the 90% selective separation of PVC from ASR plastics, with 82% purity. While, simple mixing with a nanometallic Ca/CaO/PO4 dispersion mixture immobilized 95-100% of heavy metals in ASR soil/residues. The quantity of heavy metals leached from thermal residues after treatment by nanometallic Ca/CaO/PO4 was lower than the Korean standard regulatory limit for hazardous waste landfills. Microwave treatment can be a simple and effective method for PVC separation from ASR plastics.

Keywords: Automotive shredder residue, microwave treatment, chlorinated plastics, separation, heavy metals, Immobilization, separation.

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Authors: Shuimiao Wan, Chao Yuan, Baoguang Tian

Abstract:

In statistics parameter theory, usually the parameter estimations have two kinds, one is the least-square estimation (LSE), and the other is the best linear unbiased estimation (BLUE). Due to the determining theorem of minimum variance unbiased estimator (MVUE), the parameter estimation of BLUE in linear model is most ideal. But since the calculations are complicated or the covariance is not given, people are hardly to get the solution. Therefore, people prefer to use LSE rather than BLUE. And this substitution will take some losses. To quantize the losses, many scholars have presented many kinds of different relative efficiencies in different views. For the linear weighted regression model, this paper discusses the relative efficiencies of LSE of β to BLUE of β. It also defines two new relative efficiencies and gives their lower bounds.

Keywords: Linear weighted regression, Relative efficiency, Lower bound, Parameter estimation.

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