Search results for: double sampling

Authors: Mahmoud I. Syam, Kamarulzaman Ibrahim, Amer I. Al-Omari

Abstract:

Stratified double extreme ranked set sampling (SDERSS) method is introduced and considered for estimating the population mean. The SDERSS is compared with the simple random sampling (SRS), stratified ranked set sampling (SRSS) and stratified simple set sampling (SSRS). It is shown that the SDERSS estimator is an unbiased of the population mean and more efficient than the estimators using SRS, SRSS and SSRS when the underlying distribution of the variable of interest is symmetric or asymmetric.

Keywords: double extreme ranked set sampling, extreme ranked set sampling, ranked set sampling, stratified double extreme ranked set sampling

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Authors: A. D. Abdellatif, A. N. Ahmed, M. E. Abdelaziz

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The main purpose of this paper is to design a double acceptance sampling plan under the time truncated life test when the product lifetime follows an exponentiated transmuted Weibull distribution. Here, the motive is to meet both the consumer’s risk and producer’s risk simultaneously at the specified quality levels, while the termination time is specified. A comparison between the results of the double and single acceptance sampling plans is conducted. We demonstrate the applicability of our results to real data sets.

Keywords: double sampling plan, single sampling plan, producer’s risk, consumer’s risk, exponentiated transmuted weibull distribution, time truncated experiment, single, double, Marshal-Olkin

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Authors: Mahmoud I. Syam

Abstract:

Stratified double median ranked set sampling (SDMRSS) method is suggested for estimating the population mean. The SDMRSS is compared with the simple random sampling (SRS), stratified simple random sampling (SSRS), and stratified ranked set sampling (SRSS). It is shown that SDMRSS estimator is an unbiased of the population mean and more efficient than SRS, SSRS, and SRSS. Also, by SDMRSS, we can increase the efficiency of mean estimator for specific value of the sample size. SDMRSS is applied on real life examples, and the results of the example agreed the theoretical results.

Keywords: efficiency, double ranked set sampling, median ranked set sampling, ranked set sampling, stratified

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Authors: Michael B. C. Khoo, J. L. Khoo, W. C. Yeong, W. L. Teoh

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The Shewhart Xbar control chart is a useful process monitoring tool in manufacturing industries to detect the presence of assignable causes. However, it is insensitive in detecting small process shifts. To circumvent this problem, adaptive control charts are suggested. An adaptive chart enables at least one of the chart’s parameters to be adjusted to increase the chart’s sensitivity. Two common adaptive charts that exist in the literature are the double sampling (DS) Xbar and variable sampling interval (VSI) Xbar charts. This paper compares the performances of the DS and VSI Xbar charts, based on the average time to signal (ATS) criterion. The ATS profiles of the DS Xbar and VSI Xbar charts are obtained using the Mathematica and Statistical Analysis System (SAS) programs, respectively. The results show that the VSI Xbar chart is generally superior to the DS Xbar chart.

Keywords: adaptive charts, average time to signal, double sampling, charts, variable sampling interval

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Authors: Davood Shishebori, Mohammad Saber Fallah Nezhad, Sina Seifi

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In this paper, a variable multiple dependent state (MDS) sampling plan is developed based on the process capability index using Bayesian approach. The optimal parameters of the developed sampling plan with respect to constraints related to the risk of consumer and producer are presented. Two comparison studies have been done. First, the methods of double sampling model, sampling plan for resubmitted lots and repetitive group sampling (RGS) plan are elaborated and average sample numbers of the developed MDS plan and other classical methods are compared. A comparison study between the developed MDS plan based on Bayesian approach and the exact probability distribution is carried out.

Keywords: MDS sampling plan, RGS plan, sampling plan for resubmitted lots, process capability index (PCI), average sample number (ASN), Bayesian approach

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Authors: Tomas Menard

Abstract:

The design of control-law for engineering systems has been investigated for many decades. While many results are concerned with continuous systems with continuous output, nowadays, many controlled systems have to transmit their output measurements through network, hence making it discrete-time. But it is well known that the sampling of a system whose control-law is based on the continuous output may render the system unstable, especially when this sampling period is long compared to the system dynamics. The control design then has to be adapted in order to cope with this issue. In this paper, we consider systems which can be modeled as double integrator with uncertainty on the input since many mechanical systems can be put under such form. We present a control scheme based on an observer using only discrete time measurement and which provides continuous time estimation of the state, combined with a continuous control law, which stabilized a system with second-order dynamics even in the presence of uncertainty. It is further shown that arbitrarily long sampling periods can be dealt with properly setting the control scheme parameters.

Keywords: dynamical system, control law design, sampled output, observer design

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Authors: Raghunath Arnab

Abstract:

The two-phase sampling which is also known as double sampling was introduced in 1938. In two-phase sampling, samples are selected in phases. In the first phase, a relatively large sample of size is selected by some suitable sampling design and only information on the auxiliary variable is collected. During the second phase, a sample of size is selected either from, the sample selected in the first phase or from the entire population by using a suitable sampling design and information regarding the study and auxiliary variable is collected. Evidently, two phase sampling is useful if the auxiliary information is relatively easy and cheaper to collect than the study variable as well as if the strength of the relationship between the variables and is high. If the sample is selected in more than two phases, the resulting sampling design is called a multi-phase sampling. In this article we will consider how one can use data collected at the first phase sampling at the stages of estimation of the parameter, stratification, selection of sample and their combinations in the second phase in a unified setup applicable to any sampling design and wider classes of estimators. The problem of the estimation of variance will also be considered. The variance of estimator is essential for estimating precision of the survey estimates, calculation of confidence intervals, determination of the optimal sample sizes and for testing of hypotheses amongst others. Although, the variance is a non-negative quantity but its estimators may not be non-negative. If the estimator of variance is negative, then it cannot be used for estimation of confidence intervals, testing of hypothesis or measure of sampling error. The non-negativity properties of the variance estimators will also be studied in details.

Keywords: auxiliary information, two-phase sampling, varying probability sampling, unbiased estimators

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Authors: Heung Sun Yoon, Jong Tae Kim

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In this paper, we present an activity diagram model for double-loop control self-adaptive braking system. Since activity diagram helps to improve visibility of self-adaption, we can easily find where improvement is needed on double-loop control. Double-loop control is adopted since the design conditions and actual conditions can be different. The system is reconfigured in runtime by using double-loop control. We simulated to verify and validate our model by using MATLAB. We compared single-loop control model with double-loop control model. Simulation results show that double-loop control provides more consistent brake power control than single-loop control.

Keywords: activity diagram, automotive, braking system, double-loop, self-adaptive, UML, vehicle

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Authors: Nadia Akkari

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This paper presents the analysis and simulation of the control of double star induction motor, using direct torque control (DTC) based on RST regulator. The DTC is an excellent solution for general- purpose induction drives in very wide range the short sampling time required by the TC schemes makes them suited to a very fast torque and flux controlled drives as well the simplicity of the control algorithm. DTC is inherently a motion sensorless control method. The RST regulator can improve the double star induction motor performance in terms of overshoot, rapidity, cancellation of disturbance, and capacity to maintain a high level of performance. Simulation results indicate that the proposed regulator has better performance responses. The implementation of the DTC applied to a double star induction motor based on RST regulator is validated with simulated results.

Keywords: Direct Torque Control (DTC), Double Star Induction Motor (DSIM), RST Regulator

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Authors: J. K. Chawla, S. K. Jain, M. K. Mishra

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Ion-acoustic double layers have been studied in magnetized plasma. The modified Korteweg-de Vries (m-KdV) equation using reductive perturbation method is derived. It is found that for the selected set of parameters, the system supports rarefactive double layers depending upon the value of nonthermal parameters. It is also found that the magnetization affects only the width of the double layer. For a given set of parameter values, increases in the magnetization and the obliqueness angle (θ) between wave vector and magnetic field, affect the width of the double layers, however the amplitude of the double layers have no effect. An increase in the values of nonthermal parameter decreases the amplitude of the rarefactive double layer. The effect of the ion temperature ratio on the amplitude and width of the double layers are also discussed in detail.

Keywords: ion-acoustic double layers, magnetized electronegative plasma, reductive perturbation method, the modified Korteweg-de Vries (KdV) equation

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Authors: S. P. Sharma, Som Nath Saha

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This study investigates the effect of Global Solar Radiation (GSR) on the performance of double flow corrugated absorber solar air heater. A mathematical model of a double flow solar air heater, in which air is flowing simultaneously over and under the absorbing plate is presented and solved by developing a computer program in C++ language. The performance evaluation is studied in terms of air temperature rise, energy, effective and exergy efficiencies. The performance of double flow corrugated absorber is compared with double flow flat plate and conventional solar air heaters. It is found that double flow effectively increases the air temperature rise and efficiencies in comparison to a conventional collector. However, corrugated absorber is more superior to that of flat plate double flow solar air heater. The results show that increasing the solar radiation leads to achieve higher air temperature rise and efficiencies.

Keywords: corrugated absorber, double flow, flat plate, solar air heater

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Authors: Suresh Prasad Sharma, Som Nath Saha

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This paper deals with the effect of Global Solar Radiation (GSR) on the performance of double flow solar air heater having corrugated plate as an absorber. An analytical model of a double flow solar air heater has been presented, and a computer program in C++ language has been developed to calculate the outlet air temperature, heat gain, pressure drop for estimating the thermal and thermohydraulic efficiencies. The performance of double flow corrugated absorber is compared with double flow flat plate and conventional solar air heaters. It is found that the double flow arrangement effectively increases the air temperature rise and efficiencies in comparison to a conventional collector. However, corrugated absorber is more superior to that of flat plate double flow solar air heater. The results indicate that increasing the solar radiation leads to achieve higher air temperature rise and efficiencies.

Keywords: corrugated absorber, double flow, flat plate, solar air heater

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Authors: Manjit Singh

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Multiscale entropy (MSE) is an extensively used index to provide a general understanding of multiple complexity of physiologic mechanism of heart rate variability (HRV) that operates on a wide range of time scales. Accurate selection of electrocardiogram (ECG) sampling frequency is an essential concern for clinically significant HRV quantification; high ECG sampling rate increase memory requirements and processing time, whereas low sampling rate degrade signal quality and results in clinically misinterpreted HRV. In this work, the impact of ECG sampling frequency on MSE based HRV have been quantified. MSE measures are found to be sensitive to ECG sampling frequency and effect of sampling frequency will be a function of time scale.

Keywords: ECG (electrocardiogram), heart rate variability (HRV), multiscale entropy, sampling frequency

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Authors: Hsiang-Wen Tang, Cheng-Ying Lo

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In this study, the static behavior of super elliptical Winkler plate is analyzed by applying the double side approach method. The lack of information about super elliptical Winkler plates is the motivation of this study and we use the double side approach method to solve this problem because of its superior ability on efficiently treating problems with complex boundary shape. The double side approach method has the advantages of high accuracy, easy calculation procedure and less calculation load required. Most important of all, it can give the error bound of the approximate solution. The numerical results not only show that the double side approach method works well on this problem but also provide us the knowledge of static behavior of super elliptical Winkler plate in practical use.

Keywords: super elliptical winkler plate, double side approach method, error bound, mechanic

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Authors: Said Ali Al-Hadhrami, Amer Ibrahim Al-Omari

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In this paper, Bayesian estimation for the mean of exponential distribution is considered using Moving Extremes Ranked Set Sampling (MERSS). Three priors are used; Jeffery, conjugate and constant using MERSS and Simple Random Sampling (SRS). Some properties of the proposed estimators are investigated. It is found that the suggested estimators using MERSS are more efficient than its counterparts based on SRS.

Keywords: Bayesian, efficiency, moving extreme ranked set sampling, ranked set sampling

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Authors: S. P. Sharma, Som Nath Saha

Abstract:

This paper deals with the analytical investigation of thermal and thermohydraulic performance of double flow solar air heaters with corrugated and flat plate absorber. A mathematical model of double flow solar air heater has been presented, and a computer program in C⁺⁺ language is developed to estimate the outlet temperature of air for the evaluation of thermal and thermohydraulic efficiency by solving the governing equations numerically using relevant correlations for heat transfer coefficients. The results obtained from the mathematical model is compared with the available experimental results and it is found to be reasonably good. The results show that the double flow solar air heaters have higher efficiency than conventional solar air heater, although the double flow corrugated absorber is superior to that of flat plate double flow solar air heater. It is also observed that the thermal efficiency increases with increase in mass flow rate; however, thermohydraulic efficiency increases with increase in mass flow rate up to a certain limit, attains the maximum value, then thereafter decreases sharply.

Keywords: corrugated absorber, double flow, solar air heater, thermos-hydraulic efficiency

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Authors: S. P. Sharma, Som Nath Saha

Abstract:

This paper presents the performance, based on exergy analysis of double flow solar air heaters with corrugated and flat plate absorber. A mathematical model of double flow solar air heater based on energy balance equations has been presented and the results obtained have been compared with that of a conventional flat-plate solar air heater. The double flow corrugated absorber solar air heater performs thermally better than the flat plate double flow and conventional flat-plate solar air heater under same operating conditions. However, the corrugated absorber leads to higher pressure drop thereby increasing pumping power. The results revealed that the energy and exergy efficiencies of double flow corrugated absorber solar air heater is much higher than conventional solar air heater with the concept involving of increase in heat transfer surface area and turbulence in air flow. The results indicate that the energy efficiency increases, however, exergy efficiency decreases with increase in mass flow rate.

Keywords: corrugated absorber, double flow, exergy efficiency, solar air heater

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Authors: Negar Riazifar, Nigel G. Stocks

Abstract:

This paper proposes strategies in level crossing (LC) sampling and reconstruction that provide alias-free high-fidelity signal reconstruction for speech signals without exponentially increasing sample number with increasing bit-depth. We introduce methods in LC sampling that reduce the sampling rate close to the Nyquist frequency even for large bit-depth. The results indicate that larger variation in the sampling intervals leads to an alias-free sampling scheme; this is achieved by either reducing the bit-depth or adding jitter to the system for high bit-depths. In conjunction with windowing, the signal is reconstructed from the LC samples using an efficient Toeplitz reconstruction algorithm.

Keywords: alias-free, level crossing sampling, spectrum, trigonometric polynomial

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Authors: Thana Ananacha

Abstract:

This paper reports the numerical and experimental performances of Double Glass Wall are investigated. Two configurations were considered namely, the Double Clear Glass Wall (DCGW) and the Double Translucent Glass Wall (DTGW). The coupled governing equations as well as boundary conditions are solved using the finite element method (FEM) via COMSOLTM Multiphysics. Temperature profiles and flow field of the DCGW and DTGW are reported and discussed. Different constant heat fluxes were considered namely 400 and 800 W.m-2 the corresponding initial condition temperatures were to 30.5 and 38.5 ºC respectively. The results show that the simulation results are in agreement with the experimental data. Conclusively, the model considered in this study could reasonable be used simulate the thermal and ventilation performance of the DCGW and DTGW configurations.

Keywords: thermal simulation, Double Glass Wall, velocity field, finite element method (FEM)

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Authors: Qian Zhang, Dongkai Shen, Yan Shi

Abstract:

A new mechanical ventilator with automatic secretion clearance function can improve the secretion clearance safely and efficiently. However, in recent modeling studies on various mechanical ventilators, it was considered that human had one lung, and the coupling effect of double lungs was never illustrated. In this paper, to expound the coupling effect of double lungs, a mathematical model of a ventilation system of a bi-level positive airway pressure (BiPAP) controlled ventilator with secretion clearance was set up. Moreover, an experimental study about the mechanical ventilation system of double lungs on BiPAP ventilator was conducted to verify the mathematical model. Finally, the coupling effect of double lungs of the mathematical ventilation was studied by simulation and orthogonal experimental design. This paper adds to previous studies and can be referred to optimization methods in medical researches.

Keywords: double lungs, coupling effect, secretion clearance, orthogonal experimental design

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Authors: C. W. Kwak, I. J. Park, D. I. Jang

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The importance of cost-wise effective application and construction is getting increase due to the surge of traffic volume in the metropolitan cities. Accordingly, the necessity of the tunnel has large section becomes more critical. Double deck tunnel can be one of the most appropriate solutions to the necessity. The dynamic stability of double deck tunnel is essential against seismic load since it has large section and connection between perimeter lining and interim slab. In this study, 3-dimensional dynamic numerical analysis was conducted based on the Finite Difference Method to investigate the seismic behavior of double deck tunnel. Seismic joint for dynamic stability and the mitigation of seismic impact on the lining was considered in the modeling and analysis. Consequently, the mitigation of acceleration, lining displacement and stress were verified successfully.

Keywords: double deck tunnel, interim slab, 3-dimensional dynamic numerical analysis, seismic joint

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Authors: Barenten Suciu, Akio Miyamura

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In this paper, following the study-case of an inclined plane gravitational machine, efficiency of a double-cone gravitational motor and generator is evaluated. Two types of efficiency ratios, called translational efficiency and rotational efficiency, are defined relative to the intended duty of the gravitational machine, which can be either the production of translational kinetic energy, or rotational kinetic energy. One proved that, for pure rolling movement of the double- cone, in the absence of rolling friction, the total mechanical energy is conserved. In such circumstances, as the motion of the double-cone progresses along rails, the translational efficiency decreases and the rotational efficiency increases, in such way that sum of the rotational and translational efficiencies remains unchanged and equal to 1. Results obtained allow a comparison of the gravitational machine with other types of motor-generators, in terms of the achievable efficiency.

Keywords: efficiency, friction, gravitational motor and generator, rolling and sliding, truncated double-cone

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Authors: Jiwoo Park, Junseok Yoon, Jeong Kim, Beomsoo Kang

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Multi-Point Stretch Forming (MPSF) process is suitable for flexible manufacturing, and it has several advantages including that it could be applied to various forming such as sheet metal forming, single curved surface forming and double curved one. In this study, a systematic numerical simulation was carried out for atypical double curved surface forming using the multiple die stretch forming process. In this simulation, urethane pads were defined based on hyper-elastic material model as a cushion for the smooth forming surface. The deformation behaviour on elastic recovery was also investigated to consider the exact result after the last forming process, and then the experiment was also carried out to confirm the formability of this forming process. By comparing the simulation and experiment results, the suitability of the multiple die stretch forming process for the atypical double curved surface was verified. Consequently, it is confirmed that the multi-point stretch forming process has the capability and feasibility of being used to manufacture the double curved surfaces of sheet metal.

Keywords: multi-point stretch forming, double curved surface, numerical simulation, manufacturing

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Authors: A. Calvin Antony, Sakthi Kumar Arul Prakash, V. R. Sanal Kumar

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In this paper a unique alpha-beta double piston 'stirling engine' is designed, manufactured and conducted laboratory test to ameliorate the efficiency of the stirling engine. The paper focuses on alpha and beta type engines, capturing their benefits and eradicating their short comings; along with the output observed from the flywheel. In this model alpha engine is kinematically with a piston cylinder arrangement which works quite like a beta engine. The piston of the new cylinder is so designed that it replicates a glued displacer and power piston as similar to that of beta engine. The bigger part of the piston is the power piston, which has a gap around it, while the smaller part of the piston is tightly fit in the cylinder and acts like the displacer piston. We observed that the alpha-beta double piston stirling engine produces 25% increase in power compare to a conventional alpha stirling engine. This working model is a pointer towards for the design and development of an alpha-beta double piston Stirling engine for industrial applications for producing electricity from the heat producing exhaust gases.

Keywords: alpha-beta double piston stirling engine , alpha stirling engine , beta double piston stirling engine , electricity from stirling engine

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Authors: N. Saranya

Abstract:

The difference in characteristic behavior of clay minerals for different electrolyte solution is dictated by the corresponding variation occurring at its diffused double layer thickness (DDL). The diffused double layer of clay mineral has two distinct regions; the inner region is termed as ‘Stern layer’ where ions are strongly attached to the clay surface. In the outer region, the ions are not strongly bonded with the clay surface, and this region is termed as ‘diffuse layer’. Within the diffuse layer, there is a plane that forms a boundary between the moving ions and the ions attached to the clay surface, which is termed as slipping or shear plane, and the potential of this plane is defined as zeta potential (ζ). Therefore, the variation in diffused double layer properties of clay mineral for different electrolyte solutions can be modeled if the corresponding variation in surface charge, surface potential, and zeta potential are computed. In view of this, the present study has attempted to characterize the diffused double layer properties of three different clay minerals interacting with different pore fluids by measuring the corresponding variation in surface charge, surface potential, and zeta potential. Further, the obtained variation in the diffused double layer property is compared with the Gouy-Chapman model, which is the widely accepted theoretical model to characterize the diffused double layer properties of clay minerals.

Keywords: DDL, surface charge, surface potential, zeta potential

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Authors: F. Ait Ahsene-Aissat, Y. Kerchiche, Y. Moussaoui, M. Hachemi

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Environmental pollution is at the heart of the debate today, the pollutants released into the atmosphere must be measured and reduced to the norms of international releases. The industries pollution is caused by emissions of SO₂, CO and heavy metals in volatile form that must be quantified and monitored. This study presents a qualitative and quantitative analysis However, the collection of volatile heavy metals were performed by active sampling using an isokinetic. SO₂ gas for the maximum is reached for a value of 343 mg / m³, the SO₂ concentration far exceeds the standard releases SO₂ followed by incineration industries in Algeria. the concentration of Cr exceeds 8 times the standard, the Pb concentration in the excess of 6 times, the concentration of Fe has reached very high values exceeding the standard 30 times, the Zn concentration in the excess of 5 times, and the Ni the excess of 4 times and finally that of Cu is almost double of the standard.

Keywords: SO₂, CO, volatiles metals, active sampling isokinetic

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Authors: Khattab Al Qaisi, Nicholas Bowring

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This paper presents the simulation results of the effects of sampling frequency on the total harmonic distortion (THD) of three-phase inverters using the space vector pulse width modulation (SVPWM) and space vector control (SVC) algorithms. The relationship between the variables was studied using curve fitting techniques, and it has been shown that, for 50 Hz inverters, there is an exponential relation between the sampling frequency and THD up to around 8500 Hz, beyond which the performance of the model becomes irregular, and there is an negative exponential relation between the sampling frequency and the marginal improvement to the THD. It has also been found that the performance of SVPWM is better than that of SVC with the same sampling frequency in most frequency range, including the range where the performance of the former is irregular.

Keywords: DSI, SVPWM, THD, DC-AC converter, sampling frequency, performance

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Authors: Ashish Kumar Jain, Deepak Mishra

Abstract:

The objective of the present investigation was to prepare and evaluate a vesicular dual drug delivery system for effective management of mucosal ulcer. Inner encapsulating and Double liposomes were prepared by glass bead and reverse phase evaporation method respectively. The formulation consisted of inner liposomes bearing Ranitidine Bismuth Citrate (RBC) and outer liposomes encapsulating Amoxicillin trihydrate (AMOX). The optimized inner liposomes and double liposomes were extensively characterized for vesicle size, morphology, zeta potential, vesicles count, entrapment efficiency and in vitro drug release. In vitro, the double liposomes demonstrated a sustained release of AMOX and RBC viz 91.4±1.8% and 77.2±2.1% respectively at the end of 72 hr. Furthermore binding specificity and targeting propensity toward H. pylori (SKP-56) was confirmed by agglutination and in situ adherence assay. Reduction of the absolute alcohol induced ulcerogenic index from 3.01 ± 0.25 to 0.31 ± 0.09 and 100% H. pylori clearance rate was observed. These results suggested that double liposomes are potential vector for the development of dual drug delivery for effective treatment of H. pylori-associated peptic ulcer.

Keywords: double liposomes, H. pylori targeting, PE liposomes, glass-beads method, peptic ulcers

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Authors: Mohamed Moustafa Mahmoud Sedky

Abstract:

The double-fed induction generator wind turbine has recently received a great attention. The steady state performance and response of double fed induction generator (DFIG) based wind turbine are now well understood. This paper presents the analysis of stator and rotor flux linkage dq models operation of DFIG under different faults and at different locations.

Keywords: double fed induction motor, wind energy, flux linkage, short circuit

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Authors: T. Pathinathan, M. Peter

Abstract:

Fuzzy graphs incorporate concepts from graph theory with fuzzy principles. In this paper, we make a study on the properties of fuzzy graphs which are non-cyclic and are of two-dimensional in structure. In particular, this paper presents 2D structure or the structure of double layer for a non-cyclic fuzzy graph whose underlying crisp graph is non-cyclic. In any graph structure, introducing 2D structure may lead to an inherent cycle. We propose relevant conditions for 2D structured non-cyclic fuzzy graphs. These conditions are extended even to fuzzy graphs of the 3D structure. General theoretical properties that are studied for any fuzzy graph are verified to 2D structured or double layered fuzzy graphs. Concepts like Order, Degree, Strong and Size for a fuzzy graph are studied for 2D structured or double layered non-cyclic fuzzy graphs. Using different types of fuzzy graphs, the proposed concepts relating to 2D structured fuzzy graphs are verified.

Keywords: double layered fuzzy graph, double layered non–cyclic fuzzy graph, order, degree and size

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