Search results for: Particle filter

Authors: Wilfred Fritz

Abstract:

Grid connected solar PV inverters need to be compliant to standard regulations regarding unwanted harmonic generation. This paper gives an introduction to harmonics, solar PV inverter voltage regulation and balancing through compensation and investigates the behaviour of harmonic generation at different power levels. Practical measurements of harmonics and power levels with a power quality data logger were made, on a test network at a university in Germany. The test setup and test results are discussed. The major finding was that between the morning and afternoon load peak windows when the PV inverters operate under low solar insolation and low power levels, more unwanted harmonics are generated. This has a huge impact on the power quality of the grid as well as capital and maintenance costs. The design of a single-tuned harmonic filter towards harmonic mitigation is presented.

Keywords: Harmonics, power quality, pulse width modulation, total harmonic distortion.

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Authors: V. K. Singh, P. K. Padhy

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This paper describes identification of the two poles unstable SOPDT process, especially with large time delay. A new modified relay feedback identification method for two poles unstable SOPDT process is proposed. Furthermore, for the two poles unstable SOPDT process, an additional Derivative controller is incorporated parallel with relay to relax the constraint on the ratio of delay to the unstable time constant, so that the exact model parameters of unstable processes can be identified. To cope with measurement noise in practice, a low pass filter is suggested to get denoised output signal toimprove the exactness of model parameter of unstable process. PID Lead-lag tuning formulas are derived for two poles unstable (SOPDT) processes based on IMC principle. Simulation example illustrates the effectiveness and the simplicity of the proposed identification and control method.

Keywords: IMC structure, PID Lead-lag controller, Relayfeedback, SOPDT

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Authors: Jung-Chuan Chou, Wei-Chuan Chen, Chien-Cheng Chen

Abstract:

This study is concerned with pH solution detection using 2 × 4 flexible sensor array based on a plastic polyethylene terephthalate (PET) substrate that is coated a conductive layer and a ruthenium dioxide (RuO2) sensitive membrane with the technologies of screen-printing and RF sputtering. For data analysis, we also prepared a dynamic measurement system for acquiring the response voltage and analyzing the characteristics of the working electrodes (WEs), such as sensitivity and linearity. In this condition, an array measurement system was designed to acquire the original signal from sensor array, and it is based on the method of digital signal processing (DSP). The DSP modifies the unstable acquisition data to a direct current (DC) output using the technique of digital filter. Hence, this sensor array can obtain a satisfactory yield, 62.5%, through the design measurement and analysis system in our laboratory.

Keywords: Flexible sensor array, PET, RuO2, dynamic measurement, data analysis.

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Authors: Amir Rastegarnia, Mohammad Ali Tinati, Azam Khalili

Abstract:

In this paper we consider the issue of distributed adaptive estimation over sensor networks. To deal with more realistic scenario, different variance for observation noise is assumed for sensors in the network. To solve the problem of different variance of observation noise, the proposed method is divided into two phases: I) Estimating each sensor-s observation noise variance and II) using the estimated variances to obtain the desired parameter. Our proposed algorithm is based on a diffusion least mean square (LMS) implementation with linear combiner model. In the proposed algorithm, the step-size parameter the coefficients of linear combiner are adjusted according to estimated observation noise variances. As the simulation results show, the proposed algorithm considerably improves the diffusion LMS algorithm given in literature.

Keywords: Adaptive filter, distributed estimation, sensor network, diffusion.

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Authors: Thomas Paris, Vincent Bruyere, Patrick Namy

Abstract:

A numerical model is developed to simulate gas blowdowns through a thin tube and a filter (porous media), separating a high pressure gas filled reservoir to low pressure ones. Based on a previous work, a one-dimensional approach is developed by using the finite element method to solve the transient compressible flow and to predict the pressure and temperature evolution in space and time. Mass, momentum, and energy conservation equations are solved in a fully coupled way in the reservoirs, the pipes and the porous media. Numerical results, such as pressure and temperature evolutions, are firstly compared with experimental data to validate the model for different configurations. Couplings between porous media and pipe flow are then validated by checking mass balance. The influence of the porous media and the nature of the gas is then studied for different initial high pressure values.

Keywords: Fluid mechanics, compressible flow, heat transfer, porous media.

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Authors: Walid S. Alfuhaid, Saud A. Alghamdi, John M. Watkins, M. Edwin Sawan

Abstract:

Designing a controller for stochastic decentralized interconnected large scale systems usually involves a high degree of complexity and computation ability. Noise, observability, and controllability of all system states, connectivity, and channel bandwidth are other constraints to design procedures for distributed large scale systems. The quasi-steady state model investigated in this paper is a reduced order model of the original system using singular perturbation techniques. This paper results in an optimal control synthesis to design an observer based feedback controller by standard stochastic control theory techniques using Linear Quadratic Gaussian (LQG) approach and Kalman filter design with less complexity and computation requirements. Numerical example is given at the end to demonstrate the efficiency of the proposed method.

Keywords: Decentralized, optimal control, output, singular perturb.

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Authors: Nik N. Nik Daud, Nur H. Izehar, B. Yusuf, Thamer A. Mohamed, A. Ahsan

Abstract:

An experiment was conducted using two aeration methods (water-into-air and air-into-water) and followed by filtration processes using manganese greensand material. The properties of groundwater such as pH, dissolved oxygen, turbidity and heavy metal concentration (iron and manganese) will be assessed. The objectives of this study are i) to determine the effective aeration method and ii) to assess the effectiveness of manganese greensand as filter media in removing iron and manganese concentration in groundwater. Results showed that final pH for all samples after treatment are in range from 7.40 and 8.40. Both aeration methods increased the dissolved oxygen content. Final turbidity for groundwater samples are between 3 NTU to 29 NTU. Only three out of eight samples achieved iron concentration of 0.3mg/L and less and all samples reach manganese concentration of 0.1mg/L and less. Air-into-water aeration method gives higher percentage of iron and manganese removal compare to water-into-air method.

Keywords: Aeration, filtration, groundwater, water quality.

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Authors: Edward Aris D. Fajardo, Hamdi Muhyuddin D. Barra

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This study employs the use of the fourth order Numerov scheme to determine the eigenstates and eigenvalues of particles, electrons in particular, in single and double delta function potentials. For the single delta potential, it is found that the eigenstates could only be attained by using specific potential depths. The depth of the delta potential well has a value that varies depending on the delta strength. These depths are used for each well on the double delta function potential and the eigenvalues are determined. There are two bound states found in the computation, one with a symmetric eigenstate and another one which is antisymmetric.

Keywords: Double Delta Potential, Eigenstates, Eigenvalue, Numerov Method, Single Delta Potential

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Authors: N. Kotabin, Y. Tahara, K. Issakul, O. Chunhachart

Abstract:

Cadmium (II) (Cd) is one of the major toxic elemental pollutants, which is hazardous for humans, animals and plants. γ- Polyglutamic acid (γ-PGA) is an extracellular biopolymer produced by several species of Bacillus which has been reported to be an effective biosorbent for metal ions. The effect of γ-PGA on growth of rice grown under laboratory conditions was investigated. Rice seeds were germinated and then grown at 30±1°C on filter paper soaked with Cd solution and γ-PGA for 7 days. The result showed that Cd significantly inhibited the growth of roots, shoots by reducing root, and shoot lengths. Fresh and dry weights also decreased compared with control; however, the addition of 500 mg·L-1 γ-PGA alleviated rice seedlings from the adverse effects of Cd. The analysis of physiological traits revealed that Cd caused a decrease in the total chlorophyll and soluble protein contents and amylase activities in all treatments. The Cd content in seedling tissues increased for the Cd 250 μM treatment (P<0.05) but the addition of 500 mg·L-1 γ-PGA resulted in a noticeable decrease in Cd (P<0.05).

Keywords: Polyglutamic acid, Cadmium, Rice, Bacillus subtilis.

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Authors: Sepehr Aslani, Homayoun Mahdavi-Nasab

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Automated motion detection and tracking is a challenging task in traffic surveillance. In this paper, a system is developed to gather useful information from stationary cameras for detecting moving objects in digital videos. The moving detection and tracking system is developed based on optical flow estimation together with application and combination of various relevant computer vision and image processing techniques to enhance the process. To remove noises, median filter is used and the unwanted objects are removed by applying thresholding algorithms in morphological operations. Also the object type restrictions are set using blob analysis. The results show that the proposed system successfully detects and tracks moving objects in urban videos.

Keywords: Optical flow estimation, moving object detection, tracking, morphological operation, blob analysis.

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Authors: Lloyd G. Allred

Abstract:

The distribution of velocities of particles in plasma is a well understood discipline of plasma physics. Boltzmann’s law and the Maxwell-Boltzmann distribution describe the distribution of velocity of a particle in plasma as a function of mass and temperature. Particles with the same mass tend to have the same velocity. By expressing the same law in terms of energy alone, the author obtains a distribution independent of mass. In summary, for particles in plasma, the energies tend to equalize, independent of the masses of the individual particles. For high-energy plasma, the original law predicts velocities greater than the speed of light. If one uses Einstein’s formula for energy (E=mc²), then a relativistic correction is not required.

Keywords: Cosmology, EMP, Euclidean, plasma physics, relativity.

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Authors: Anurag Gaur, Neha Sharma

Abstract:

In this work, we have synthesized BaTiO₃ via sol gel method by sintering at different temperatures (600, 700, 800, 900, 1000⁰C) and studied their structural, optical and ferroelectric properties through X-ray diffraction (XRD), UV-Vis spectrophotometer and PE Loop Tracer. X-ray diffraction patterns of barium titanate samples show that the peaks of the diffractogram are successfully indexed with the tetragonal and cubic structure of BaTiO₃. The Optical band gap calculated through UV Visible spectrophotometer varies from 4.37 to 3.80 eV for the samples sintered at 600 to 1000⁰C, respectively. The particle size calculated through transmission electron microscopy varies from 20 to 40 nm for the samples sintered at 600 to 1000⁰C, respectively. Moreover, it has been observed that the ferroelectricity increases as we increase the sintering temperature.

Keywords: Nanostructures, Ferroelectricity, Sol-gel method.

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Authors: Toshiaki Yanada, Kazumi Ishikawa

Abstract:

The present paper deals with the analysis and development of noise-reduction transformer that has a filter function for conductive noise transmission. Two types of prototype noise-reduction transformers with two different output voltages are proposed. To determine an optimum design for the noise-reduction transformer, noise attenuation characteristics are discussed based on the experiments and the equivalent circuit analysis. The analysis gives a relation between the circuit parameters and the noise attenuation. High performance step-down noise-reduction transformer for direct power supply to electronics equipment is developed. The input voltage of the transformer is 100 V and the output voltage is 5 V. Frequency characteristics of noise attenuation are discussed, and prevention of pulse noise transmission is demonstrated. Normal mode noise attenuation of this transformer is –80 dB, and common mode exceeds –90 dB. The step-down noise-reduction transformer eliminates pulse noise efficiently.

Keywords: conductive noise, EMC, EMI, noise attenuation, transformer.

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Authors: Widi Astuti, Agus Prasetya, Endang Tri Wahyuni, I Made Bendiyasa

Abstract:

Coal fly ash (CFA) generated by coal-based thermal power plants is mainly composed of quartz, mullite, and unburned carbon. In this study, the effect of unburned carbon on CFA toward its adsorption capacity was investigated. CFA with various carbon content was obtained by refluxing it with sulfuric acid having various concentration at various temperature and reflux time, by heating at 400-800°C, and by sieving into 100-mesh in particle size. To evaluate the effect of unburned carbon on CFA toward its adsorption capacity, adsorption of methyl violet solution with treated CFA was carried out. The research shows that unburned carbon leads to adsorption capacity decrease. The highest adsorption capacity of treated CFA was found 5.73 x 10-4mol.g-1.

Keywords: CFA, carbon, methyl violet, adsorption capacity.

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Authors: Hung-Ming Lai, Andreas Albrecht, Kathleen Steinhöfel

Abstract:

Cancers could normally be marked by a number of differentially expressed genes which show enormous potential as biomarkers for a certain disease. Recent years, cancer classification based on the investigation of gene expression profiles derived by high-throughput microarrays has widely been used. The selection of discriminative genes is, therefore, an essential preprocess step in carcinogenesis studies. In this paper, we have proposed a novel gene selector using information-theoretic measures for biological discovery. This multivariate filter is a four-stage framework through the analyses of feature relevance, feature interdependence, feature redundancy-dependence and subset rankings, and having been examined on the colon cancer data set. Our experimental result show that the proposed method outperformed other information theorem based filters in all aspect of classification errors and classification performance.

Keywords: Colon cancer, feature interdependence, feature subset selection, gene selection, microarray data analysis.

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Authors: A. Naceri, M. S. Bouglada, P. Grosseau

Abstract:

The setting agent Ca(OH)2 for activation of slag cement is used in the proportions of 0%, 2%, 4%, 6%, 8% and 10% by various methods (substitution and addition by mass of slag cement). The physical properties of slag cement activated by the calcium hydroxide at anhydrous and hydrated states (fineness, particle size distribution, consistency of the cement pastes and setting times) were studied. The activation method by the mineral activator of slag cement (latent hydraulicity) accelerates the hydration process and reduces the setting times of the cement activated.

Keywords: Mineral activator, slag cement, Anhydrous and hydrated states, physical characteristics.

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Authors: Mina Alibeigi, Sattar Hashemi, Ali Hamzeh

Abstract:

Since dealing with high dimensional data is computationally complex and sometimes even intractable, recently several feature reductions methods have been developed to reduce the dimensionality of the data in order to simplify the calculation analysis in various applications such as text categorization, signal processing, image retrieval, gene expressions and etc. Among feature reduction techniques, feature selection is one the most popular methods due to the preservation of the original features. In this paper, we propose a new unsupervised feature selection method which will remove redundant features from the original feature space by the use of probability density functions of various features. To show the effectiveness of the proposed method, popular feature selection methods have been implemented and compared. Experimental results on the several datasets derived from UCI repository database, illustrate the effectiveness of our proposed methods in comparison with the other compared methods in terms of both classification accuracy and the number of selected features.

Keywords: Feature, Feature Selection, Filter, Probability Density Function

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Authors: V. J. Pillewan, D. N. Raut, K. N. Patil, D. K. Shinde

Abstract:

Forging, milling, turning, grinding and shaping etc. are the various industrial manufacturing processes which generate the metal waste. Grinding is extensively used in the finishing operation. The waste generated contains significant impurities apart from the metal particles. Due to these significant impurities, it becomes difficult to process and gets usually dumped in the landfills which create environmental problems. Therefore, it becomes essential to reuse metal waste to create value added products. Powder injection molding process is used for producing the porous metal matrix framework. This paper discusses the presented design of the porous framework to be used for the liquid filter application. Different parameters are optimized to obtain the better strength framework with variable porosity. Carbon nanotubes are used as reinforcing materials to enhance the strength of the metal matrix framework.

Keywords: Grinding waste, powder injection molding, carbon nanotubes, metal matrix composites.

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Authors: R. Blythman, N. Jeffers, T. Persoons, D. B. Murray

Abstract:

The exploitation of flow pulsation in micro- and mini-channels is a potentially useful technique for enhancing cooling of high-end photonics and electronics systems. It is thought that pulsation alters the thickness of the hydrodynamic and thermal boundary layers, and hence affects the overall thermal resistance of the heat sink. Although the fluid mechanics and heat transfer are inextricably linked, it can be useful to decouple the parameters to better understand the mechanisms underlying any heat transfer enhancement. Using two-dimensional, two-component particle image velocimetry, the current work intends to characterize the heat transfer mechanisms in pulsating flow with a mean Reynolds number of 48 by experimentally quantifying the hydrodynamics of a generic liquid-cooled channel geometry. Flows circulated through the test section by a gear pump are modulated using a controller to achieve sinusoidal flow pulsations with Womersley numbers of 7.45 and 2.36 and an amplitude ratio of 0.75. It is found that the transient characteristics of the measured velocity profiles are dependent on the speed of oscillation, in accordance with the analytical solution for flow in a rectangular channel. A large velocity overshoot is observed close to the wall at high frequencies, resulting from the interaction of near-wall viscous stresses and inertial effects of the main fluid body. The steep velocity gradients at the wall are indicative of augmented heat transfer, although the local flow reversal may reduce the upstream temperature difference in heat transfer applications. While unsteady effects remain evident at the lower frequency, the annular effect subsides and retreats from the wall. The shear rate at the wall is increased during the accelerating half-cycle and decreased during deceleration compared to steady flow, suggesting that the flow may experience both enhanced and diminished heat transfer during a single period. Hence, the thickness of the hydrodynamic boundary layer is reduced for positively moving flow during one half of the pulsation cycle at the investigated frequencies. It is expected that the size of the thermal boundary layer is similarly reduced during the cycle, leading to intervals of heat transfer enhancement.

Keywords: Heat transfer enhancement, particle image velocimetry, localized and time-resolved velocity, photonics and electronics cooling, pulsating flow, Richardson’s annular effect.

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Authors: N. Benabdeslam, N. Bouzidi, F. Atmani, R. Boucif, A. Sakhri

Abstract:

The objective of this study was to provide answers for a better understanding of the mechanisms involved during grinding. To obtain a phosphate powder, we carry out sieving - grinding circuits for each parameter influencing the process. The analysis of the average particle size of the different tests carried out served in the first place as a basis for the determination of the granulometric curve area, the characteristics and the granular coefficients, then the exploitation of the different results for the calculation of the energies consumed for the fragmentation of different ore types, the energy coefficients as well as the ability to grind. Indeed, a time of 5 to 10 minutes can be chosen as the optimal grinding time in a disc mill for a % in weight of the highest pass. However, grinding time can influence the granular characteristics of ore.

Keywords: Energy, granular characteristics, grinding, mineralogical composition, phosphate ore.

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Authors: Kyung Hyun, Choi, Minh Ngoc, Nong, M. Asif Ali, Rehmani

Abstract:

This present paper proposes the modified Elastic Strip method for mobile robot to avoid obstacles with a real time system in an uncertain environment. The method deals with the problem of robot in driving from an initial position to a target position based on elastic force and potential field force. To avoid the obstacles, the robot has to modify the trajectory based on signal received from the sensor system in the sampling times. It was evident that with the combination of Modification Elastic strip and Pseudomedian filter to process the nonlinear data from sensor uncertainties in the data received from the sensor system can be reduced. The simulations and experiments of these methods were carried out.

Keywords: Collision avoidance, Avoidance obstacle, Elastic Strip, Real time collision avoidance.

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Authors: Vahid Mohammadi Saffarzadeh, Pourya Jafarzadeh, Masoud Mazloom

Abstract:

This paper presents a hybrid approach for solving nqueen problem by combination of PSO and SA. PSO is a population based heuristic method that sometimes traps in local maximum. To solve this problem we can use SA. Although SA suffer from many iterations and long time convergence for solving some problems, By good adjusting initial parameters such as temperature and the length of temperature stages SA guarantees convergence. In this article we use discrete PSO (due to nature of n-queen problem) to achieve a good local maximum. Then we use SA to escape from local maximum. The experimental results show that our hybrid method in comparison of SA method converges to result faster, especially for high dimensions n-queen problems.

Keywords: PSO, SA, N-queen, CSP

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Authors: Marzieh. Savoj, S. Amirhassan. Monadjemi

Abstract:

Iris localization is a very important approach in biometric identification systems. Identification process usually is implemented in three levels: iris localization, feature extraction, and pattern matching finally. Accuracy of iris localization as the first step affects all other levels and this shows the importance of iris localization in an iris based biometric system. In this paper, we consider Daugman iris localization method as a standard method, propose a new method in this field and then analyze and compare the results of them on a standard set of iris images. The proposed method is based on the detection of circular edge of iris, and improved by fuzzy circles and surface energy difference contexts. Implementation of this method is so easy and compared to the other methods, have a rather high accuracy and speed. Test results show that the accuracy of our proposed method is about Daugman method and computation speed of it is 10 times faster.

Keywords: Convolution, Edge detector filter, Fuzzy circle, Identification

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Authors: Benjamin Y. M. Kwan, Hon Keung Kwan

Abstract:

Early detection of lung cancer through chest radiography is a widely used method due to its relatively affordable cost. In this paper, an approach to improve lung nodule visualization on chest radiographs is presented. The approach makes use of linear phase high-frequency emphasis filter for digital filtering and histogram equalization for contrast enhancement to achieve improvements. Results obtained indicate that a filtered image can reveal sharper edges and provide more details. Also, contrast enhancement offers a way to further enhance the global (or local) visualization by equalizing the histogram of the pixel values within the whole image (or a region of interest). The work aims to improve lung nodule visualization of chest radiographs to aid detection of lung cancer which is currently the leading cause of cancer deaths worldwide.

Keywords: Chest radiographs, Contrast enhancement, Digital filtering, Lung nodule detection

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Authors: Madina Hamiane, Amina Khunji

Abstract:

Detecting changes in multiple images of the same scene has recently seen increased interest due to the many contemporary applications including smart security systems, smart homes, remote sensing, surveillance, medical diagnosis, weather forecasting, speed and distance measurement, post-disaster forensics and much more. These applications differ in the scale, nature, and speed of change. This paper presents an application of image processing techniques to implement a real-time change detection system. Change is identified by comparing the RGB representation of two consecutive frames captured in real-time. The detection threshold can be controlled to account for various luminance levels. The comparison result is passed through a filter before decision making to reduce false positives, especially at lower luminance conditions. The system is implemented with a MATLAB Graphical User interface with several controls to manage its operation and performance.

Keywords: Image change detection, Image processing, image filtering, thresholding, B/W quantization.

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Authors: Jefrey Pilusa, Edison Muzenda

Abstract:

This research investigated treatment of crude carbon black produced from pyrolysis of waste tyres in order to evaluate its quality and possible industrial applications. A representative sample of crude carbon black was dry screened to determine the initial particle size distribution. This was followed by pulverizing the crude carbon black and leaching in hot concentrated sulphuric acid for the removal of heavy metals and other contaminants. Analysis of the refined carbon black showed a significant improvement of the product quality compared to crude carbon black. It was discovered that refined carbon black can be further classified into multiple high value products for various industrial applications such as filler, paint pigment, activated carbon and fuel briquettes.

Keywords: Activated Carbon, Briquettes, Fuel, Filler, Pyrolysis.

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Authors: S. Jalilzadeh, A. Kimiyaghalam, A. Ashouri

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This paper presents a mathematical model and a methodology to analyze the losses in transmission expansion planning (TEP) under uncertainty in demand. The methodology is based on discrete particle swarm optimization (DPSO). DPSO is a useful and powerful stochastic evolutionary algorithm to solve the large-scale, discrete and nonlinear optimization problems like TEP. The effectiveness of the proposed idea is tested on an actual transmission network of the Azerbaijan regional electric company, Iran. The simulation results show that considering the losses even for transmission expansion planning of a network with low load growth is caused that operational costs decreases considerably and the network satisfies the requirement of delivering electric power more reliable to load centers.

Keywords: DPSO, TEP, Uncertainty

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Authors: M. Ziółkowska, J. T. Duda, J. Milewska-Duda

Abstract:

This paper describes an approach to the adsorption phenomena modeling aimed at specifying the adsorption mechanisms on localized or nonlocalized adsorbent sites, when applied to the nanocarbons. The concept comes from the fundamental thermodynamic description of adsorption equilibrium and is based on numerical calculations of the hydrogen adsorbed particles volume on the surface of selected nanocarbons: single-walled nanotube and nanocone. This approach enables to obtain information on adsorption mechanism and then as a consequence to take appropriate mathematical adsorption model, thus allowing for a more reliable identification of the material porous structure. Theoretical basis of the approach is discussed and newly derived results of the numerical calculations are presented for the selected nanocarbons.

Keywords: Adsorption, mathematical modeling, nanocarbons, numerical analysis.

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Authors: Merve Küçük, M. Lütfi Öveçoğlu

Abstract:

Zinc oxide particles were synthesized using the sol-gel method and dip coated on polyester fabric. X-ray diffraction (XRD) analysis revealed a single crystal phase of ZnO particles. Chemical characteristics of the polyester fabric surface were investigated using attenuated total reflection-Fourier transform infrared (ATR-FTIR) measurements. Morphology of ZnO coated fabric was analyzed using field emission scanning electron microscopy (FESEM). After particle analysis, the aqueous ZnO solution resulted in a narrow size distribution at submicron levels. The deposit of ZnO on polyester fabrics yielded a homogeneous spread of spherical particles. Energy dispersive X-ray spectroscopy (EDX) results also affirmed the presence of ZnO particles on the polyester fabrics.

Keywords: Dip coating, polyester fabrics, sol-gel, zinc oxide.

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Authors: Paul O'Leary, Matthew Harker

Abstract:

This paper presents unified theory for local (Savitzky- Golay) and global polynomial smoothing. The algebraic framework can represent any polynomial approximation and is seamless from low degree local, to high degree global approximations. The representation of the smoothing operator as a projection onto orthonormal basis functions enables the computation of: the covariance matrix for noise propagation through the filter; the noise gain and; the frequency response of the polynomial filters. A virtually perfect Gram polynomial basis is synthesized, whereby polynomials of degree d = 1000 can be synthesized without significant errors. The perfect basis ensures that the filters are strictly polynomial preserving. Given n points and a support length ls = 2m + 1 then the smoothing operator is strictly linear phase for the points xi, i = m+1. . . n-m. The method is demonstrated on geometric surfaces data lying on an invariant 2D lattice.

Keywords: Gram polynomials, Savitzky-Golay Smoothing, Discrete Polynomial Moments

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