Search results for: attractive solution

Authors: Yanmin Zhao, Siu Ming Yiu

Abstract:

To claim the ownership for an executable program is a non-trivial task. An emerging direction is to add a watermark to the program such that the watermarked program preserves the original program’s functionality and removing the watermark would heavily destroy the functionality of the watermarked program. In this paper, the first watermarking signature scheme with the watermark and the constraint function hidden in the symmetric key setting is constructed. The scheme uses well-known techniques of lattice trapdoors and a lattice evaluation. The watermarking signature scheme is unforgeable under the Short Integer Solution (SIS) assumption and satisfies other security requirements such as the unremovability security property.

Keywords: Short integer solution problem, signatures, the symmetric-key setting, watermarking schemes.

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Authors: Khaja Kamaluddin, Muhammed Yousoof

Abstract:

Bandwidth allocation in wired network is less complex and to allocate bandwidth in wireless networks is complex and challenging, due to the mobility of source end system.This paper proposes a new approach to bandwidth allocation to higher and lower priority mobile nodes.In our proposal bandwidth allocation to new mobile node is based on bandwidth utilization of existing mobile nodes.The first section of the paper focuses on introduction to bandwidth allocation in wireless networks and presents the existing solutions available for allocation of bandwidth. The second section proposes the new solution for the bandwidth allocation to higher and lower priority nodes. Finally this paper ends with the analytical evaluation of the proposed solution.

Keywords: Layered Approach, Bandwidth allocation, CBR, ABR, QOS.

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Authors: Khairil Iskandar Othman, Zarina Bibi Ibrahim, Mohamed Suleiman

Abstract:

A parallel block method based on Backward Differentiation Formulas (BDF) is developed for the parallel solution of stiff Ordinary Differential Equations (ODEs). Most common methods for solving stiff systems of ODEs are based on implicit formulae and solved using Newton iteration which requires repeated solution of systems of linear equations with coefficient matrix, I - hβJ . Here, J is the Jacobian matrix of the problem. In this paper, the matrix operations is paralleled in order to reduce the cost of the iterations. Numerical results are given to compare the speedup and efficiency of parallel algorithm and that of sequential algorithm.

Keywords: Backward Differentiation Formula, block, ordinarydifferential equations.

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Authors: Faheem Ahmed, Fareed Ahmed, Yongheng Guo, Yong Yang

Abstract:

This paper deals with a high-order accurate Runge Kutta Discontinuous Galerkin (RKDG) method for the numerical solution of the wave equation, which is one of the simple case of a linear hyperbolic partial differential equation. Nodal DG method is used for a finite element space discretization in 'x' by discontinuous approximations. This method combines mainly two key ideas which are based on the finite volume and finite element methods. The physics of wave propagation being accounted for by means of Riemann problems and accuracy is obtained by means of high-order polynomial approximations within the elements. High order accurate Low Storage Explicit Runge Kutta (LSERK) method is used for temporal discretization in 't' that allows the method to be nonlinearly stable regardless of its accuracy. The resulting RKDG methods are stable and high-order accurate. The L1 ,L2 and L∞ error norm analysis shows that the scheme is highly accurate and effective. Hence, the method is well suited to achieve high order accurate solution for the scalar wave equation and other hyperbolic equations.

Keywords: Nodal Discontinuous Galerkin Method, RKDG, Scalar Wave Equation, LSERK

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Authors: Weihua Ruan, Kuan-Chou Chen

Abstract:

This paper is concerned with a system of Hamilton-Jacobi-Bellman equations coupled with an autonomous dynamical system. The mathematical system arises in the differential game formulation of political economy models as an infinite-horizon continuous-time differential game with discounted instantaneous payoff rates and continuously and discretely varying state variables. The existence of a weak solution of the PDE system is proven and a computational scheme of approximate solution is developed for a class of such systems. A model of democratization is mathematically analyzed as an illustration of application.

Keywords: Differential games, Hamilton-Jacobi-Bellman equations, infinite horizon, political-economy models.

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Authors: M. Jahanandish, M. B. Zeydabadinejad

Abstract:

In this paper, von Mises and Drucker-Prager yield criteria, as typical ones that consider the effect of intermediate principal stress σ2, have been selected and employed for investigating the influence of σ2 on the solution of a typical stability problem. The bearing capacity factors have been calculated under plane strain condition (strip footing) and axisymmetric condition (circular footing) using the method of stress characteristics together with the criteria mentioned. Different levels of σ2 relative to the other two principal stresses have been considered. While a higher σ2 entry in yield criterion gives a higher bearing capacity; its entry in equilibrium equations (axisymmetric) causes substantial reduction.

Keywords: Intermediate principal stress, plane strain, axisymmetric, yield criteria.

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Authors: Jihyung Kim, Taejin Kim, Sungho Park, Jun-Dong Cho

Abstract:

In this paper, the problem of reducing switching activity in on-chip buses at the stage of high-level synthesis is considered, and a high-level low power bus binding based on dynamic bit reordering is proposed. Whereas conventional methods use a fixed bit ordering between variables within a bus, the proposed method switches a bit ordering dynamically to obtain a switching activity reduction. As a result, the proposed method finds a binding solution with a smaller value of total switching activity (TSA). Experimental result shows that the proposed method obtains a binding solution having 12.0-34.9% smaller TSA compared with the conventional methods.

Keywords: bit reordering, bus binding, low power, switching activity matrix

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Authors: Mukesh Kumar Shah, Tushar Gupta

Abstract:

An Upgraded Cuckoo Search Algorithm is proposed here to solve optimization problems based on the improvements made in the earlier versions of Cuckoo Search Algorithm. Short comings of the earlier versions like slow convergence, trap in local optima improved in the proposed version by random initialization of solution by suggesting an Improved Lambda Iteration Relaxation method, Random Gaussian Distribution Walk to improve local search and further proposing Greedy Selection to accelerate to optimized solution quickly and by “Study Nearby Strategy” to improve global search performance by avoiding trapping to local optima. It is further proposed to generate better solution by Crossover Operation. The proposed strategy used in algorithm shows superiority in terms of high convergence speed over several classical algorithms. Three standard algorithms were tested on a 6-generator standard test system and the results are presented which clearly demonstrate its superiority over other established algorithms. The algorithm is also capable of handling higher unit systems.

Keywords: Economic dispatch, Gaussian selection operator, prohibited operating zones, ramp rate limits, upgraded cuckoo search.

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Authors: Yue-Der Lin, Wei-Ting Liu, Ching-Che Tsai, Wen-Hsiu Chen

Abstract:

PPG is a potential tool in clinical applications. Among such, the relationship between respiration and PPG signal has attracted attention in past decades. In this research, a bivariate AR spectral estimation method was utilized for the coherence analysis between these two signals. Ten healthy subjects participated in this research with signals measured at different respiratory rates. The results demonstrate that high coherence exists between respiration and PPG signal, whereas the coherence disappears in breath-holding experiments. These results imply that PPG signal reveals the respiratory information. The utilized method may provide an attractive alternative approach for the related researches.

Keywords: Coherence analysis, photoplethysmography (PPG), bivariate AR spectral estimation.

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Authors: M. Klimavicius

Abstract:

This paper proposes a modeling methodology for the development of data analysis solution. The Author introduce the approach to address data warehousing issues at the at enterprise level. The methodology covers the process of the requirements eliciting and analysis stage as well as initial design of data warehouse. The paper reviews extended business process model, which satisfy the needs of data warehouse development. The Author considers that the use of business process models is necessary, as it reflects both enterprise information systems and business functions, which are important for data analysis. The Described approach divides development into three steps with different detailed elaboration of models. The Described approach gives possibility to gather requirements and display them to business users in easy manner.

Keywords: Data warehouse, data analysis, business processmanagement.

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Authors: A. K. Al-Othman, H. A. Al-Mekhaizim

Abstract:

Multilevel inverters supplied from equal and constant dc sources almost don-t exist in practical applications. The variation of the dc sources affects the values of the switching angles required for each specific harmonic profile, as well as increases the difficulty of the harmonic elimination-s equations. This paper presents an extremely fast optimal solution of harmonic elimination of multilevel inverters with non-equal dc sources using Tanaka's fuzzy linear regression formulation. A set of mathematical equations describing the general output waveform of the multilevel inverter with nonequal dc sources is formulated. Fuzzy linear regression is then employed to compute the optimal solution set of switching angles.

Keywords: Multilevel converters, harmonics, pulse widthmodulation (PWM), optimal control.

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Authors: Shiyang Zhu, G. Q. Lo, D. L. Kwong

Abstract:

Silicon photonics is merging as a unified platform for driving photonic based telecommunications and for local photonic based interconnect but it suffers from large footprint as compared with the nanoelectronics. Plasmonics is an attractive alternative for nanophotonics. In this work, two CMOS compatible plasmonic waveguide platforms are compared. One is the horizontal metal-insulator-Si-insulator-metal nanoplasmonic waveguide and the other is metal-insulator-Si hybrid plasmonic waveguide. Various passive and active photonic devices have been experimentally demonstrated based on these two plasmonic waveguide platforms.

Keywords: Plasmonics, on-chip integration, Silicon photonics.

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Authors: Takaaki Ishibashi

Abstract:

Frequency domain independent component analysis has a scaling indeterminacy and a permutation problem. The scaling indeterminacy can be solved by use of a decomposed spectrum. For the permutation problem, we have proposed the rules in terms of gain ratio and phase difference derived from the decomposed spectra and the source-s coarse directions. The present paper experimentally clarifies that the gain ratio and the phase difference work effectively in a real environment but their performance depends on frequency bands, a microphone-space and a source-microphone distance. From these facts it is seen that it is difficult to attain a perfect solution for the permutation problem in a real environment only by either the gain ratio or the phase difference. For the perfect solution, this paper gives a solution to the problems in a real environment. The proposed method is simple, the amount of calculation is small. And the method has high correction performance without depending on the frequency bands and distances from source signals to microphones. Furthermore, it can be applied under the real environment. From several experiments in a real room, it clarifies that the proposed method has been verified.

Keywords: blind source separation, frequency domain independent component analysys, permutation correction, scale adjustment, target extraction.

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Authors: A. Tannai, V. Herbert, C. Rufin-Soler

Abstract:

Since the beginning of the 21st century, we have been observing in some seaside resorts aging demography, combined with an increase in second homes. These seaside resorts are said to have become places undergoing profound changes, leading to hybridization of functions (personal services, health, residential, etc.) and practices. All of these issues are part of the challenges of silver tourism, which stems from the silver economy. The Hauts-de-France region is made up of numerous seaside resorts that have a significant proportion of second homes in their real estate stock. The seaside resorts have tourist offers based on sports and leisure activities. They also offer a suitable environment for the installation of this category of the population. This set of attractive criteria in the choice of installation in seaside resorts is likely to be replaced by personal and health services due to the advanced age of the population. The resorts of Le Touquet Paris-Plage, Bray-Dunes, Neufchâtel-Hardelot and Le Crotoy seem to be evolving towards other functions of residential resorts, as opposed to seaside resorts This paper will be an opportunity to present the results of the surveys we conducted in 4 seaside resorts in the Hauts-de-France region, where more than 420 retired secondary residents were questioned. The results show that nearly 90% of retirees spend their time in their second home at any time of the year. The criteria that lead them there are school vacations and the weather. More than 40% of them have been living there for more than 20 years. The reasons for the installations are the living environment (83%) and the quality of life (79%). Their activities are walking and strolling, as well as sports. More than 99% of the respondents do not take into account the health service offers. Personal services are also little taken into account - around 60% of respondents say they do not know whether personal services exist in the resort. 80% of respondents answer that their grandchildren benefit from activities organized by the commune and the tourist offices during their stay. To conclude, the influx of retired secondary residents will not lead to a change in the functions of the seaside resorts. Their classic tourist offers - leisure and sports activities, the environment - will remain the attractive criteria of the seaside resorts.  The results of the study prove that personal services and health services are not the first choice criteria in the installation of retired secondary residents, quite the contrary. We can even complete that retirees in secondary residences are demanding and concerned about living in a calm, safe and clean environment and quality of life.

Keywords: Health services, people care, second home, seniors, silver tourism, tourism, tourist functions.

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Authors: Praveen Saraswat, Vipin Kumar Verma, Rudraman Singh

Abstract:

The unsteady transient free convection flow of an incompressible dissipative viscous fluid between parallel plates at different distances have been investigated under porous medium. Due to presence of heat flux under the influence of uniform transverse magnetic field the velocity distribution and the temperature distribution, is shown graphically. Since exact solution is not possible so we find parametrical solution by perturbation technique. The result is shown in graph for different parameters. We notice that heat generation effects fluid velocity keeping in which of free convection which cools.

Keywords: Transient, Convection, MHD, Viscous, Porous.

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Authors: Ali Reza Pouladkhan, Jalil Emadi, Hamed Habibolahiyan

Abstract:

This paper presents an exact solution and a finite element method (FEM) for a Piezoceramic Rod under static load. The cylindrical rod is made from polarized ceramics (piezoceramics) with axial poling. The lateral surface of the rod is traction-free and is unelectroded. The two end faces are under a uniform normal traction. Electrically, the two end faces are electroded with a circuit between the electrodes, which can be switched on or off. Two cases of open and shorted electrodes (short circuit and open circuit) will be considered. Finally, a finite element model will be used to compare the results with an exact solution. The study uses ABAQUS (v.6.7) software to derive the finite element model of the ceramic rod.

Keywords: Finite element method, Ceramic rod; Axial poling, Normal traction, Short circuit, Open circuit.

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Authors: M. Hossain, A. H. Khan, M. A. R. Sarkar

Abstract:

Primary containment structure is one of the five safety layers of a nuclear facility which is needed to be designed in such a manner that it can withstand the pressure and excessive radioactivity during accidental situations. It is also necessary to ensure minimization of cost with maximum possible safety in order to make the design economically feasible and attractive. This paper attempts to identify the optimum design conditions for primary containment structure considering both mechanical and radiation safety keeping the economic aspects in mind. This work takes advantage of commercial simulation software to identify the suitable conditions without the requirement of costly experiments. Generated data may be helpful for further studies.

Keywords: PWR, concrete containment, finite element approach, neutron attenuation, Von Mises Stress.

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Authors: Chinwendu. B. Eleje, Udechukwu P. Egbuhuzor

Abstract:

One of the difficulties encountered in solving nonlinear Boundary Value Problems (BVP) by many researchers is finding approximated solutions with minimum deviations from the exact solutions without so much rigor and complications. In this paper, we propose an approach to solve a two point BVP which involves a combination of Taylor series expansion method and Newton Raphson method. Furthermore, the fourth and sixth order approximated solutions are obtained and we compare their relative error and rate of convergence to the exact solution. Finally, some numerical simulations are presented to show the behavior of the solution and its derivatives.

Keywords: Newton Raphson method, non-linear boundary value problem, Taylor series approximation, Michaelis-Menten equation.

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Authors: Kwang-Wook Kim, Geun-Il Park, Eil-Hee Lee, Kune-Woo Lee, Kee-Chan Song

Abstract:

Electrolytic dissolution characteristics of UO2 and SIMFUEL electrodes were studied at several potentials in carbonate solutions of a high concentration at several pHs. The electrolytic uranium dissolution was much affected by a corrosion product of UO2CO3 generated at the electrode during the dissolution in carbonate solution. The corrosion product distorted the voltammogram at UO2 and SIMFUEL electrodes in the potential region of oxygen evolution and increased the overpotential of oxygen evolution at the electrode. The effective dissolution in a carbonate solution could be obtained at an applied potential such as +4 V (vs SSE) or more which had an overpotential of oxygen evolution high enough to rupture the corrosion product on the electrode surface.

Keywords: Anodic, Electrolytic, Dissolution, SIMFUEL, Uranium dioxide, Carbonate

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Authors: Hafizah Che Hasan, Fateen Nazwa Yusof, Maslina Daud

Abstract:

Internet of Things (IoT) is a powerful industry system, which end-devices are interconnected and automated, allowing the devices to analyze data and execute actions based on the analysis. The IoT technology leverages the technology of Radio-Frequency Identification (RFID) and Wireless Sensor Network (WSN), including mobile and sensor. These technologies contribute to the evolution of IoT. However, due to more devices are connected each other in the Internet, and data from various sources exchanged between things, confidentiality of the data becomes a major concern. This paper focuses on one of the major challenges in IoT; authentication, in order to preserve data integrity and confidentiality are in place. A few solutions are reviewed based on papers from the last few years. One of the proposed solutions is securing the communication between IoT devices and cloud servers with Elliptic Curve Cryptograhpy (ECC) based mutual authentication protocol. This solution focuses on Hyper Text Transfer Protocol (HTTP) cookies as security parameter.  Next proposed solution is using keyed-hash scheme protocol to enable IoT devices to authenticate each other without the presence of a central control server. Another proposed solution uses Physical Unclonable Function (PUF) based mutual authentication protocol. It emphasizes on tamper resistant and resource-efficient technology, which equals a 3-way handshake security protocol.

Keywords: Internet of Things, authentication, PUF ECC, keyed hash scheme protocol.

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Authors: H.Seidi, M.Jalali Azizpour, S.A.Zahedi

Abstract:

Today, Hydroforming technology provides an attractive alternative to conventional matched die forming, especially for cost-sensitive, lower volume production, and for parts with irregular contours. In this study the critical fluid pressures which lead to rupture in the workpiece has been investigated by theoretical and finite element methods. The axisymmetric analysis was developed to investigate the tearing phenomenon in cylindrical Hydroforming Deep Drawing (HDD). By use of obtained equations the effect of anisotropy, drawing ratio, sheet thickness and strain hardening exponent on tearing diagram were investigated.

Keywords: Hydroforming deep drawing, Pressure path, Axisymmetric analysis, Finite element simulation.

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Authors: Boutahar Lhoucine, El Bikri Khalid, Benamar Rhali

Abstract:

The effects of large vibration amplitudes on the first axisymetric mode shape of thin isotropic annular plates having both edges clamped are examined in this paper. The theoretical model based on Hamilton’s principle and spectral analysis by using a basis of Bessel’s functions is adapted اhere to the case of annular plates. The model effectively reduces the large amplitude free vibration problem to the solution of a set of non-linear algebraic equations.

The governing non-linear eigenvalue problem has been linearised in the neighborhood of each resonance and a new one-step iterative technique has been proposed as a simple alternative method of solution to determine the basic function contributions to the non-linear mode shape considered.

Numerical results are given for the first non-linear mode shape for a wide range of vibration amplitudes. For each value of the vibration amplitude considered, the corresponding contributions of the basic functions defining the non-linear transverse displacement function and the associated non-linear frequency, the membrane and bending stress distributions are given. By comparison with the iterative method of solution, it was found that the present procedure is efficient for a wide range of vibration amplitudes, up to at least 1.8 times the plate thickness,

Keywords: Non-linear vibrations, Annular plates, Large vibration amplitudes.

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Authors: Masayoshi Matsui, Akiko Nakahara, Akiko Takatsu, Kenji Kato, Naoki Matsuda

Abstract:

The state and stability of hemoglobin adsorbed on the glass surface was investigated using slab optical waveguide (SOWG) spectroscopy. The peak position of the absorption band of hemoglobin adsorbed on the glass surface was same as that of the hemoglobin in solution. This result suggests that no significant denaturation occurred by adsorption. The adsorption of hemoglobin is relatively strong that the hemoglobin molecules even remained adsorbed after rinsing the cell with buffer solution. The peak shift caused by the reduction of adsorbed hemoglobin was also observed.

Keywords: hemoglobin, reduction, slab optical waveguide spectroscopy, solid/liquid interface.

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Authors: Alireza Rezaei, Fatemeh Baharifard, Kourosh Parand

Abstract:

In this paper we improve the quasilinearization method by barycentric Lagrange interpolation because of its numerical stability and computation speed to achieve a stable semi analytical solution. Then we applied the improved method for solving the Fin problem which is a nonlinear equation that occurs in the heat transferring. In the quasilinearization approach the nonlinear differential equation is treated by approximating the nonlinear terms by a sequence of linear expressions. The modified QLM is iterative but not perturbative and gives stable semi analytical solutions to nonlinear problems without depending on the existence of a smallness parameter. Comparison with some numerical solutions shows that the present solution is applicable.

Keywords: Quasilinearization method, Barycentric lagrange interpolation, nonlinear ODE, fin problem, heat transfer.

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Authors: Jieer Wu, Zheshu Ma

Abstract:

Nondestructive testing in engineering is an inverse Cauchy problem for Laplace equation. In this paper the problem of nondestructive testing is expressed by a Laplace-s equation with third-kind boundary conditions. In order to find unknown values on the boundary, the method of fundamental solution is introduced and realized. Because of the ill-posedness of studied problems, the TSVD regularization technique in combination with L-curve criteria and Generalized Cross Validation criteria is employed. Numerical results are shown that the TSVD method combined with L-curve criteria is more efficient than the TSVD method combined with GCV criteria. The abstract goes here.

Keywords: ill-posed, TSVD, Laplace's equation, inverse problem, L-curve, Generalized Cross Validation.

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Authors: L. Temdrara, A. Khelifi, A. Addoun

Abstract:

Activated carbons were produced from olive stones by a chemical process. The activated carbon (AC) were modified by nitric acid and used as adsorbents for the removal of methylene blue dye from aqueous solution. The activated carbons were characterized by nitrogen adsorption and enthalpy of immersion. Batch adsorption experiments were carried out to study the effect of initial different concentrations solution on dye adsorption properties. Isotherms were fitted to Langmuir model, and corresponding parameters were determined. The results showed that the increase of ration of ZnCl₂ leads to increase in apparent surface areas and produces activated carbons with pore structure more developed. However, the maximum MB uptakes for all carbons were determined and correlated with activated carbons characteristics. 

Keywords: Adsorption, activated carbon, chemical activation, enthalpy of immersion.

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Authors: Smarajit Ghosh , Karma Sonam Sherpa

Abstract:

This paper reports a new and accurate method for load-flow solution of radial distribution networks with minimum data preparation. The node and branch numbering need not to be sequential like other available methods. The proposed method does not need sending-node, receiving-node and branch numbers if these are sequential. The proposed method uses the simple equation to compute the voltage magnitude and has the capability to handle composite load modelling. The proposed method uses the set of nodes of feeder, lateral(s) and sub lateral(s). The effectiveness of the proposed method is compared with other methods using two examples. The detailed load-flow results for different kind of load-modellings are also presented.

Keywords: Load−flow, Feeder, Lateral, Power, Voltage, Composite, Exponential

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Authors: B. Medjahed, M. A. Didi, B. Guezzen

Abstract:

In the present work, emulsion liquid membrane (ELM) technique was applied for the extraction of cadmium(II) present in aqueous samples. Aliquat 336 (Chloride tri-N-octylmethylammonium) was used as carrier to extract cadmium(II). The main objective of this work is to investigate the influence of various parameters affected the ELM formation and its stability and testing the performance of the prepared ELM on removal of cadmium by using synthetic solution with different concentrations. Experiments were conducted to optimize pH of the feed solution and it was found that cadmium(II) can be extracted at pH 6.5. The influence of the carrier concentration and treat ratio on the extraction process was investigated. The obtained results showed that the optimal values are respectively 3% (Aliquat 336) and a ratio (feed: emulsion) equal to 1:1.

Keywords: Cadmium, carrier, emulsion liquid membrane, surfactant.

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Authors: R. Mkahl, A. Nait-Sidi-Moh, M. Wack

Abstract:

Batteries of electric vehicles (BEV) are becoming more attractive with the advancement of new battery technologies and promotion of electric vehicles. BEV batteries are recharged on board vehicles using either the grid (G2V for Grid to Vehicle) or renewable energies in a stand-alone application (H2V for Home to Vehicle). This paper deals with the modeling, sizing and control of a photovoltaic stand-alone application that can charge the BEV at home. The modeling approach and developed mathematical models describing the system components are detailed. Simulation and experimental results are presented and commented.

Keywords: Electric vehicles, photovoltaic energy, lead-acid batteries, charging process, modeling, simulation, experimental tests.

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Authors: Fu E. Tang, Chung W. Tong

Abstract:

“Garbage enzyme", a fermentation product of kitchen waste, water and brown sugar, is claimed in the media as a multipurpose solution for household and agricultural uses. This study assesses the effects of dilutions (5% to 75%) of garbage enzyme in reducing pollutants in domestic wastewater. The pH of the garbage enzyme was found to be 3.5, BOD concentration about 150 mg/L. Test results showed that the garbage enzyme raised the wastewater-s BOD in proportion to its dilution due to its high organic content. For mixtures with more than 10% garbage enzyme, its pH remained acidic after the 5-day digestion period. However, it seems that ammonia nitrogen and phosphorus could be removed by the addition of the garbage enzyme. The most economic solution for removal of ammonia nitrogen and phosphorus was found to be 9%. Further tests are required to understand the removal mechanisms of the ammonia nitrogen and phosphorus.

Keywords: Wastewater treatment, garbage enzyme, wastewater additives, ammonia nitrogen, phosphorus.

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