Search results for: solitary wave solution

Authors: Djemai Bara, Mohamed Faouzi Mahboub, Djamila Bennaceur-Doumaz

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In this work, the role of the preformed plasma created on the front face of a target, irradiated by a high intensity short pulse laser, in the framework of ion acceleration process, modeled by Target Normal Sheath Acceleration (TNSA) mechanism, is studied. This plasma is composed of cold ions governed by fluid equations and non-thermal & trapped with densities represented by a "Cairns-Gurevich" equation. The self-similar solution of the equations shows that electronic trapping and the presence of non-thermal electrons in the pre-plasma are both responsible in ion acceleration as long as the proportion of energetic electrons is not too high. In the case where the majority of electrons are energetic, the electrons are accelerated directly by the ponderomotive force of the laser without the intermediate of an accelerating plasma wave.

Keywords: Cairns-Gurevich Equation, ion acceleration, plasma expansion, pre-plasma.

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Authors: M.Imanova, G.Mehdiyeva, V.Ibrahimov

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Solution of some practical problems is reduced to the solution of the integro-differential equations. But for the numerical solution of such equations basically quadrature methods or its combination with multistep or one-step methods are used. The quadrature methods basically is applied to calculation of the integral participating in right hand side of integro-differential equations. As this integral is of Volterra type, it is obvious that at replacement with its integrated sum the upper limit of the sum depends on a current point in which values of the integral are defined. Thus we receive the integrated sum with variable boundary, to work with is hardly. Therefore multistep method with the constant coefficients, which is free from noted lack and gives the way for finding it-s coefficients is present.

Keywords: Volterra integro-differential equations, multistepmethods, finite-difference methods, initial value problem

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Authors: Nicolas Zufferey

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Ant algorithms are well-known metaheuristics which have been widely used since two decades. In most of the literature, an ant is a constructive heuristic able to build a solution from scratch. However, other types of ant algorithms have recently emerged: the discussion is thus not limited by the common framework of the constructive ant algorithms. Generally, at each generation of an ant algorithm, each ant builds a solution step by step by adding an element to it. Each choice is based on the greedy force (also called the visibility, the short term profit or the heuristic information) and the trail system (central memory which collects historical information of the search process). Usually, all the ants of the population have the same characteristics and behaviors. In contrast in this paper, a new type of ant metaheuristic is proposed, namely SMART (for Solution Methods with Ants Running by Types). It relies on the use of different population of ants, where each population has its own personality.

Keywords: Optimization, Metaheuristics, Ant Algorithms, Evolutionary Procedures, Population-Based Methods.

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Authors: Meng Hu, Lili Wang

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In this paper, based on the estimation of the Cauchy matrix of linear impulsive differential equations, by using Banach fixed point theorem and Gronwall-Bellman-s inequality, some sufficient conditions are obtained for the existence and exponential stability of almost periodic solution for Cohen-Grossberg shunting inhibitory cellular neural networks (SICNNs) with continuously distributed delays and impulses. An example is given to illustrate the main results.

Keywords: Almost periodic solution, exponential stability, neural networks, impulses.

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Authors: A.Khaja Kamaluddin, B.Muhammed Yousoof

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Routing places an important role in determining the quality of service in wireless networks. The routing methods adopted in wireless networks have many drawbacks. This paper aims to review the current routing methods used in wireless networks. This paper proposes an innovative solution to overcome the problems in routing. This solution is aimed at improving the Quality of Service. This solution is different from others as it involves the resuage of the part of the virtual circuits. This improvement in quality of service is important especially in propagation of multimedia applications like video, animations etc. So it is the dire need to propose a new solution to improve the quality of service in ATM wireless networks for multimedia applications especially during this era of multimedia based applications.

Keywords: Packet buffering, Routing Table, Virtual Circuits (VC)

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Authors: S. Botman, D. Borchevkin, V. Petrov, E. Bogdanov, M. Patrushev, N. Shusharina

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In this paper, we report the development of the device for diagnostics of cardiovascular system state and associated automated workstation for large-scale medical measurement data collection and analysis. It was shown that optimal design for the monitoring device is wristband as it represents engineering trade-off between accuracy and usability. Monitoring device is based on the infrared reflective photoplethysmographic sensor, which allows collecting multiple physiological parameters, such as heart rate and pulsing wave characteristics. Developed device uses BLE interface for medical and supplementary data transmission to the coupled mobile phone, which processes it and send it to the doctor's automated workstation. Results of this experimental model approbation confirmed the applicability of the proposed approach.

Keywords: Cardiovascular diseases, health monitoring systems, photoplethysmography, pulse wave, remote diagnostics.

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Authors: Thidarat Wongsawa, Ura Pancharoen, Anchaleeporn Waritswat Lothongkum

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The separation of silver ions from medicinal wastewater via hollow fiber supported liquid membrane (HFSLM) was examined to promote the performance of this technique. The wastewater consisting of 30mg/L silver ions and 120mg/L ferric ions was used as the feed solution. LIX84I dissolving in kerosene and sodium thiosulfate pentahydrate solution were used as the liquid membrane and stripping solution, respectively. In order to access the highest performance of HFSLM, the optimum condition was investigated via several influential variables. Final concentration of silver ions in feed solution was obtained 0.2mg/L which was lower than the discharge limit of Thailand’s mandatory.

Keywords: Hollow fiber, Liquid membrane, Separation, Silver ions.

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Authors: Khaled M. EL-Naggar

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This paper presents a new method for estimating the mean curve of impulse voltage waveforms that are recorded during impulse tests. In practice, these waveforms are distorted by noise, oscillations and overshoot. The problem is formulated as an estimation problem. Estimation of the current signal parameters is achieved using a fast and accurate technique. The method is based on discrete dynamic filtering algorithm (DDF). The main advantage of the proposed technique is its ability in producing the estimates in a very short time and at a very high degree of accuracy. The algorithm uses sets of digital samples of the recorded impulse waveform. The proposed technique has been tested using simulated data of practical waveforms. Effects of number of samples and data window size are studied. Results are reported and discussed.

Keywords: Digital Filtering, Estimation, Impulse wave, Stochastic filtering.

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Authors: Abu Qudeiri Jaber, Yamamoto Hidehiko Rizauddin Ramli

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To create a solution for a specific problem in machine learning, the solution is constructed from the data or by use a search method. Genetic algorithms are a model of machine learning that can be used to find nearest optimal solution. While the great advantage of genetic algorithms is the fact that they find a solution through evolution, this is also the biggest disadvantage. Evolution is inductive, in nature life does not evolve towards a good solution but it evolves away from bad circumstances. This can cause a species to evolve into an evolutionary dead end. In order to reduce the effect of this disadvantage we propose a new a learning tool (criteria) which can be included into the genetic algorithms generations to compare the previous population and the current population and then decide whether is effective to continue with the previous population or the current population, the proposed learning tool is called as Keeping Efficient Population (KEP). We applied a GA based on KEP to the production line layout problem, as a result KEP keep the evaluation direction increases and stops any deviation in the evaluation.

Keywords: Genetic algorithms, Layout problem, Machinelearning, Production system.

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Authors: Figen Eraslan, Abdel Karim Hassan Awad Elkarim, Aydın Gunes, Ali Inal

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A greenhouse experiment was conducted to investigate the effects of different types of nutrients induced salinity on the growth, membrane permeability, nitrate reductase activity, proline content and macronutrient concentrations of tomato plants. The plants were subjected to six different treatments: 1 (control) containing basic solution, 2 basic solution+40mM of NaCl, 3 basic solution+40 mM of KNO3, 4 basic solution+20 mM of Ca(NO3)2.4H2O, 5 basic solution+20 mM of Mg(NO3)2.6H2O and 6 basic solution+20 mM of KNO3+5 mM of Ca(NO3)2.4H2O+5 mM of Mg(NO3)2.6H2O. Membrane permeability was increased significantly only with addition of NaCl, and then decreased to its lower level with addition of Ca(NO3)2.4H2O and Mg(NO3)2.6H2O. Proline accumulation were followed the same trend of results when they had been exposed to NaCl salinity. Nitrate reductase activity (NRA) was significantly affected by addition of different types of nutrient induced salinity.

Keywords: Membrane Permeability, Nitrate Reductase Activity, Nutrient induced salinity, Proline.

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Authors: Anil Kumar, S. Deswal

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The mathematical equation for Separation of the binary aqueous solution is developed by using the Spiegler- Kedem theory. The characteristics of a B-9 hollow fibre module of Du Pont are determined by using these equations and their results are compared with the experimental results of Ohya et al. The agreement between these results is found to be excellent.

Keywords: Binary aqueous solution, modeling, reverse osmosis module, Spiegler-Kedem theory.

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Authors: Milan Hladik

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The symmetric solution set Σ sym is the set of all solutions to the linear systems Ax = b, where A is symmetric and lies between some given bounds A and A, and b lies between b and b. We present a contractor for Σ sym, which is an iterative method that starts with some initial enclosure of Σ sym (by means of a cartesian product of intervals) and sequentially makes the enclosure tighter. Our contractor is based on polyhedral approximation and solving a series of linear programs. Even though it does not converge to the optimal bounds in general, it may significantly reduce the overestimation. The efficiency is discussed by a number of numerical experiments.

Keywords: Linear interval systems, solution set, interval matrix, symmetric matrix.

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Authors: Aichun Feng, Zhi-Min Chen, Jing Tang Xing

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A two-dimensional linear wave-body interaction problem can be solved using a desingularized integral method by placing free surface Rankine sources over calm water surface and satisfying boundary conditions at prescribed collocation points on the calm water surface. A new free-surface Rankine source distribution scheme, determined by the intersection points of free surface and body surface, is developed to reduce numerical computation cost. Associated with this, a new treatment is given to the intersection point. The present scheme results are in good agreement with traditional numerical results and measurements.

Keywords: Source point distribution, panel method, Rankine source, desingularized algorithm.

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Authors: M. Y. Ismail, M. Inam, A. F. M. Zain, N. Misran

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Progressive phase distribution is an important consideration in reflectarray antenna design which is required to form a planar wave in front of the reflectarray aperture. This paper presents a detailed mathematical model in order to determine the required reflection phase values from individual element of a reflectarray designed in Ku-band frequency range. The proposed technique of obtaining reflection phase can be applied for any geometrical design of elements and is independent of number of array elements. Moreover the model also deals with the solution of reflectarray antenna design with both centre and off-set feed configurations. The theoretical modeling has also been implemented for reflectarrays constructed on 0.508mm thickness of different dielectric substrates. The results show an increase in the slope of the phase curve from 4.61°/mm to 22.35°/mm by varying the material properties.

Keywords: Mathematical modeling, Progressive phase distribution, Reflectarray antenna, Reflection phase.

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Authors: Nebi Gedik

Abstract:

One of the significant and continual public health problems in the world is breast cancer. Early detection is very important to fight the disease, and mammography has been one of the most common and reliable methods to detect the disease in the early stages. However, it is a difficult task, and computer-aided diagnosis (CAD) systems are needed to assist radiologists in providing both accurate and uniform evaluation for mass in mammograms. In this study, a multiresolution statistical method to classify mammograms as normal and abnormal in digitized mammograms is used to construct a CAD system. The mammogram images are represented by wave atom transform, and this representation is made by certain groups of coefficients, independently. The CAD system is designed by calculating some statistical features using each group of coefficients. The classification is performed by using support vector machine (SVM).

Keywords: Wave atom transform, statistical features, multi-resolution representation, mammogram.

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Authors: J. Costa, M. Ortigueira, A. Batista, T. Paiva

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Sleep spindles are the most interesting hallmark of stage 2 sleep EEG. Their accurate identification in a polysomnographic signal is essential for sleep professionals to help them mark Stage 2 sleep. Sleep Spindles are also promising objective indicators for neurodegenerative disorders. Visual spindle scoring however is a tedious workload. In this paper three different approaches are used for the automatic detection of sleep spindles: Short Time Fourier Transform, Wavelet Transform and Wave Morphology for Spindle Detection. In order to improve the results, a combination of the three detectors is presented and comparison with human expert scorers is performed. The best performance is obtained with a combination of the three algorithms which resulted in a sensitivity and specificity of 94% when compared to human expert scorers.

Keywords: EEG, Short Time Fourier Transform, Sleep Spindles, Wave Morphology for Spindle Detection, Wavelet Transform.

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Authors: A. G. Sifalakis, E. P. Papadopoulou, Y. G. Saridakis

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A generalized Dirichlet to Neumann map is one of the main aspects characterizing a recently introduced method for analyzing linear elliptic PDEs, through which it became possible to couple known and unknown components of the solution on the boundary of the domain without solving on its interior. For its numerical solution, a well conditioned quadratically convergent sine-Collocation method was developed, which yielded a linear system of equations with the diagonal blocks of its associated coefficient matrix being point diagonal. This structural property, among others, initiated interest for the employment of iterative methods for its solution. In this work we present a conclusive numerical study for the behavior of classical (Jacobi and Gauss-Seidel) and Krylov subspace (GMRES and Bi-CGSTAB) iterative methods when they are applied for the solution of the Dirichlet to Neumann map associated with the Laplace-s equation on regular polygons with the same boundary conditions on all edges.

Keywords: Elliptic PDEs, Dirichlet to Neumann Map, Global Relation, Collocation, Iterative Methods, Jacobi, Gauss-Seidel, GMRES, Bi-CGSTAB.

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Authors: Wanna Saikaew, Pairat Kaewsarn, Wuthikorn Saikaew

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The ability of pomelo peel, a natural biosorbent, to remove Cd(II) ions from aqueous solution by biosorption was investigated. The experiments were carried out by batch method at 25 °C. The influence of solution pH, initial cadmium ion concentrations and contact times were evaluated. Cadmium ion removal increased significantly as the pH of the solution increased from pH 1 to pH 5. At pH 5, the cadmium ion removal reached a maximum value. The equilibrium process was described well by the Langmuir isotherm model, with a maximum biosorption capacity of 21.83 mg/g. The biosorption was relatively quick, (approx. 20 min). Biosorption kinetics followed a pseudo-second-order model. The result showed that pomelo peel was effective as a biosorbent for removing cadmium ions from aqueous solution. It is a low cost material that shows potential to be applied in wastewater technology for remediation of heavy metal contamination.

Keywords: Pomelo peel, biosorption, Cadmium ions.

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Authors: Suprijanto, Linda Sari, Vebi Nadhira , IGN. Merthayasa. Farida I.M

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Detection of human emotions has many potential applications. One of application is to quantify attentiveness audience in order evaluate acoustic quality in concern hall. The subjective audio preference that based on from audience is used. To obtain fairness evaluation of acoustic quality, the research proposed system for multimodal emotion detection; one modality based on brain signals that measured using electroencephalogram (EEG) and the second modality is sequences of facial images. In the experiment, an audio signal was customized which consist of normal and disorder sounds. Furthermore, an audio signal was played in order to stimulate positive/negative emotion feedback of volunteers. EEG signal from temporal lobes, i.e. T3 and T4 was used to measured brain response and sequence of facial image was used to monitoring facial expression during volunteer hearing audio signal. On EEG signal, feature was extracted from change information in brain wave, particularly in alpha and beta wave. Feature of facial expression was extracted based on analysis of motion images. We implement an advance optical flow method to detect the most active facial muscle form normal to other emotion expression that represented in vector flow maps. The reduce problem on detection of emotion state, vector flow maps are transformed into compass mapping that represents major directions and velocities of facial movement. The results showed that the power of beta wave is increasing when disorder sound stimulation was given, however for each volunteer was giving different emotion feedback. Based on features derived from facial face images, an optical flow compass mapping was promising to use as additional information to make decision about emotion feedback.

Keywords: Multimodal Emotion Detection, EEG, Facial Image, Optical Flow, compass mapping, Brain Wave

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Authors: Alhasan Hakami, Arun Kumar, Sung J Shim, Yousef Abu Nahleh

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In recent years, many high intensity earthquakes have occurred around the world, such as the 2011 earthquake in Tohoku, Japan. These large-scale disasters caused huge casualties and losses. In addition, inefficient disaster response operations also caused the second wave of casualties and losses, and expanded the damage. Effective disaster management can be used to respond to the chaotic situation, and reduce the damage; however, some inefficient disaster response operations are still used. Therefore, this case study chose the 921 earthquake for analyzing disaster emergency logistics problems and proposed the Soft Systems Methodology (SSM) to solve disaster emergency logistics problems. Moreover, it analyses the effect of human factors on system operation, and suggests a solution to improve the system.

Keywords: Soft systems methodology, emergency logistics.

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Authors: Sperisa Distantina, Fadilah Fadilah, Mujtahid Kaavessina

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Hydrogel films were prepared from kappa carrageenan by crosslinking with glutaraldehyde. Carrageenan films extracted from Kappaphycus alvarezii seaweed were immersed in glutaraldehyde solution for 2 min and then cured at 110 °C for 25 min. The obtained crosslinked films were washed with ethanol to remove the unreacted glutaraldehyde and then air dried to constant weights. The aim of this research was to study the swelling degree behaviour of the hydrogel film to neutral salts solution, namely NaCl, KCl, and CaCl₂. The results showed that swelling degree of crosslinked films varied non-monotonically with salinity of NaCl. Swelling degree decreased with the increasing of KCl concentration. Swelling degree of crosslinked film in CaCl₂ solution was lower than that in NaCl and in KCl solutions.

Keywords: Hydrogel, carrageenan, glutaraldehyde, swelling, salt.

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Authors: Khaled M. Khader, Mamdouh I. Elimy, Omayma A. Nada

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Sustainable development is the nominal goal of most countries at present. In general, fossil fuels are the development mainstay of most world countries. Regrettably, the fossil fuel consumption rate is very high, and the world is facing the problem of conventional fuels depletion soon. In addition, there are many problems of environmental pollution resulting from the emission of harmful gases and vapors during fuel burning. Thus, clean, renewable energy became the main concern of most countries for filling the gap between available energy resources and their growing needs. There are many renewable energy sources such as wind, solar and wave energy. Energy can be obtained from the motion of sea waves almost all the time. However, power generation from solar or wind energy is highly restricted to sunny periods or the availability of suitable wind speeds. Moreover, energy produced from sea wave motion is one of the cheapest types of clean energy. In addition, renewable energy usage of sea waves guarantees safe environmental conditions. Cheap electricity can be generated from wave energy using different systems such as oscillating bodies' system, pendulum gate system, ocean wave dragon system and oscillating water column device. In this paper, a multi-criteria model has been developed using Analytic Hierarchy Process (AHP) to support the decision of selecting the most effective system for generating power from sea waves. This paper provides a widespread overview of the different design alternatives for sea wave energy converter systems. The considered design alternatives have been evaluated using the developed AHP model. The multi-criteria assessment reveals that the off-shore Oscillating Water Column (OWC) system is the most appropriate system for generating power from sea waves. The OWC system consists of a suitable hollow chamber at the shore which is completely closed except at its base which has an open area for gathering moving sea waves. Sea wave's motion pushes the air up and down passing through a suitable well turbine for generating power. Improving the power generation capability of the OWC system is one of the main objectives of this research. After investigating the effect of some design modifications, it has been concluded that selecting the appropriate settings of some effective design parameters such as the number of layers of Wells turbine fans and the intermediate distance between the fans can result in significant improvements. Moreover, simple dynamic analysis of the Wells turbine is introduced. Furthermore, this paper strives for comparing the theoretical and experimental results of the built experimental prototype.

Keywords: Renewable energy, oscillating water column, multi-criteria selection, wells turbine.

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Authors: Sun H. Hwang, Young E. Lee, Yunhan Ga, Gilwon Yoon

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EEG is a very complex signal with noises and other bio-potential interferences. EOG is the most distinct interfering signal when EEG signals are measured and analyzed. It is very important how to process raw EEG signals in order to obtain useful information. In this study, the EEG signal processing techniques such as EOG filtering and outlier removal were examined to minimize unwanted EOG signals and other noises. The two different mental states of resting and focusing were examined through EEG analysis. A focused state was induced by letting subjects to watch a red dot on the white screen. EEG data for 32 healthy subjects were measured. EEG data after 60-Hz notch filtering were processed by a commercially available EOG filtering and our presented algorithm based on the removal of outliers. The ratio of beta wave to theta wave was used as a parameter for determining the degree of focusing. The results show that our algorithm was more appropriate than the existing EOG filtering.

Keywords: EEG, focus, mental state, outlier, signal processing.

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Authors: Alfonso Bahillo, Juan Blas, Santiago Mazuelas, Patricia Fernanadez, Ruben Mateo Lorenzo, Evaristo Jose Abril

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The wide increase and diffusion on telecommunication technologies have caused a huge spread of electromagnetic sources in most European Countries. Since the public is continuously being exposed to electromagnetic radiation the possible health effects have become the focus of population concerns. As a result, electromagnetic field monitoring stations which control field strength in commercial frequency bands are being placed on the flat roof of many buildings. However there is no guidance on where to place them. This paper presents an analysis of frequency, polarization and angles of incidence of a plane wave which impinges on a flat roof security wall and its dependence on electromagnetic field strength meters placement.

Keywords: EM field exposition, EM field strength meter, FDTD method, flat roof security wall, plane wave propagation.

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Authors: Ritu Shitak

Abstract:

Humans are social mammals, of the primate order. Our biology, our behaviour and our pathologies are unique to us. In our desire to understand, reduce solitary confinement one source of information is the many reports of social isolation of other social mammals, especially primates. A behavioural study was conducted in the department of pharmacology at Indira Gandhi Medical College, Shimla in Himachalpradesh province in India using white albino mice. Different behavioural parameters were observed by using open field, tail suspension, tests for aggressive behaviour and social interactions and the effect of isolation was studied. The results were evaluated and the standard statistics were applied. The said study was done to establish facts that isolation itself impairs social behaviour and can lead to alcohol dependence as well as related drug dependence.

Keywords: Albino Mice, Drug Dependence, Social isolation.

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Authors: André Trudel, Haiyi Zhang

Abstract:

Over the years, many implementations have been proposed for solving IA networks. These implementations are concerned with finding a solution efficiently. The primary goal of our implementation is simplicity and ease of use. We present an IA network implementation based on finite domain non-binary CSPs, and constraint logic programming. The implementation has a GUI which permits the drawing of arbitrary IA networks. We then show how the implementation can be extended to find all the solutions to an IA network. One application of finding all the solutions, is solving probabilistic IA networks.

Keywords: Constraint logic programming, CSP, logic, temporalreasoning.

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Authors: Minghui Wang

Abstract:

Based on the classical algorithm LSQR for solving (unconstrained) LS problem, an iterative method is proposed for the least-squares like-minimum-norm symmetric solution of AXB+CYD=E. As the application of this algorithm, an iterative method for the least-squares like-minimum-norm biymmetric solution of AXB=E is also obtained. Numerical results are reported that show the efficiency of the proposed methods.

Keywords: Matrix equation, bisymmetric matrix, least squares problem, like-minimum norm, iterative algorithm.

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Authors: S. Levitsky, R. Bergman

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Fluid rheology may have essential impact on sound propagation in a liquid-filled pipe, especially, in a low frequency range. Rheological parameters of liquid are temperature-sensitive, which ultimately results in a temperature dependence of the wave speed and attenuation in the waveguide. The study is devoted to modeling of this effect at sound propagation in an elastic pipe with polymeric liquid, described by generalized Maxwell model with non-zero high-frequency viscosity. It is assumed that relaxation spectrum is distributed according to the Spriggs law; temperature impact on the liquid rheology is described on the basis of the temperature-superposition principle and activation theory. The dispersion equation for the waveguide, considered as a thin-walled tube with polymeric solution, is obtained within a quasi-one-dimensional formulation. Results of the study illustrate the influence of temperature on sound propagation in the system.

Keywords: Elastic tube, sound propagation, temperature effect, viscoelastic liquid.

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Authors: Sahar Noori, Seyed Amir Hossein, Mohammad Ebrahimi

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This paper is devoted to predict laminar and turbulent heating rates around blunt re-entry spacecraft at hypersonic conditions. Heating calculation of a hypersonic body is normally performed during the critical part of its flight trajectory. The procedure is of an inverse method, where a shock wave is assumed, and the body shape that supports this shock, as well as the flowfield between the shock and body, are calculated. For simplicity the normal momentum equation is replaced with a second order pressure relation; this simplification significantly reduces computation time. The geometries specified in this research, are parabola and ellipsoids which may have conical after bodies. An excellent agreement is observed between the results obtained in this paper and those calculated by others- research. Since this method is much faster than Navier-Stokes solutions, it can be used in preliminary design, parametric study of hypersonic vehicles.

Keywords: Aerodynamic Heating, Blunt Body, Hypersonic Flow, Laminar, Turbulent.

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Authors: K. L. Verma

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Analysis for the propagation of elastic waves in arbitrary anisotropic plates is investigated, commencing with a formal analysis of waves in a layered plate of an arbitrary anisotropic media, the dispersion relations of elastic waves are obtained by invoking continuity at the interface and boundary of conditions on the surfaces of layered plate. The obtained solutions can be used for material systems of higher symmetry such as monoclinic, orthotropic, transversely isotropic, cubic, and isotropic as it is contained implicitly in the analysis. The cases of free layered plate and layered half space are considered separately. Some special cases have also been deduced and discussed. Finally numerical solution of the frequency equations for an aluminum epoxy is carried out, and the dispersion curves for the few lower modes are presented. The results obtained theoretically have been verified numerically and illustrated graphically.

Keywords: Anisotropic, layered, dispersion, elastic waves, frequency equations.

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