Search results for: initial lining

Authors: Xinhui Wang, Xiuyong Ding

Abstract:

This paper addresses the controller synthesis problem of discrete-time switched positive systems with bounded time-varying delays. Based on the switched copositive Lyapunov function approach, some necessary and sufficient conditions for the existence of state-feedback controller are presented as a set of linear programming and linear matrix inequality problems, hence easy to be verified. Another advantage is that the state-feedback law is independent on time-varying delays and initial conditions. A numerical example is provided to illustrate the effectiveness and feasibility of the developed controller.

Keywords: Switched copositive Lyapunov functions, positive linear systems, switched systems, time-varying delays, stabilization.

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Authors: Roli Saini, Pradeep Kumar

Abstract:

A coagulation/flocculation process was adopted for the reduction of carbamate insecticide (carbofuran) from aqueous solution. Ferric chloride (FeCl₃) was used as a coagulant to treat the carbofuran. To exploit the reduction efficiency of pesticide concentration and COD, the jar-test experiments were carried out and process was optimized through response surface methodology (RSM). The effects of two independent factors; i.e., FeCl₃ dosage and pH on the reduction efficiency were estimated by using central composite design (CCD). The initial COD of the 30 mg/L concentrated solution was found to be 510 mg/L. Results exposed that the maximum reduction occurred at an optimal condition of FeCl₃ = 80 mg/L, and pH = 5.0, from which the reduction of concentration and COD 75.13% and 65.34%, respectively. The present study also predicted that the obtained regression equations could be helpful as the theoretical basis for the coagulation process of pesticide wastewater.

Keywords: Carbofuran, coagulation, optimization, response surface methodology.

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Authors: Abdelkarim Ait Brik, Abdelaziz Khoukh, Mustapha Jammali, Hamid Chaikhy

Abstract:

The energy audit is the essential initial step to ensure a good definition of energy control actions. The in-depth study of the various energy-consuming equipments makes it possible to determine the actions and investments with best cost for the company. The analysis focuses on the energy consumption of production equipment and utilities (lighting, heating, air conditioning, ventilation, transport). Successful implementation of this approach requires, however, to take into account a number of prerequisites. This paper proposes a number of useful recommendations concerning the energy audit in order to achieve better results, and a case study concerning the lighting audit of a Moroccan company by showing the gains that can be made through this audit.

Keywords: Energy audit, energy diagnosis, consumption, electricity, energy efficiency, lighting audit.

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Authors: C. Nobre, C. C. Castro, A.-L. Hantson, J. A. Teixeira, L. R. Rodrigues, G. De Weireld

Abstract:

Fructo-oligosaccharides (FOS) are produced from sucrose by Aureobasidium pullulans in yields between 40-60% (w/w). To increase the amount of FOS it is necessary to remove the small, non-prebiotic sugars, present. Two methods for producing high-purity FOS have been developed: the use of microorganisms able to consume small saccharides; and the use of continuous chromatography to separate sugars: simulated moving bed (SMB). It is herein proposed the combination of both methods. The aim of this study is to optimize the composition of the fermentative broth (in terms of salts and sugars) that will be further purified by SMB. A yield of 0.63 gFOS.gSucrose^-1 was obtained with A. pullulans using low amounts of salts in the initial fermentative broth. By removing the small sugars, Saccharomyces cerevisiae and Zymomonas mobilis increased the percentage of FOS from around 56.0% to 83% (w/w) in average, losing only 10% (w/w) of FOS during the recovery process.

Keywords: Fructo-oligosaccharides, microbial treatment, Saccharomyces cerevisiae, Zymomonas mobilis.

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Authors: Stefania Arguelles Reyes, Octavio José Salcedo Parra, Alberto Acosta López

Abstract:

This paper presents a web application for the improvement of images through recognition. The web application is based on the analysis of picture-based recognition methods that allow an improvement on the physical appearance of people posting in social networks. The basis relies on the study of tools that can correct or improve some features of the face, with the help of a wide collection of user images taken as reference to build a facial profile. Automatic facial profiling can be achieved with a deeper study of the Object Detection Library. It was possible to improve the initial images with the help of MATLAB and its filtering functions. The user can have a direct interaction with the program and manually adjust his preferences.

Keywords: Application, MATLAB, make up, model, recognition.

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Authors: Sanjeeb Kumar Kar

Abstract:

The optimal control problem of a linear distributed parameter system is studied via shifted Legendre polynomials (SLPs) in this paper. The partial differential equation, representing the linear distributed parameter system, is decomposed into an n - set of ordinary differential equations, the optimal control problem is transformed into a two-point boundary value problem, and the twopoint boundary value problem is reduced to an initial value problem by using SLPs. A recursive algorithm for evaluating optimal control input and output trajectory is developed. The proposed algorithm is computationally simple. An illustrative example is given to show the simplicity of the proposed approach.

Keywords: Optimal control, linear systems, distributed parametersystems, Legendre polynomials.

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Authors: A. M. Tahsini

Abstract:

Solid fuel transient burning behavior under oxidizer gas flow is numerically investigated. It is done using analysis of the regression rate responses to the imposed sudden and oscillatory variation at inflow properties. The conjugate problem is considered by simultaneous solution of flow and solid phase governing equations to compute the fuel regression rate. The advection upstream splitting method is used as flow computational scheme in finite volume method. The ignition phase is completely simulated to obtain the exact initial condition for response analysis. The results show that the transient burning effects which lead to the combustion instabilities and intermittent extinctions could be observed in solid fuels as the solid propellants.

Keywords: Extinction, Oscillation, Regression rate, Response, Transient burning.

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Authors: K. Dimitropoulos, N. Grammalidis, I. Gragopoulos, H. Gao, Th. Heuer, M. Weinmann, S. Voit, C. Stockhammer, U. Hartmann, N. Pavlidou

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Existing ground movement surveillance technologies at airports are subjected to limitations due to shadowing effects or multiple reflections. Therefore, there is a strong demand for a new sensing technology, which will be cost effective and will provide detection of non-cooperative targets under any weather conditions. This paper aims to present a new intelligent system, developed within the framework of the EC-funded ISMAEL project, which is based on a new magnetic sensing technology and provides detection, tracking and automatic classification of targets moving on the airport surface. The system is currently being installed at two European airports. Initial experimental results under real airport traffic demonstrate the great potential of the proposed system.

Keywords: Air traffic management, magnetic sensors, multitracking, A-SMGCS.

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Authors: Shonal Singh, Bibhya Sharma, Jito Vanualailai

Abstract:

This paper considers the design of a motion planner that will simultaneously accomplish control and motion planning of a n-link nonholonomic mobile manipulator, wherein, a n-link holonomic manipulator is coupled with a nonholonomic mobile platform, within an obstacle-ridden environment. This planner, derived from the Lyapunov-based control scheme, generates collision-free trajectories from an initial configuration to a final configuration in a constrained environment cluttered with stationary solid objects of different shapes and sizes. We demonstrate the efficiency of the control scheme and the resulting acceleration controllers of the mobile manipulator with results through computer simulations of an interesting scenario.

Keywords: Artificial potential fields, Lyapunov-based control scheme, Lyapunov stability, nonholonomic manipulator, minimum distance technique, kinodynamic constraints.

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Authors: M. Bahgat, F. M. Awan, H. A. Hanafy, O. N. Alzeghaibi

Abstract:

Strontium hexaferrite (SrFe12O19; Sr-ferrite) is one of the well-known materials for permanent magnets. In this study, Mtype strontium ferrite was prepared by following the conventional ceramic method from steelmaking by-product. Initial materials; SrCO3 and by-product, were mixed together in the composition of SrFe12O19 in different Sr/Fe ratios. The mixtures of these raw materials were dry-milled for 6h. The blended powder was presintered (i.e. calcination) at 1000°C for different times periods, then cooled down to room temperature. These pre-sintered samples were re-milled in a dry atmosphere for 1h and then fired at different temperatures in atmospheric conditions, and cooled down to room temperature. The produced magnetic powder has a dense hexagonal grain shape structure. The calculated energy product values for the produced samples ranged from 0.3 to 2.4 MGOe.

Keywords: Ceramic route, Hard magnetic materials, Strontium ferrite.

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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: S.A.M. Yatim, Z.B. Ibrahim, K.I. Othman, F. Ismail

Abstract:

The implicit block methods based on the backward differentiation formulae (BDF) for the solution of stiff initial value problems (IVPs) using variable step size is derived. We construct a variable step size block methods which will store all the coefficients of the method with a simplified strategy in controlling the step size with the intention of optimizing the performance in terms of precision and computation time. The strategy involves constant, halving or increasing the step size by 1.9 times the previous step size. Decision of changing the step size is determined by the local truncation error (LTE). Numerical results are provided to support the enhancement of method applied.

Keywords: Backward differentiation formulae, block backwarddifferentiation formulae, stiff ordinary differential equation, variablestep size.

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Authors: Cherif Haddad, Faouzi Ben Charrada

Abstract:

On a such wide-area environment as a Grid, data placement is an important aspect of distributed database systems. In this paper, we address the problem of initial placement of database no-replicated fragments in Grid architecture. We propose a graph based approach that considers resource restrictions. The goal is to optimize the use of computing, storage and communication resources. The proposed approach is developed in two phases: in the first phase, we perform fragment grouping using knowledge about fragments dependency and, in the second phase, we determine an efficient placement of the fragment groups on the Grid. We also show, via experimental analysis that our approach gives solutions that are close to being optimal for different databases and Grid configurations.

Keywords: Grid computing, Distributed systems, Data resourcesmanagement, Database systems, Database placement.

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Authors: Ahmet Denker, Tuğrul Adıgüzel

Abstract:

This paper presents a solution for a robotic manipulation problem. We formulate the problem as combining target identification, tracking and interception. The task in our solution is sensing a target on a conveyor belt and then intercepting robot-s end-effector at a convenient rendezvous point. We used an object recognition method which identifies the target and finds its position from visualized scene picture, then the robot system generates a solution for rendezvous problem using the target-s initial position and belt velocity . The interception of the target and the end-effector is executed at a convenient rendezvous point along the target-s calculated trajectory. Experimental results are obtained using a real platform with an industrial robot and a vision system over it.

Keywords: Object recognition, rendezvous planning, robotics.

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Authors: Eunji Choi, Borang Park, Youngjae Choi, Jinwoo Moon

Abstract:

In this study, a predictive model for estimating the metabolism (MET) of human body was developed for the optimal control of indoor thermal environment. Human body images for indoor activities and human body joint coordinated values were collected as data sets, which are used in predictive model. A deep learning algorithm was used in an initial model, and its number of hidden layers and hidden neurons were optimized. Lastly, the model prediction performance was analyzed after the model being trained through collected data. In conclusion, the possibility of MET prediction was confirmed, and the direction of the future study was proposed as developing various data and the predictive model.

Keywords: Deep learning, indoor quality, metabolism, predictive model.

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Authors: Thana Ananacha

Abstract:

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

Keywords: Thermal simulation, Double Glass Wall, Velocity field.

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Authors: M.Sushanth Babu, P.Krishna, U.Venu, M.Ranjith

Abstract:

In this paper, we evaluate the choice of suitable quantization characteristics for both the decoder messages and the received samples in Low Density Parity Check (LDPC) coded systems using M-QAM (Quadrature Amplitude Modulation) schemes. The analysis involves the demapper block that provides initial likelihood values for the decoder, by relating its quantization strategy of the decoder. A mapping strategy refers to the grouping of bits within a codeword, where each m-bit group is used to select a 2m-ary signal in accordance with the signal labels. Further we evaluate the system with mapping strategies like Consecutive-Bit (CB) and Bit-Reliability (BR). A new demapper version, based on approximate expressions, is also presented to yield a low complexity hardware implementation.

Keywords: Low Density parity Check, Mapping, Demapping, Quantization, Quadrature Amplitude Modulation

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Authors: Hans H. Diel

Abstract:

In this paper a functional interpretation of quantum theory (QT) with emphasis on quantum field theory (QFT) is proposed. Besides the usual statements on relations between a functions initial state and final state, a functional interpretation also contains a description of the dynamic evolution of the function. That is, it describes how things function. The proposed functional interpretation of QT/QFT has been developed in the context of the author-s work towards a computer model of QT with the goal of supporting the largest possible scope of QT concepts. In the course of this work, the author encountered a number of problems inherent in the translation of quantum physics into a computer program. He came to the conclusion that the goal of supporting the major QT concepts can only be satisfied, if the present model of QT is supplemented by a "functional interpretation" of QT/QFT. The paper describes a proposal for that

Keywords: Computability, Foundation of Quantum Mechanics, Measurement Problem, Models of Physics.

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Authors: S. Liepina, A. Jemeljanovs

Abstract:

Tasks of the work were study the possible E.coli contamination in red deer meat, identify pathogenic strains from isolated E.coli, determine their incidence in red deer meat and determine the presence of VT1, VT2 and eaeA genes for the pathogenic E.coli. 8 (10%) samples were randomly selected from 80 analysed isolates of E.coli and PCR reaction was performed on them. PCR was done both on initial materials – samples of red deer meat - and for already isolated liqueurs. Two of analysed venison samples contain verotoxin-producing strains of E. coli. It means that this meat is not safe to consumer. It was proven by the sequestration reaction of E. coli and by comparison of the obtained results with the database of microorganism genome available on the internet that the isolated culture corresponds to region 16S rDNS of E. coli thus presenting correctness of the microbiological methods.

Keywords: Deer meat, pathogenic Escherichia coli

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Authors: J. Ierache, N. A. Mangiarua, S. A. Bevacqua, N. N. Verdicchio, M. E. Becerra, D. R. Sanz, M. E. Sena, F. M. Ortiz, N. D. Duarte, S. Igarza

Abstract:

Augmented Reality is a technology that involves the overlay of virtual content, which is context or environment sensitive, on images of the physical world in real time. This paper presents the development of a catalog system that facilitates and allows the creation, publishing, management and exploitation of augmented multimedia contents and Augmented Reality applications, creating an own space for anyone that wants to provide information to real objects in order to edit and share it then online with others. These spaces would be built for different domains without the initial need of expert users. Its operation focuses on the context of Web 2.0 or Social Web, with its various applications, developing contents to enrich the real context in which human beings act permitting the evolution of catalog’s contents in an emerging way.

Keywords: Augmented Reality, Catalog System, Computer Graphics, Mobile Application.

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Authors: M. Heydari, S. A. Torabi

Abstract:

The problem of lot sizing, sequencing and scheduling multiple products in flow line production systems has been studied by several authors. Almost all of the researches in this area assumed that setup times and costs are sequence –independent even though sequence dependent setups are common in practice. In this paper we present a new mixed integer non linear program (MINLP) and a heuristic method to solve the problem in sequence dependent case. Furthermore, a genetic algorithm has been developed which applies this constructive heuristic to generate initial population. These two proposed solution methods are compared on randomly generated problems. Computational results show a clear superiority of our proposed GA for majority of the test problems.

Keywords: Economic lot scheduling problem, finite horizon, genetic algorithm, mixed zero-one nonlinear programming, sequence-dependent.

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Authors: N. Choosri, N. Swadchaipong, T. Utistham, U. W. Hartley

Abstract:

Performance of a cobalt doped sol-gel derived silica (Co/SiO2) catalyst for Fischer–Tropsch synthesis (FTS) in slurryphase reactor was studied using paraffin wax as initial liquid media. The reactive mixed gas, hydrogen (H2) and carbon monoxide (CO) in a molar ratio of 2:1, was flowed at 50 ml/min. Braunauer-Emmett- Teller (BET) surface area and X-ray diffraction (XRD) techniques were employed to characterize both the specific surface area and crystallinity of the catalyst, respectively. The reduction behavior of Co/SiO2 catalyst was investigated using the Temperature Programmmed Reduction (TPR) method. Operating temperatures were varied from 493 to 533K to find the optimum conditions to maximize liquid fuels production, gasoline and diesel.

Keywords: Fischer Tropsch synthesis, slurry phase, Co/SiO2, operating temperature.

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Authors: S. H. Mirhossaini, H. Godini, A. Jafari

Abstract:

Biological Ammonia removal (nitrification), the oxidation of ammonia to nitrate catalyzed by bacteria, is a key part of global nitrogen cycling. In the first step of nitrification, chemolithoautotrophic ammonia oxidizer transform ammonia to nitrite, this subsequently oxidized to nitrate by nitrite oxidizing bacteria. This process can be affected by several factors. In this study the effect of influent COD on biological ammonia removal in a bench-scale biological reactor was investigated. Experiments were carried out using synthetic wastewater. The initial ammonium concentration was 25mgNH4 +-N L-1. The effect of COD between 247.55±1.8 and 601.08±3.24mgL-1 on biological ammonia removal was investigated by varying the COD loading supplied to reactor. From the results obtained in this study it could be concluded in the range of 247.55±1.8 to 351.35±2.05mgL-1, there is a direct relationship between amount of COD and ammonia removal. However more than 351.35±2.05 up to 601.08±3.24mgL-1 were found an indirect relationship between them.

Keywords: Ammonia biological removal, Nitrification, InfluentCOD.

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Authors: Kartikaningsih Danis, Yao-Hui Huang

Abstract:

Various techniques including conventional and advanced have been employed for the boron treatment from water and wastewater. The electrocoagulation involves an electrolytic reactor for coagulation/flotation with aluminium as anode and cathode. There is aluminium as coagulant to be used for removal which may induce secondary pollution in chemical coagulation. The purpose of this study is to investigate and compare the performance between electrocoagulation and chemical coagulation on boron removal from synthetic wastewater. The effect of different parameters, such as pH reaction, coagulant dosage, and initial boron concentration were examined. The results show that the boron removal using chemical coagulation was lower. At the optimum condition (e.g. pH 8 and 0.8 mol coagulant dosage), boron removal efficiencies for chemical coagulation and electrocoagulation were 61% and 91%, respectively. In addition, the electrocoagulation needs no chemical reagents and makes the boron treatment easy for application.

Keywords: Electrocoagulation, chemical coagulation, aluminum electrode, boron removal.

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Authors: Vanessa Matias Leite, Jandira Guenka Palma, Flávio Henrique de Oliveira

Abstract:

This paper presents a model-oriented development approach to software development in the Model-View-Controller (MVC) architectural standard. This approach aims to expose a process of extractions of information from the models, in which through rules and syntax defined in this work, assists in the design of the initial model and its future conversions. The proposed paper presents a syntax based on the natural language, according to the rules agreed in the classic grammar of the Portuguese language, added to the rules of conversions generating models that follow the norms of the Object Management Group (OMG) and the Meta-Object Facility MOF.

Keywords: Model driven architecture, model-view-controller, bnf syntax, model, transformation, UML.

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Authors: B. Noruziaan, A. Shvarzman, R. Leahy

Abstract:

An innovative flooring underlayment was produced and tested. The composite system is made of common OSB boards and a layer of eco-friendly non-cement gypsum based material (GeoGypTM). It was found that the shear bond between the two materials is sufficient to secure the composite interaction between the two. The very high compressive strength and relatively high tensile strength of the non-cement based component together with its high modulus of elasticity provides enough strength and stiffness for the composite product to cover wider spacing between the joists. The initial findings of this study indicate that with joist spacing as wide as 800 mm, the flooring system provides enough strength without compromising the serviceability requirements of the building codes.

Keywords: Composite, floor deck, gypsum based, lumber joist, non-cement, oriented strandboard, shear bond.

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Authors: Esraa A. Khalil, Mohamed N. AbouZeid

Abstract:

Building materials selection is critical for the sustainability of any project. The choice of building materials has a huge impact on the built environment and cost of projects. Building materials emit huge amount of carbon dioxide (CO₂) due to the use of cement as a basic component in the manufacturing process and as a binder, which harms our environment. Energy consumption from buildings has increased in the last few years; a huge amount of energy is being wasted from using unsustainable building and finishing materials, as well as from the process of heating and cooling of buildings. In addition, the construction sector in Egypt is taking a good portion of the economy; however, there is a lack of awareness of buildings environmental impacts on the built environment. Using advanced building materials and different wall systems can help in reducing heat consumption, the project’s initial and long-term costs, and minimizing the environmental impacts. Red Bricks is one of the materials that are being used widely in Egypt. There are many other types of bricks such as Autoclaved Aerated Concrete (AAC); however, the use of Red Bricks is dominating the construction industry due to its affordability and availability. This research focuses on the New Egyptian Administrative Capital as a case study to investigate the potential of the influence of using different wall systems such as AAC on the project’s cost and the environment. The aim of this research is to conduct a comparative analysis between the traditional and most commonly used bricks in Egypt, which is Red Bricks, and AAC wall systems. Through an economic and environmental study, the difference between the two wall systems will be justified to encourage the utilization of uncommon techniques in the construction industry to build more affordable, energy efficient and sustainable buildings. The significance of this research is to show the potential of using AAC in the construction industry and its positive influences. The study analyzes the factors associated with choosing suitable building materials for different projects according to the need and criteria of each project and its nature without harming the environment and wasting materials that could be saved or recycled. The New Egyptian Administrative Capital is considered as the country’s new heart, where ideas regarding energy savings and environmental benefits are taken into consideration. Meaning that, Egypt is taking good steps to move towards more sustainable construction. According to the analysis and site visits, there is a potential in reducing the initial costs of buildings by 12.1% and saving energy by using different techniques up to 25%. Interviews with the mega structures project engineers and managers reveal that they are more open to introducing sustainable building materials that will help in saving the environment and moving towards green construction as well as to studying more effective techniques for energy conservation.

Keywords: AAC blocks, building material, environmental impact, modern construction, New Egyptian Administrative Capital.

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Authors: Mohd Safee M. K., Wan Abas W. A. B, Ibrahim F., Abu Osman N. A., Abdul Malik N. A.

Abstract:

This paper investigates the activity of the rectus femoris (RF) and biceps femoris (BF) in healthy subjects during salat (prostration) and specific exercise (squat exercise) using electromyography (EMG). A group of undergraduates aged between 19 to 25 years voluntarily participated in this study. The myoelectric activity of the muscles were recorded and analyzed. The finding indicated that there were contractions of the muscles during the salat and exercise with almost same EMG’s level. From the result, Wilcoxon’s Rank Sum test showed significant difference between prostration and squat exercise (p<0.05) but the differences was very small; RF (8.63%MVC) and BF (11.43%MVC). Therefore, salat may be useful in strengthening exercise and also in rehabilitation programs for lower limb activities. This pilot study conducted initial research into the biomechanical responses of human muscles in various positions of salat.

Keywords: Electromyography, exercise, muscle, salat.

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Authors: Basheer M. Al-Maqaleh, Kamal K. Bharadwaj

Abstract:

Automated discovery of hierarchical structures in large data sets has been an active research area in the recent past. This paper focuses on the issue of mining generalized rules with crisp hierarchical structure using Genetic Programming (GP) approach to knowledge discovery. The post-processing scheme presented in this work uses flat rules as initial individuals of GP and discovers hierarchical structure. Suitable genetic operators are proposed for the suggested encoding. Based on the Subsumption Matrix(SM), an appropriate fitness function is suggested. Finally, Hierarchical Production Rules (HPRs) are generated from the discovered hierarchy. Experimental results are presented to demonstrate the performance of the proposed algorithm.

Keywords: Genetic Programming, Hierarchy, Knowledge Discovery in Database, Subsumption Matrix.

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

Abstract:

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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