Search results for: initial consonants

Authors: Hager Kammoun, Jean Charles Lamirel, Mohamed Ben Ahmed

Abstract:

In this paper, a model for an information retrieval system is proposed which takes into account that knowledge about documents and information need of users are dynamic. Two methods are combined, one qualitative or symbolic and the other quantitative or numeric, which are deemed suitable for many clustering contexts, data analysis, concept exploring and knowledge discovery. These two methods may be classified as inductive learning techniques. In this model, they are introduced to build “long term" knowledge about past queries and concepts in a collection of documents. The “long term" knowledge can guide and assist the user to formulate an initial query and can be exploited in the process of retrieving relevant information. The different kinds of knowledge are organized in different points of view. This may be considered an enrichment of the exploration level which is coherent with the concept of document/query structure.

Keywords: Information Retrieval Systems, machine learning, classification, Galois lattices, Self Organizing Map.

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Authors: C. Ardil

Abstract:

This paper introduces a new method for multiplecriteria decision making (MCDM) that avoids order reversal and ensures consistency in decision-making. The proposed method involves range targeting of benefit and cost criteria vectors for range normalization of the initial decision matrix. The Reference Linear Combination (RLC) is used to avoid the rank reversal problem. The preference order generated from the target score matrix does not require relative comparisons between alternatives but relies on a chosen reference solution point after transforming the original decision matrix into an MCDM problem by specifying the minimum and maximum bounds of each criterion. The efficiency and applicability of the proposed RLC method were demonstrated in the selection of commercial passenger aircraft. 

Keywords: Aircraft selection, reference linear combination (RLC), multiple criteria decision-making, MCDM

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Authors: S. Ahmadnejad, Z. Monjamed, M. Pakravannejad, A. Malekian

Abstract:

The investigating and assessing the effects of relaxation training on the levels of state anxiety concerning first year female nursing students at their initial experience in clinical setting. This research is a quasi experimental study that was carried out in nursing and midwifery faculty of Tehran university of medical sciences .The sample of research consists 60 first term female nursing students were selected through convenience and random sampling. 30 of them were the experimental group and 30 of them were in control group. The Instruments of data-collection has been a questionnaire which consists of 3 parts. The first part includes 10 questions about demographic characteristics .the second part includes 20 question about anxiety (test 'Spielberg' ). The 3rd part includes physiological indicators of anxiety (BP, P, R, body temperature). The statistical tests included t-test and
 and fisher test, Data were analyzed by SPSS software.

Keywords: Anxiety, Nursing students, Relaxation

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Authors: S. O. Adeosun, O. S. Sanni

Abstract:

Study on corrosion propensity of welded mild steel- bar in soil media around the coastal area of University of Lagos has been carried out using gravimetric method. Six (6) samples each for welded and unwelded mild steels were cut, their initial weights were recorded and buried in two selected soil. The weight losses of these coupons were measured at regular intervals for a period of six months (180 days).

The corrosiveness of the soil media varied widely depending on the potency level of its constituents. The results revealed that soil in the studied area have marked variations in composition and contents. Soil medium with a lower pH and higher chloride ion concentration aggressively attacked the coupons with the welded steel coupon corroding faster than unwelded one. The medium resistivity to the flow of current is another strong factor affecting corrosion rate.

Keywords: Coastal area, corrosion rate, mild steel, soil media, welds.

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Authors: S. Kazemzadeh Hannani, A. Azimi, S. Nikoofard

Abstract:

To simulate heating systems in buildings, a research oriented computer code has been developed in Sharif University of Technology in Iran where the climate, existing heating equipment in buildings, consumer behavior and their interactions are considered for simulating energy consumption in conventional systems such as heaters, radiators and fan-coils. In order to validate the computer code, the available data of five buildings was used and the computed consumed energy was compared with the estimated energy extracted from monthly bills. The initial heating system was replaced by the alternative system and the effect of this change was observed on the energy consumption. As a result, the effect of changing heating equipment on energy consumption was investigated in different climates. Changing heater to radiator renders energy conservation up to 50% in all climates and changing radiator to fan-coil decreases energy consumption in climates with cold and dry winter.

Keywords: Energy consumption, heating system, energy simulation.

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Authors: S. Kazemzadeh Hannani, A. Azimi, S. Nikoofard

Abstract:

To simulate heating systems in buildings, a research oriented computer code has been developed in Sharif University of Technology in Iran where the climate, existing heating equipment in buildings, consumer behavior and their interactions are considered for simulating energy consumption in conventional systems such as heaters, radiators and fan-coils. In order to validate the computer code, the available data of five buildings was used and the computed consumed energy was compared with the estimated energy extracted from monthly bills. The initial heating system was replaced by the alternative system and the effect of this change was observed on the energy consumption. As a result, the effect of changing heating equipment on energy consumption was investigated in different climates. Changing heater to radiator renders energy conservation up to 50% in all climates and changing radiator to fan-coil decreases energy consumption in climates with cold and dry winter.

Keywords: Energy consumption, heating system, energy simulation.

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Authors: Ahmad. A. Kardan, Amir Narimani, Foozhan Ataiefard

Abstract:

Recommender Systems have been developed to provide contents and services compatible to users based on their behaviors and interests. Due to information overload in online discussion forums and users diverse interests, recommending relative topics and threads is considered to be helpful for improving the ease of forum usage. In order to lead learners to find relevant information in educational forums, recommendations are even more needed. We present a hybrid thread recommender system for MOOC forums by applying social network analysis and association rule mining techniques. Initial results indicate that the proposed recommender system performs comparatively well with regard to limited available data from users' previous posts in the forum.

Keywords: Association rule mining, hybrid recommender system, massive open online courses, MOOCs, social network analysis.

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Authors: B.M.N. Nik Hisyamudin, S. Yokoyama, M. Umemoto

Abstract:

In the current study, we have conducted an experimental investigation on the utilization of electronic arc furnace (EAF) reducing slag for the absorption of CO2 via wet grinding method. It was carried out by various grinding conditions. The slag was ground in the vibrating ball mill in the presence of CO2 and pure water under ambient temperature. The reaction behavior was monitored with constant pressure method, and the changes of experimental systems volume as a function of grinding time were measured. It was found that the CO2 absorption occurred as soon as the grinding started. The CO2 absorption was significantly increased in the case of wet grinding compare to the dry grinding. Generally, the amount of CO2 absorption increased as the amount of water, weight of slag and initial pressure increased. However, it was decreased when the amount of water exceeds 200ml and when smaller balls were used. The absorption of CO2 occurred simultaneously with the start of the grinding and it stopped when the grinding was stopped. According to this research, the CO2 reacted with the CaO inside the slag, forming CaCO3.

Keywords: CO2 absorption, EAF reducing slag, vibration ball mill, wet grinding.

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Authors: Adnan Y. Rojeab

Abstract:

This hypothesis shows that the induction and the remanent of magnetic properties govern the mechanism processes of DNA replication and the shortening of the telomere. The solenoid–like formation of each parental DNA strand, which exists at the initial stage of the replication process, enables an electric charge transformation through the strand to produce a magnetic field. The magnetic field, in turn, induces the surrounding medium to form a new (replicated) strand by a remanent magnetisation. Through the remanent [residual] magnetisation process, the replicated strand possesses a similar information pattern to that of the parental strand. In the same process, the remanent amount of magnetisation forms the medium in which it has less of both repetitive and pattern magnetisation than that of the parental strand, therefore the replicated strand shows a shortening in the length of its telomeres.

Keywords: DNA replication, magnetic properties, residual magnetisation, shortening of the telomere.

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Authors: Yury Nikulin

Abstract:

A multicriteria linear programming problem with integer variables and parameterized optimality principle "from lexicographic to Slater" is considered. A situation in which initial coefficients of penalty cost functions are not fixed but may be potentially a subject to variations is studied. For any efficient solution, appropriate measures of the quality are introduced which incorporate information about variations of penalty cost function coefficients. These measures correspond to the so-called stability and accuracy functions defined earlier for efficient solutions of a generic multicriteria combinatorial optimization problem with Pareto and lexicographic optimality principles. Various properties of such functions are studied and maximum norms of perturbations for which an efficient solution preserves the property of being efficient are calculated.

Keywords: Stability and accuracy, multicriteria optimization, lexicographic optimality.

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Authors: Lejla A. Bexheti, Visar S. Shehu, Adrian A. Besimi

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The Learning Management Systems present learning environment which offers a collection of e-learning tools in a package that allows a common interface and information sharing among the tools. South East European University initial experience in LMS was with the usage of the commercial LMS-ANGEL. After a three year experience on ANGEL usage because of expenses that were very high it was decided to develop our own software. As part of the research project team for the in-house design and development of the new LMS, we primarily had to select the features that would cover our needs and also comply with the actual trends in the area of software development, and then design and develop the system. In this paper we present the process of LMS in-house development for South East European University, its architecture, conception and strengths with a special accent on the process of migration and integration with other enterprise applications.

Keywords: e-learning tools, LMS, migration, user feedback.

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Authors: M. W. Siddiqi, M. Ilyas

Abstract:

Availability and mobilization of revenue is the main essential with which an economy is managed and run. While planning or while making the budgets nations set revenue targets to be achieved. But later when the accounts are closed the actual collections of revenue through taxes or even the non-tax revenue collection would invariably be different as compared to the initial estimates and targets set to be achieved. This revenue-gap distorts the whole system and the economy disturbing all the major macroeconomic indicators. This study is aimed to find out short and long term impact of revenue gap on budget deficit, debt burden and economic growth on the economy of Pakistan. For this purpose the study uses autoregressive distributed lag approach to cointegration and error correction mechanism on three different models for the period 1980 to 2009. The empirical results show that revenue gap has a short and long run relationship with economic growth and budget deficit. However, revenue gap has no impact on debt burden.

Keywords: Revenue Gap, Economic Growth, Budget Deficit, Debt Burden

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Authors: Haluk Eren, Mucahit Karaduman

Abstract:

This paper presents 15-year trends for scientific studies in a scientific database considering 3D and vehicle words. Two words are selected to find their associated publications in IEEE scholar database. Both of keywords are entered individually for the years 2002, 2012, and 2016 on the database to identify the preferred subjects of researchers in same years. We have classified closer research fields after searching and listing. Three years (2002, 2012, and 2016) have been investigated to figure out progress in specified time intervals. The first one is assumed as the initial progress in between 2002-2012, and the second one is in 2012-2016 that is fast development duration. We have found very interesting and beneficial results to understand the scholars’ research field preferences for a decade. This information will be highly desirable in smart city-based research purposes consisting of 3D and vehicle-related issues.

Keywords: Vehicle, 3D, smart city, scholarly search, semantic.

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Authors: Fazeera Ujin, Kamran Shavarebi Ali, Zarina Yasmin Hanur Harith

Abstract:

This research paper reports on the feasibility and viability of eggshells ash and its effects on the water content and setting time of cement. An experiment was carried out to determine the quantity of water required in order to follow standard cement paste of normal consistency in accordance with MS EN 196-3:2007. The eggshells ash passing the 90µm sieve was used in the investigation. Eggshells ash with percentage of 0%, 0.1%, 0.5%, 1.0%, 1.5% and 2.0% were constituted to replace the cement. Chemical properties of both eggshells ash and cement are compared. From the results obtained, both eggshells ash and cement have the same chemical composition and primary composition which is the calcium compounds. Results from the setting time show that by adding the eggshells ash to the cement, the setting time of the cement decreases. In short, the higher amount of eggshells ash, the faster the rate of setting and apply to all percentage of eggshells ash that were used in this investigation. Both initial and final setting times fulfill the setting time requirements by Malaysian Standard. Hence, it is suggested that eggshells ash can be used as an admixture in concrete mix.

Keywords: Construction Materials, Eggshells Ash, Solid Waste, Setting Time.

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Authors: Maziar Ramezani, Thomas Neitzert

Abstract:

This paper gives an overview of a deep drawing process by pressurized liquid medium separated from the sheet by a rubber diaphragm. Hydroforming deep drawing processing of sheet metal parts provides a number of advantages over conventional techniques. It generally increases the depth to diameter ratio possible in cup drawing and minimizes the thickness variation of the drawn cup. To explore the deformation mechanism, analytical and numerical simulations are used for analyzing the drawing process of an AA6061-T4 blank. The effects of key process parameters such as coefficient of friction, initial thickness of the blank and radius between cup wall and flange are investigated analytically and numerically. The simulated results were in good agreement with the results of the analytical model. According to finite element simulations, the hydroforming deep drawing method provides a more uniform thickness distribution compared to conventional deep drawing and decreases the risk of tearing during the process.

Keywords: Deep drawing, Hydroforming, Rubber diaphragm

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Authors: Kalyankumar M. Matti, Chandrashekhar J. Savanurmath, Shivayogeppa B. Hinchigeri

Abstract:

A rare phenomenon of SDS-induced activation of a latent protease activity associated with the purified silkworm excretory red fluorescent protein (SE-RFP) was noticed. SE-RFP aliquots incubated with SDS for different time intervals indicated that the protein undergoes an obligatory breakdown into a number of subunits which exhibit autoproteolytic (acting upon themselves) and/or heteroproteolytic (acting on other proteins) activities. A strong serine protease activity of SE-RFP subunits on Bombyx mori nucleopolyhedrovirus (BmNPV) polyhedral protein was detected by zymography technique. A complete inhibition of BmNPV infection to silkworms was observed by the oral administration assay of the SE-RFP. Here, it is proposed that the SE-RFP prevents the initial infection of BmNPV to silkworms by obliterating the polyhedral protein. This is the first report on a silkworm red fluorescent protein that exhibits a protease activity on exposure to SDS. The present studies would help in understanding the antiviral mechanism of silkworm red fluorescent proteins.

Keywords: BmNPV, polyhedra, SE-RFP, SDS-induced protease activity, zymography.

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Authors: S. Kavitha, Nirmala P. Ratchagar

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This paper presents the novel deterministic dynamic programming approach for solving optimization problem with quadratic objective function with linear equality and inequality constraints. The proposed method employs backward recursion in which computations proceeds from last stage to first stage in a multi-stage decision problem. A generalized recursive equation which gives the exact solution of an optimization problem is derived in this paper. The method is purely analytical and avoids the usage of initial solution. The feasibility of the proposed method is demonstrated with a practical example. The numerical results show that the proposed method provides global optimum solution with negligible computation time.

Keywords: Backward recursion, Dynamic programming, Multi-stage decision problem, Quadratic objective function.

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Authors: Biswajit Biswas

Abstract:

Demand of energy is increasing faster than the generation. It leads shortage of power in all sectors of society. At peak hours this shortage is higher. Unless we utilize energy efficient technology, it is very difficult to minimize the shortage of energy. So energy efficiency program and energy conservation has an important role. Energy efficient technologies are cost intensive hence it is always not possible to implement in country like India. In the recent study, an educational building with operating hours from 10:00 a.m. to 05:00 p.m. has been selected to quantify the possibility of lighting energy conservation. As the operating hour is in daytime, integration of daylight with artificial lighting system will definitely reduce the lighting energy consumption. Moreover the initial investment has been given priority and hence the existing lighting installation was unaltered. An automatic controller has been designed which will be operated as a function of daylight through windows and the lighting system of the room will function accordingly. The result of the study of integrating daylight gave quite satisfactory for visual comfort as well as energy conservation.

Keywords: Lighting energy, energy efficiency, daylight, illumination, energy conservation.

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Authors: Khawtar Hasan Ahmed, Sasha Omanovic

Abstract:

Polarization modulation infrared reflection absorption spectroscopy (PM-IRRAS) in combination with electrochemistry, was employed to study the influence of surface charge (potential) on the kinetics of bovine serum albumin (BSA) adsorption on a biomedical-grade 316LVM stainless steel surface is discussed. The BSA adsorption kinetics was found to greatly depend on the surface potential. With an increase in surface potential towards more negative values, both the BSA initial adsorption rate and the equilibrium (saturated) surface concentration also increased. Both effects were explained on the basis of replacement of well-ordered water molecules at the 316LVM / solution interface, i.e. by the increase in entropy of the system.

Keywords: adsorption, biomedical grade stainless steel, bovine serum albumin (BSA), electrode surface potential / charge, kinetics, PM-IRRAS, protein/surface interactions

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Authors: Mohd Ariff Admon, Abdul Rahman Mohd Kasim, Sharidan Shafie

Abstract:

This paper considers the effect of heat generation proportional l to (T - T∞ )p , where T is the local temperature and T∞ is the ambient temperature, in unsteady free convection flow near the stagnation point region of a three-dimensional body. The fluid is considered in an ambient fluid under the assumption of a step change in the surface temperature of the body. The non-linear coupled partial differential equations governing the free convection flow are solved numerically using an implicit finite-difference method for different values of the governing parameters entering these equations. The results for the flow and heat characteristics when p ≤ 2 show that the transition from the initial unsteady-state flow to the final steadystate flow takes place smoothly. The behavior of the flow is seen strongly depend on the exponent p.

Keywords: Free convection, Boundary layer flow, Stagnationpoint, Heat generation

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Authors: Nina Robson, Kenneth John Faller II, Vishalkumar Ahir, Mustafa Mhawesh, Reza Langari

Abstract:

This paper describes the development of a model of an impaired human arm performing a reaching motion, which will be used to predict hand path trajectories for people with reduced arm joint mobility. Assuming that the arm was in contact with a surface during the entire movement, the contact conditions at the initial and final task locations were determined and used to generate the entire trajectory. The model was validated by comparing it to experimental data, which simulated an arm joint impairment by physically constraining the joint motion with a brace. Future research will include using the model in the development of physical training protocols that avoid early recruitment of “healthy” Degrees-Of-Freedom (DOF) for reaching motions, thus facilitating an Active Range-Of-Motion Recovery (AROM) for a particular impaired joint.

Keywords: Higher order kinematic specifications, human motor coordination, impaired movement, kinematic synthesis.

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

Abstract:

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

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

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Authors: I. Kruashvili, I. Inashvili, K. Bziava, M. Lomishvili

Abstract:

Seepage capillary anomalies in the active layer of soil, related to the soil water movement, often cause variation of soil hydrophysical properties and become one of the main objectives of the hydroecology. It is necessary to mention that all existing equations for computing the seepage flow particularly from soil channels, through dams, bulkheads, and foundations of hydraulic engineering structures are preferable based on the linear seepage law. Regarding the existing beliefs, anomalous seepage is based on postulates according to which the fluid in free volume is characterized by resistance against shear deformation and is presented in the form of initial gradient. According to the above-mentioned information, we have determined: Equation to calculate seepage coefficient when the velocity of transition flow is equal to seepage flow velocity; by means of power function, equations for the calculation of average and maximum velocities of seepage flow have been derived; taking into consideration the fluid continuity condition, average velocity for calculation of average velocity in capillary tube has been received.

Keywords: Seepage, soil, velocity, water.

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Authors: Vera Pujani, Alfitman, Refdinal Nazir

Abstract:

E-travel is travel agency-s companies employing internet and website as e-commerce context. This study presents numerous initial key factors of electronic travel model based on small travel agencies perspectives. Browsing previous studies related to website travel activities are conducted. Five small travel agencies in Indonesia has been deeply interviewed in case studies. The finding of this research is identifying numerous characteristics and dimension factors and travel website operations including ownermanager roles, business experiences, characteristically business, and technological aspects. This study is the preliminary research related to travel website adoption in Indonesia. The further study would be conducted in questionnaires of the quantitative research in Indonesia contexts as a developing country.

Keywords: Tourism, travel agency, e-commerce, website, developing country, small business, case study.

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Authors: V. D. Thi, M. Li, M. Khelifa, M. El Ganaoui, Y. Rogaume

Abstract:

This paper presents a two-dimensional model to study the heat and moisture transfer through porous building materials. Dynamic and static coupled models of heat and moisture transfer in porous material under low temperature are presented and the coupled models together with variable initial and boundary conditions have been considered in an analytical way and using the finite element method. The resulting coupled model is converted to two nonlinear partial differential equations, which is then numerically solved by an implicit iterative scheme. The numerical results of temperature and moisture potential changes are compared with the experimental measurements available in the literature. Predicted results demonstrate validation of the theoretical model and effectiveness of the developed numerical algorithms. It is expected to provide useful information for the porous building material design based on heat and moisture transfer model.

Keywords: Finite element method, heat transfer, moisture transfer, porous materials, wood.

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Authors: Shuen-Tai Wang, Chin-Hung Li, Ying-Chuan Chen

Abstract:

In recent years there has been renewal of interest in the relation between Green IT and Cloud Computing. The growing use of computers in cloud platform has caused marked energy consumption, putting negative pressure on electricity cost of cloud data center. This paper proposes an effective mechanism to reduce energy utilization in cloud computing environments. We present initial work on the integration of resource and power management that aims at reducing power consumption. Our mechanism relies on recalling virtualization services dynamically according to user-s virtualization request and temporarily shutting down the physical machines after finish in order to conserve energy. Given the estimated energy consumption, this proposed effort has the potential to positively impact power consumption. The results from the experiment concluded that energy indeed can be saved by powering off the idling physical machines in cloud platforms.

Keywords: Green IT, Cloud Computing, virtualization, power consumption.

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Authors: V. Goremikins, K. Rocens, D. Serdjuks

Abstract:

One of the main problems of suspended cable structures is initial shape change under the action of non uniform load. The problem can be solved by increasing of weight of construction or by using of prestressing. But this methods cause increasing of materials consumption of suspended cable structure. The cable truss usage is another way how the problem of shape change under the action of non uniform load can be fixed. The cable trusses with the vertical and inclined suspensions, cross web and single cable were analyzed as the main load-bearing structures of suspension bridge. It was shown, that usage of cable truss allows to reduce the vertical displacements up to 32% in comparison with the single cable in case of non uniformly distributed load. In case of uniformly distributed load single cable is preferable.

Keywords: Cable trusses, Non uniform load, Suspension bridge, Vertical displacements.

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Authors: Nerijus Remeikis, Ignas Skucas, Vida Melninkaite

Abstract:

Text categorization - the assignment of natural language documents to one or more predefined categories based on their semantic content - is an important component in many information organization and management tasks. Performance of neural networks learning is known to be sensitive to the initial weights and architecture. This paper discusses the use multilayer neural network initialization with decision tree classifier for improving text categorization accuracy. An adaptation of the algorithm is proposed in which a decision tree from root node until a final leave is used for initialization of multilayer neural network. The experimental evaluation demonstrates this approach provides better classification accuracy with Reuters-21578 corpus, one of the standard benchmarks for text categorization tasks. We present results comparing the accuracy of this approach with multilayer neural network initialized with traditional random method and decision tree classifiers.

Keywords: Text categorization, decision trees, neural networks, machine learning.

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Authors: Munther I. Kandah, Fahmi A. Abu Al-Rub, Lucy Bawarish, Mira Bawarish, Hiba Al-Tamimi, Reem Khalil, Raja'a Sa, ada

Abstract:

In this project cadmium ions were adsorbed from aqueous solutions onto either date pits; a cheap agricultural and nontoxic material, or chemically activated carbon prepared from date pits using phosphoric acid. A series of experiments were conducted in a batch adsorption technique to assess the feasibility of using the prepared adsorbents. The effects of the process variables such as initial cadmium ions concentration, contact time, solution pH and adsorbent dose on the adsorption capacity of both adsorbents were studied. The experimental data were tested using different isotherm models such as Langmuir, Freundlich, Tempkin and Dubinin- Radushkevich. The results showed that although the equilibrium data could be described by all models used, Langmuir model gave slightly better results when using activated carbon while Freundlich model, gave better results with date pits.

Keywords: Adsorption, Cadmium, Chemical Activation, DatePits.

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Authors: Abdu Masanawa Sagir

Abstract:

In this paper, linear multistep technique using power series as the basis function is used to develop the block methods which are suitable for generating direct solution of the special second order ordinary differential equations of the form y′′ = f(x,y), a < = x < = b with associated initial or boundary conditions. The continuaous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain two different three discrete schemes, each of order (4,4,4)T, which were used in block form for parallel or sequential solutions of the problems. The computational burden and computer time wastage involved in the usual reduction of second order problem into system of first order equations are avoided by this approach. Furthermore, a stability analysis and efficiency of the block method are tested on linear and non-linear ordinary differential equations whose solutions are oscillatory or nearly periodic in nature, and the results obtained compared favourably with the exact solution.

Keywords: Block Method, Hybrid, Linear Multistep Method, Self – starting, Special Second Order.

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