Search results for: positive solution.

Authors: Haksoon Kim

Abstract:

The paper investigates the relationship between the foreign direct investment (FDI) and the corporate governance or transparency by investigating the country-level FDI flows, FDI inward performance, corporate governance and transparency variables. From the regression analysis with Newey-West estimator of 28 country panel data from 1990- 2002, we find strong positive relationships between corporate governance or transparency level of hosting countries and FDI inward performance within hosting countries. A strong positive relationship is found between anti-director rights level or number of analysts of hosting countries and FDI inward performance within hosting countries. Also, we find a positive relationship between the number of analysts of hosting countries and FDI inflows. The empirical results are consistent with stock market liberalizations and corporate governance explanations of reasons for FDI.

Keywords: corporate governance, corporate transparency, FDIflows, FDI inward performance

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Authors: Imran S.Bajwa

Abstract:

The trends of design and development of information systems have undergone a variety of ongoing phases and stages. These variations have been evolved due to brisk changes in user requirements and business needs. To meet these requirements and needs, a flexible and agile business solution was required to come up with the latest business trends and styles. Another obstacle in agility of information systems was typically different treatment of same diseases of two patients: business processes and information services. After the emergence of information technology, the business processes and information systems have become counterparts. But these two business halves have been treated under totally different standards. There is need to streamline the boundaries of these both pillars that are equally sharing information system's burdens and liabilities. In last decade, the object orientation has evolved into one of the major solutions for modern business needs and now, SOA is the solution to shift business on ranks of electronic platform. BPM is another modern business solution that assists to regularize optimization of business processes. This paper discusses how object orientation can be conformed to incorporate or embed SOA in BPM for improved information systems.

Keywords: Object Oriented Business Solutions, Services forBusiness Processes; Mixing SOA and BPM.

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Authors: Xia Cui, Guang-wei Yuan, Jing-yan Yue

Abstract:

A Picard-Newton iteration method is studied to accelerate the numerical solution procedure of a class of two-dimensional nonlinear coupled parabolic-hyperbolic system. The Picard-Newton iteration is designed by adding higher-order terms of small quantity to an existing Picard iteration. The discrete functional analysis and inductive hypothesis reasoning techniques are used to overcome difficulties coming from nonlinearity and coupling, and theoretical analysis is made for the convergence and approximation properties of the iteration scheme. The Picard-Newton iteration has a quadratic convergent ratio, and its solution has second order spatial approximation and first order temporal approximation to the exact solution of the original problem. Numerical tests verify the results of the theoretical analysis, and show the Picard-Newton iteration is more efficient than the Picard iteration.

Keywords: Nonlinearity, iterative acceleration, coupled parabolic hyperbolic system, quadratic convergence, numerical analysis.

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Authors: Zare Aliabadi, Hassan, Mirzaei, Somaye

Abstract:

The use of amine mixtures employing methyldiethanolamine (MDEA), monoethanolamine (MEA), and diethanolamine (DEA) have been investigated for a variety of cases using a process simulation program called HYSYS. The results show that, at high pressures, amine mixtures have little or no advantage in the cases studied. As the pressure is lowered, it becomes more difficult for MDEA to meet residual gas requirements and mixtures can usually improve plant performance. Since the CO2 reaction rate with the primary and secondary amines is much faster than with MDEA, the addition of small amounts of primary or secondary amines to an MDEA based solution should greatly improve the overall reaction rate of CO2 with the amine solution. The addition of MEA caused the CO2 to be absorbed more strongly in the upper portion of the column than for MDEA along. On the other hand, raising the concentration for MEA to 11%wt, CO2 is almost completely absorbed in the lower portion of the column. The addition of MEA would be most advantageous. Thus, in areas where MDEA cannot meet the residual gas requirements, the use of amine mixtures can usually improve the plant performance.

Keywords: CO2, H2S, Methyldiethanolamine, Monoethanolamine

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Authors: S. A. Mousavi Rad, S. A. Mirbagheri, T. Mohammadi

Abstract:

In this paper, removal of chromium(VI) from aqueous solution has been researched using reverse osmosis. The influence of transmembrane pressure and feed concentration on permeate flux, water recovery, permeate concentration, and salt rejection was studied. The results showed that according to the variation of transmembrane pressure and feed concentration, the permeate flux and salt rejection were in the range 19.17 to 58.75 l/m2.min and 99.51 to 99.8 %, respectively. The highest permeate flux, 58.75 l/m2.min, and water recovery, 42.47 %, were obtained in the highest pressure and the lowest feed concentration. On the other hand, the lowest permeate concentration, 0.01 mg/l, and the highest salt rejection, 99.8 %, were obtained in the highest pressure and the lowest feed concentration.

Keywords: solution, Chromium, Removal, Reverse osmosis.

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Authors: Ahmet Güven, Ö. Özgür Bozkurt, Oya Kalıpsız

Abstract:

Number of documents being created increases at an increasing pace while most of them being in already known topics and little of them introducing new concepts. This fact has started a new era in information retrieval discipline where the requirements have their own specialties. That is digging into topics and concepts and finding out subtopics or relations between topics. Up to now IR researches were interested in retrieving documents about a general topic or clustering documents under generic subjects. However these conventional approaches can-t go deep into content of documents which makes it difficult for people to reach to right documents they were searching. So we need new ways of mining document sets where the critic point is to know much about the contents of the documents. As a solution we are proposing to enhance LSI, one of the proven IR techniques by supporting its vector space with n-gram forms of words. Positive results we have obtained are shown in two different application area of IR domain; querying a document database, clustering documents in the document database.

Keywords: Document clustering, Information Extraction, Information Retrieval, LSI, n-gram.

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Authors: Christiono Utomo, Arazi Idrus, Madzlan Napiah, Mohd. Faris Khamidi

Abstract:

This paper presents a conceptual model of agreement options on negotiation support for civil engineering decision. The negotiation support facilitates the solving of group choice decision making problems in civil engineering decision to reduce the impact of mud volcano disaster in Sidoarjo, Indonesia. The approach based on application of analytical hierarchy process (AHP) method for multi criteria decision on three level of decision hierarchy. Decisions for reducing impact is very complicated since many parties involved in a critical time. Where a number of stakeholders are involved in choosing a single alternative from a set of solution alternatives, there are different concern caused by differing stakeholder preferences, experiences, and background. Therefore, a group choice decision support is required to enable each stakeholder to evaluate and rank the solution alternatives before engaging into negotiation with the other stakeholders. Such civil engineering solutions as alternatives are referred to as agreement options that are determined by identifying the possible stakeholder choice, followed by determining the optimal solution for each group of stakeholder. Determination of the optimal solution is based on a game theory model of n-person general sum game with complete information that involves forming coalitions among stakeholders.

Keywords: Agreement options, AHP, agent, negotiation, multicriteria, game theory, and coalition.

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Authors: Mohammad Koushafar, Amir Hossein Khoshgoftarmanesh

Abstract:

Due to water shortage, application of saline water for irrigation is an urgent in agriculture. In this study the effect of calcium and potassium application as additive in saline root media for reduce salinity adverse effects was investigated on tomato growth in a hydroponic system with unequal distribution of salts in the root media, which was divided in to two equal parts containing full Johnson nutrient solution and 40 mMNaCl solution, alone or in combination with KCl (6 mM), CaCl2 (4 mM), K+Ca (3+2 mM) or half-strength Johnson nutrient solution. The root splits were exchanged every 7 days. Results showed that addition of calcium, calcium-potassium and nutrition elements equivalent to half the concentration of Johnson formula to the saline-half of culture media minimized the reduction in plant growth caused by NaCl, although addition of potassium to culture media wasn’t effective. The greatest concentration of sodium was observed at the shoot of treatments which had smallest growth. According to the results of this study, in case of dynamic and non-uniform distribution of salts in the root media, by addition of additive to the saline solution, it would be possible to use of saline water with no significant growth reduction.

Keywords: Calcium, Hydroponic, Local salinity, Potassium, Saline water, Tomato.

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Authors: M. Zarebnia, S. Khani

Abstract:

In this paper first, a numerical method based on quasiinterpolation for solving nonlinear Fredholm integral equations of the Hammerstein-type is presented. Then, we approximate the solution of Hammerstein integral equations by Nystrom’s method. Also, we compare the methods with some numerical examples.

Keywords: Hammerstein integral equations, quasi-interpolation, Nystrom’s method.

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Authors: Alexander Urbach, Mukharbij Banov, Vladislav Turko

Abstract:

Fatigue tests of specimen-s with numerous holes are presented. The tests were made up till fatigue cracks have been created on both sides of the hole. Their extension was stopping with pressed plastic deformation at the mouth of the detected crack. It is shown that the moments of occurrence of cracks on holes are stochastically dependent. This dependence has positive and negative correlation relations. Shown that the positive correlation is formed across of the applied force, while negative one – along it. The negative relationship extends over a greater distance. The mathematical model of dependence area formation is represented as well as the estimating of model parameters. The positive correlation of fatigue cracks origination can be considered as an extension of one main crack. With negative correlation the first crack locates the place of its origin, leading to the appearance of multiple cracks; do not merge with each other.

Keywords: Correlation analysis, fatigue damage accumulation, local area, mathematical model.

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Authors: Jindong Gu, Matthias Schubert, Volker Tresp

Abstract:

In many outlier detection tasks, only training data belonging to one class, i.e., the positive class, is available. The task is then to predict a new data point as belonging either to the positive class or to the negative class, in which case the data point is considered an outlier. For this task, we propose a novel corrupted Generative Adversarial Network (CorGAN). In the adversarial process of training CorGAN, the Generator generates outlier samples for the negative class, and the Discriminator is trained to distinguish the positive training data from the generated negative data. The proposed framework is evaluated using an image dataset and a real-world network intrusion dataset. Our outlier-detection method achieves state-of-the-art performance on both tasks.

Keywords: Outlier detection, generative adversary networks, semi-supervised learning.

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Authors: S.N.Paul, G.Pakira, B.Paul, B.Ghosh

Abstract:

Nonlinear propagation of ion-acoustic waves in a selfgravitating dusty plasma consisting of warm positive ions, isothermal two-temperature electrons and negatively charged dust particles having charge fluctuations is studied using the reductive perturbation method. It is shown that the nonlinear propagation of ion-acoustic waves in such plasma can be described by an uncoupled third order partial differential equation which is a modified form of the usual Korteweg-deVries (KdV) equation. From this nonlinear equation, a new type of solution for the ion-acoustic wave is obtained. The effects of two-temperature electrons, gravity and dust charge fluctuations on the ion-acoustic solitary waves are discussed with possible applications.

Keywords: Charge fluctuations, gravitating dusty plasma, Ionacoustic solitary wave, Two-temperature electrons

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Authors: Marian Dragomir, Alin Dragomir

Abstract:

In the paper, two fault location algorithms are presented for transmission lines which use the line parameters to estimate the distance to the fault. The first algorithm uses only the measurements from one end of the line and the positive and zero sequence parameters of the line, while the second one uses the measurements from both ends of the line and only the positive sequence parameters of the line. The algorithms were tested using a transmission grid transposed in MATLAB. In a first stage it was established a fault location base line, where the algorithms mentioned above estimate the fault locations using the exact line parameters. After that, the positive and zero sequence resistance and reactance of the line were calculated again for different ground resistivity values and then the fault locations were estimated again in order to compare the results with the base line results. The results show that the algorithm which uses the zero sequence impedance of the line is the most sensitive to the line parameters modifications. The other algorithm is less sensitive to the line parameters modification.

Keywords: Estimation algorithms, fault location, line parameters, simulation tool.

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Authors: M. Chumburidze, D. Lekveishvili

Abstract:

We have considered the harmonic oscillations and general dynamic (pseudo oscillations) systems of theory generalized Green-Lindsay of couple-stress thermo-elasticity for isotropic, homogeneous elastic media. Approximate solution of some mixed boundary value problems for finite domain, bounded by the some closed surface are constructed.

Keywords: The couple-stress thermo-elasticity, boundary value problems.

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Authors: A.R. Rahmani, M.T. Samadi, R. Noroozi

Abstract:

The present work was conducted for the synthesis of nano size zerovalent iron (nZVI) and hexavalent chromium (Cr(VI)) removal as a highly toxic pollutant by using this nanoparticles. Batch experiments were performed to investigate the effects of Cr(VI), nZVI concentration, pH of solution and contact time variation on the removal efficiency of Cr(VI). nZVI was synthesized by reduction of ferric chloride using sodium borohydrid. SEM and XRD examinations applied for determination of particle size and characterization of produced nanoparticles. The results showed that the removal efficiency decreased with Cr(VI) concentration and pH of solution and increased with adsorbent dosage and contact time. The Langmuir and Freundlich isotherm models were used for the adsorption equilibrium data and the Langmuir isotherm model was well fitted. Nanoparticle ZVI presented an outstanding ability to remove Cr(VI) due to high surface area, low particle size and high inherent activity.

Keywords: Adsorption, aqueous solution, Chromium, nZVI, removal.

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Authors: Aziza Benaboud, Alfred Rufer

Abstract:

In this paper the authors propose a flexible electronic solution, to improve the energetic efficiency of a thermo plant. This is achieved by replacing the mechanical gear box, placed traditionally between a gas turbine and a synchronous generator; by a power electronic converter. After reminding problematic of gear boxes and interest of a proposed electronic solution in high power plants, the authors describe a new control strategy for an indirect frequency converter, which is characterized by its high efficiency due to the use of SWM: Square Wave Modulation. The main advantage of this mode is the quasi absence of switching losses. A control method is also proposed to resolve some problems incurred by using square wave modulation, in particular to reduce the harmonics distortion of the output inverter voltage and current. Simulation examples as well as experimental results are included.

Keywords: Angle shift, high efficiency, indirect converter, gas turbine, NPC three level converter, square wave modulation SWM, switching angle.

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Authors: Julio Kauss, Miguel Cadillo, David Mauricio

Abstract:

E-commerce is a business model that allows companies to optimize the processes of buying, selling, transferring goods and exchanging services through computer networks or the Internet. In Peru, the electronic commerce is used infrequently. This situation is due, in part to the fact that there is no model that allows companies to implement an e-commerce solution, which means that most SMEs do not have adequate knowledge to adapt to electronic commerce. In this work, a reference model is proposed for the implementation of an e-commerce solution in Peruvian SMEs in the retail sector. It consists of five phases: Business Analysis, Business Modeling, Implementation, Post Implementation and Results. The present model was validated in a SME of the Peruvian retail sector through the implementation of an electronic commerce platform, through which the company increased its sales through the delivery channel by 10% in the first month of deployment. This result showed that the model is easy to implement, is economical and agile. In addition, it allowed the company to increase its business offer, adapt to e-commerce and improve customer loyalty.

Keywords: E-commerce, retail, SMEs, reference model.

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Authors: Nur Razia Mohd Suradi, Hema Subramaniam, Marina Hassan, Siti Fatimah Omar

Abstract:

Knowledge sharing culture contributes to a positive working environment. Currently, there is no platform for the Faculty of Industrial Information Technology (FIIT), Unisel academic staff to share knowledge among them. As it is done manually, the sharing process is through common meeting or by any offline discussions. There is no repository for future retrieval. However, with open source solution the development of knowledge based application may reduce the cost tremendously. In this paper we discuss about the domain on which this knowledge portal is being developed and also the deployment of open source tools such as JOOMLA, PHP programming language and MySQL. This knowledge portal is evidence that open source tools also reliable in developing knowledge based portal. These recommendations will be useful to the open source community to produce more open source products in future.

Keywords: Knowledge management, Portal, ContentManagement, JOOMLA.

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Authors: Sayeed Salam

Abstract:

An effort to develop a unit commitment approach capable of handling large power systems consisting of both thermal and hydro generating units offers a large profitable return. In order to be feasible, the method to be developed must be flexible, efficient and reliable. In this paper, various proposed methods have been described along with their strengths and weaknesses. As all of these methods have some sort of weaknesses, a comprehensive algorithm that combines the strengths of different methods and overcomes each other-s weaknesses would be a suitable approach for solving industry-grade unit commitment problem.

Keywords: Unit commitment, Solution methods, and Comprehensive algorithm.

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Authors: Diptendu Das, Vikas Kumar Rahi, V. A. Juvekar, R. Bhattacharya

Abstract:

Extraction of Fe(III) from aqueous solution using Trin- butyl Phosphate (TBP) as carrier needs a highly acidic medium (>6N) as it favours formation of chelating complex FeCl3.TBP. Similarly, stripping of Iron(III) from loaded organic solvents requires neutral pH or alkaline medium to dissociate the same complex. It is observed that TBP co-extracts acids along with metal, which causes reversal of driving force of extraction and iron(III) is re-extracted back from the strip phase into the feed phase during Liquid Emulsion Membrane (LEM) pertraction. Therefore, rate of extraction of different mineral acids (HCl, HNO3, H2SO4) using TBP with and without presence of metal Fe(III) was examined. It is revealed that in presence of metal acid extraction is enhanced. Determination of mass transfer coefficient of both acid and metal extraction was performed by using Bulk Liquid Membrane (BLM). The average mass transfer coefficient was obtained by fitting the derived model equation with experimentally obtained data. The mass transfer coefficient of the mineral acid extraction is in the order of kHNO3 = 3.3x10-6m/s > kHCl = 6.05x10-7m/s > kH2SO4 = 1.85x10-7m/s. The distribution equilibria of the above mentioned acids between aqueous feed solution and a solution of tri-n-butyl-phosphate (TBP) in organic solvents have been investigated. The stoichiometry of acid extraction reveals the formation of TBP.2HCl, HNO3.2TBP, and TBP.H2SO4 complexes. Moreover, extraction of Iron(III) by TBP in HCl aqueous solution forms complex FeCl3.TBP.2HCl while in HNO3 medium forms complex 3FeCl3.TBP.2HNO3

Keywords: Bulk Liquid Membrane (BLM) Transport, Iron(III) extraction, Tri-n-butyl Phosphate, Mass Transfer coefficient.

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Authors: József Valyon, Gábor Horváth

Abstract:

In comparison to the original SVM, which involves a quadratic programming task; LS–SVM simplifies the required computation, but unfortunately the sparseness of standard SVM is lost. Another problem is that LS-SVM is only optimal if the training samples are corrupted by Gaussian noise. In Least Squares SVM (LS–SVM), the nonlinear solution is obtained, by first mapping the input vector to a high dimensional kernel space in a nonlinear fashion, where the solution is calculated from a linear equation set. In this paper a geometric view of the kernel space is introduced, which enables us to develop a new formulation to achieve a sparse and robust estimate.

Keywords: Support Vector Machines, Least Squares SupportVector Machines, Regression, Sparse approximation.

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Authors: Onur Ayaz, Nuray Ucar, Elif Bahar, Oguzhan Ucar, Mustafa Oksuz, Aysen Onen, Mehmet Ucar, Ezgi İşmar, Ali Demir

Abstract:

In this study, single nozzle method used for electrospinning technique which composite polymer solution with cellulose nanowiskers (CNW) was treated by ultrasonic sonificator have been compared with coaxial (double) nozzle method, in terms of mechanical, thermal and morphological properties of composite nanofiber. The effect of water content in composite polymer solution on properties of nanofiber has also been examined. It has been seen that single nozzle method which polymer solution does not contain water has better results than that of coaxial method, in terms of mechanical, thermal and morphological properties of nanofiber. However, it is necessary to make an optimization study on setting condition of ultrasonic treatment to get better dispersion of CNW in composite nanofiber and to get better mechanical and thermal properties

Keywords: cellulose nanowhiskers, coaxial nozzle, composite nanofiber, electrospinning

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Authors: Pavel Pešout, Miroslav Andrle

Abstract:

Frauds in insurance industry are one of the major sources of operational risk of insurance companies and constitute a significant portion of their losses. Every reasonable company on the market aims for improving their processes of uncovering frauds and invests their resources to reduce them. This article is addressing fraud management area from the view of extension of existing Business Intelligence solution. We describe the frame of such solution and would like to share with readers all benefits brought to insurance companies by adopting this approach in their fight against insurance frauds.

Keywords: business intelligence, insurance fraud, fraudmanagement

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Authors: Mohammad Taghi Darvishi, Mohammad Najafi

Abstract:

This paper considers the (2+1)-dimensional breaking soliton equation in its bilinear form. Some exact solutions to this equation are explicitly derived by the idea of three-wave solution method with the assistance of Maple. We can see that the new idea is very simple and straightforward.

Keywords: Soliton solution, computerized symbolic computation, painleve analysis, (2+1)-dimensional breaking soliton equation, Hirota's bilinear form.

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Authors: Chun Wen, Tingzhu Huang

Abstract:

We present a new numerical method for the computation of the steady-state solution of Markov chains. Theoretical analyses show that the proposed method, with a contraction factor α, converges to the one-dimensional null space of singular linear systems of the form Ax = 0. Numerical experiments are used to illustrate the effectiveness of the proposed method, with applications to a class of interesting models in the domain of tandem queueing networks.

Keywords: Markov chains, tandem queueing networks, convergence, effectiveness.

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Authors: Zhijie Ma, Qinglin Zhao, Hongning Dai, Huan Zhang

Abstract:

This paper proposes an APPLE scheme that aims at providing absolute and proportional throughput guarantees, and maximizing system throughput simultaneously for wireless LANs with homogeneous and heterogenous traffic. We formulate our objectives as an optimization problem, present its exact and approximate solutions, and prove the existence and uniqueness of the approximate solution. Simulations validate that APPLE scheme is accurate, and the approximate solution can well achieve the desired objectives already.

Keywords: IEEE 802.11e, throughput guarantee, priority.

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Authors: Dimitar Georgiev, Bogdan Bogdanov, Yancho Hristov, Irena Markovska

Abstract:

In this study the adsorption of Cu (II) ions from aqueous solutions on synthetic zeolite NaA was evaluated. The effect of solution temperature and the determination of the kinetic parameters of adsorption of Cu(II) from aqueous solution on zeolite NaA is important in understanding the adsorption mechanism. Variables of the system include adsorption time, temperature (293- 328K), initial solution concentration and pH for the system. The sorption kinetics of the copper ions were found to be strongly dependent on pH (the optimum pH 3-5), solute ion concentration and temperature (293 – 328 K). It was found, the pseudo-second-order model was the best choice among all the kinetic models to describe the adsorption behavior of Cu(II) onto ziolite NaA, suggesting that the adsorption mechanism might be a chemisorptions process The activation energy of adsorption (Ea) was determined as Cu(II) 13.5 kJ mol-1. The low value of Ea shows that Cu(II) adsorption process by zeolite NaA may be an activated chemical adsorption. The thermodynamic parameters (ΔG0, ΔH0, and ΔS0) were also determined from the temperature dependence. The results show that the process of adsorption Cu(II) is spontaneous and endothermic process and rise in temperature favors the adsorption.

Keywords: Zeolite NaA, adsorption, adsorption capacity, kinetic sorption

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Authors: Suresh Thokchom, Partha Ghosh, Somnath Ghosh

Abstract:

This paper presents the findings of an experimental investigation to study the effect of alkali content in geopolymer mortar specimens exposed to sulphuric acid. Geopolymer mortar specimens were manufactured from Class F fly ash by activation with a mixture of sodium hydroxide and sodium silicate solution containing 5% to 8% Na2O. Durability of specimens were assessed by immersing them in 10% sulphuric acid solution and periodically monitoring surface deterioration and depth of dealkalization, changes in weight and residual compressive strength over a period of 24 weeks. Microstructural changes in the specimens were studied with Scanning electron microscopy (SEM) and EDAX. Alkali content in the activator solution significantly affects the durability of fly ash based geopolymer mortars in sulphuric acid. Specimens manufactured with higher alkali content performed better than those manufactured with lower alkali content. After 24 weeks in sulphuric acid, specimen with 8% alkali still recorded a residual strength as high as 55%.

Keywords: Alkali content, acid attack, compressive strength, geopolymer

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Authors: Me. Sistaninia, G.H.Farrahi, Ma. Sistaninia

Abstract:

Thermoelastic temperature, displacement, and stress in heat transfer during laser surface hardening are solved in Eulerian formulation. In Eulerian formulations the heat flux is fixed in space and the workpiece is moved through a control volume. In the case of uniform velocity and uniform heat flux distribution, the Eulerian formulations leads to a steady-state problem, while the Lagrangian formulations remains transient. In Eulerian formulations the reduction to a steady-state problem increases the computational efficiency. In this study also an analytical solution is developed for an uncoupled transient heat conduction equation in which a plane slab is heated by a laser beam. The thermal result of the numerical model is compared with the result of this analytical model. Comparing the results shows numerical solution for uncoupled equations are in good agreement with the analytical solution.

Keywords: Coupled thermoelasticity, Finite element, Laser surface hardening, Eulerian formulation.

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Authors: Yongxin Yuan

Abstract:

The problem of updating damped gyroscopic systems using measured modal data can be mathematically formulated as following two problems. Problem I: Given Ma ∈ Rn×n, Λ = diag{λ1, ··· , λp} ∈ Cp×p, X = [x1, ··· , xp] ∈ Cn×p, where p<n and both Λ and X are closed under complex conjugation in the sense that λ2j = λ¯2j−1 ∈ C, x2j = ¯x2j−1 ∈ Cn for j = 1, ··· , l, and λk ∈ R, xk ∈ Rn for k = 2l + 1, ··· , p, find real-valued symmetric matrices D,K and a real-valued skew-symmetric matrix G (that is, GT = −G) such that MaXΛ2 + (D + G)XΛ + KX = 0. Problem II: Given real-valued symmetric matrices Da, Ka ∈ Rn×n and a real-valued skew-symmetric matrix Ga, find (D, ˆ G, ˆ Kˆ ) ∈ SE such that Dˆ −Da2+Gˆ−Ga2+Kˆ −Ka2 = min(D,G,K)∈SE (D− Da2 + G − Ga2 + K − Ka2), where SE is the solution set of Problem I and · is the Frobenius norm. This paper presents an iterative algorithm to solve Problem I and Problem II. By using the proposed iterative method, a solution of Problem I can be obtained within finite iteration steps in the absence of roundoff errors, and the minimum Frobenius norm solution of Problem I can be obtained by choosing a special kind of initial matrices. Moreover, the optimal approximation solution (D, ˆ G, ˆ Kˆ ) of Problem II can be obtained by finding the minimum Frobenius norm solution of a changed Problem I. A numerical example shows that the introduced iterative algorithm is quite efficient.

Keywords: Model updating, iterative algorithm, gyroscopic system, partially prescribed spectral data, optimal approximation.

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