Search results for: micellar solutions

Authors: S. Henine, A. Youkana

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This work is devoted to study the global existence and asymptotic behavior of solutions for Gierer-Meinhardt systems arising in biological phenomena. We prove that the solutions are global and uniformly bounded by a positive constant independent of the time. Our technique is based on Lyapunov functional argument. Under suitable conditions, we established a result on the asymptotic behavior of solutions. These results are valid for any positive continuous initial data, and improve some recently results established.

Keywords: asymptotic behavior, Gierer-Meinhardt systems, global existence, Lyapunov functional

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Authors: Flavia Smarrazzo

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Initial-boundary value problems for nonlinear parabolic equations having a Radon measure as initial data have been widely investigated, looking for solutions which for positive times take values in some function space. On the other hand, if the diffusivity degenerates too fast at infinity, it is well known that function-valued solutions may not exist, singularities may persist, and it looks very natural to consider solutions which, roughly speaking, for positive times describe an orbit in the space of the finite Radon measures. In this general framework, our purpose is to introduce a concept of measure-valued solution which is consistent with respect to regularizing and smoothing approximations, in order to develop an existence theory which does not depend neither on the level of degeneracy of diffusivity at infinity nor on the choice of the initial measures. In more detail, we prove existence of suitably defined measure-valued solutions to the homogeneous Dirichlet initial-boundary value problem for a class of nonlinear parabolic equations without strong coerciveness. Moreover, we also discuss some qualitative properties of the constructed solutions concerning the evolution of their singular part, including conditions (depending both on the initial data and on the strength of degeneracy) under which the constructed solutions are in fact unction-valued or not.

Keywords: degenerate parabolic equations, measure-valued solutions, Radon measures, young measures

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Authors: T. Boonraksa, B. Marungsri

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This paper presents the experimental results on role of ionic solutions affect water treeing propagation in cross-linked polyethylene insulation for high voltage cable. To study the water treeing expansion due to the ionic solutions, discs of 4mm thickness and 4cm diameter were taken from 115 kV XLPE insulation cable and were used as test specimen in this study. Ionic solutions composed of CuSO4, FeSO4, Na2SO4 and K2SO4 were used. Each specimen was immersed in 0.1 mole ionic solutions and was tested for 120 hrs. under a voltage stress at 7 kV AC rms, 1000 Hz. The results show that Na2SO4 and CuSO4solutions play an important role in the expansion of water treeing and cause degradation of the cross-linked polyethylene (XLPE) in the presence of the applied electric field.

Keywords: ionic solutions, water treeing, water treeing expansion, cross-linked polyethylene (XLPE)

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Authors: Shankar Kambhampaty, Harish Rohan Kambhampaty

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Data in IT systems in enterprises has been growing at a phenomenal pace. This has provided opportunities to run analytics to gather intelligence on key business parameters that enable them to provide better products and services to customers. While there are several artificial intelligence (AI/ML) and business intelligence (BI) tools and technologies available in the marketplace to run analytics, there is a need for an integrated view when developing intelligent solutions in enterprises. This paper progressively elaborates a reference model for enterprise solutions, builds an integrated view of data, information, and intelligence components, and presents a reference architecture for intelligent enterprise solutions. Finally, it applies the reference architecture to an insurance organization. The reference architecture is the outcome of experience and insights gathered from developing intelligent solutions for several organizations.

Keywords: architecture, model, intelligence, artificial intelligence, business intelligence, AI, BI, ML, analytics, enterprise

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Authors: Kamel Al-Khaled

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In this paper, numerical solutions for the nonlinear coupled Korteweg-de Vries, (abbreviated as KdV) equations are calculated by Sinc-collocation method. This approach is based on a global collocation method using Sinc basis functions. First, discretizing time derivative of the KdV equations by a classic finite difference formula, while the space derivatives are approximated by a $\theta-$weighted scheme. Sinc functions are used to solve these two equations. Soliton solutions are constructed to show the nature of the solution. The numerical results are shown to demonstrate the efficiency of the newly proposed method.

Keywords: Nonlinear coupled KdV equations, Soliton solutions, Sinc-collocation method, Sinc functions

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Authors: Nhabhat Chaimongkol

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Human capital is one of the factors that are vital for economic growth. This is especially true as humans will face increasingly more forms of disruptive technology in the near future. Therefore, there is a need to develop human capital in order to overcome the current uncertainty in the global economy and the future of jobs. In recent years, Thailand has increasingly devoted more attention to developing its human capital. The Thai government has raised this issue in its national agenda, which is part of its 20-year national strategy. Currently, there are multiple challenges and solutions regarding this issue. This study aims to find out what are the challenges and solutions to human capital development in Thailand. The research in this study uses mixed methods consisting of quantitative and qualitative research methods. The results show that while Thailand has many plans to develop human capital, it is still lacking the necessary actions and integrations that are required to achieve its goals. Finally, the challenges and solutions will be discussed in detail.

Keywords: challenges, human capital, solutions, Thailand

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Authors: Doo Ki Lee, Man Young Kim

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The Urea-Selective Catalytic Reduction (SCR) system is considered to be the most promising technology to fulfill the stringent emission regulation. In the Urea-SCR system, the urea solutions are used as the reducing agent, which is a eutectic composition (32.5wt% of urea). The advantage of this eutectic compositions is that it has a low freezing point approximately at -11 ℃, however, the problem of freezing occurs at low-temperature levels below that freezing point. To prevent freezing of urea solutions, we need heating systems that can melt by heating the frozen urea solutions in urea storage tank at low-temperature environment. In this study, therefore, a numerical investigation of three-dimensional unsteady heating problems analyzed to find the melting characteristics of the urea solutions on melting process. In this work, it can be found that the urea melting initiated by heat conduction from the heater is enhanced by the natural convection inside the melted liquid urea solutions due to the temperature difference. Also, liquid urea solutions are initially concentrated on the upper parts of the urea sender module.

Keywords: urea solution, melting, heat conduction, natural convection, liquid fraction, phase change

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Authors: Mehtap Lafcı

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In recent years, oscillation, periodicity and convergence of solutions of linear differential equations with piecewise constant arguments have been significantly considered but there are only a few papers for impulsive differential equations with piecewise constant arguments. In this paper, a first order nonlinear impulsive differential equation with piecewise constant arguments is studied and the existence of solutions and periodic solutions of this equation are investigated by using Carvalho’s method. Finally, an example is given to illustrate these results.

Keywords: Carvalho's method, impulsive differential equation, periodic solution, piecewise constant arguments

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Authors: D. Abid, A. Guettar, A. Toubane, A. Bouda, K. Daoud

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The aim of this work is to study coating formulations rheology. Fourteen solutions were prepared with Hydroxypropyl methylcellulose (HPMC) percentage which varies from 2 to 20 %, Ethyl cellulose (EC) percentage varying from 1 to 3 % and Titanium dioxide (TiO2) percentage which vary from 1 to 3%, Opadry solution (25%) was used as a reference for this study. Two behaviors appeared obviously ‘pseudo plastic’ and ‘dilatant’ related to the percentage of HPMC, this allowed us to define that HPMC is the polymer which influence the behavior of coating solutions.

Keywords: rheology, opadry, HPMC, B1-B6 tablets

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Authors: Yang-Kuei Lin, Yin-Yi Chou

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In this research, we have considered operating room scheduling problem. The objective is to minimize total operating cost. The total operating cost includes idle cost and overtime cost. We have proposed a dispatching rule that can guarantee to find feasible solutions for the studied problem efficiently. We compared the proposed dispatching rule with the optimal solutions found by solving Inter Programming, and other solutions found by using modified existing dispatching rules. The computational results indicates that the proposed heuristic can find near optimal solutions efficiently.

Keywords: assignment, dispatching rule, operation rooms, scheduling

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Authors: A. C. Amaro de Faria Jr, A. M. Canone

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Considering a scenario where our universe is taken as a 3d domain wall embedded in a 5d dimensional Minkowski space-time, we explore the existence of a richer class of solitonic solutions and their consequences for accelerating universes driven by collisions of bulk particle excitations with the walls. In particular it is shown that some of these solutions should play a fundamental role at the beginning of the expansion process. We present some of these solutions in cosmological scenarios that can be applied to models that describe the inflationary period of the Universe.

Keywords: solitons, topological defects, branes, kinks, accelerating universes in brane scenarios

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Authors: Mustafa Hasan Omar

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The destruction effect of hydrocarbon solutions on concrete besides its high permeability have led researchers to try to improve the performance of concrete exposed to these solutions, hence improving the durability and usability of oil concrete structures. Recently, polymer concrete is considered one of the most important types of concrete, and its behavior after exposure to oil products is still unknown. In the present work, an experimental study has been carried out, in which the prepared epoxy polymer concrete immersed in different types of hydrocarbon exposure solutions (gasoline, kerosene, and gas oil) for 120 days and compared with the reference concrete left in the air. The results for outdoor specimens indicate that the mechanical properties are increased after 120 days, but the specimens that were immersed in gasoline, kerosene, and gas oil for the same period show a reduction in compressive strength by -21%, -27% and -23%, whereas in splitting tensile strength by -19%, -24% and -20%, respectively. The reductions in ultrasonic pulse velocity for cubic specimens are -17%, -22% and -19% and in cylindrical specimens are -20%, -25% and -22%, respectively.

Keywords: epoxy resin, hydrocarbon solutions, mechanical properties, polymer concrete, ultrasonic pulse velocity

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Authors: Igor Izosimov

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This work is devoted to applications of the Time-resolved laser-induced luminescence (TRLIF) spectroscopy and time-resolved laser-induced chemiluminescence spectroscopy for detection of lanthanides and actinides. Results of the experiments on Eu, Sm, U, and Pu detection in solutions are presented. The limit of uranyl detection (LOD) in urine in our TRLIF experiments was up to 5 pg/ml. In blood plasma LOD was 0.1 ng/ml and after mineralization was up to 8pg/ml – 10pg/ml. In pure solution, the limit of detection of europium was 0.005ng/ml and samarium, 0.07ng/ml. After addition urine, the limit of detection of europium was 0.015 ng/ml and samarium, 0.2 ng/ml. Pu, Np, and some U compounds do not produce direct luminescence in solutions, but when excited by laser radiation, they can induce chemiluminescence of some chemiluminogen (luminol in our experiments). It is shown that multi-photon scheme of chemiluminescence excitation makes chemiluminescence not only a highly sensitive but also a highly selective tool for the detection of lanthanides/actinides in solutions.

Keywords: actinides/lanthanides detection, laser spectroscopy with time resolution, luminescence/chemiluminescence, solutions

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Authors: Muna Alghabshi, Edmana Krishnan

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A nonlinear Schrodinger equation has been considered for solving by mapping methods in terms of Jacobi elliptic functions (JEFs). The equation under consideration has a linear evolution term, linear and nonlinear dispersion terms, the Kerr law nonlinearity term and three terms representing the contribution of meta materials. This equation which has applications in optical fibers is found to have soliton solutions, shock wave solutions, and singular wave solutions when the modulus of the JEFs approach 1 which is the infinite period limit. The equation with special values of the parameters has also been solved using the tanh method.

Keywords: Jacobi elliptic function, mapping methods, nonlinear Schrodinger Equation, tanh method

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Authors: Xu Runzhang, Yang Yanbing, Niu Yi, Zhang Mingyou, Liu Yu

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For a class of semilinear parabolic equations with linear dynamical boundary conditions in a bounded domain, we obtain both global solutions and finite time blow-up solutions when the initial data varies in the phase space H1(Ω). Our main tools are the comparison principle, the potential well method and the concavity method. In particular, we discuss the behavior of the solutions with the initial data at critical and high energy level.

Keywords: high energy level, critical energy level, linear dynamical boundary condition, semilinear parabolic equation

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Authors: Geraldine O’Neill

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Work-integrated learning is a valuable learning experience for students in higher education. However, the fairness of the assessment process has been identified as a challenge. This study explored solutions to this challenge through interviews with expert authors in the field and workshops across nine different disciplines in Ireland. In keeping with the use of a participatory and action research methodology, the key stakeholders in the process, the students, educators, and practitioners, identified some solutions. The solutions included the need to: clarify the assessments’ expectations; enhance the flexibility of the competencies, reduce the number of competencies; use grading scales with lower specificity; support practitioner training, and empower students in the assessment process. The results are discussed as they relate to interactional, procedural, and distributive fairness.

Keywords: competencies, fairness, grading scales, work-integrated learning

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Authors: Angelo I. Aquino, Luis Ma. T. Bo-ot

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We use the Homotopy Analysis Method (HAM) to solve the system of equations modeling the two-level system and extract results which will pinpoint to turbulent behavior. We look at multi-valued solutions as indicative of turbulence or turbulent-like behavior. We take dierent specic cases which result in multi-valued velocities. The solutions are in series form and application of HAM ensures convergence in some region.

Keywords: multivalued solutions, homotopy analysis method, two-level system, equation

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Authors: Mario Calabrese, Francesca Iandolo, Pietro Vito, Raffaele D'Amore, Francesco Caputo

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This article presents a synopsis of Nature-Based Solutions (NBS), a fresh and emerging concept in mitigating and adapting to climate change. It outlines a classification of NBS, from the least intrusive to the most advanced engineering, and provides illustrations of each. Moreover, it gives an overview of the 'Life Metro Adapt' initiative, which dealt with the climatic challenges faced by the Milan Metropolitan City and encouraged the development of climate change adaptation methods using alternative, nature-focused solutions. Lastly, the article emphasizes the necessity of raising awareness about environmental issues to ensure that NBS becomes a regular practice today and can be refined in the future.

Keywords: nature-based solutions, urban resilience, climate change adaptation, life metro adapt initiative

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Authors: Abderrahim Siam, Ramdane Maamri, Zaidi Sahnoun

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The development of adaptive user interfaces (UI) presents for a long time an important research area in which researcher attempt to call upon the full resources and skills of several disciplines. The adaptive UI community holds a thorough knowledge regarding the adaptation of UIs with users and with contexts of use. Several solutions, models, formalisms, techniques, and mechanisms were proposed to develop adaptive UI. In this paper, we propose an approach based on the fuzzy set theory for modeling the concept of the appropriateness of different solutions of UI adaptation with different situations for which interactive systems have to adapt their UIs.

Keywords: adaptive user interfaces, adaptation solution’s appropriateness, fuzzy sets

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Authors: Sh. Gofurov, O. Ismailova, U. Makhmanov, A. Kokhkharov

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The refractometric method has been used to determine optical properties of concentration features of aqueous solutions of ethanol, tetrahydrofuran and dimethylformamide at the room temperature. Changes in dielectric permittivity of aqueous solutions of ethanol, tetrahydrofuran and dimethylformamide in a wide range of concentrations (0÷1.0 molar fraction) have been studied using molecular dynamics method. The curves depending on the concentration of experimental data on excess refractive indices and excess dielectric permittivity were compared. It has been shown that stable heteromolecular complexes in binary solutions are formed in the concentration range of 0.3÷0.4 mole fractions. The real and complex part of dielectric permittivity was obtained from dipole-dipole autocorrelation functions of molecules. At the concentrations of C = 0.3 / 0.4 m.f. the heteromolecular structures with hydrogen bonds are formed. This is confirmed by the extremum values of excessive dielectric permittivity and excessive refractive index of aqueous solutions.

Keywords: refractometric method, aqueous solution, molecular dynamics, dielectric constant

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Authors: Palwinder Singh, Munish Sandhir, Tejinder Singh

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The ordinary differential equations (ODE) represent a natural framework for mathematical modeling of many real-life situations in the field of engineering, control systems, physics, chemistry and astronomy etc. Such type of differential equations can be solved by analytical methods or by numerical methods. If the solution is calculated using analytical methods, it is done through calculus theories, and thus requires a longer time to solve. In this paper, we compare the numerical accuracy of the solutions given by the three main types of one-step initial value solvers: Taylor’s Series Method, Euler’s Method and Runge-Kutta Fourth Order Method (RK4). The comparison of accuracy is obtained through comparing the solutions of ordinary differential equation given by these three methods. Furthermore, to verify the accuracy; we compare these numerical solutions with the exact solutions.

Keywords: Ordinary differential equations (ODE), Taylor’s Series Method, Euler’s Method, Runge-Kutta Fourth Order Method

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Authors: Zoran Visak, Joana Lopes, Vesna Najdanovic-Visak

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Within this study, the separation of nicotine from its aqueous solutions, using inorganic salt sodium chloride or ionic liquid (molten salt) ECOENG212® as salting-out media, was carried out. Thus, liquid-liquid equilibria of the ternary solutions (nicotine+water+NaCl) and (nicotine+water+ECOENG212®) were determined at ambient pressure, 0.1 MPa, at three temperatures. The related phase diagrams were constructed in two manners: by adding the determined cloud-points and by the chemical analysis of phases in equilibrium (tie-line data). The latter were used to calculate two important separation parameters - partition coefficients of nicotine and separation factors. The impacts of the initial compositions of the mother solutions and of temperature on the liquid-liquid phase separation and partition coefficients were analyzed and discussed. The results obtained clearly showed that both investigated salts are good salting-out media for the efficient and sustainable separation of nicotine from its solutions with water. However, when compared, sodium chloride exhibited much better separation performance than the ionic liquid.

Keywords: nicotine, liquid-liquid separation, inorganic salt, ionic liquid

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Authors: Jay Xiong, Li Lin

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Existing software modeling and visualization approaches using UML are outdated, which are outcomes of reductionism and the superposition principle that the whole of a system is the sum of its parts, so that with them all tasks of software modeling and visualization are performed linearly, partially, and locally. This paper introduces revolutionary solutions for modeling and visualization of complex software systems, which make complex software systems much easy to understand, test, and maintain. The solutions are based on complexity science, offering holistic, automatic, dynamic, virtual, and executable approaches about thousand times more efficient than the traditional ones.

Keywords: complex systems, software maintenance, software modeling, software visualization

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Authors: Elena M. Kopteva, Pavlina Jaluvkova, Zdenek Stuchlik

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In spite of the numerous attempts to close the discussion about the influence of cosmological expansion on local gravitationally bounded systems, this question arises in literature again and again and remains still far from its final resolution. Here one of the main problems is the problem of obtaining a physically adequate model of strongly gravitating object immersed in non-static cosmological background. Such objects are usually called ‘cosmological’ black holes and are of great interest in wide set of cosmological and astrophysical areas. In this work the set of new exact solutions of the Einstein equations is derived for the flat space that generalizes the known Lemaitre-Tolman-Bondi solution for the case of nonzero pressure. The solutions obtained are pretending to describe the black hole immersed in nonstatic cosmological background and give a possibility to investigate the hot problems concerning the effects of the cosmological expansion in gravitationally bounded systems, the structure formation in the early universe, black hole thermodynamics and other related problems. It is shown that each of the solutions obtained contains either the Reissner-Nordstrom or the Schwarzschild black hole in the central region of the space. It is demonstrated that the approach of the mass function use in solving of the Einstein equations allows clear physical interpretation of the resulting solutions, that is of much benefit to any their concrete application.

Keywords: exact solutions of the Einstein equations, cosmological black holes, generalized Lemaitre-Tolman-Bondi solutions, nonzero pressure

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Authors: Arash Esmaeili, Zhibang Liu, Yang Xiang, Jimmy Yun, Lei Shao

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A high pressure carbon dioxide (CO₂) absorption from a specific gas in a conventional column has been evaluated by the Aspen HYSYS simulator using a wide range of single absorbents and blended solutions to estimate the outlet CO₂ concentration, absorption efficiency and CO₂ loading to choose the most proper solution in terms of CO₂ capture for environmental concerns. The property package (Acid Gas-Chemical Solvent) which is compatible with all applied solutions for the simulation in this study, estimates the properties based on an electrolyte non-random two-liquid (E-NRTL) model for electrolyte thermodynamics and Peng-Robinson equation of state for the vapor and liquid hydrocarbon phases. Among all the investigated single amines as well as blended solutions, piperazine (PZ) and the mixture of piperazine and monoethanolamine (MEA) have been found as the most effective absorbents respectively for CO₂ absorption with high reactivity based on the simulated operational conditions.

Keywords: absorption, amine solutions, Aspen HYSYS, carbon dioxide, simulation

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Authors: Turan Çalban, Oral Laçin, Abdüsselam Kurtbaş

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The experimental production methods Chevreul’s salt being a intermediate stage product for copper recovery were investigated by dealing with the articles written on this topic. Chevreul’s salt, Cu2SO3.CuSO3.2H2O, being a mixed valence copper sulphite compound has been obtained by using different methods and reagents. Chevreul’s salt has a intense brick-red color. It is a highly stable and expensive salt. The production of Chevreul’s salt plays a key role in hiydrometallurgy. In recent years, researchs on this compound have been intensified. Silva et al. reported that this salt is thermally stable up to 200oC. Çolak et al. precipitated the Chevreul’s salt by using ammonia and sulphur dioxide. Çalban et al. obtained at the optimum conditions by passing SO2 from leach solutions with NH3-(NH4)2SO4. Yeşiryurt and Çalban investigated the optimum precipitation conditions of Chevreul’s salt from synthetic CuSO4 solutions including Na2SO3. Çalban et al. achieved the precipitation of Chevreul’s salt at the optimum conditions by passing SO2 from synthetic CuSO4 solutions. Çalban et al. examined the precipitation conditions of Chevreul’s salt using (NH4)2SO3 from synthetic aqueous CuSO4 solutions. In light of these studies, it can be said that Chevreul’s salt can be produced practically from both a leach solutions including copper and synthetic CuSO4 solutions.

Keywords: Chevreul’s salt, ammonia, copper sulpfite, sodium sülfite, optimum conditions

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Authors: Hussaini Doko Ibrahim, Hamilton Cyprian Chinwenyi, Henrietta Nkem Ude

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In this paper, efforts were made to examine and compare the algorithmic iterative solutions of the conjugate gradient method as against other methods such as Gauss-Seidel and Jacobi approaches for solving systems of linear equations of the form Ax=b, where A is a real n×n symmetric and positive definite matrix. We performed algorithmic iterative steps and obtained analytical solutions of a typical 3×3 symmetric and positive definite matrix using the three methods described in this paper (Gauss-Seidel, Jacobi, and conjugate gradient methods), respectively. From the results obtained, we discovered that the conjugate gradient method converges faster to exact solutions in fewer iterative steps than the two other methods, which took many iterations, much time, and kept tending to the exact solutions.

Keywords: conjugate gradient, linear equations, symmetric and positive definite matrix, gauss-seidel, Jacobi, algorithm

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Authors: Mehdi Asgarkhani

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Today, investment on Information Technology (IT) solutions in most organizations is the largest component of capital expenditure. As capital investment on IT continues to grow, IT managers and strategists are expected to develop and put in practice effective decision making models (frameworks) that improve decision-making processes for the use of IT in organizations and optimize the investment on IT solutions. To be exact, there is an expectation that organizations not only maximize the benefits of adopting IT solutions but also avoid the many pitfalls that are associated with rapid introduction of technological change. Different organizations depending on size, complexity of solutions required and processes used for financial management and budgeting may use different techniques for managing strategic investment on IT solutions. Decision making processes for strategic use of IT within organizations are often referred to as IT Governance (or Corporate IT Governance). This paper examines IT governance - as a tool for best practice in decision making about IT strategies. Discussions in this paper represent phase I of a project which was initiated to investigate trends in strategic decision making on IT strategies. Phase I is concerned mainly with review of literature and a number of case studies, establishing that the practice of IT governance, depending on the complexity of IT solutions, organization's size and organization's stage of maturity, varies significantly – from informal approaches to sophisticated formal frameworks.

Keywords: IT governance, corporate governance, IT governance frameworks, IT governance components, aligning IT with business strategies

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Authors: Stavros Poulopoulos, Aphrodite Tetorou, Constantine Philippopoulos

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Day after day more pharmaceutical compounds that are not efficiently removed by conventional treatment methods are found in treated wastewaters and drinking waters. Due to their refractory nature, they escape conventional wastewater treatment facilities, and thus advanced oxidation processes have to be utilized to effectively eliminate them. In the present study, the removal of Ibuprofen from aqueous solutions containing the commercial drug Algofren (non-steroidal, anti-inflammatory) using UV irradiation, hydrogen peroxide, titanium dioxide and ferric ions was examined. All experiments were conducted in a batch photoreactor operated for 120 min. The main target was to select the most effective operating conditions for the mineralization of the solutions treated. The combination of Fe(III)/ H₂O₂/UV proved to be very efficient in terms of total organic carbon removal and ibuprofen conversion. For solutions containing 5 mg/L ibuprofen and initial total carbon 51.1 mg/L, complete mineralization was achieved by means of 2.2 ppm Fe(III) and 333 mg/L H₂O₂.

Keywords: pharmaceuticals, photocatalytic, photo-Fenton, TiO₂

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Authors: Muhammad Danish Khan, Imran Naeem, Mudassar Imran

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In this article, we study time-space Fractional Advection-Dispersion (FADE) equation and time-space Fractional Whitham-Broer-Kaup (FWBK) equation that have a significant role in hydrology. We introduce suitable transformations to convert fractional order derivatives to integer order derivatives and as a result these equations transform into Partial Differential Equations (PDEs). Then the Lie symmetries and corresponding optimal systems of the resulting PDEs are derived. The symmetry reductions and exact independent solutions based on optimal system are investigated which constitute the exact solutions of original fractional differential equations.

Keywords: modified Riemann-Liouville fractional derivative, lie-symmetries, optimal system, invariant solutions

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