Search results for: Automated solution

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

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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

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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

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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

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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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Authors: Augustine Chioma Affam, Shamsul Rahman M. Kutty, Malay Chaudhuri

Abstract:

The feasibility of employing solar radiation for enhanced Fenton process in degradation of combined chlorpyrifos, cypermethrin and chlorothalonil pesticides was examined. The effect of various operating conditions of the process on biodegradability improvement and mineralization of the pesticides were also evaluated. The optimum operating conditions for treatment of aqueous solution containing 100, 50 and 250 mg L-1 chlorpyrifos cypermethrin and chlorothalonil, respectively were observed to be H2O2/COD molar ratio 2, H2O2/Fe2+ molar ratio 25 and pH 3. Under the optimum operating conditions, complete degradation of the pesticides occurred in 1 min. Biodegradability (BOD5/COD) increased from zero to 0.36 in 60 min, and COD and TOC removal were 74.19 and 58.32%, respectively in 60 min. Due to mineralization of organic carbon, decrease in ammonia-nitrogen from 22 to 4.3 mg L-1 and increase in nitrate from 0.7 to 18.1 mg L-1 in 60 min were recorded. The study indicated that solar photo-Fenton process can be used for pretreatment of chlorpyrifos, cypermethrin and chlorothalonil pesticides in aqueous solution for further biological treatment.

Keywords: Chlorpyrifos, Cypermethrin, Chlorothalonil, Solar photo-Fenton

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Authors: N. M. Kamoh, M. C. Soomiyol

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In this work, a five step continuous method for the solution of third order ordinary differential equations was developed in block form using collocation and interpolation techniques of the shifted Legendre polynomial basis function. The method was found to be zero-stable, consistent and convergent. The application of the method in solving third order initial value problem of ordinary differential equations revealed that the method compared favorably with existing methods.

Keywords: Shifted Legendre polynomials, third order block method, discrete method, convergent.

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Authors: Mpai Mokoena, Nsenda Lukumwena

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South Africa is one of the driest countries in the world and is facing a water crisis. In addition to inadequate infrastructure and poor planning, the country is experiencing high rates of water wastage due to pipe leaks. This study outlines the level of water wastage and develops a smart solution to efficiently manage and reduce the effects of pipe leaks, while monitoring the situation before and after fixing the pipe leaks. To understand the issue in depth, a literature review of journal papers and government reports was conducted. A questionnaire was designed and distributed to the general public. Additionally, the municipality office was contacted from a managerial perspective. The analysis from the study indicated that the majority of the citizens are aware of the water crisis and are willing to participate positively to decrease the level of water wasted. Furthermore, the response from the municipality acknowledged that more practical solutions are needed to reduce water wastage, and resources to attend to pipe leaks swiftly. Therefore, this paper proposes a specific solution for municipalities, local plumbers and citizens to minimize the effects of pipe leaks. The solution provides web and mobile application platforms to report and manage leaks swiftly. The solution is beneficial to the country in achieving water security and would promote a culture of responsibility toward water usage.

Keywords: Urban Distribution Networks, leak management, mobile application, responsible citizens, water crisis, water security.

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Authors: Nedjima Mouhoubi, Souad Sassi Boudemagh

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In this paper, we will try to demonstrate the importance of the project approach in the urban to deal with uncertainty, the importance of the involvement of all stakeholders in the urban project process and that the absence of an actor can lead to project failure but also the importance of the urban project management. These points are handled through the following questions: Does the urban adhere to the theory of complexity? Does the project approach bring hope and solution to make urban planning "sustainable"? How converging visions of actors for the same project? Is the management of urban project the solution to support the urban project approach?

Keywords: Strategic planning, project, urban project stakeholders, management.

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Authors: T. Moremedi, L. Katata-Seru, S. Sardar, A. Bandyopadhyay, E. Makhado, M. Joseph Hato

Abstract:

The rapid industrialisation and population growth have led to a steady fall in freshwater supplies worldwide. As a result, water systems are affected by modern methods upon use due to secondary contamination. The application of novel adsorbents derived from natural polymer holds a great promise in addressing challenges in water treatment. In this study, the UV irradiation technique was used to prepare acrylamide (AAm) monomer, and acrylic acid (AA) monomer grafted xanthan gum (XG) copolymer. Furthermore, the factors affecting rhodamine B (RhB) adsorption from aqueous media, such as pH, dosage, concentration, and time were also investigated. The FTIR results confirmed the formation of graft copolymer by the strong vibrational bands at 1709 cm^-1 and 1612 cm^-1 for AA and AAm, respectively. Additionally, more irregular, porous and wrinkled surface observed from SEM of XG-g-AAm/AA indicated copolymerization interaction of monomers. The optimum conditions for removing RhB dye with a maximum adsorption capacity of 313 mg/g at 25 ⁰C from aqueous solution were pH approximately 5, initial dye concentration = 200 ppm, adsorbent dose = 30 mg. Also, the detailed investigation of the isothermal and adsorption kinetics of RhB from aqueous solution showed that the adsorption of the dye followed a Freundlich model (R² = 0.96333) and pseudo-second-order kinetics. The results further indicated that this absorbent based on XG had the universality to remove dye through the mechanism of chemical adsorption. The outstanding adsorption potential of the grafted copolymer could be used to remove cationic dyes from aqueous solution as a low-cost product.

Keywords: Xanthan gum, adsorbents, rhodamine B, Freundlich model.

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Authors: N. Bachok, N. L. Aleng, N. M. Arifin, A. Ishak, N. Senu

Abstract:

The problem of laminar fluid flow which results from the shrinking of a permeable surface in a nanofluid has been investigated numerically. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. A similarity solution is presented which depends on the mass suction parameter S, Prandtl number Pr, Lewis number Le, Brownian motion number Nb and thermophoresis number Nt. It was found that the reduced Nusselt number is decreasing function of each dimensionless number.

Keywords: Boundary layer, Nanofluid, Shrinking sheet, Brownian motion, Thermophoresis, Similarity solution.

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Authors: L. Wong, H. Asrah, M.E. Rahman, M.A. Mannan

Abstract:

The storage of chemical fertilizers in concrete building often leads to durability problems due to chemical attack. The damage of concrete is mostly caused by certain ammonium salts. The main purpose of the research is to investigate the durability properties of concrete being exposed to ammonium nitrate solution. In this investigation, experiments are conducted on concrete type G50 and G60. The leaching process is achieved by the use of 20% concentration solution of ammonium nitrate. The durability properties investigated are water absorption, volume of permeable voids, and sorptivity. Compressive strength, pH value, and degradation depth are measured after a certain period of leaching. A decrease in compressive strength and an increase in porosity are found through the conducted experiments. Apart from that, the experimental data shows that pH value decreases with increased leaching time while the degradation depth of concrete increases with leaching time. By comparing concrete type G50 and G60, concrete type G60 is more resistant to ammonium nitrate attack.

Keywords: Normal weight concrete durability, Aggressive Ammonium Nitrate Solution, G50 & G60 concretes, Chemical attack.

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Authors: S. Sudhakar, Geetha Manjunath, Siva Teja Kakileti, Himanshu Madhu

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Diagnosis of breast cancer at early stages has seen better clinical and survival outcomes. Survival rates in developing countries like India are very low due to accessibility and affordability issues of screening tests such as Mammography. In addition, Mammography is not much effective in younger women with dense breasts. This leaves a gap in current screening methods. Thermalytix is a new technique for detecting breast abnormality in a non-contact, non-invasive way. It is an AI-enabled computer-aided diagnosis solution that automates interpretation of high resolution thermal images and identifies potential malignant lesions. The solution is low cost, easy to use, portable and is effective in all age groups.  This paper presents the results of a retrospective comparative analysis of Thermalytix over Mammography and Clinical Breast Examination for breast cancer screening. Thermalytix was found to have better sensitivity than both the tests, with good specificity as well. In addition, Thermalytix identified all malignant patients without palpable lumps.

Keywords: Breast Cancer Screening, Radiology, Thermalytix, Artificial Intelligence, Thermography.

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Authors: Nikol Žižková, Šárka Keprdová, Rostislav Drochytka

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The paper focuses on the study of the properties of cement-based composites produced using secondary crystallization (crystalline additive). In this study, cement mortar made with secondary crystallization was exposed to an aggressive environment and the influence of secondary crystallization on the degradation of the cementitious composite was investigated. The results indicate that the crystalline additive contributed to increasing the resistance of the cement-based composite to the attack of the selected environments (sodium sulphate solution and ammonium chloride solution).

Keywords: Secondary crystallization, cement-based composites, durability.

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Authors: Muhammad A.Rauf, I.Shehadeh, Amal Ahmed, Ahmed Al-Zamly

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Removal of Methylene Blue (MB) from aqueous solution by adsorbing it on Gypsum was investigated by batch method. The studies were conducted at 25°C and included the effects of pH and initial concentration of Methylene Blue. The adsorption data was analyzed by using the Langmuir, Freundlich and Tempkin isotherm models. The maximum monolayer adsorption capacity was found to be 36 mg of the dye per gram of gypsum. The data were also analyzed in terms of their kinetic behavior and was found to obey the pseudo second order equation.

Keywords: Adsorption, Dye, Gypsum, Kinetics, Methylene Blue.

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Authors: Jalil Rashidinia, Reza Jalilian

Abstract:

In this paper we use quintic non-polynomial spline functions to develop numerical methods for approximation to the solution of a system of fourth-order boundaryvalue problems associated with obstacle, unilateral and contact problems. The convergence analysis of the methods has been discussed and shown that the given approximations are better than collocation and finite difference methods. Numerical examples are presented to illustrate the applications of these methods, and to compare the computed results with other known methods.

Keywords: Quintic non-polynomial spline, Boundary formula, Convergence, Obstacle problems.

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Authors: Ghassan Kbar, Shady Aly, Ibraheem Elsharawy, Akshay Bhatia, Nur Alhasan, Ronaldo Enriquez

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The Smart Help for persons with disability (PWD) is a part of the project SMARTDISABLE which aims to develop relevant solution for PWD that target to provide an adequate workplace environment for them. It would support PWD needs smartly through smart help to allow them access to relevant information and communicate with other effectively and flexibly, and smart editor that assist them in their daily work. It will assist PWD in knowledge processing and creation as well as being able to be productive at the work place. The technical work of the project involves design of a technological scenario for the Ambient Intelligence (AmI) - based assistive technologies at the workplace consisting of an integrated universal smart solution that suits many different impairment conditions and will be designed to empower the Physically disabled persons (PDP) with the capability to access and effectively utilize the ICTs in order to execute knowledge rich working tasks with minimum efforts and with sufficient comfort level. The proposed technology solution for PWD will support voice recognition along with normal keyboard and mouse to control the smart help and smart editor with dynamic auto display interface that satisfies the requirements for different PWD group. In addition, a smart help will provide intelligent intervention based on the behavior of PWD to guide them and warn them about possible misbehavior. PWD can communicate with others using Voice over IP controlled by voice recognition. Moreover, Auto Emergency Help Response would be supported to assist PWD in case of emergency. This proposed technology solution intended to make PWD very effective at the work environment and flexible using voice to conduct their tasks at the work environment. The proposed solution aims to provide favorable outcomes that assist PWD at the work place, with the opportunity to participate in PWD assistive technology innovation market which is still small and rapidly growing as well as upgrading their quality of life to become similar to the normal people at the workplace. Finally, the proposed smart help solution is applicable in all workplace setting, including offices, manufacturing, hospital, etc.

Keywords: Ambient Intelligence, ICT, Persons with disability PWD, Smart application.

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Authors: Marko Niinimaki

Abstract:

Cryptocurrencies are getting increasingly popular, but very few of them can be conveniently used in daily mobile phone purchases. To solve this problem, we demonstrate how to build a functional prototype of a mobile cryptocurrency-based e-commerce application the communicates with Near-Field Communication (NFC) tags. Using the system, users are able to purchase physical items with an NFC tag that contains an e-commerce URL. The payment is done simply by touching the tag with a mobile device and accepting the payment. Our method is constructive: we describe the design and technologies used in the implementation and evaluate the security and performance of the solution. Our main finding is that the analysis and measurements show that our solution is feasible for e-commerce.

Keywords: Cryptocurrency, e-commerce, NFC, mobile devices.

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Authors: Changjin Xu

Abstract:

In this paper, using the Gaines and Mawhin,s continuation theorem of coincidence degree theory on time scales, the existence of periodic solutions for a two-prey one-predator system is studied. Some sufficient conditions for the existence of positive periodic solutions are obtained. The results provide unified existence theorems of periodic solution for the continuous differential equations and discrete difference equations.

Keywords: Time scales, competitive system, periodic solution, coincidence degree, topological degree.

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Authors: Zhouhong Li

Abstract:

In this paper, by applying Mawhin-s continuation theorem of coincidence degree theory, we study the existence of almost periodic solutions for neural multi-delay logarithmic population model and obtain one sufficient condition for the existence of positive almost periodic solution for the above equation. An example is employed to illustrate our result.

Keywords: Almost periodic solution, Multi-delay, Logarithmic population model, Coincidence degree.

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Authors: A. Giniatoulline

Abstract:

A nonlinear model of the mathematical fluid dynamics which describes the motion of an incompressible viscous rotating fluid in a homogeneous gravitational field is considered. The model is a generalization of the known Navier-Stokes system with the addition of the Coriolis parameter and the equations for changeable density. An explicit algorithm for the solution is constructed, and the proof of the existence and uniqueness theorems for the strong solution of the nonlinear problem is given. For the linear case, the localization and the structure of the spectrum of inner waves are also investigated.

Keywords: Galerkin method, Navier-Stokes equations, nonlinear partial differential equations, Sobolev spaces, stratified fluid.

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Authors: R. B. Ogunrinde

Abstract:

This paper presents the development, analysis and implementation of an inverse polynomial numerical method which is well suitable for solving initial value problems in first order ordinary differential equations with applications to sample problems. We also present some basic concepts and fundamental theories which are vital to the analysis of the scheme. We analyzed the consistency, convergence, and stability properties of the scheme. Numerical experiments were carried out and the results compared with the theoretical or exact solution and the algorithm was later coded using MATLAB programming language.

Keywords: Differential equations, Numerical, Initial value problem, Polynomials.

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Authors: H. Pahlavanzadeh, A.R.Jahangiri, I. Noshadi

Abstract:

In this paper, the solubility of CO2 in AMP solution have been measured at temperature range of ( 293, 303 ,313,323) K.The amine concentration ranges studied are (2.0, 2.8, and 3.4) M. A solubility apparatus was used to measure the solubility of CO2 in AMP solution on samples of flue gases from Thermal and Central Power Plants of Esfahan Steel Company. The modified Kent Eisenberg model was used to correlate and predict the vapor-liquid equilibria of the (CO2 + AMP + H2O) system. The model predicted results are in good agreement with the experimental vapor-liquid equilibrium measurements.

Keywords: AMP, Carbon dioxide; loading, Flue gases, Modified Kent Eisenberg model

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Authors: Chang Liu, Zishu He

Abstract:

Adaptive echo cancellers with two-path algorithm are applied to avoid the false adaptation during the double-talk situation. In the two-path algorithm, several transfer logic solutions have been proposed to control the filter update. This paper presents an improved transfer logic solution. It improves the convergence speed of the two-path algorithm, and allows the reduction of the memory elements and computational complexity. Results of simulations show the improved performance of the proposed solution.

Keywords: Acoustic echo cancellation, Echo return lossenhancement (ERLE), Two-path algorithm, Transfer logic

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Authors: W. Thepsuwan, N. Monmaturapoj

Abstract:

Calcium phosphate cement (CPC) is one of the most attractive bioceramics due to its moldable and shape ability to fill complicated bony cavities or small dental defect positions. In this study, CPC was produced by using mixture of tetracalcium phosphate (TTCP, Ca4O(PO4)2) and dicalcium phosphate anhydrous (DCPA, CaHPO4) in equimolar ratio (1/1) with aqueous solutions of acetic acid (C2H4O2) and disodium hydrogen phosphate dehydrate (Na2HPO4.2H2O) in combination with sodium alginate in order to improve theirs moldable characteristic. The concentration of the aqueous solutions and sodium alginate were varied to investigate the effect of different aqueous solutions and alginate on properties of the cements. The cement paste was prepared by mixing cement powder (P) with aqueous solution (L) in a P/L ratio of 1.0g/0.35ml. X-ray diffraction (XRD) was used to analyses phase formation of the cements. Setting time and compressive strength of the set CPCs were measured using the Gilmore apparatus and Universal testing machine, respectively. The results showed that CPCs could be produced by using both basic (Na2HPO4.2H2O) and acidic (C2H4O2) solutions. XRD results show the precipitation of hydroxyapatite in all cement samples. No change in phase formation among cements using difference concentrations of Na2HPO4.2H2O solutions. With increasing concentration of acidic solutions, samples obtained less hydroxyapatite with a high dicalcium phosphate dehydrate leaded to a shorter setting time. Samples with sodium alginate exhibited higher crystallization of hydroxyapatite than that of without alginate as a result of shorten setting time in a basic solution but a longer setting time in an acidic solution. The stronger cement was attained from samples using the acidic solution with sodium alginate; however the strength was lower than that of using the basic solution.

Keywords: Calcium phosphate cements, TTCP, DCPA, hydroxyapatite, properties.

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Authors: Mahmoud Zarrini, Sanaz Torkaman

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In this paper, we have proposed a numerical method for solving fuzzy Fredholm integral equation of the second kind. In this method a combination of orthonormal Bernstein and Block-Pulse functions are used. In most cases, the proposed method leads to the exact solution. The advantages of this method are shown by an example and calculate the error analysis.

Keywords: Fuzzy Fredholm Integral Equation, Bernstein, Block-Pulse, Orthonormal.

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Authors: Lv Yuhua

Abstract:

In this paper, by constructing a special cone and using fixed point theorem and fixed point index theorem of cone, we get the existence of positive solution for a class of singular eigenvalue value problems with p-Laplace operator, which improved and generalized the result of related paper.

Keywords: Cone, fixed point index, eigenvalue problem, p-Laplace operator, positive solutions.

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Authors: Meghal Desai, Jigisha Parikh

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Aggregation behavior of sodium salicylate and sodium cumene sulfonate was studied in aqueous solution at different temperature. Specific conductivity and relative viscosity were measured at different temperature to find minimum hydrotropic concentration. The thermodynamic parameters (free energy, enthalpy and entropy) were evaluated in the temperature range of 30°C-70°C. The free energy decreased with increase in temperature. The aggregation was found to be exothermic in nature and favored by positive value of entropy.

Keywords: Hydrotropes, Enthalpy, Entropy, Free Energy, Minimum Hydrotropic Concentration.

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Authors: Alberto Hananel

Abstract:

The aim of this work is to modelize the occlusion of a person with temporomandibular disorders as an evolutionary equation and approach its solution by the construction and characterizing of discrete variational splines. To formulate the problem, certain boundary conditions have been considered. After showing the existence and the uniqueness of the solution of such a problem, a convergence result of a discrete variational evolutionary spline is shown. A stress analysis of the occlusion of a human jaw with temporomandibular disorders by finite elements is carried out in FreeFem++ in order to prove the validity of the presented method.

Keywords: Approximation, evolutionary PDE, finite element method, temporomandibular disorders, variational spline.

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