Search results for: kinetic equation

Authors: Amina Ramdani, Abdelkader Kadeche, Zoubida Taleb, Safia Taleb

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The aim of this present study is to evaluate the adsorption capacity of a dye, Malachite green, on a local Algerian montmorillonite clay mineral (raw, purified and Cr-pillared). Various parameters influencing the dye adsorption process ie contact time, adsorbent dose, initial concentration of dye, pH of the solution and temperature. Cr pillared clay has been obtained with a better surface character than purified and natural clay. An increase in basal spacing from 12.45 Å (Mont-Na) to 22.88 Å (Mont-PLCr), surface area from 67 m2 /g (Mont-Na) to 102 m2 /g (Mont-PLCr). The experimental results show that the dye adsorption kinetic were fast: 5 min for Cr-pillared clay mineral, and 30 min for raw and purified clay mineral (RC and Mont-Na). The removal efficiency on Mont-PLCr (98.64%) is greater than that of Mont-Na (86.20%) and RC (82.09%). The acidity and basicity of the medium considerably affect the adsorption of the dye. It attained its maximum at pH 4.8. The equilibrium and kinetic data were found to fit well the Langmuir model and the pseudo-second-order model.

Keywords: Dye removal, pillared clay, isotherm, kinetic

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Authors: Mishu Gupta, Rama Gupta

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It has been elucidated here that non- autonomous discrete non-linear Schrödinger equation is associated with saturable non-linearity through photo-refractive media. We have investigated the localized solution of non-autonomous saturable discrete non-linear Schrödinger equations. The similarity transformation has been involved in converting non-autonomous saturable discrete non-linear Schrödinger equation to constant-coefficient saturable discrete non-linear Schrödinger equation (SDNLSE), whose exact solution is already known. By back substitution, the solution of the non-autonomous version has been obtained. We have analysed our solution for the hyperbolic and periodic form of gain/loss term, and interesting results have been obtained. The most important characteristic role is that it helps us to analyse the propagation of electromagnetic waves in glass fibres and other optical wave mediums. Also, the usage of SDNLSE has been seen in tight binding for Bose-Einstein condensates in optical mediums. Even the solutions are interrelated, and its properties are prominently used in various physical aspects like optical waveguides, Bose-Einstein (B-E) condensates in optical mediums, Non-linear optics in photonic crystals, and non-linear kerr–type non-linearity effect and photo refracting medium.

Keywords: B-E-Bose-Einstein, DNLSE-Discrete non linear schrodinger equation, NLSE-non linear schrodinger equation, SDNLSE - saturable discrete non linear Schrodinger equation

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Authors: Ch. Surawut, D. Sukawat

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In order to utilize results from global climate models, dynamical and statistical downscaling techniques have been developed. For dynamical downscaling, usually a limited area numerical model is used, with associated high computational cost. This research proposes dynamic equation for specific space-time regional climate downscaling from the Educational Global Climate Model (EdGCM) for Southeast Asia. The equation is for surface air temperature. These equations provide downscaling values of surface air temperature at any specific location and time without running a regional climate model. In the proposed equations, surface air temperature is approximated from ground temperature, sensible heat flux and 2m wind speed. Results from the application of the equation show that the errors from the proposed equations are less than the errors for direct interpolation from EdGCM.

Keywords: dynamic equation, downscaling, inverse distance, weight interpolation

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Authors: B. Guezzen, M. A. Didi, B. Medjahed

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An organoclay (HDTMA-B) was prepared from sodium bentonite (Na-B). The starting material was modified using the hexadecyltrimethylammonium ion (HDTMA⁺) in the amounts corresponding to 100 % of the CEC value. Batch experiments were carried out in order to model and optimize the sorption of Congo red dye from aqueous solution. The pseudo-first order and pseudo-second order kinetic models have been developed to predict the rate constant and the sorption capacity at equilibrium with the effect of temperature, the solid/solution ratio and the initial dye concentration. The equilibrium time was reached within 60 min. At room temperature (20 °C), optimum dye sorption of 49.4 mg/g (98.9%) was achieved at pH 6.6, sorbent dosage of 1g/L and initial dye concentration of 50 mg/L, using surfactant modified bentonite. The optimization of adsorption parameters mentioned above on dye removal was carried out using Box-Behnken design. The sorption parameters were analyzed statistically by means of variance analysis by using the Statgraphics Centurion XVI software.

Keywords: adsorption, dye, factorial design, kinetic, organo-bentonite

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Authors: Jawad Zakir, Syed Irtiza Ali Shah, Rana Shaharyar, Sidra Mahmood

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Y-force equation comprises aerodynamic forces, drag and side force with side slip angle β and weight component along with the coupled roll (φ) and pitch angles (θ). This research deals with the linearization of Y-force equation using Small Disturbance theory assuming equilibrium flight conditions for different state variables of aircraft. By using assumptions of Small Disturbance theory in non-linear Y-force equation, finally reached at linearized lateral rigid body equation of motion; which says that in linearized Y-force equation, the lateral acceleration is dependent on the other different aerodynamic and propulsive forces like vertical tail, change in roll rate (Δp) from equilibrium, change in yaw rate (Δr) from equilibrium, change in lateral velocity due to side force, drag and side force components due to side slip, and the lateral equation from coupled rotating frame to decoupled rotating frame. This paper describes implementation of this lateral linearized equation for aircraft control systems. Another significant parameter considered on which y-force equation depends is ‘c’ which shows that any change bought in the weight of aircrafts wing will cause Δφ and cause lateral force i.e. Y_c. This simplification also leads to lateral static and dynamic stability. The linearization of equations is required because much of mathematics control system design for aircraft is based on linear equations. This technique is simple and eases the linearization of the rigid body equations of motion without using any high-speed computers.

Keywords: Y-force linearization, small disturbance theory, side slip, aerodynamic force drag, lateral rigid body equation of motion

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Authors: Jorge Gonzalez Camus, Valentin Keyantuo, Mahamadi Warma

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In this work, we obtain representation results for solutions of a time-fractional differential equation involving the discrete fractional Laplace operator in terms of generalized Wright functions. Such equations arise in the modeling of many physical systems, for example, chain processes in chemistry and radioactivity. The focus is on the linear problem of the simplified Moore - Gibson - Thompson equation, where the discrete fractional Laplacian and the Caputo fractional derivate of order on (0,2] are involved. As a particular case, we obtain the explicit solution for the discrete heat equation and discrete wave equation. Furthermore, we show the explicit solution for the equation involving the perturbed Laplacian by the identity operator. The main tool for obtaining the explicit solution are the Laplace and discrete Fourier transforms, and Stirling's formula. The methodology mainly is to apply both transforms in the equation, to find the inverse of each transform, and to prove that this solution is well defined, using Stirling´s formula.

Keywords: discrete fractional Laplacian, explicit representation of solutions, fractional heat and wave equations, fundamental

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Authors: Ilija Plecas, Dalibor Arbutina

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The leaching rate of 60Co from spent mix bead (anion and cation) exchange resins in a cement-bentonite matrix has been studied. Transport phenomena involved in the leaching of a radioactive material from a cement-bentonite matrix are investigated using three methods based on theoretical equations. These are: the diffusion equation for a plane source, an equation for diffusion coupled to a first order equation and an empirical method employing a polynomial equation. The results presented in this paper are from a 25-year mortar and concrete testing project that will influence the design choices for radioactive waste packaging for a future Serbian radioactive waste disposal center.

Keywords: cement, concrete, immobilization, leaching, permeability, radioactivity, waste

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Authors: Alireza Bahramian

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High-purity TiO₂ nanoparticles (NPs) with size ranging between 50 nm and 100 nm are synthesized from titanium slag through sulphate route under sonochemical procedure. The effect of dissolution parameters such as the sulfuric acid/slag weight ratio, caustic soda concentration, digestion temperature and time, and initial particle size of the dried slag on the extraction efficiency of TiO₂ and removal of iron are examined. By optimizing the digestion conditions, a rutile TiO₂ powder with surface area of 42 m²/g and mean pore diameter of 22.4 nm were prepared. A thermo-kinetic analysis showed that the digestion temperature has an important effect, while the acid/slag weight ratio and initial size of the slag has a moderate effect on the dissolution rate. The shrinking-core model including both chemical surface reaction and surface diffusion is used to describe the leaching process. A low value of activation energy, 38.12 kJ/mol, indicates the surface chemical reaction model is a rate-controlling step. The kinetic analysis suggested a first order reaction mechanism with respect to the acid concentrations.

Keywords: TiO₂ nanoparticles, titanium slag, dissolution rate, sonochemical method, thermo-kinetic study

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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: Rhoda Afriyie Mensah, Lin Jiang, Solomon Asante-Okyere, Xu Qiang, Cong Jin

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Flammability analysis of extruded polystyrene (XPS) has become crucial due to its utilization as insulation material for energy efficient buildings. Using the Kissinger-Akahira-Sunose and Flynn-Wall-Ozawa methods, the degradation kinetics of two pure XPS from the local market, red and grey ones, were obtained from the results of thermogravity analysis (TG) and microscale combustion calorimetry (MCC) experiments performed under the same heating rates. From the experiments, it was discovered that red XPS released more heat than grey XPS and both materials showed two mass loss stages. Consequently, the kinetic parameters for red XPS were higher than grey XPS. A comparative evaluation of activation energies from MCC and TG showed an insignificant degree of deviation signifying an equivalent apparent activation energy from both methods. However, different activation energy profiles as a result of the different chemical pathways were presented when the dependencies of the activation energies on extent of conversion for TG and MCC were compared.

Keywords: flammability, microscale combustion calorimetry, thermogravity analysis, thermal degradation, kinetic analysis

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Authors: Aid Asma, Dahdouh Nadjib, Amokrane Samira, Ladjali Samir, Nibou Djamel

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The present work has for main objective the elimination of the textile dye Maxilon Red (MR) by two processes, adsorption on activated clay followed by photocatalysis in presence of ZnO as a photocatalyst. The influence of the physical parameters like the initial pH, adsorbent dose of the activated clay, the MR concentration and temperature has been studied. The best adsorption yield occurs at neutral pH ~ 7 within 60 min with an uptake percentage of 97% for a concentration of 25 mg L⁻¹ and a dose of 0.5 g L⁻¹. The adsorption data were suitably fitted by the Langmuir model with a maximum capacity of 176 mg g⁻¹. The MR adsorption is well described by the pseudo second order kinetic. The second part of this work was dedicated to the photocatalytic degradation onto ZnO under solar irradiation of the residual MR concentration, remained after adsorption. The effect of ZnO dose and MR concentration has also been investigated. The parametric study showed that the elimination is very effective by this process, based essentially on the in situ generation of free radicals *OH which are non-selective and very reactive. The photodegradation process follows a first order kinetic model according to the Langmuir-Hinshelwood model.

Keywords: maxilon red, adsorption, photodegradation, ZnO, coupling

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Authors: Aziz Sezgin

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We consider the problem of stabilization of an unstable heat equation in a 2-D, 3-D and generally n-D domain by deriving a generalized backstepping boundary control design methodology. To stabilize the systems, we design boundary backstepping controllers inspired by the 1-D unstable heat equation stabilization procedure. We assume that one side of the boundary is hinged and the other side is controlled for each direction of the domain. Thus, controllers act on two boundaries for 2-D domain, three boundaries for 3-D domain and ”n” boundaries for n-D domain. The main idea of the design is to derive ”n” controllers for each of the dimensions by using ”n” kernel functions. Thus, we obtain ”n” controllers for the ”n” dimensional case. We use a transformation to change the system into an exponentially stable ”n” dimensional heat equation. The transformation used in this paper is a generalized Volterra/Fredholm type with ”n” kernel functions for n-D domain instead of the one kernel function of 1-D design.

Keywords: backstepping, boundary control, 2-D, 3-D, n-D heat equation, distributed parameter systems

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Authors: Naila Nasreen, Dianchen Lu

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This paper explores the dynamical behavior of the (2+1)-dimensional Boussinesq equation, which is a nonlinear water wave equation and is used to model wave packets in dispersive media with weak nonlinearity. This equation depicts how long wave made in shallow water propagates due to the influence of gravity. The (2+1)- dimensional Boussinesq equation combines the two-way propagation of the classical Boussinesq equation with the dependence on a second spatial variable, as that occurs in the two-dimensional Kadomstev- Petviashvili equation. This equation provides a description of head- on collision of oblique waves and it possesses some interesting properties. The governing model is discussed by the assistance of Ricatti equation mapping method, a relatively integration tool. The solutions have been extracted in different forms the solitary wave solutions as well as hyperbolic and periodic solutions. Moreover, the sensitivity analysis is demonstrated for the designed dynamical structural system’s wave profiles, where the soliton wave velocity and wave number parameters regulate the water wave singularity. In addition to being helpful for elucidating nonlinear partial differential equations, the method in use gives previously extracted solutions and extracts fresh exact solutions. Assuming the right values for the parameters, various graph in different shapes are sketched to provide information about the visual format of the earned results. This paper’s findings support the efficacy of the approach taken in enhancing nonlinear dynamical behavior. We believe this research will be of interest to a wide variety of engineers that work with engineering models. Findings show the effectiveness simplicity, and generalizability of the chosen computational approach, even when applied to complicated systems in a variety of fields, especially in ocean engineering.

Keywords: (2+1)-dimensional Boussinesq equation, solitary wave solutions, Ricatti equation mapping approach, nonlinear phenomena

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Authors: Yaping Zhao

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In the present study, the exact solutions for the steady response of quasi-linear systems under non-white wide-band random excitation are considered by means of the stochastic averaging method. The non linearity of the systems contains the power-law damping and the cross-product term of the power-law damping and displacement. The drift and diffusion coefficients of the Fokker-Planck-Kolmogorov (FPK) equation after averaging are obtained by a succinct approach. After solving the averaged FPK equation, the joint probability density function and the marginal probability density function in steady state are attained. In the process of resolving, the eigenvalue problem of ordinary differential equation is handled by integral equation method. Some new results are acquired and the novel method to deal with the problems in nonlinear random vibration is proposed.

Keywords: random vibration, stochastic averaging method, FPK equation, transition probability density

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Authors: Miroslaw Wendeker, Piotr Kacejko, Marcin Szlachetka, Mariusz Duk

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This paper discusses a model of fuel economy in a city bus driving in a dynamic urban environment. Rapid changes in speed result in a constantly changing kinetic energy accumulated in a bus mass and an increased fuel consumption due to hardly recuperated kinetic energy. The model is based on the bench test results achieved from chassis dynamometer, airport and city street researches. The verified model was applied to simulate the behavior of a bus during the Japanese JE05 Emission Test Cycle. The fuel consumption was calculated for three separate research stages, i.e. urban, downtown and motorway. The simulations were performed for several values of vehicle mass and electrical load applied to on-board devices. The research results show fuel consumption is impacted by driving dynamics.

Keywords: city bus, heavy duty vehicle, Japanese JE05 test cycle, kinetic energy

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Authors: Sumit Kumar Vishwakarma

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The aim of the paper is to investigate the influence of inhomogeneity associated with the elastic constants and density of the orthotropic medium. The inhomogeneity is considered as exponential function of depth. The impact of gravity had been discussed. Using the concept of separation of variables, the system of a partial differential equation (equation of motion) has been converted into ordinary differential equation, which is coupled in nature. It further reduces to a biquadratic equation whose roots were found by using MATLAB. A suitable boundary condition is employed to derive the dispersion equation in a closed-form. Numerical simulations had been performed to show the influence of the inhomogeneity parameter. It was observed that as the numerical values of increases, the phase velocity of Rayleigh waves decreases at a particular wavenumber. Graphical illustrations were drawn to visualize the effect of the increasing and decreasing values of the inhomogeneity parameter. It can be concluded that it has a remarkable bearing on the phase velocity as well as damping velocity.

Keywords: Rayleigh waves, orthotropic medium, gravity field, inhomogeneity

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Authors: Fahrudin Nugroho, Halim Hamadi, Yusril Yusuf, Pekik Nurwantoro, Ari Setiawan, Yoshiki Hidaka

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We investigate the Nikolaevskiy equation numerically using exponential time differencing method and pseudo-spectral method. This equation develops a long-wavelength modulation that behaves as a Nambu–Goldstone mode, and short-wavelength instability and exhibit turbulence. Using the autocorrelation analysis, the statistical properties of the turbulence governed by the equation are investigated. The autocorrelation then has been fitted with The Kohlrausch– Williams–Watts (KWW) expression. By varying the control parameter, we show a transition from compressed to stretched exponential for the auto-correlation function of Nikolaevskiy turbulence. The compressed exponential is an indicator of the existence of dynamical heterogeneity while the stretched indicates aging process. Thereby, we revealed the existence of dynamical heterogeneity and aging in the turbulence governed by Nikolaevskiy equation.

Keywords: compressed exponential, dynamical heterogeneity, Nikolaevskiy equation, stretched exponential, turbulence

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Authors: Onur Karaman, Ceren Karaman

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In this study, the adsorption of Methylene Blue (MB), a cationic dye, onto Orange Peel Derived Activated Carbon (OPAC) and chitosan(OPAC/Chitosan composite) composite (a low-cost absorbent) was carried out using a batch system. The composite was characterised using IR spectra, XRD, FESEM and Pore size studies. The effects of initial pH, adsorbent dose rate and initial dye concentration on the initial adsorption rate, capacity and dye removal efficiency were investigated. The Langmuir and Freundlich adsorption models were used to define the adsorption equilibrium of dye-adsorbent system mathematically and it was decided that the Langmuir model was more suitable to describe the adsorption equilibrium for the system. In addition, first order, second order and saturation type kinetic models were applied to kinetic data of adsorption and kinetic constants were calculated. It was concluded that the second order and the saturation type kinetic models defined the adsorption data more accurately. Finally, the evaluated thermodynamic parameters of adsorption show a spontaneous and exothermic behavior. Overall, this study indicates OPAC/Chitosan composite as an effective and low-cost adsorbent for the removal of MB dye from aqueous solutions.

Keywords: activated carbon, adsorption, chitosan, methylene blue, orange peel

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Authors: Norhashidah Hj Mohd Ali, Teng Wai Ping

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In this paper, the formulation of a new group explicit method with a fourth order accuracy is described in solving the two-dimensional Helmholtz equation. The formulation is based on the nine-point fourth-order compact finite difference approximation formula. The complexity analysis of the developed scheme is also presented. Several numerical experiments were conducted to test the feasibility of the developed scheme. Comparisons with other existing schemes will be reported and discussed. Preliminary results indicate that this method is a viable alternative high accuracy solver to the Helmholtz equation.

Keywords: explicit group method, finite difference, Helmholtz equation, five-point formula, nine-point formula

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Authors: Aria Ratmandanu

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Boson stars can be viewed as zero temperature ground state, Bose-Einstein condensates, characterized by enormous occupation numbers. Time-dependent spherically symmetric spacetime can be a model of Boson Star. We use (3+1) split of Einstein equation (ADM formulation of general relativity) to solve Einstein field equation coupled to a complex scalar field (Einstein-Klein-Gordon Equation) on time-dependent spherically symmetric spacetime, We get the result that Boson stars are pulsating stars with the frequency of oscillation equal to its density. We search for interior solution of Boson stars and get the T.O.V. (Tollman-Oppenheimer-Volkoff) equation for Boson stars. Using T.O.V. equation, we get the equation of state and the relation between pressure and density, its total mass and along with its gravitational Mass. We found that the hypothetical particle Axion could form a Boson star with the size of a milky way galaxy and make it a candidate for a dark galaxy, (a galaxy that consists almost entirely of dark matter).

Keywords: axion, boson star, dark galaxy, time-dependent spherically symmetric spacetime

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Authors: Sajad Haghanifar, Seyed-Farshid Kashani Bozorg

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Nano-crystalline Mg2Ni-based powder was produced by mechanical alloying technique using binary and ternary powder mixtures with stoichiometric compositions of Mg2Ni, Mg1.9C0.1Ni and Mg2C0.1Ni0.9. The structures and morphologies of the milled products were studied by XRD, SEM and HRTEM. Their electrochemical hydrogen storage characteristics were investigated in 6 M KOH solution. X-Ray diffraction, scanning and transmission electron microscopy of the milled products showed the formation of Mg2Ni-based nano-crystallites after 5, 15 and 30 h of milling using the initial powder mixtures of Mg1.9C0.1Ni, Mg2Ni and Mg2C0.1Ni0.9, respectively. It was found that partial substitution of C for Mg has beneficial effect on the formation kinetic of nano-crystalline Mg2Ni. Contrary to this, partial substitution of C for Ni was resulted in retardation of formation kinetic of nano-crystalline Mg2Ni. In addition, the negative electrode made from Mg1.9C0.1Ni ternary milled product after 30 hour of milling exhibited the highest initial discharge capacity and longest discharge life. Thus, partial substitution of C for Mg is beneficial to electrode properties of the Mg2Ni-based crystallites. The relation between the discharge capacity and cycling number of mechanically alloyed products was proposed on the basis of the fact that the degradation of discharge capacity was mainly caused by the oxidation of magnesium and nickel. The experimental data fitted the deduced equation well.

Keywords: Mg2Ni, hydrogen absorbing materials, electrochemical properties, nano-crystalline, amorphous, mechanical alloying, carbon

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Authors: Kitjapat Phuvoravan, Phattaraphong Ponsorn

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In the design of Castellated beams (CB), the web post buckling acted by horizontal shear force is one of the important failure modes that have to be considered. It is also a dominant governing mode when design following the AISC 31 design guideline which is just published. However, the equation of the web post buckling given by the guideline is still questionable for most of the engineers. So the purpose of this paper is to study and provide a proposed equation for design the web post buckling with more simplified and convenient to use. The study is also including the improper of the safety factor given by the guideline. The proposed design equation is acquired by regression method based on the results of finite element analysis. An amount of Cellular beam simulated to study is modelled by using shell element, analysis with both geometric and material nonlinearity. The results of the study show that the use of the proposed equation to design the web post buckling in Castellated beams is more simple and precise for computation than the equations provided from the guideline.

Keywords: castellated beam, web opening, web post buckling, design equation

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Authors: Olayiwola Moruf Oyedunsi

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This paper discusses the Modified Variational Iteration Method (MVIM) for the solution of nonlinear Burgers’ equation arising in longitudinal dispersion phenomena in fluid flow through porous media. The method is an elegant combination of Taylor’s series and the variational iteration method (VIM). Using Maple 18 for implementation, it is observed that the procedure provides rapidly convergent approximation with less computational efforts. The result shows that the concentration C(x,t) of the contaminated water decreases as distance x increases for the given time t.

Keywords: modified variational iteration method, Burger’s equation, porous media, partial differential equation

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Authors: Owamah Hilary, O. C. Izinyon

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Many existing biogas kinetic models are difficult to apply to substrates they were not developed for, as they are substrate specific. Biodegradability kinetic (BIK) model and maximum biogas production potential and stability assessment (MBPPSA) model were therefore developed in this study for the anaerobic co-digestion of food waste and maize husk. Biodegradability constant (k) was estimated as 0.11d-1 using the BIK model. The results of maximum biogas production potential (A) obtained using the MBPPSA model corresponded well with the results obtained using the popular but complex modified Gompertz model for digesters B-1, B-2, B-3, B-4, and B-5. The (If) value of MBPPSA model also showed that digesters B-3, B-4, and B-5 were stable, while B-1 and B-2 were unstable. Similar stability observation was also obtained using the modified Gompertz model. The MBPPSA model can therefore be used as alternative model for anaerobic digestion feasibility studies and plant design.

Keywords: biogas, inoculum, model development, stability assessment

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Authors: M. A. Sohaly, M. A. Elfouly

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Parkinson's disease (PD) is a heterogeneous movement disorder that often appears in the elderly. PD is induced by a loss of dopamine secretion. Some drugs increase the secretion of dopamine. In this paper, we will simply study the stability of PD models as a nonlinear delay differential equation. After a period of taking drugs, these act as positive feedback and increase the tremors of patients, and then, the differential equation has positive coefficients and the system is unstable under these conditions. We will present a set of suggested modifications to make the system more compatible with the biodynamic system. When giving a set of numerical examples, this research paper is concerned with the mathematical analysis, and no clinical data have been used.

Keywords: Parkinson's disease, stability, simulation, two delay differential equation

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Authors: Mohamed El Hattab

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The Supercritical carbon dioxide (SFE) and the focused microwave-assisted hydrodistillation (FMAHD) were employed to isolate the volatile fraction of the brown alga Dictyopteris membranacea from the crude extract. The volatiles fractions obtained were analyzed by GC/MS. The major compounds in this case: dictyopterene A, 6-butylcyclohepta-1,4-diene, Undec-1-en-3-one, Undeca-1,4-dien-3-one, (3-oxoundec-4-enyl) sulphur, tetradecanoic acid, hexadecanoic acid, 3-hexyl-4,5-dithia-cycloheptanone and albicanol (this later is present only in the FMAHD oil) are identified by comparing their mass spectra with those reported on the commercial MS data base and also on our previously work. A kinetic study realized on both extraction processes and followed by an external standard quantification has allowed the study of the mass percent evolution of the major compounds in the two oils, an empirical mathematical modelling was used to describe their kinetic extraction.

Keywords: dictyopteris membranacea, extraction techniques, mathematical modeling, volatile oils

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Authors: Elvis Adam Alhassan, Kaiyu Tian, Akos Konadu, Ernest Zamanah, Michael Jackson Adjabui, Ibrahim Justice Musah, Esther Agyeiwaa Owusu, Emmanuel K. A. Agyeman

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In this paper, how to solve simultaneous equations using the Elvis improved method is shown. The Elvis improved method says; to make one variable in the first equation the subject; make the same variable in the second equation the subject; equate the results and simplify to obtain the value of the unknown variable; put the value of the variable found into one equation from the first or second steps and simplify for the remaining unknown variable. The difference between our Elvis improved method and the substitution method is that: with Elvis improved method, the same variable is made the subject in both equations, and the two resulting equations equated, unlike the substitution method where one variable is made the subject of only one equation and substituted into the other equation. After describing the Elvis improved method, findings from 100 secondary students and the views of 5 secondary tutors to demonstrate the effectiveness of the method are presented. The study's purpose is proved by hypothetical examples.

Keywords: simultaneous equations, substitution method, elimination method, graphical method, Elvis improved method

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Authors: Ali Dehgan Moroozeh, B. Farhadi Bansouleh

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Evapotranspiration is one of the most important components of the hydrological cycle. Evapotranspiration (ETo) is an important variable in water and energy balances on the earth’s surface, and knowledge of the distribution of ET is a key factor in hydrology, climatology, agronomy and ecology studies. Many researchers have a valid relationship, which is a function of climate factors, to estimate the potential evapotranspiration presented to the plant water stress or water loss, prevent. The FAO-Penman method (PM) had been recommended as a standard method. This method requires many data and these data are not available in every area of world. So, other methods should be evaluated for these conditions. When sufficient or reliable data to solve the PM equation are not available then Hargreaves equation can be used. The Hargreaves equation (HG) requires only daily mean, maximum and minimum air temperature extraterrestrial radiation .In this study, Hargreaves method (HG) were evaluated in 12 stations in the North West region of Iran. Results of HG and M.HG methods were compared with results of PM method. Statistical analysis of this comparison showed that calibration process has had significant effect on efficiency of Hargreaves method.

Keywords: evapotranspiration, hargreaves, equation, FAO-Penman method

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Authors: A. Zerarka, W. Djoudi

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The method developed in this work uses a generalised coth and csch funtions method to construct new exact travelling solutions to the nonlinear lattice equation. The technique of the homogeneous balance method is used to handle the appropriated solutions.

Keywords: coth functions, csch functions, nonlinear partial differential equation, travelling wave solutions

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Authors: Ceren Efe, Hale Sütçü

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In this study, the pyrolysis of bituminous coal, peat and their blends formed by mixing various ratios of them were examined by thermogravimetric analysis method. Thermogravimetric analyses of peat, bituminous coal and their blends in the proportions of 25 %, 50 % and 75 % were performed at heating rate of 10 °C/min and from the room temperature until to 800 °C temperature, in a nitrogen atmosphere of 100 ml/min. Kinetic parameters for the pyrolysis process were calculated using Coats&Redfern kinetic model.

Keywords: bituminous coal, peat, pyrolysis, thermogravimetric analysis, Coats&Redfern

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