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A fourth-order accurate finite difference scheme for the extended-Fisher-Kolmogorov equation
Tlili Kadri,Khaled Omrani 대한수학회 2018 대한수학회보 Vol.55 No.1
In this paper, a nonlinear high-order difference scheme is proposed to solve the Extended-Fisher-Kolmogorov equation. The existence, uniqueness of difference solution and priori estimates are obtained. Furthermore, the convergence of the difference scheme is proved by utilizing the energy method to be of fourth-order in space and second-order in time in the discrete $L^{\infty}$-norm. Some numerical examples are given in order to validate the theoretical results.
A FOURTH-ORDER ACCURATE FINITE DIFFERENCE SCHEME FOR THE EXTENDED-FISHER-KOLMOGOROV EQUATION
Kadri, Tlili,Omrani, Khaled Korean Mathematical Society 2018 대한수학회보 Vol.55 No.1
In this paper, a nonlinear high-order difference scheme is proposed to solve the Extended-Fisher-Kolmogorov equation. The existence, uniqueness of difference solution and priori estimates are obtained. Furthermore, the convergence of the difference scheme is proved by utilizing the energy method to be of fourth-order in space and second-order in time in the discrete $L^{\infty}-norm$. Some numerical examples are given in order to validate the theoretical results.
Ali Tlili,Mongi Felhi,Nabil Fattah,Mabrouk Montacer 한국지질과학협의회 2011 Geosciences Journal Vol.15 No.1
Thick Ypresian marly clays and silica rich rocks constitute the so-called interbedded facies of phosphatic series, in the Gafsa-Metlaoui basin, southwestern Tunisia. Mineralogical and geochemical investigations are carried out on selected samples from Kef Eddour section. The data obtained by using X-ray diffraction (XRD), scanning electron microscopy (SEM), and Energy Dispersive X-ray microanalysis (EDX) and chemical analysis and IR of clay fractions indicate that the bulk rock samples are composed of cristobalite-tridymite and dolomite. Observation by SEM showed the occurrence of dolomite as a well-crystallized and a weathered shape. Whereas, cristobalite-tridymite observed in the cherty bed appears as a spheres, filling the pore spaces. However, samples which contain moderately a significant amount of feldspars, clinoptilolite and pyrite occur in the upper part of Kef Eddour section. Clay minerals consist mainly of smectite, palygorskite, and sepiolite. In this clay assemblages, the N-alkane (m/z = 57) distributions, revealed that organic matter has phytoplankton and bacterial origin. The Pristane/Phytane ratio indicated that the organic matter is deposited in a reduced environment. In this latter, sulfate-reducing bacteria generate hydrogen sulfur, which is incorporated on the organic biomolecules that occurred at the lower part of Kef Eddour section. However, the high Fe activity on the depositional environment favored the occurrence of pyrite in the upper part.
Ali Sghaier Tlili 제어·로봇·시스템학회 2017 International Journal of Control, Automation, and Vol.15 No.4
This paper proposes developing a H∞ dynamic output-feedback decentralized control design methodfor nonlinear interconnected systems subject to time-varying parameters and external disturbances. The designedcontroller is formulated as an optimization problem subject to linear matrix inequalities (LMIs) for the concurrentcomputation of the decentralized observation and control gains, and for the external disturbance mitigation by meansof a H∞ performance criterion minimization. The propounded optimization problem, designed in LMI conditions,is expeditiously resolved by a one-step procedure to override the conservatism generated by using many step-basedprocedures often used in the analysis and synthesis of interconnected systems. The effectiveness of the developedcontrol scheme is demonstrated through simulation results of multimachine power systems.
Fluoride removal from diluted solutions by Donnan dialysis using full factorial design
Ali Boubakri,Nawel Helali,Mohamed Tlili,Mohamed Ben Amor 한국화학공학회 2014 Korean Journal of Chemical Engineering Vol.31 No.3
Excessive fluoride concentration in potable water can lead to fluorosis of teeth and bones. In the presentstudy, Donnan dialysis (DD) is applied for the removal of fluoride ions from diluted sodium fluoride solutions. A fourfactor two level (24) full factorial design was used to investigate the influence of different physico-chemical parameterson fluoride removal efficiency (YF) and fluoride flux (JF) through anion exchange membrane. The statistical designdetermines factors which have the important effects on Donnan dialysis performance and studies all interactions amongthe considered parameters. The four significant factors were initial fluoride concentration, feed flow rate, temperatureand agitation speed. The experimental results and statistical analysis show that the temperature and agitation speedhave positive effects on fluoride removal efficiency and the initial fluoride concentration has a negative effect. In thecase of fluoride flux, feed flow rate and initial concentration are the main effect and all factors have a positive effect. The interaction between studied parameters was not negligible on two responses. A maximum fluoride removal of 75.52%was obtained under optimum conditions and the highest value of fluoride flux obtained was 2.4 mg/cm2·h. Empiricalregression models were also obtained and used to predict the flux and the fluoride removal profiles with satisfactoryresults.