Fluorine is a very common element in the Earth’s crust and is present in the air, food, and in natural waters. It never meets in the free state in nature due to its high reactivity, and it comes in the form of fluorides. Depending on the concentration of fluorine absorbed, it may be beneficial or harmful to human health. Similar to any trace element, fluoride ion is beneficial for the human body at low levels, but as soon as its concentration becomes too high, it is toxic, inducing dental and bone fluorosis. The lowering of fluoride concentrations that exceed the recommended standards in drinking water is practiced in various ways around the world. The adsorption process has been classified as one of the most efficient methods for the removal of fluoride from water as it is environmentally friendly, easy to operate, and cost-effective. The present study deals with fluoride ion adsorption on modified zeolite. There are several influential parameters, such as zeolite particle size, stirring rate, solution pH, initial concentration of fluoride, contact time, and solution temperature. The maximum removal efficiency of the modified zeolite adsorbent was 94% at 5 mg/L fluoride initial concentration, pH 6.3, and 0.5 g modified zeolite mass. The adsorption rate increases accordingly with increases in the stirring rate and pH value and decreases when the initial fluoride concentration is increased. The evaluation was enhanced by the study of adsorption isotherms using the Langmuir and Freundlich models. The Langmuir isotherm corresponds with the experimental results of the fluoride ions adsorption with a correlation value of 0.994. The kinetic analysis results of the fluoride ions adsorption on modified zeolite allowed us to demonstrate that the process primarily follows a pseudo-second-order and then, in the next step, follows a pseudo-first-order model. Thermodynamic parameters were calculated, and the ΔG° value is found to be in the range of −0.266 kJ/mol up to 1.613 kJ/mol amidst an increase in temperature from 298.2 to 331.7 K. The negative values of the free enthalpy ΔG° mean that the adsorption of fluoride ions on the modified zeolite is spontaneous, and the positive value of the enthalpy ∆H° shows that the adsorption process is endothermic. The ∆S° values of entropy indicate the fluoride adsorption randomness characteristics at the zeolite-solution interface.
Purpose -The purpose of this paper is to discuss a widespread idea in the financial literature: information in financial markets is free. Indeed, whenever an investor wants to intervene to purchase and/or to sell, he/she faces the need to access the information, which he/she judges to ensure an optimal decision. Design/methodology/approach -The paper uses the entropy statistics in order to estimate the information cost of the assets of the Tunisian stock market over the period extending from 2002 to 2005. Findings -The obtained results show that the information costs follow a Brownian motion. This finding lends empirical support to the theoretical position that has always been adopted in the relevant literature: in finance, as in economy, the majority of the series follow a Brownian motion. Practical implications -The proposed methodology offers investors the opportunity to estimate the information cost by taking into account the quotation probability, a simple approach that can be used not only by fund managers, but also by financial market investors. Originality/value -The paper uses entropy as a relatively new tool applied in financial theory. It offers a new understanding of information cost. The paper will be of interest for financial market investors and academics.
The aim of the current study is to investigate the spread of the COVID-19 pandemic as a multiphase percolation process. Mathematical equations have been developed to describe the time dependence of the number of cumulative infected individuals, , and the velocity of the pandemic, , as well as to calculate epidemiological characteristics. The study focuses on the use of sigmoidal growth models to investigate multiwave COVID-19. Hill, logistic dose response and sigmoid Boltzmann models fitted successfully a pandemic wave. The sigmoid Boltzmann model and the dose response model were found to be effective in fitting the cumulative number of COVID-19 cases over time 2 waves spread ( N = 2). However, for multiwave spread ( N > 2), the dose response model was found to be more suitable due to its ability to overcome convergence issues. The spread of N successive waves has also been described as multiphase percolation with a period of pandemic relaxation between two successive waves. Graphical abstract
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