Abstract. In this study, the adsorption of Ni(II) and Cu(II) ions from
aqueous solutions by powdered Delonix regia pods and leaves was investigated using batch
adsorption techniques. The effects of operating conditions such as pH,
contact time, adsorbent dosage, metal ion concentration and the presence of
sodium ions interfering with the sorption process were investigated. The
results obtained showed that equilibrium sorption was attained within 30 min of interaction, and an increase in the initial concentration of the
adsorbate, pH and adsorbent dosage led to an increase in the amount of Ni(II)
and Cu(II) ions adsorbed. The adsorption process followed the
pseudo-second-order kinetic model for all metal ions' sorption. The
equilibrium data fitted well with both the Langmuir and Freundlich
isotherms; the monolayer adsorption capacity (Q0 mg g−1) of the Delonix regia pods and
leaves was 5.88 and 5.77 mg g−1 for Ni(II) ions respectively and
9.12 and 9.01 mg g−1 for Cu(II) ions respectively. The efficiency of the
powdered pods and leaves of Delonix regia with respect to the removal of Ni(II) and Cu(II) ions was
greater than 80 %, except for the sorption of Ni(II) ions onto the leaves.
The desorption study revealed that the percentage of metal ions recovered
from the pods was higher than that recovered from the leaves at various nitric acid concentrations. This study proves that Delonix regia biomass, an agricultural waste product (“agro-waste”), could be
used to remove Ni(II) and Cu(II) ions from aqueous solution.
Interest rate paths experience discontinuities in the presence of certain factors. Much of the work on interest rate modelling has no consideration for effects of such unexpected occurrences in real life. A good risk manager needs to have a better model that considers possibility of unexpected occurrences. In this paper, we discuss step by step extension of Vasicek model to both jump model and jumpdiffusion model using Itô’s formula as the major tool. We also derive the greeks ‘delta’ and ‘vega’ that measure sensitivity of the interest rate with respect to both changes in its initial interest rate and volatility in an interbank rate.
In this article, a new implicit continuous block method is developed using the interpolation and collocation techniques via Power series as the basis function. A constant step length within a seven-step interval of integration was adopted. The selected grid points were evaluated to get a continuous linear multistep method. The evaluation of the continuous method at the non-interpolation points produces the discrete schemes which form the block. The basic properties of the block method were investigated and found to be consistent, zero stable and hence convergent. The new method was tested on real life problems namely: SIR and Growth model. The results were found to compare favourably with the existing methods in terms of accuracy and efficiency. Keywords: Block method, Growth Model, implicit, power series and SIR model.
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