Sorptive potential of sunflower stem for Cr(III) ions from aqueous solutions and its kinetic and thermodynamic profile

The sorptive potential of sunflower stem (180-300 μm) for Cr(III) ions has been investigated in detail. The maximum sorption (≥85%) of Cr(III) ions (70.2 μM) has been accomplished using 30 mg of high density sunflower stem in 10 min from 0.001 M nitric and 0.0001 M hydrochloric acid solutions. The accumulation of Cr(III) ions on the sorbent follows Dubinin-Radushkevich (D-R), Freundlich and Langmuir isotherms. The isotherm yields D-R saturation capacity X_m = 1.60 ± 0.23 mmol g⁻¹, β = −0.00654 ± 0.00017 kJ² mol⁻², mean free energy E = 8.74 ± 0.12 kJ mol⁻¹, Freundlich sorption capacity K_F = 0.24 ± 0.11 mol g⁻¹, 1/n = 0.90 ± 0.04 and of Langmuir constant K_L = 6800 ± 600 dm³ mol⁻¹ and C_m = 120 ± 18 μmol g⁻¹. The variation of sorption with temperature (283-323 K) gives ΔH = −23.3 ± 0.8 kJ mol⁻¹, ΔS = −64.0 ± 2.7 J mol⁻¹ K⁻¹ and ΔG_298k = −4.04 ± 0.09 kJ mol⁻¹. The negative enthalpy and free energy envisage exothermic and spontaneous nature of sorption, respectively. Bisulphate, Fe(III), molybdate, citrate, Fe(II), Y(III) suppress the sorption significantly. The selectivity studies indicate that Cr(III), Eu(III) and Tb(III) ions can be separated from Tc(VII) and I(I). Sunflower stem can be used for the preconcentration and removal of Cr(III) ions from aqueous medium. This cheaper and novel sorbent has potential applications in analytical and environmental chemistry, in water decontamination, industrial waste treatment and in pollution abatement. A possible mechanism of biosorption of Cr(III) ions onto the sunflower stem has been proposed.     

Fullerene‐Catalyzed Reduction of Azo Derivatives in Water under UV Irradiation

Metal‐free fullerene (C₆₀) was found to be an effective catalyst for the reduction of azo groups in basic aqueous solution under UV irradiation in the presence of NaBH₄. Use of NaBH₄ by itself is not sufficient to reduce the azo dyes without the assistance of a metal catalyst such as Pd and Ag. Experimental and theoretical results suggest that C₆₀ catalyzes this reaction by using its vacant orbital to accept the electron in the bonding orbital of azo dyes, which leads to the activation of the N?N bond. UV irradiation increases the ability of C₆₀ to interact with electron‐donor moieties in azo dyes.     

On Difference Fields with Quantifier Elimination

This paper proves that a difference field (E, ) admits quantifierelimination if and only if E is an algebraically closed field,and is an integer power of the Frobenius automorphism. 1991Mathematics Subject Classification 03C60, 12H10.     

BEST PROXIMITY POINT THEOREMS FOR SINGLE- AND SET-VALUED NON-SELF MAPPINGS

We study the existence of best proximity points for single-valued non-self map-pings. Also, we prove a best proximity point theorem for set-valued non-self mappings in metric spaces with an appropriate geometric property. Examples are given to support the usability of our results.     

Solving nonlinear parabolic PDEs via extended hybrid BDF methods

The details of new methods based on backward differentiation formulas (BDF) for the MOL solution of one-dimensional nonlinear time dependent PDEs are presented. In these extended hybrid BDF methods, we say EHBDF, one additional stage point (or off-step point) together with one step point have been used in the first derivative of the solution. All presented methods, of order p, p = 2,3,..., 12, are A(α)-stable whereas they have wide stability regions comparing with those of some known methods such as BDF, extended BDF (EBDF) and modified EBDF (MEBDF) methods.     

Proximal Weakly Contractive and Proximal Nonexpansive Non-self-Mappings in Metric and Banach Spaces

In this work, we consider two classes of non-self-mappings, which are called proximal weakly contractive and proximal nonexpansive mappings, and study the existence of solutions of a minimization problem. Existence results of best proximity points for these two classes of non-self-mappings in metric and Banach spaces are also obtained.     

Forced Folding of a Disordered Protein Accesses an Alternative Folding Landscape

Intrinsically disordered proteins (IDPs) are involved in diverse cellular functions. Many IDPs can interact with multiple binding partners, resulting in their folding into alternative ligand‐specific functional structures. For such multi‐structural IDPs, a key question is whether these multiple structures are fully encoded in the protein sequence, as is the case in many globular proteins. To answer this question, here we employed a combination of single‐molecule and ensemble techniques to compare ligand‐induced and osmolyte‐forced folding of α‐synuclein. Our results reveal context‐dependent modulation of the protein′s folding landscape, suggesting that the codes for the protein′s native folds are partially encoded in its primary sequence, and are completed only upon interaction with binding partners. Our findings suggest a critical role for cellular interactions in expanding the repertoire of folds and functions available to disordered proteins.     

Electron–electron interaction induced spin thermalization in quasi-low-dimensional spin valves

We study the spin thermalization, i.e., the inter-spin energy relaxation mediated by electron–electron scattering in small spin valves. When one or two of the dimensions of the spin valve spacer are smaller than the thermal coherence length, the direct spin energy exchange rate diverges and needs to be regularized by the sample dimensions. Here we consider two model systems: a long quasi-1D wire and a thin quasi-2D sheet.     

New class of hybrid BDF methods for the computation of numerical solutions of IVPs

A new class of hybrid BDF-like methods is presented for solving systems of ordinary differential equations (ODEs) by using the second derivative of the solution in the stage equation of class 2 + 1hybrid BDF-like methods to improve the order and stability regions of these methods. An off-step point, together with two step points, has been used in the first derivative of the solution, and the stability domains of the new methods have been obtained by showing that these methods are A-stable for order p, p =?3,4,5,6,7and A(α)-stable for order p, 8 ≤ p ≤?14. The numerical results are also given for four test problems by using variable and fixed step-size implementations.