A novel method for non-destructive Compton scatter imaging based on the genetic algorithm

Compton scattering tomography is widely used in numerous applications such as biomedical imaging, nondestructive industrial testing and environmental survey, etc. This paper proposes the use of the genetic algorithm (GA), which utilizes bio-inspired mathematical models, to construct an image of the insides of a test object via the scattered photons, from a voxel within the object. A NaI(Tl) scintillation detector and a 185 MBq ¹³⁷Cs gamma ray source were used in the experimental measurements. The obtained results show that the proposed GA based method performs well in constructing images of objects.     

A driven damped harmonic oscillator in the ket-vector representation of the density operator

By virtue of the entangled-state basis and the ket-vector representation of the density operator, we solve the master equation of a driven damped harmonic oscillator. In this representation, the density operators are mapped to vectors of a two-mode Fock space whose first mode is the system mode and the second mode is a fictitious one. We derive the Glauber–Sudarshan P function of the quantum state.     

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 computer program to calculate the symmetry of molecules

In this paper we, present some MATLAB and GAP programs and use them to find the automorphism group of the Euclidean graph of the C₈₀ fullerence with connectivity and geometry of I _h symmetry point group. It is proved that this group has order 120 and is isomorphic to I _h ≊Z₂×A₅, where Z₂ is, a cyclic group of order 2 and A₅ is the alternating group on five symbols.     

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.     

Full Non-rigid Group of Sponge and Pina

The non-rigid molecule group theory (NRG) in which the dynamical symmetry operations are defined as physical operations is a new field in chemistry. Smeyers and Villa computed the r-NRG of the triple equivalent methyl rotation in pyramidal trimethylamine with inversion and proved that the r-NRG of this molecule is a group of order 648, containing a subgroup of order 324 without inversions (see J. Math. Chem. 28(4) (2000) 377–388). In this work, a computational method is described, by means of which it is possible to calculate the symmetry group of molecules. We study the full non-rigid group (f-NRG) of Sponge and Pina molecules with C ₂ and C _i point groups, respectively. It proved that these are groups of order 162 and 13122 with 54 and 3240 conjugacy classes, respectively. The character tables of these groups are also computed.     

Fluorine-Boosted Kinetic and Selective Molecular Sieving of C6 Derivatives

Porous molecular sorbents have excellent selectivity towards hydrocarbon separation with energy saving techniques. However, to realize commercialization, molecular sieving processes should be faster and more efficient compared to extended frameworks. In this work, we show that utilizing fluorine to improve the hydrophobic profile of leaning pillararenes affords a substantial kinetic selective adsorption of benzene over cyclohexane (20 : 1 for benzene). The crystal structure shows a porous macrocycle that acts as a perfect match for benzene in both the intrinsic and extrinsic cavities with strong interactions in the solid state. The fluorinated leaning pillararene surpasses all reported organic molecular sieves and is comparable to the extended metal–organic frameworks that were previously employed for this separation such as UIO-66. Most importantly, this sieving system outperformed the well-known zeolitic imidazolate frameworks under low pressure, which opens the door to new generations of molecular sieves that can compete with extended frameworks for more sustainable hydrocarbon separation.     

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.     

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.