Single- and coupled-channel radial inverse scattering with supersymmetric transformations

The present status of the coupled-channel inverse-scattering method with supersymmetric transformations is reviewed. We first revisit in a pedagogical way the single-channel case, where the supersymmetric approach is shown to provide a complete solution to the inverse-scattering problem. A special emphasis is put on the differences between conservative and non-conservative transformations. In particular, we show that for the zero initial potential, a non-conservative transformation is always equivalent to a pair of conservative transformations. These single-channel results are illustrated on the inversion of the neutron-proton triplet eigenphase shifts for the S and D waves. We then summarize and extend our previous works on the coupled-channel case and stress remaining difficulties and open questions. We mostly concentrate on two-channel examples to illustrate general principles while keeping mathematics as simple as possible. In particular, we discuss the difference between the equal-threshold and different-threshold problems. For equal thresholds, conservative transformations can provide non-diagonal Jost and scattering matrices. Iterations of such transformations are shown to lead to practical algorithms for inversion. A convenient technique where the mixing parameter is fitted independently of the eigenphases is developed with iterations of pairs of conjugate transformations and applied to the neutron-proton triplet S-D scattering matrix, for which exactly-solvable matrix potential models are constructed. For different thresholds, conservative transformations do not seem to be able to provide a non-trivial coupling between channels. In contrast, a single non-conservative transformation can generate coupled-channel potentials starting from the zero potential and is a promising first step towards a full solution to the coupled-channel inverse problem with threshold differences.Comment: Topical review, 84 pages, 7 figures, 93 reference

Synthesis of Bis(1,2,3-triazolyl)alkanes in Superbasic and Solvent-Free Conditions

Nucleophilic substitution reactions between 1,2,3-triazole and dibromomethane or 1,2-dirbomoethane in a superbasic medium potassium hydroxide–dimethyl sulfoxide gave mixtures of the isomeric bis(1,2,3-triazolyl)alkanes, in which (1,2,3-triazol-1-yl)(1,2,3-triazol-2-yl)alkanes and bis(1,2,3-triazol-2-yl)alkanes were the dominating products, while bis(triazol-1-yl)alkanes were detected only in trace amounts. The same products could also be obtained under solvent-free conditions in a neat reaction mixture. The proposed methods are economically feasible, do not require using toxic solvents or catalysts, and make the (1,2,3-triazol-2-yl)-derivatives, inaccessible by alkyne-azide cycloaddition (click) reactions, readily available

Synthesis, Crystal Structure, and Luminescence of Cadmium(II) and Silver(I) Coordination Polymers Based on 1,3-Bis(1,2,4-triazol-1-yl)adamantane

Coordination polymers with a new rigid ligand 1,3-bis(1,2,4-triazol-1-yl)adamantane (L) were prepared by its reaction with cadmium(II) or silver(I) nitrates. Crystal structure of the coordination polymers was determined using single-crystal X-ray diffraction analysis. Silver formed two-dimensional coordination polymer [Ag(L)NO3]n, in which metal ions are linked by 1,3-bis(1,2,4-triazol-1-yl)adamantane ligands, coordinated by nitrogen atoms at positions 2 and 4 of 1,2,4-triazole rings. Layers of the coordination polymer consist of rare 18- and 30-membered {Ag2L2} and {Ag4L4} metallocycles. Cadmium(II) nitrate formed two kinds of one-dimensional coordination polymers depending on the metal-to-ligand ratio used in the synthesis. Coordination polymer [Cd(L)2(NO3)2]n was obtained in case of a 1:2 M:L ratio, while for M:L = 2:1 product {[Cd(L)(NO3)2(CH3OH)]·0.5CH3OH}n was isolated. All coordination polymers demonstrated ligand-centered emission near 450 nm upon excitation at 370 nm

Bio-damaged Wood Processing in Microcrystalline Cellulose Production

Bio-damaged wood was studied as a potential raw material for the production of hydrolytic degradation cellulose products. Conditions for obtaining fine-dispersed microcrystalline cellulose (MCC) based on hydrolytic treatment of cellulose from bio-damaged wood were determined. A comparative analysis of the quantitative values of the degree of polymerization of default commercial cellulose and cellulose from damaged wood was performed. The objective of the work was to study the possibilities of obtaining MCC from bio-damaged wood possessing quantitative characteristics close to those obtained from the commercial wood, reducing the concentration of inorganic acid during the hydrolytic degradation. The experimental analysis showed that with an increase in the pulp refining degree from 15 °SR to 75 °SR, the time for the hydrolysis process decreased from 150 to 90 min, the temperature of chemical treatment decreased from 100 °C to 80 °C, and acid concentration by 0.5 N. The polymerisation degree of microcrystalline cellulose, regardless of the type of raw material, also decreased with an increase in the refining degree