How One can Repair Non-integrable Kahan Discretizations. II. A Planar System with Invariant Curves of Degree 6

Mathematical Physics, Analysis and Geometry - In this paper, we develop the dressing method to study the modified Camassa-Holm equation with the help of reciprocal transformation and the associated...     

Influence of the Degree of Deacetylation of Chitosan and BMP-2 Concentration on Biocompatibility and Osteogenic Properties of BMP-2/PLA Granule-Loaded Chitosan/β-Glycerophosphate Hydrogels

Compositions based on chitosan/β-glycerophosphate hydrogels with highly porous polylactide granules can be used to obtain moldable bone graft materials that have osteoinductive and osteoconductive properties. To eliminate the influence of such characteristics as chain length, degree of purification, and molecular weight on a designed material, the one-stock chitosan sample was reacetylated to degrees of deacetylation (DD%) of 19.5, 39, 49, 55, and 56. A study of the chitosan/β-glycerophosphate hydrogel with chitosan of a reduced DD% showed that a low degree of deacetylation increased the MSCs (multipotent stromal cells) viability rate in vitro and reduced the leukocyte infiltration in subcutaneous implantation to Wistar rats in vivo. The addition of 12 wt% polylactide granules resulted in optimal composite mechanical and moldable properties, and increased the modulus of elasticity of the hydrogel-based material by approximately 100 times. Excessive filling of the material with PLA (polylactide) granules (more than 20%) led to material destruction at a ~10% strain. Osteoinductive and osteoconductive properties of the chitosan hydrogel-based material with reacetylated chitosan (39 DD%) and highly porous polylactide granules impregnated with BMP-2 (bone morphogenetic protein-2) have been demonstrated in models of orthotopic and ectopic bone formation. When implanted into a critical-size calvarial defect in rats, the optimal concentration of BMP-2 was 10 μg/mL: bone tissue areas filled the entire material’s thickness. Implantation of the material with 50 μg/mL BMP-2 was accompanied with excessive growth of bone tissue and material displacement beyond the defect. Significant osteoinductive and osteoconductive properties of the material with 10 μg/mL of BMP-2 were also shown in subcutaneous implantation.     

Thermal properties of rare earth dodecaborides

We have measured heat capacity and thermal expansion of rare earth dodecaborides REB₁₂ (RE=Y, Tb-Tm, Lu). YB₁₂ and LuB₁₂ are diamagnetics whereas the other dodecaborides are ordered antiferromagnetically. The amplitude of the heat capacity discontinuity at the Néel temperature and the shape of the heat capacity variation in the critical region for all these antiferromagnetics are characteristics for amplitude-modulated magnetic structures. In the ordered state TbB₁₂ reveals two first-order phase transitions, most likely due to magnetic structure changes. The heat capacity of ErB₁₂ just below the Néel point shows an anomaly of unclear origin. From the Schottky contribution to the heat capacity we have determined crystal field parameters. They are completely different than that is estimated from Point Charge Model.     

Multireference spin-adapted variant of density functional theory

A new Kohn-Sham formalism is developed for studying the lowest molecular electronic states of given space and spin symmetry whose densities are represented by weighted sums of several reference configurations. Unlike standard spin-density functional theory, the new formalism uses total spin conserving spin-density operators and spin-invariant density matrices so that the method is fully spin-adapted and solves the so-called spin-symmetry dilemma. The formalism permits the use of an arbitrary set of reference (noninteracting) configurations with any number of open shells. It is shown that the requirement of degeneracy of the total noninteracting energies of the reference configurations (or configuration state functions) is equivalent to the stationary condition of the exact energy relative to the weights of the configurations (or configuration state functions). Consequently, at any molecular geometry, the weights can be determined by minimization of the energy, and, for given reference weights, the Kohn-Sham orbitals can be determined. From this viewpoint, the developed theory can be interpreted as an analog of the multiconfiguration self-consistent field approach within density functional theory.     

Adsorption of metal halides from ethanol solutions by a 3-n-propylpyridiniumsilsesquioxane chloride-coated silica gel surface

3-n-propylpyridiniumsilsesquioxane chloride polymer, abbreviated as SiPy+Cl-, was used to coat a porous silica gel, SiO2, surface to form the chemically modified solid SiO2/SiPy+Cl-. The resulting polymer film was well adhered to the surface and presented an ion exchange capacity of 0.74 mmol g(-1). Metal halides, MClz [M=Fe(III), Cu(II), and Zn(II)], were adsorbed by the modified solid from ethanol solutions as neutral species by forming the surface anionic complexes described by the equation: mSiO2/SiPy+Cl-+ MClz <=> (SiO2/SiPy+)m[MCl(z+m)]m-, where the [MCl(z+m)]m- species adsorbed on the surface are FeCl4-, ZnCl4(2-), and CuCl4(2-). Accurate estimates of the specific sorption capacities and the heterogeneous stability constants of the immobilized metal complexes were determined with the aid of computational procedures.     

A parallel solution-phase synthesis of substituted 3,7-diazabicyclo[3.3.1]nonanes

The parallel solution-phase synthesis of a series of building blocks and combinatorial libraries based on natural bispidine scaffold has been accomplished. Key reactions include catalytic hydrogenation of the (-)-cytisine heterocyclic system, followed by alkali-mediated ring cleavage. Using this approach, a series of new bispidine core building blocks for combinatorial synthesis with three points of diversity were effectively synthesized. The libraries from libraries were then obtained in good yields and purities using solution-phase acylation reactions. Obtained combinatorial libraries of 3,4,7-trisubstituted bispidines are potentially useful in the discovery of novel physiologically active compounds.     

Alkyl radical adducts of aromatic N-oxides as hydrogen-abstracting agents: The reactivity of phenazine-N,N′-dioxide-methyl radical adduct

An O-methylated analog of protonated phenazine-di-N-oxide radical anion abstracts hydrogen from primary and secondary alcohols in a slow (k ₁ < 500 M⁻¹ s⁻¹) bimolecular reaction. No kinetic evidence has been found for the unimolecular release of free methoxyl radicals through the homolytic N-OMe bond cleavage in these species. DFT calculations at the UB3LYP 6-31G(d) level indicate that protonated and O-alkylated radical anions of pyrazine, quinoxaline and phenazine di-N-oxides are close analogues of aromatic nitroxyl radicals with the highest spin density localized on the oxygen and nitrogen of the nitrone moiety.