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.     

Chloroaqua Complexes [M3S4(H2O)9?xClx](4?x)+ (M = Mo, W; x = 4, 6, 7) and Their Supramolecular Compounds with Cucur[8]uril

Compounds of trigonal cluster chloroaqua complexes with cucurbit[8]uril were synthesized by slowly evaporating HCl solutions of chalcogenides heterometallic cubane cluster complexes of molybdenum and tungsten with cucurbit[8]uril in air; the complexes were characterized by X-ray diffraction analysis: (H₃O)₈[Mo₃S₄(H₂O)_2.5Cl_6.5]₂Cl(PdCl₄)·(C₄₈H₄₈N₃₂O₁₆)· 29H₂O (a = 13.3183(17) Å, b = 13.7104(18) Å, c = 18.225(3) Å; α = 80.263(3)°, β = 77. 958(3)°, γ = 87.149(4)°, V = 3207.4(7) ų, space group P , Z = 1, ρ(calc) = 1.900 g/cm³), (H₃O)₄ [Mo₃S₄(H₂O)₃Cl₆]₂·(C₄₈H₄₈N₃₂O₁₆)₃·68H₂O (a = 21.413(6) Å, c = 49.832(10) Å; γ = 120°, V = 19788(8) ų, space group R , Z = 3, ρ(calc) = 1.695 g/cm³), (H₃O)₆ [Mo₃S₄(H₂O)₃Cl₆]₂Cl₂·(C₄₈H₄₈N₃₂O₁₆)·12H₂O (a = 15.881(2) Å, b = 17.191(2) Å, c = 23.276(4) Å; β = 98.865(15)°, V = 6278.7(15) ų, space group P2₁/c, Z = 2, ρ(calc) = 1.638 g/cm³), [W₃S₄(H₂O)₅Cl₄]₂·(C₄₈H₄₈N₃₂O₁₆)₃·35H₂O (a = 21.038(3) Å; α = 61.20(1)°, V = 6762.0(14) ų, space group R , Z = 1, ρ(calc) = 1.582 g/cm³). The [Mo₃S₄(H₂O)₃Cl₆]²⁻ anion complex was isolated as three geometrical isomers.Original Russian Text Copyright © 2004 by E. V. Chubarova, D. G. Samsonenko, H. G. Platas, F. M. Dolgushin, A. V. Gerasimenko, M. N. Sokolov, Z. A. Starikova, M. Yu. Antipin, and V. P. Fedin__________Translated from Zhurnal Strukturnoi Khimii, Vol. 45, No. 6, pp. 1049–1058, November–December, 2004.     

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.     

Inclusion of Two PhP(O)(OH) 2 Guest Molecules into the Cavity of Macrocyclic Cavidand Cucurbit[8]uril

A new inclusion compound which is a supramolecular adduct of cucurbit[8]uril with two guest molecules of phenylphosphonic acid, PhP(O)(OH)₂, included into the cavity as ``two guests in host'' is reported. The guests match both size and hydrophilicity/hydrophobicity requirements. Two phenyl groups of molecules of PhP(O)(OH)₂ are directed toward the center of the large hydrophobic cavity whereas the PO(OH)₂ groups are outward-looking and bound with each hydrophilic portal of cucurbit[8]uril by a short hydrogen bond.     

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.     

Currents of the second kind in quasielastic scattering ofv(\tilde v) by free polarized nucleons

Expressions are obtained for the cross sections for scattering of high-energy (E _v Mc², where M is the nucleon mass) neutrinos and antineutrinos by free polarized nucleons with currents of the second kind taken into account. The effect of the axial-tensor form factor F_T of these currents on the spin asymmetry coefficients A_L and A_S and on the charge asymmetry coefficient is considered. It is shown that experimental study of the energy dependence of these coefficients can improve the accuracy of the bounds on the form factor.Russian University of the Friendship of Nations. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 36–40, January, 1993.     

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.     

Synthesis and Crystal Structure of Supramolecular Adducts of Macrocyclic Cavitand Cucurbituril with Chromium(III) and Nickel(II) Aqua Complexes

Supramolecular compounds {[Cr(H₂O)₆](C₃₆H₃₆N₂₄O₁₂)}(NO₃)₃ · 13H₂O (I) and {[Ni(H₂O)₆]₂(C₃₆H₃₆N₂₄O₁₂)}(SO₄)₂ · 16H₂O (II) were obtained from aqueous solutions of chromium nitrate or nickel sulfate and the macrocyclic cavitand cucurbituril. According to X-ray diffraction analysis data, the cucurbituril molecule is closed from both sides by metal aqua complexes due to the formation of hydrogen bonding between the cucurbituril CO groups and aqua ligands. Compound I has a chain structure, while the structure of compound II is layered. Modes of cucurbituril coordination, depending on the size and charge of the metal cation, are discussed.