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.     

On hyperbolicity cones associated with elementary symmetric polynomials

Elementary symmetric polynomials can be thought of as derivative polynomials of . Their associated hyperbolicity cones give a natural sequence of relaxations for . We establish a recursive structure for these cones, namely, that the coordinate projections of these cones are themselves hyperbolicity cones associated with elementary symmetric polynomials. As a consequence of this recursion, we give an alternative characterization of these cones, and give an algebraic characterization for one particular dual cone associated with together with its self-concordant barrier functional.     

Numerical solution of multiple nonlinear Volterra integral equations

We analyze a discretization method for solving nonlinear integral equations that contain multiple integrals. These equations include integral equations with a Volterra series, instead of a single integral term, on one side of the equation. We prove existence and uniqueness of solutions, and convergence and estimates of the order of convergence for the numerical methods of solution.     

Time-fractional radial heat conduction in a cylinder and associated thermal stresses

The theory of thermal stresses based on the heat conduction equation with the Caputo time-fractional derivative of order 0 < α ≤ 2 is used to investigate axisymmetic thermal stresses in a cylinder. The solution is obtained applying the Laplace and finite Hankel integral transforms. The Dirichlet and two types of Neumann problems with the prescribed boundary value of the temperature, the normal derivative of the temperature, and the heat flux are considered. Numerical results are illustrated graphically.     

Capillary cavity flow past a circular cylinder

Cavity flow past a circular cylinder is considered accounting for the surface tension on the cavity boundary. The fluid is assumed to be inviscid and incompressible, and the flow is assumed to be irrotational. The solution is based on two derived governing expressions, which are the complex velocity and the derivative of the complex potential defined in an auxiliary parameter region. An integral equation in the velocity magnitude along the free surface is derived from the dynamic boundary condition. The Brillouin–Villat criterion is employed to determine the location of the point of flow separation. The cases of zero surface tension and zero cavitation number are obtained as limiting cases of the solution. Numerical results concerning the effects of surface tension and cavitation development on the cavity detachment, the drag force and the geometry of the free boundaries are presented over a wide range of the Weber and the cavitation numbers.     

The Neumann boundary problem for axisymmetric fractional heat conduction equation in a solid with?cylindrical hole and associated thermal stress

The theory of thermoelasticity based on the heat conduction equation with the Caputo time-fractional derivative of order α is used to study thermal stress in an infinite medium with a cylindrical hole. Two types of Neumann boundary conditions are considered: the constant value of the normal derivative of the temperature and constant heat flux at the surface of a cavity. The solution is obtained applying Laplace and Weber integral transforms. Numerical results are illustrated graphically.     

Intermediate carbene formation in the reaction of thioamides with phosphorus (III) derivatives: Quantum chemical investigation

The reactions of perfluoroalkyl thioamides with trimethyl phosphine, trimethyl phosphite, and tris(dimethylamino)phosphine have been analyzed by means of quantum chemical (DFT and MP2) calculations. The reaction seems to proceed via the nucleophilic attack of the electrophilic carbon atom by the phosphorus lone pair with the formation of cyclic or acyclic adducts. The latter releases the thiophosphate molecule forming perfluoroalkylaminocarbene as the short‐lived intermediate. The reaction of the carbene with the second molecule of trialkyl phosphite yields phosphorus ylide. The ylide undergoes a migration of fluorine from carbon to phosphorus. The reactions of perfluoroalkyl thioamides with phosphines and tris(dimethylamino)phosphine probably proceeds differently. Using alkyl thioamides or amides instead of perfluoroalkyl thioamides also makes the reaction less favorable. The only combination of perfluoroalkyl thioamides with trialkyl phosphite fulfills both the kinetic requirements (moderate activation energies and relative energies for intermediates) and the thermodynamic aspects (higher stabilities of the reaction products compared with the starting materials). © 2013 Wiley Periodicals, Inc.     

Fast protonic conductivity in crystalline benzenehexasulfonic acid hydrates

We report on the crystal structures of two hydrates of benzenehexasulfonic acid, its water sorption isotherm, temperature- and humidity-dependent conductivity, along with ¹H NMR studies. At comparable humidities and temperatures, this crystalline material shows conductivity similar to Nafion, which conducts protons via liquid water channels. We believe that the presented discovery of fast protonic conductivity in benzenehexasulfonic acid at low humidities is encouraging for further efforts in developing highly sulfonated polymers as membranes for fuel cells.