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.     

Estimates of the albedo of powderlike surfaces in the geometrical optics approximation

Results of computer simulation of light scattering by powderlike media composed of large semitransparent particles of different shapes are presented. The geometrical optics approach is used. The cases of particles of spherical, cubic, and random shapes are considered. The one-dimensional geometrical optics model of light scattering by powderlike media, which finds application in investigations of planetary surfaces, meteorites, and lunar samples, is briefly described. The numerical simulation allowed us to estimate the error of this model, which turned out to be within the limits of several percent. The albedo calculated by using the one-dimensional model is shown to be closest to the “three-dimensional” reflectance of the surfaces at a phase angle of about 60°. This albedo also approximates fairly well the integrated reflectance, which in laboratory measurements is determined with the help of an integrating sphere.     

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.     

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.     

On the closure of the first Grigorchuk group

We consider the closure (in the natural topology) of the well-known periodic self-similar group. A finitely generated group that is not isomorphic to the Grigorchuk group and has the same closure is constructed.     

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.     

On Truncated Matricial Stieltjes Type Moment Problems

We study two slightly different versions of truncated generalized matricial moment problems of Stieltjes type. A central topic is the construction and investigation of distinguished solutions of both moment problems under consideration. These solutions turn out to be nonnegative Hermitian Borel measures on the real axis which are concentrated on a finite number of points. Our approach is mainly algebraic. It is based on the use of particular matrix polynomials constructed from a nonnegative Hermitian block Hankel matrix.     

Carbon monoxide laser emitting nanosecond pulses with 10 MHz repetition rate

Actively mode-locked electron-beam-sustained-discharge CO laser producing a train of ∼5-15 ns (FWHM) spikes following with repetition rate 10 MHz for both single-line and multiline mode of operation in the mid-IR range of ∼5 μm was experimentally studied. Total laser pulse duration was ∼0.5 ms for both mode-locked and free-running laser. Specific output energy in multiline CO laser mode of operation was up to 20 Jl⁻¹ Amagat⁻¹ and the laser efficiency up to 3.5%. The active mode-locking was achieved for single-line CO laser mode of operation in spectral range 5.2-5.3 μm. This sort of radiation can be used for pumping an optical parametric amplifier for optical stochastic cooling in relativistic heavy ion collider, for laser ablation, and for studying vibrational and rotational relaxation of CO and NO molecules.