The influence of the length and concentration of chopped carbon fiber on physical and mechanical properties of siloxane matrix

In this paper, the influence of the concentration and length of chopped carbon fiber on the physical and mechanical characteristics of siloxane matrix was investigated. It is shown that the highest values can be achieved at 2–5 wt % loading of chopped carbon fiber with a length of 3 mm. In this case, the elastic modulus increases by five to eight times in comparison with unmodified composite. Destruction of such materials takes place in accordance with an adhesive–cohesive mechanism, which testifies to the existence of relative adhesion of siloxane binder to carbon fiber.     

Oligomer–oligomer modification upon the synthesis of epoxy polymers with a “shape-memory” effect

The results of studies of the oligomer–oligomer modification of epoxyamine compositions with amine adducts, oligomers, block oligomers, and oligocyclocarbonates differing in their structure and molecular weight upon hardening under the conditions of a general epoxide–amine polycondensation reaction, and competitive epoxide–amine and cyclocarbonate–amine reactions are given. The parameters of the structure and the elastic-deformation properties required for the preparation of high-quality thermally contracting epoxy polymers with a “shape-memory” and for their reliable application are established.     

Evaluation of the biosafety of cyanoacrylate adhesive in vitro

This paper considers the evaluation of the biosafety of cyanoacrylate adhesive in vitro on human multipotent mesenchymal stem cells. This adhesive is intended for medical use, in particular, for X-ray and endovascular interventions. A toxicity study was carried out in a culture of multipotent mesenchymal stem cells isolated from human subcutaneous fat. As a result of the work, the concentration of cyanoacrylate adhesive in lipiodol was chosen, which has the lowest toxicity.     

Determination of the heat resistance of polymer construction materials by the dynamic mechanical method

Russian and foreign standards for the techniques for the determination of the heat resistance of polymer materials are analyzed and the incorrectness of their use for polymer construction materials is shown. The determination of the heat resistance by the low-frequency dynamic mechanical method based on the temperature derivative extrema of the dynamic modulus of elasticity and the dynamic loss modulus under the transition of polymer matrices from the glassy to the highly elastic state is experimentally substantiated for multicomponent polymer compositions with dispersed or fibrous fillers.     

The influence of stabilizers on the properties of silicone rubber

The influence of various stabilizers on the properties of rubber based on silicone rubber SKTV is studied. It is established that the use of the Ca/Zn stabilizer in the resin composition makes it possible to increase thermal resistance and physico-mechanical characteristics of the rubber used to make sealing elements in the automotive industry.     

The one-dimensional Riemann problem on an elliptic curve

A one-dimensional generalization of the Riemann–Hilbert problem from the Riemann sphere to an elliptic curve is considered. A criterion for its positive solvability is obtained and the explicit form of all possible solutions is found. As in the spherical case, the solutions turn out to be isomonodromic.     

Spectral analysis of operator polynomials and higher-order difference operators

The study of the spectral properties of operator polynomials is reduced to the study of the spectral properties of the operator specified by the operator matrix. The results obtained are applied to higher-order difference operators. Conditions for their invertibility and for them to be Fredholm, as well as the asymptotic representation for bounded solutions of homogeneous difference equations are obtained.     

Sharp estimates of the error of interpolation by bilinear splines for some classes of functions

On a two-point homogeneous space X, we consider the problem of describing the set of continuous functions having zero integrals over all spheres enclosing the given ball. We obtain the solution of this problem and its generalizations for an annular domain in X. By way of applications, we prove new uniqueness theorems for functions with zero spherical means.     

Classification of Toeplitz operators on hardy spaces of bounded domains in the plane

We construct an orthonormal basis for the class of square integrable functions on bounded domains in the plane in terms of the classical kernel functions in potential theory. Then we generalize the results of Brown and Halmos about algebraic properties of Toeplitz operators and Laurent operators on the unit disc to general bounded domains. This is a complete classification of Laurent operators and Toeplitz operators for bounded domains.     

Finding the coefficients in the new representation of the solution of the Riemann–Hilbert problem using the Lauricella function

The solution of the Riemann–Hilbert problem for an analytic function in a canonical domain for the case in which the data of the problem is piecewise constant can be expressed as a Christoffel–Schwartz integral. In this paper, we present an explicit expression for the parameters of this integral obtained by using a Jacobi-type formula for the Lauricella generalized hypergeometric function F _D ^(N). The results can be applied to a number of problems, including those in plasma physics and the mechanics of deformed solids.