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.     

A strengthening of a theorem of Bourgain and Kontorovich. V

It is proved that the denominators of finite continued fractions all of whose partial quotients belong to an arbitrary finite alphabet A with parameter δ > 0.7807... (i.e., such that the set of infinite continued fractions with partial quotients from this alphabet is of Hausdorff dimension δ with δ > 0.7807... ) contain a positive proportion of positive integers. Earlier, a similar theorem has been obtained only for alphabets with somewhat greater values of δ. Namely, the first result of this kind for an arbitrary finite alphabet with δ > 0.9839... is due to Bourgain and Kontorovich (2011). Then, in 2013, D.A. Frolenkov and the present author proved such a theorem for an arbitrary finite alphabet with δ > 0.8333.... The preceding result of 2015 of the present author concerned an arbitrary finite alphabet with δ > 0.7862....     

Estimates of Wiman–Valiron type for evolution equations

We establish estimates of Wiman–Valiron type for solutions of evolution equations with a pseudodifferential operator of the Hörmander class in a Hilbert space. Estimates of this type characterize the behavior of the solution of the problem as t→∞ or t → 0 depending on the decay or growth rate of the Fourier coefficients of the initial data.     

Students as toolmakers: refining the results in the accuracy and precision of a trigonometric activity

Smartphones used as tools provide opportunities for the teaching of the concepts of accuracy and precision and the mathematical concept of arctan. The accuracy and precision of a trigonometric experiment using entirely mechanical tools is compared to one using electronic tools, such as a smartphone clinometer application and a laser pointer. This research has demonstrated how two classroom activities based on tool-making can enhance student measurement and application of accuracy and precision considerations through a trigonometric activity investigating arctan.     

Non-accretive Schrödinger operators and exponential decay of their eigenfunctions

We consider non-self-adjoint electromagnetic Schrödinger operators on arbitrary open sets with complex scalar potentials whose real part is not necessarily bounded from below. Under a suitable sufficient condition on the electromagnetic potential, we introduce a Dirichlet realisation as a closed densely defined operator with non-empty resolvent set and show that the eigenfunctions corresponding to discrete eigenvalues satisfy an Agmon-type exponential decay.     

Generalized Kondo lattice model and its spin-polaron realization by the projection method for cuprates

The spin–fermion model, which is an effective low-energy realization of the three-band Emery model after passing to the Wannier representation for the p_x and p_y orbitals of the subsystem of oxygen ions, reduces to the generalized Kondo lattice model. A specific feature of this model is the existence of spin-correlated hoppings of the current carriers between distant cells. Numerical calculations of the spectrum of spin-electron excitations highlight the important role of the long-range spin-correlated hoppings.     

Bergman Subspaces and Subkernels: Degenerate $$L^p$$ Mapping and Zeroes

Regularity and irregularity of the Bergman projection on \(L^p\) spaces is established on a natural family of bounded, pseudoconvex domains. The family is parameterized by a real variable \(\gamma \). A surprising consequence of the analysis is that, whenever \(\gamma \) is irrational, the Bergman projection is bounded only for \(p=2\).     

Stokes constants of an oblate ellipsoid of revolution with equidensites homothetic to its surface

The theory of equilibrium figures was actively developed in the 19th century, when it was found that the observed massive celestial bodies (the Sun, planets, and satellites) had an almost ellipsoidal form. The existence of exactly ellipsoidal figures was also established. The gravitational potential of these figures is represented by a Laplace series with its coefficients (Stokes’ constants I _n ) determined by some integral operator. The general term of the series was found for a homogeneous ellipsoid of revolution and the first terms of the series were found for some other mass distributions. Here, we have obtained the general term of the series for an arbitrary mass distribution given that the equidensites (surfaces of equal density) are homothetic to the outer surface of the ellipsoid of revolution. Simple estimates and an asymptotics of I _n have also been obtained.     

A maximum of the first eigenvalue of semibounded differential operator with a parameter

We consider a self-adjoint differential operator in Hilbert space. Then the domain of the operator is changed by the perturbation of the boundary conditions so that a given neighborhood “is cleared” from the points of the spectrum of the perturbed operator. For the Sturm–Liouville operator on the segment and the Laplace operator on the square such a possibility is attained via integral perturbations of boundary conditions.