Nonlinear second-order equations with functional implicit impulses and nonlinear functional boundary conditions

In this paper we deal with nonlinear second-order boundary value problems with impulses. The impulsive functions depend implicitly on the different considered variables and the boundary value conditions are nonlinear. In both cases functional dependence on the solution is allowed. The existence results follow from the existence of a pair of well-ordered lower and upper solutions.     

Some remarks on general commutators theorems

The paper proves some general facts on commutators that refer to Fuglede-Putnam classical theorem in the spectral theory of not necessarily selfadjoint operators.     

Observation of a “giant” step of the field electron emission current from a high-temperature superconductor

An abrupt rise of the field electron emission (FEE) current from a high-temperature superconductor (HTSC) being in the normal state has been detected. The current amplification with a factor reaching ∼10⁶ occurs as an HTSC emitter is heated in the temperature range 110–170 K. The features of the temperature dependence of FEE are discussed. Measured parameters of the effect observed are presented. Possible mechanisms of the process under consideration are discussed. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 13–16, May, 2007.     

Quantum graph of Sierpinski gasket type: Computational experiment

A continuous model of the Sierpinski gasket (SG) is suggested. The Laplace operator on the SG is defined. An effective computational algorithm for solving the scattering problem is suggested. The self-similarity of the graph of transmission coefficient via the wave number k is observed. A violation of symmetry of the SG is considered. The results are compared with the discrete SG model. In memoriam V. A. Geyler     

Production of high purity proteins by elution of individual fractions from two-dimensional gels.

Results are presented on the production of purified myocardial proteins from two-dimensional (2-D) gels. Proteins were fixed in a native condition using potassium acetate and then eluted into an aqueous solution. Homogeneous tropomyosin and myosin light chain fractions and a number of nonidentified myocardial proteins present on 2-D gels were obtained.     

Modification of silica gels with small admixtures of titanium ions

Microporous silica gels containing small amounts of titanium ions are synthesized. Addition of Ti ions to the silica gels during the sol-forming step is demonstrated to increase the specific surface area and decrease the volume of sorptive pores. Spectral results indicate that Ti ions uniformly distribute in the silica gel matrix and isomorphously replace Si.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 10, pp. 2217–2222, October, 1991.     

On the deficiency index of a certain class of differential operators

This paper studies problems on the behavior of solutions for a certain class of differential equations of the form l _n y = λy as x → +0, where l _n is a scalar, formally self-adjoint, quasidifferential expression of an arbitrary order with complex coefficients. The results obtained allow us to find the defficiency index of the operator generated by the expression l _n . __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 36, Suzdal Conference-2004, Part 2, 2005.     

Shadowing with multidimensional time in Banach spaces

We study linear dynamical systems with multidimensional time in Banach spaces. Using Taylor functional calculus we prove that under additional assumptions hyperbolic systems have shadowing property.