Asymptotic behavior of the mean square displacement of the Brownian parametric oscillator near the singular point

A parametric oscillator with damping driven by white noise is studied. The mean square displacement (MSD) in the long-time limit is derived analytically for the case that the static force vanishes, which was not treated in the past work \cite{tashiro07}. The formula is asymptotic but is applicable to a general periodic function. On the basis of this formula, some periodic functions reducing MSD remarkably are proposed

New global stability estimates for the Gel'fand-Calderon inverse problem

We prove new global stability estimates for the Gel'fand-Calderon inverse problem in 3D. For sufficiently regular potentials this result of the present work is a principal improvement of the result of [G. Alessandrini, Stable determination of conductivity by boundary measurements, Appl. Anal. 27 (1988), 153-172]

Numbers of donors and acceptors from transport measurements in graphene

A method is suggested to separately determine the surface density of positively and negatively charged impurities that limit the mobility in a graphene monolayer. The method is based on the exact result for the transport cross-section, according to which the massless carriers are scattered more strongly when they are attracted to a charged impurity than when they are repelled from it.Comment: 3 pages, 1 figur

Hydrodynamic Flow as Congruence of Geodesic Lines in Riemannian Space-Time

It is shown that small elements of perfect fluid in adiabatic processes move along geodesic lines of a Riemannian space-time.Comment: 5 pages, Latex. Final versio

The electrification of spacecraft

Physical and applied aspects of the electrification of space vehicles and natural celestial objects are discussed, the factors resulting in electrification of spacecraft are analyzed, and methods of investigating various phenomena associated with this electrification and ways of protecting spacecraft against the influence of static electricity are described. The booklet is intended for the general reader interested in present day questions of space technology

Weighted Radon transforms for which the Chang approximate inversion formula is precise

We describe all weighted Radon transforms on the plane for which the Chang approximate inversion formula is precise. Some subsequent results, including the Cormack type inversion for these transforms, are also given

Groebner-Shirshov basis for HNN extensions of groups and for the alternating group

In this paper, we generalize the Shirshov's Composition Lemma by replacing the monomial order for others. By using Groebner-Shirshov bases, the normal forms of HNN extension of a group and the alternating group are obtained

New global stability estimates for monochromatic inverse acoustic scattering

We give new global stability estimates for monochromatic inverse acoustic scattering. These estimates essentially improve estimates of [P. Hahner, T. Hohage, SIAM J. Math. Anal., 33(3), 2001, 670-685] and can be considered as a solution of an open problem formulated in the aforementioned work