Excitation of localized spatial structures of different symmetry in a system of two thin films

We consider spatial dissipative solitons arising in the system of two nonlinear thin films which interact resonantly with light. Symmetric and nonsymmetric solitons and methods of their exciting and switching are studied.     

Nonstandard analysis and compact Abelian groups

Gor'kii. Translated fromSibirskii Matematicheskii Zhurnal, Vol. 32, No. 2, pp. 26–40, March–April 1991.     

Convergence of Weighted Sums and Laws of Large Numbers in D([0,1]; E)

Convergence properties of weighted sums of functions in D([0, 1]; E) (E a Banach space) are investigated. We show that convergence in the Skorokhod J₁-topology of a sequence (x_n) in D([0, 1]; E) does not imply convergence of a sequence ( _n) of averages. Convergence in the J₁-topology of a sequence ( _n) of averages is shown, under the growth condition x_n ∞ = o(n), to be equivalent to the convergence of ( _n) in the uniform topology. Convergence of a sequence (x_n,) is shown to imply convergence of the sequence ( _n) of averages in the M₁ and M₂ topologies. The strong law of large numbers in D[0, 1] is considered and an example is constructed to show that different definitions of the strong law of large numbers are nonequivalent.     

Realisation and metrological characterisation of thickness standards below 100 nm

High-accuracy film thickness measurements in the range below 100 nm can be made by various complex methods like spectral ellipsometry (SE), scanning force microscopy (SFM), grazing incidence X-ray reflectometry (GIXR), or X-ray fluorescence analysis (XRF). The measurement results achieved with these methods are based on different interactions between the film and the probe. A key question in nanotechnology is how to achieve consistent results on a level of uncertainty below one nanometre with different techniques.Two different types of thickness standards are realised. Metal film standards for X-ray techniques in the thickness range 10 to 50 nm are calibrated by GIXR with monochromatised synchrotron radiation of 8048 eV. The results obtained at four different facilities show excellent agreement. SiO₂ on Si standards for SE and SFM in the thickness range 6 to 1000 nm are calibrated by GIXR with monochromatised synchrotron radiation of 1841 eV and with a metrological SFM. Consistent results within the combined uncertainties are obtained with the two methods. Surfaces and interfaces of both types of standards are additionally investigated by transmission electron microscopy (TEM). PACS 61.10.Kw; 68.55.Jk; 06.20.Fn; 06.60.Mr; 07.79.Lh     

The lay-out of the photon collider at the international linear collider

One of the interaction regions at the linear colliders should be compatible both with e ⁺ e ⁻ and γγ, γe modes of operation. In this paper, the differences in requirements and possible design solutions are discussed.      

Utilization of waste solutions in perovskite technology

A scheme for utilization of chloride solutions of complex composition with α-and β-activity of up to 35 and 28 kBq 1^?1, respectively, is suggested.