Discretization of the Lebesgue-Kolmogorov theorem

It is well-known that if f(x) belongs to the spaceW ^r of 2π-periodic functions, the r-th derivatives of which are continuous and satisfy the inequality |f ^(r)(x)| ≤ 1, then the modulus of the remainder term in the Fourier series of f(x) has independent of x finite upper bound. Besides, for any natural r A. N. Kolmogorov has proved the asymptotic formula

Propagation of sound waves through a spatially homogeneous but smoothly time-dependent medium

The propagation of sound through a spatially homogeneous but non-stationary medium is investigated within the framework of fluid dynamics. For a non-vortical fluid, especially, a generalized wave equation is derived for the (scalar) potential of the fluid velocity distribution in dependence of the equilibrium mass density of the fluid and the sound wave velocity. A solution of this equation for a finite   transition period τ$\tau$ is determined in terms of the hypergeometric function for a phenomenologically realistic, sigmoidal change of the mass density and sound wave velocity. Using this solution, it is shown that the energy flux of the sound wave is not conserved but increases always   for the propagation through a non-stationary medium, independent of whether the equilibrium mass density is increased or decreased. It is found, moreover, that this amplification of the transmitted wave arises from an energy exchange with the medium and that its flux is equal to the (total) flux of the incident and the reflected wave. An interpretation of the reflected wave as a propagation of sound backward in time is given in close analogy to Feynman and Stueckelberg for the propagation of anti-particles. The reflection and transmission coefficients of sound propagating through a non-stationary medium is analyzed in more detail for hypersonic waves with transition periods τ$\tau$ between 15 and 200 ps as well as the transformation of infrasound waves in non-stationary oceans.     

Nonlinear approximation of functions from the class L r with respect to the Vilenkin system

In this paper we prove that for any function f from the class L ^r on [0, 1) one can find a function g from the same class (which differs from f on a set of arbitrarily small measure) whose greedy algorithm with respect to the Vilenkin system converges to f.     

Dimension six corrections to the vector sector of AdS/QCD model

We study the effects of dimension six terms on the predictions of the holographic model for the vector meson form factors and determine the corrections to the electric radius, the magnetic and the quadrupole moments of the ρ  -meson. We show that the only dimension six terms which contribute nontrivially to the vector meson form factors are X²F²$X^2{F}^2$ and F³$F^3$. It appears that the effect from the former term is equivalent to the metric deformation and can change only masses, decay constants and charge radii of vector mesons, leaving the magnetic and the quadrupole moments intact. The latter term gives different contributions to the three form factors of the vector meson and changes the values of the magnetic and the quadrupole moments. The results suggest that the addition of the higher dimension terms improves the holographic model.     

Dispersion-managed solitons at normal average dispersion

We find that in a dispersion-managed fiber, in which the strength of the dispersion management is above some threshold, solitons can exist with normal average dispersion. When the normal average dispersion is below some limiting value there exist two soliton solutions with the same pulse duration and different pulse energies. When the normal average dispersion is above this limiting value, no soliton exists. Both higher-energy and lower-energy solitons are dynamically stable in the parameter range that we considered.     

Effect of aminoacids on the critical micellization concentration of different surfactants

The effect of aminoacids (DL-glycine, DL-alanine, DL-serine, L-leucine, L-lysine, DL-phenylalanine, DL-tyrosine, and L-aspartic acid) on the critical micellization concentration (CMC) of nonionic, anionic, and cationic surfactants is investigated. It is established that, as the hydrophobicity of aminoacids rises, the CMC values of ionic and nonionic surfactants increase and decrease, respectively. An exception is aspartic acid, which reduces CMC values irrespective of the nature of surfactants.     

Structural and energetic properties of Ni-Cu bimetallic clusters

The lowest-energy structures for all compositions of Ni n Cu m bimetallic clusters with N = n + m up to 20 atoms, N = 23, and N = 38 atoms have been determined using a genetic algorithm for unbiased structure optimization in combination with an embedded-atom method for the calculation of the total energy for a given structure. Comparing bimetallic clusters with homoatomic clusters of the same size, it is shown that the most stable structures for each cluster size are composed entirely of Ni atoms. Among the bimetallic clusters in the size range N = 2-20, the Ni N-1 Cu 1 clusters possess the highest stability. Further, it has been established that most of the bimetallic cluster structures have geometries similar to those of pure Ni clusters. The size N = 38 presents a special case, as the bimetallic clusters undergo a dramatic structural change with increasing atom fraction of Cu. Moreover, we have identified an icosahedron, a double, and a triple icosahedron with one, two, and three Ni atoms at the centers, respectively, as particularly stable structures. We show that in all global-minimum structures Ni atoms tend to occupy mainly high-coordination inner sites, and we confirm the segregation of Cu on the surface of Ni-Cu bimetallic clusters predicted in previous studies. Finally, it is observed that, in contrast to the bulk, the ground-state structures of the 15-, 16-, and 17-atom bimetallic clusters do not experience a smooth transition between the structures of the pure copper and the pure nickel clusters as a function of the relative number of the two types of atoms. For these sizes, the concentration effect on energy is more important than the geometric one.     

On behavior of Fourier coefficients by Walsh system

The paper proves that for any ε > 0 there exists ameasurable set E ? [0, 1] with measure |E| > 1 ? ε such that for each f ∈ L¹[0, 1] there is a function \(\tilde f \in {L^1}\left[ {0,1} \right]\) coinciding with f on E whose Fourier-Walsh series converges to \(\tilde f\) in L¹[0, 1]-norm, and the sequence \(\left\{ {\left| {{c_k}\left( {\tilde f} \right)} \right|} \right\}_{n = 0}^\infty \) is monotonically decreasing, where \(\left\{ {{c_k}\left( {\tilde f} \right)} \right\}\) is the sequence of Fourier-Walsh coefficients of \(\left\{ {\left| {{c_k}\left( {\tilde f} \right)} \right|} \right\}_{n = 0}^\infty \).     

Specific features of charge relaxation in the solid solution of barium titanate stannate in the presence of a constant electric field

The electric properties of ceramic barium titanate stannate modified with chromium oxide are examined via impedance spectroscopy at frequencies ranging from 100 Hz to 1 MHz and in the temperature interval of 300–550 K. In order to reveal specific electrophysical features of polycrystalline samples that contain crystallites (interior regions of grains) and grain boundaries, a constant electric field that facilitates the accumulation of spatial charge near structural inhomogeneities is applied to the electrodes. The experimental results are interpreted using the Maxwell–Wagner double-layer capacitor model and the Schottky barrier model.