Without taking into account external friction, small transverse vibrations of a viscoelastic pipeline of unit length are described for nonnegative values of time in dimensionless variables by an ...integro-differential equation with hinged conditions at the ends and with initial conditions. The solution of this equation can be written in terms of an operator semigroup. In the present paper, we establish that this equation generates a semigroup that is analytic in some sector of the right half-plane.
We consider an operator semigroup arising in the study of an integro-differential equation modeling small transverse vibrations of a viscoelastic pipeline with allowance for Kelvin–Voigt damping. The ...explicit form of the generator of this semigroup is established, its spectrum is studied, and the norm of its resolvent is estimated. Based on these results, the analyticity of this semigroup is proved with the use of well-known facts from the theory of semigroups.
In this paper we consider an operator function being a symbol of the abstract integro-differential equation describing the oscillations of a viscoelastic tube. The operator-function spectrum ...localization is determined in the paper and its resolvent norm is estimated in a domain free of spectral points.
The problem is discussed of replacing an integral norm with respect to a given probability measure by the corresponding integral norm with respect to a discrete measure. This problem is investigated ...for elements of finite-dimensional spaces. Also, discretization of the uniform norm of functions in a given finite-dimensional subspace of continuous functions is studied. Special attention is given to the case of multivariate trigonometric polynomials with frequencies (harmonics) in a finite set with fixed cardinality. Both new results and a survey of known results are presented. Bibliography: 47 titles.
The definition of a self-similar function is extended to quasi-Banach Lebesgue spaces. A sufficient condition for a function with given self-similarity parameters to lie in some such space is given.
Chirality, an intrinsic handedness, is one of the most intriguing fundamental phenomena in nature. Materials composed of chiral molecules find broad applications in areas ranging from nonlinear ...optics and spintronics to biology and pharmaceuticals. However, chirality is usually an invariable inherent property of a given material that cannot be easily changed at will. Here, we demonstrate that ferroelectric nanodots support skyrmions the chirality of which can be controlled and switched. We devise protocols for realizing control and efficient manipulations of the different types of skyrmions. Our findings open the route for controlled chirality with potential applications in ferroelectric-based information technologies.
The relationship between the rate of approximation of a monotone function by step functions (with an increasing number of values) and the Hausdorff dimension of the corresponding Lebesgue–Stieltjes ...measure is studied. An upper bound on the dimension is found in terms of the approximation rate, and it is shown that a lower bound cannot be constructed in these terms.
Polarized Raman spectra of the epitaxial Ba
0.5
Sr
0.5
TiO
3
film, bi-color BaTiO
3
/Ba
0.5
Sr
0.5
TiO
3
superlattice and tri-color BaTiO
3
/Ba
0.5
Sr
0.5
TiO
3
/SrTiO
3
superlattice were studied in ...a broad temperature range of 80-700 K. Based on the temperature dependence of the polar modes we determined the phase transitions temperatures in the studied heterostructures. In the sub-THz frequency range of the
spectra, we revealed the coexistence of the Debye-type central peak and soft mode in bi-color BaTiO
3
/Ba
0.5
Sr
0.5
TiO
3
superlattice.
Transients in a high- and medium-voltage power-supply network due to switching operations and short circuits are accompanied by high-frequency overvoltage pulses. Their amplitude and frequency ...characteristics are needed to select proper protection devices. Only experimental study can give us reliable data on such characteristics. The paper presents overvoltage spikes experimental study data in switchgears of 6–500 kV. The spikes were measured by means of recorder with noncontact capacitive sensors. Experimental studies at power-engineering facilities showed that most hazardous phenomena are high-frequency resonances. In this case, the overvoltage values are over ten times higher than nominal voltage amplitude. The usual method of connecting protection device to mains via a conductor a few meters long was shown to be inadequate to provide equipment protection.
RC
circuits are needed for this situation.
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