Methods for estimating the input signal of a measuring device are considered. Information about the device is contained in the measurement results of a set of known test signals and the measurements were obtained in natural or in computational experiments. A method is proposed for the approximation of the measurement model by means of a piecewise linear model that is consistent with the results of measurements and the method of evaluation of the input signal and its accuracy. An example is given of the solution of a problem of the interpretation of measurements based on the approximation of a model of the photosynthetic system, in which the measured parameters are the values of saturation $\Delta$pH and the rate of ATP synthesis and the estimated parameters are the concentration of photosystem-2 and light intensity.
Show AbstractThe signals of a given form are considered as elements of the linear subspace of Euclidean space of all signals. Linear subspaces (referred to as waveforms) are built on the basis of measurements of series of test signals of the same form, accompanied by a non-zero measurement error. Completed forms are used for the classification of signals of unknown form.
Show AbstractThe scattering problem in a quantum waveguide is considered within a light-binding approach. The relationship between the stationary and time-dependent definition of an S-matrix is established.
Show AbstractThe problem of regularization and renormalization of the Casimir pressure in a finite area with a smooth boundary is considered using the example of a real scalar field in the two-dimensional case. A procedure for the renormalization of boundary pressure using a certain modified area and a method for approximate calculation of the Green’s function and its derivatives with the use of efficient surface charges are proposed. For problems that allow an exact solution, it is shown that the method has high accuracy and computational efficiency.
Show AbstractA tomographic representation of kinetic equations is constructed using the Radon transform. Liouville’s equation is considered for one and many particles. The reduced Liouville’s equation is obtained in the tomographic representation and the Bogolyubov chain is investigated in this representation. An example of the relativistic kinetic equation in the tomographic representation is considered.
Show AbstractThe problem of the excitation of electromagnetic oscillations by given charge and current distributions in a domain with a nonhomogeneous chiral filling is investigated. The domain where the problem is considered may be both a finite one bounded by an ideally conducting surface and an infinite supplement to an ideally conducting bounded object. The initial boundary value problem is shown to arise, for which the generalized formulation in a special functional space is given. The existence of a unique weak solution to the problem is proven using the Galerkin method.
Show AbstractUsing the example of a neural system that generates a conditional Markov sequence of delta pulses, the procedure for the derivation of the expression for the spectral power density of such a signal is shown.
Show AbstractThe quantum and mechanical properties of a carbon nanotube are described in a model with the use of a macroscopic parameter, viz., surface impedance. Solving the boundary problem for the impedance vibrator is reduced to solving paired integral equations for the vibrator current. The paired integral equations are solved by the Galerkin method with Chebyshev’s basis. The influence of the substrate on the amplitude and frequency characteristics of the antenna, a carbon nanotube, is investigated.
Show AbstractThe values of Dunham constants are calculated for the electronic ground state of the carbon monoxide molecule on the basis of new values of the effective rotational and centrifugal constants and the energies of the high vibrational-rotational states are predicted. The peculiarity of the approach consists in the use of vibrational-rotational levels computed according to the traditional polynomial equation of energy values as the initial data for the procedure of Dunham coefficients determination. The role of the maximum degree of the Dunham polynom in determining its coefficients is analyzed, and the energy levels up to ${v=40}$ and ${J=60}$ calculated. A comparison with the literature data is made.
Show AbstractThe luminescent properties of LiRbLa$_{2-x}$Eu$_x$(MoO$_4$)$_4$ (${x=0.002}$, 0.02, 0.1, 0.2, 0.5, 1.0, 1.5, 2.0) solid solutions are investigated under laser excitation ($\lambda_{\bf ex}=337.1$ nm). It is established that the composition containing 50 at % Eu$^{3+}$ is the brightest of the considered set of phosphors and has the highest quantum yield.
Show AbstractThe Debye-Waller factors of UO$_2$ dependence on the temperature are calculated for the Born-Mayer model in the approximation of “frozen” sublattices. It is shown that the calculation results are in good agreement with the experimental data in the temperature range from 0 to 1500 K, i.e., up to the superionic transition.
Show AbstractNew experimental data are presented on the effects of uniaxial compression of up to 4 kbar along the $[110]$ and $[1\bar10]$ crystallographic directions on the spectra of electroluminescence and the current-voltage characteristics of diodes based on $n$-Al$_x$Ga$_{1-x}$As/GaAs$_y$P$_{1-y}$/$p$-Al$_x$Ga$_{1-x}$As (${y=0.84}$) heterostructures that were designed for injection lasers. With increasing pressure, the spectra show a shift to shorter wavelengths, reaching 25 meV at 3 kbar; the intensity increases 2–3 times as well. Numerical calculations were carried out on the band structure of the investigated heterostructures under compression along the $[110]$ axis, which indicate the increase in the effective band gap in the quantum well (QW) GaAs$_y$P$_{1-y}$ , with a pressure coefficient of about 8.5 meV/kbar and reduction of the barrier height at the boundaries of the QW. The calculations predict the possibility that light and heavy holes crossover at pressures above 4.5–5 kbar. The increase in the effective band gap completely describes the experimental data on the shift of the electroluminescence spectra. The mixing of light and heavy holes when approaching the band crosspoint is the probable cause of an increase in the intensity of radiation under uniaxial compression.
Show AbstractThe Mössbauer spectra of nickel ferrite NiGa$_x$Al$_x$Fe$_{2-2x}$O$_4$ were measured with significant dilution by nonmagnetic ions (with ${x=0.5}$, 0.7, and 0.8). In the temperature range of 90–295 K, the ratio of the near- and long-range forces was experimentally found and the Curie temperatures were determined.
Show AbstractThis article describes a novel experimental system for optical recording of the polymerization of blood coagulation proteins. It was shown that the experimental method has diagnostic abilities and defines some coagulation pathologies. Using this method, new properties of the coagulation system were discovered. The experimental system described is a prototype for a clinical diagnostic system.
Show AbstractThe theory of sqwall storms is created. Results of theoretical calculations is compared with observations.
Show AbstractThe penetration of nonlinear wind waves into the depth of a liquid is investigated in a laboratory channel. It is found that the amplitude of nonlinear waves on deep water depends only on the wave steepness normalized by the wave length. An expression is found that connects the growth of the wave mass with the wave steepness.
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