No abstract available

[en] We calculate the frequency spectra of absolute optical instruments using the Wentzel–Kramers–Brillouin (WKB) approximation. The resulting eigenfrequencies approximate the actual values very accurately; in some cases they even give the exact values. Our calculations confirm the results obtained previously by a completely different method. In particular, the eigenfrequencies of absolute instruments form tight groups that are almost equidistantly spaced. We demonstrate our method and its results applied to several examples. (paper)

[en] The possibility of stable faster-than-light propagation of ultimately short (without high-frequency carrier) electromagnetic solitons, breathers, and nonresonant envelope solitons is discussed based on the simple model of two-component nonequilibrium media undergoing two-level quantum transitions with widely differing eigenfrequencies. (methodological notes)

[en] We analyse frequency spectra of absolute optical instruments and show that they have very specific properties: the eigenfrequencies form tight groups that are almost equidistantly spaced. We prove this by theoretical analysis and demonstrate by numerically calculated spectra of various examples of absolute instruments. We also show that in rotationally and spherically symmetric absolute instruments a source, its image and the centre of the device must lie on a straight line. (paper)

[en] The implications of the five minute oscillations of the sun of high degree are considered first. They are confined to the outer few thousand kilometres of the sun. Careful calculations are made of the eigenfrequencies of the modes corresponding to the observed oscillations. It is shown that the oscillation frequencies place constraints on the convection zone adiabat. One claim about the interior of the sun that has been made based upon the frequencies of oscillations is that the solar interior is considerably cooler than evolved solar models suggest. This conclusion results from identifying the observed 160 minute oscillation with the fundamental radial oscillation mode. It is shown that this identification is certainly incorrect as the sun cannot possibly have a radial mode period as long as 160 minutes. In fact the maximum possible period is not significantly greater than that of an n = 3/2 polytrope (about 100 minutes). The geophysical inversion technique used to explore the internal structure of the earth is then applied to the sun in the form of simple model calculations. Two models are constructed. These are superposed polytropic models with an n = 3 polytrope at the centre and an outer n = 3/2 polytrope of depth 25% and 20% of the radius. (author)

[en] The dynamic characteristics of the torsional system in a lathe gearbox are analyzed. The forms of vibration of the torsional system are identified, and the amplitude–frequency characteristics of the gearbox’s dynamic pliability are determined. The resonant peaks at the eigenfrequencies are considered.

[en] A method is proposed for transforming a mechanical system described by arbitrary generalized coordinates into a system described by primary coordinates. To this end, an elastic element with negative rigidity is introduced. As a result, the vibrational motion is divided into two components; the maximum vibrational frequency is decreased; and the vibrational protection of the system is improved.

[en] Based on the quantum Liouville formalism, a theory of the two-color, triply resonant four-wave mixing is developed for molecules with isotropically oriented angular momenta. The approach allows to strictly incorporate the relaxation matrices Γ^(r) (r = 0, 1, 2) into the third-order susceptibility χ⁽³⁾ whose expression acquires therewith the form of a scalar product in the line space. Thanks to this representation, isolation of all resonance terms from χ⁽³⁾ becomes a routine task. Some of these terms correspond to the case when a molecule initially interacts with two pump photons of the same frequency. Such interactions give rise to the grating line-space vectors which have the same (zero) eigenfrequency. Due to this degeneracy, the latter are easily mixed by rotationally inelastic collisions which shows up in a state-resolved coherence transfer. The satellite signals induced thereby provide a great scope to study the state-to-state inelastic rates in situ by purely optical means. If the diagonal form of Γ is assumed, the satellites become forbidden and our results reduce to conventional expressions for the main resonances. Polarization configurations are designed for direct measurements of the population (r = 0), orientation (r = 1), and alignment (r = 2) contributions to χ⁽³⁾. Finally, depending on the photon-molecule interaction sequence, the resonance terms of χ⁽³⁾ are shown to be differently affected by velocity averaging, the effect which conspicuously manifests itself when Doppler broadening becomes paramount

No abstract available

[en] This study presents an inverse procedure to identify multiple cracks in beams using an evolutionary algorithm. By considering the crack detection procedure as an optimization problem, an objective function can be constructed based on the change of the eigenfrequencies and some strain energy parameters. Each crack is modeled by a rotational spring. The changes in natural frequencies due to the presence of the cracks are related to a damage index vector. Then, the bees algorithm, a swarm-based evolutionary optimization technique, is used to optimize the objective function and find the damage index vector, whose positive components show the number and position of the cracks. A second objective function is also optimized to find the crack depths. Several experimental studies on cracked cantilever beams are conducted to ensure the integrity of the proposed method. The results show that the number of cracks as well as their sizes and locations can be predicted well through this method.