Problems of saturation of linear methods

We review some basic results of the theory of saturation of linear methods of summation of Fourier series.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 3, pp. 291–308, March, 1991.     

Influence of the Inhomogeneous Surface Relief on the Magnetic and Magnetoelastic Properties of Amorphous Iron-Based Metal Alloys

The influence of the inhomogeneous surface relief on the magnetic and magnetoelastic properties of films, wires, and strips manufactured from amorphous iron-based metal alloys is investigated. It is demonstrated that the inhomogeneous surface relief is one of the main factors determining the magnetic and magnetoelastic properties of amorphous iron-based metal alloys. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 32–39, July, 2005.     

Results of a higgs boson searches in the ATLAS and CMS experiments at the large hadron collider at energies 7 and 8 TeV

Recent achievements of the ATLAS and CMS experiments at the Large Hadron Collider searching for a Higgs boson are summarized. A new particle with the mass of 125 GeV and properties expected for the Standard Model Higgs boson was discovered three years ago in these experiments in proton-proton collisions when analyzing part of the data taken at the centre-of-mass energies 7 TeV and 8 TeV in 2011 and 2012 year exposures. Today all the data are processed and fully analyzed. Experimental results of studies of individual Higgs boson decay channels as well as their combination to extract such properties as mass, signal strength, coupling constants, spin and parity are reviewed. All experimental results are found to be compatible with the Standard Model predictions.     

Many-photon dynamics of photobleaching

A detailed dynamical theory of photobleaching by periodical sequences of laser pulses is presented. The theory is used for interpretation of recent experiments with pyrylium salts. Our simulations are based on first-principles simulations of photoabsorption cross-sections and on empirical rate constants. Two competitive channels of photobleaching, namely, photobleaching from the lowest excited singlet and triplet states and from higher excited states, are found to explain different intensity dependences of the photobleaching rates in different samples. The process includes two-photon excitation from the ground state to the first or second excited singlet states and one-photon excitation from the first singlet or triplet states to higher excited states. The fluorescence follows double-exponential dynamics with two characteristic times. The first and the shorter one is the equilibrium settling time between the ground and the lowest triplet states. The second characteristic time, the time of photobleaching, is responsible for the long-term dynamics. The effective rate of photobleaching from the first excited singlet and lowest triplet states depends differently on the irradiance in comparison with the photobleaching in higher states. The first channel is characterized by a quadratic intensity dependence in contrast to the second channel that shows a cubic dependence. The competition between these photobleaching channels is very sensitive to the rate constants as well as to the repetition rate, the pulse duration, and the peak intensity. The double-exponential decay of the fluorescence is explained by the spatial inhomogeneity of the light beam. The findings in this work are discussed in terms of the possibility of using many-photon-induced photobleaching for new three-dimensional read-write devices.     

Magnetic collapse and the change of electronic structure of FeBO3 antiferromagnet under high pressure

The effect of high pressures up to 60 GPa on single-crystal and polycrystalline samples of iron borate ⁵⁷FeBO₃ was studied by Mössbauer absorption spectroscopy (⁵⁷Fe nuclei) in a diamond anvil cell. Magnetic field H _hf at the ⁵⁷Fe nuclei increases with pressure but abruptly drops to zero at 46±2 GPa, indicating the crystal transition from the antiferromagnetic to nonmagnetic state. This is accompanied by an abrupt change in the isomer shift and quadrupole splitting. Their values in the high-pressure phase are evidence for the transition of Fe⁺³ ions from a high-spin (S=5/2, ⁶ A _1g ) to low-spin (S=1/2, ⁶ T2g) state (spin crossover). This correlates with an abrupt decrease in the unit-cell volume (by ～9%) and optical gap. The change of the magnetic and electronic structures is explained by Mott’s transition with rupturing of strong d-d-electron correlations.     

Processes in resonant domains of metal nanoparticle aggregates and optical nonlinearity of aggregates in pulsed laser fields

Optical nonlinearities in aggregates of nanoparticles formed in silver hydrosols (SHs) are studied under pico- and nanosecond pulsed laser excitation. The dependence of the nonlinear refractive index n ₂ on the degree of hydrosol aggregation is studied experimentally at the wavelength λ=1.064 μm. It is found that n ₂ changes sign when the degree of hydrosol aggregation is increased. Various physical effects occurring in resonant domains of the aggregates are analyzed using a simple physical model of two bound silver nanoparticles. The theory takes into account thermal, elastic, electrostatic, and light-induced effects. Experimental results are discussed in the context of this theory.     

New Constraints on the Axion–Photon Coupling Constant for Solar Axions

Resonance excitation of the ⁸³Kr first nuclear level (E = 9.4 keV) by solar axions formed via the Primakoff mechanism is sought. The γ- and X-ray photons and the conversion and Auger electrons arising from the excited-level relaxation are detected with a gas proportional counter of a low-background detector in the underground Baksan Neutrino Observatory. The following experimental constraint is obtained for the product of the axion–photon coupling constant and the axion mass:|g_Aγ × m_A| ≤ 6.3 × 10 ^-17 In the framework of the hadronic-axion model, this corresponds to a new axion-mass constraint of m_A ≤ 12.7 eV at 95% C.L.     

Data-sparse approximation to the operator-valued functions of elliptic operator

In previous papers the arithmetic of hierarchical matrices has been described, which allows us to compute the inverse, for instance, of finite element stiffness matrices discretising an elliptic operator The required computing time is up to logarithmic factors linear in the dimension of the matrix. In particular, this technique can be used for the computation of the discrete analogue of a resolvent

In the present paper, we consider various operator functions, the operator exponential negative fractional powers , the cosine operator function and, finally, the solution operator of the Lyapunov equation. Using the Dunford-Cauchy representation, we get integrals which can be discretised by a quadrature formula which involves the resolvents mentioned above. We give error estimates which are partly exponentially, partly polynomially decreasing.