On the scales of computability potentials of finite algebras: Results and problems

We give a review of general known results on problems concerning the structure of scales of computability potentials of n-element algebras. We also formulate a number of natural open problems. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 9, No. 3, pp. 145–164, 2003.     

On the Length of Scales of Computability Potentials for n-Element Algebras

We find the length of scales of computability potentials for n-element algebras. As a consequence, we find the length of the filter generated by the clone of a discriminant function in the lattice of clones of functions on an n-element set.     

Mechanism of submicrocrack generation in stressed polymers

Submicrocracks, free radicals, and endgroups of scissioned molecules formed in polyethylene, polypropylene, and polycaprolactam under uniaxial tension have been investigated. Measurements were carried out by small-angle x-ray scattering, electron paramagnetic resonance, and infrared spectroscopy. The concentration of submicrocracks is almost the same as that of free radicals but is smaller than the concentration of scissioned macromolecules by approximately three orders of magnitude. The number of scissions per crack proved to be close to the number of macromolecules passing through the cross section of a submicrocrack calculated on the assumption of close packing. It is concluded that submicrocracks in stressed polymers are formed as a result of chain reactions of macromolecular decomposition initiated by the active end primary free radicals.     

Electric-pulse breakdown and the breakage of granite

The breakage of granite during the action of an electric pulse is studied for a two-electrode system in the interelectrode distance range 10–300 mm and a power input of 3.6–100 J/mm per unit interelectrode length. Empirical dependences of the breakdown voltage, the breakage depth, the breakage output, and the specific energy consumption on the interelectrode distance are obtained.     

Electrical breakdown of solid dielectrics and rocks on the trailing edge of a voltage pulse

An analysis of modern notions of breakdown in condensed media opens up new possibilities for a decrease in the microsecond voltages for solid dielectric breakdown. Investigations of solid dielectric and rock breakdowns on the trailing edge of a voltage pulse in a sharply nonuniform field demonstrate that the pulse amplitude and the slope of the working voltage pulse edge can be decreased significantly.     

Principles of the kinetic approach of fracture prediction

It is shown that during crack formation in loaded solids considered as a thermofluctuational process of generation of stable cracks two stages exist, i.e. a delocalized accumulation which spontaneously results in an enlargement of cracks and a relatively fast autocatalytic growth of enlarged cracks in the field of overstresses produced by them. The change of stages takes place at the critical concentration of cracks when an average relative distance between them is equal to e. The effect of the enlargement is the increase of the energy emission during further crack formation. This effect allows to state the going of the object into the prerupturing state and to estimate its residual longevity according to acoustic emission data corresponding to the crack formation. This permits to formulate the physically valid principle of fracture prediction of elements of engineering constructions and geophysics objects.     

Electric strength of rocks at a pulsed voltage under high pressures at high temperatures

The electric strength of rocks (granite, limestone, and sandstone) for the first time has been measured under the simultaneous effect of the pressure up to 35 MPa and temperature up to 120°C in the system of rod-rod electrodes arranged on one sample surface and point-plane electrodes in the liquid medium of a drilling agent. With the simultaneous increase in pressure and temperature, the electric strength of rocks for point-plane electrodes continuously increases (especially rapidly in the pressure range of 10–24 MPa and temperature range of 35–85°C), while for rod-rod electrodes arranged on the same sample surface, the electric strength varies with a maximum at pressures of 5–12 MPa and temperatures 20–35°C.     

Luminescence and electronic excitations in KBe<Subscript>2</Subscript>BO<Subscript>3</Subscript>F<Subscript>2</Subscript> crystals

This paper reports on a study of the dynamics of electronic excitations in KBe₂BO₃F₂ (KBBF) crystals by low-temperature luminescent vacuum ultraviolet spectroscopy with nanosecond time resolution under photoexcitation by synchrotron radiation. The first data have been obtained on the kinetics of photoluminescence (PL) decay, time-resolved PL spectra, time-resolved PL excitation spectra, and reflection spectra at 7 K; the estimation has been performed for the band gap E _g = 10.6−11.0 eV; the predominantly excitonic mechanism for PL excitation at 3.88 eV has been identified; and defect luminescence bands at 3.03 and 4.30 eV have been revealed. The channels of generation and decay of electronic excitations in KBBF crystals have been discussed.     

Luminescence and electronic excitations in crystals K<Subscript>2</Subscript>Al<Subscript>2</Subscript>B<Subscript>2</Subscript>O<Subscript>7</Subscript> with defects

This paper reports on the results of the comprehensive study of the dynamics of electronic excitations in K₂Al₂B₂O₇ (KABO) crystals, obtained by low-temperature luminescence vacuum ultraviolet spectroscopy with nanosecond time resolution upon photoexcitation by synchrotron radiation. For the first time, the data have been obtained on the photoluminescence (PL) decay kinetics, PL spectra with time resolution, PL excitation spectra with time resolution, and reflection spectra at 7 K; the intrinsic nature of PL at 3.28 eV has been established; luminescence bands of defects have been separated in the visible and ultraviolet spectral regions; an intense long-wavelength PL band has been detected at 1.72 eV; channels of the formation and decay of electronic excitations in K₂Al₂B₂O₇ crystals have been discussed.