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The paper presents a technique for determining the time index of growth of the slope of reverse voltage for double insulated cables, based on the body of the theory of series. It is proved that in the vicinity of the extremum point (maximum) the function of the reverse voltage is approximated by polynomials of the nth power. It is proposed to use second-degree polynomials for practical calculations. The method for calculating relevant indicators is illustrated using real data. Analysis of deviations made it possible to conclude that the calculation method proposed in the paper is far more accurate. In the final part of the study, it was concluded that there is a promising outlook for further development of methodological guidelines for determining complex indices of the remaining life of the cable, including but not limited to the use of various mathematical methods. [ABSTRACT FROM AUTHOR]

Proteasomes hydrolyze most cellular proteins. The standard reaction to determine proteasome activity in cellular lysate or elsewhere contains AMC-conjugated peptide substrate, ATP, Mg2+, and DTT. ATP and Mg2+ are included to maintain 26S proteasome functionality. However, most cellular proteasomes are 20S proteasomes, and the effects of ATP on the turnover of fluorogenic substrates by 20S complexes are largely unknown. Here, we evaluated the effect of ATP alone or in combination with Mg2+ on the degradation of AMC-conjugated fluorogenic substrates by purified 20S proteasomes. Degradation of substrates used to determine chymotrypsin-, caspase- and trypsin-like proteasome activities was gradually decreased with the rise of ATP concentration from 0.25 to 10 mM. These effects were not associated with the blockage of the proteasome catalytic subunit active sites or unspecific alterations of AMC fluorescence by the ATP. However, ATP-induced peptide degradation slowdown was rescued by the addition of Mg2+. Moreover, the substrate degradation efficacy was proportional to the Mg2+/ATP ratio, being equal to control values when equimolar concentrations of the molecules were used. The obtained results indicate that when proteasome activity is assessed, the reciprocal effects of ATP and Mg2+ on the hydrolysis of AMC-conjugated fluorogenic substrates by the 20S proteasomes should be considered. [ABSTRACT FROM AUTHOR]

In the present paper we thoroughly investigated the dynamics, kinetics, and the transport properties of the one-dimensional (1D) mass-disordered lattice of harmonic oscillators with the number of particles N < or =5000. The thermostat is simulated by the Langevin sources. Our method is adequate to any 1D lattice with linear equations of motion. Two accurate methods to calculate the temporal behavior of pair correlation functions were developed. The feature of the considered disordered model is an existence of localized states with great relaxation times tau to their stationary states. The exponential growth tau proportional variant exp(N) is observed. A method which allows us to extend the range of computed relaxation times up to tau approximately =(10)300 is suggested. The stationary state is unique. The thermal conduction x has the nonmonotonic character versus N: for the number of particles N < 300 the thermal conduction increases as x proportional variant ln N and reaches the maximal value at N approximately =300. At larger values the decreasing asymptotic is observed: x proportional variant N -alpha, and alpha approximately 0.27. An influence of parameters on the calculated properties was analyzed. Mathematical problems associated with the computation of very large times of establishing the stationary states were extensively studied.