Dilaton black hole entropy from entropy function formalism

It has been shown that the entropy function formalism is an efficient way to calculate the entropy of black holes in string theory. We check this formalism for the extremal charged dilaton black hole. We find the general four-derivative correction on the black hole entropy from the value of the entropy function at its extremum point.

Algorithm for Determining the State of Impregnated Paper Insulation of High-Voltage Cables

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.

Simple MCBR models of chemical evolution: An application to the thin and the thick disk

Simple multistage closed-(box+reservoir) (MCBR) models of chemical evolution, formulated in an earlier attempt, are extended to the limit of dominant gas inflow or outflow with respect to gas locked up into long-lived stars and remnants. For an assigned empirical differential oxygen abundance distribution (EDOD), which can be linearly fitted, a family of theoretical differential oxygen abundance distribution (TDOD) curves is built up with the following prescriptions: (i) the initial and the ending points of the linear fit are common to all curves; (ii) the flow parameter k ranges from an extremum point to ? ?, where negative and positive k correspond to inflow and outflow, respectively; (iii) the cut parameter ?O ranges from an extremum point (which cannot be negative) to the limit (?O) ? related to |k|? + ?. For curves with increasing ?O, the gas mass fraction locked up into long-lived stars and remnants is found to attain a maximum and then decrease towards zero as |k|? + ? while the remaining parameters show a monotonic trend. The theoretical integral oxygen abundance distribution (TIOD) is also expressed. An application is made to the EDOD deduced from two different samples of disk stars, for both the thin and the thick disk. The constraints on formation and evolution are discussed in the light of the model. The evolution is tentatively subdivided into four stages, namely: assembling (A), formation (F), contraction (C), equilibrium (E). The EDOD related to any stage is fitted by all curves where 0 ? ?O ? (?O) ? for inflowing gas and (?O) ? ? ?O ? 1.2 for outflowing gas, with a single exception related to the thin disk (A stage), where the range of fitting curves is restricted to 0.35 ? ?O ? (?O) ?. The F stage may safely be described by a steady inflow regime (k= -1), implying a flat TDOD, in agreement with the results of hydrodynamical simulations. Finally, (1) the change of fractional mass due to the extension of the linear fit to the EDOD, towards both the (undetected) low-metallicity and high-metallicity tail, is evaluated and (2) the idea of a thick disk - thin disk collapse is discussed, in the light of the model.

SUVOKIAMO ATKARPOS ILGIO PRIKLAUSOMYBĖ NUO JOS ATVAIZDO VIETOS AKIES TINKLAINĖJE

Tyrimo tikslas yra patikrinti, kaip keičiasi objekto dydžio suvokimas, kintant jo projekcijos padėčiai akies tinklainėje, ir kaip objekto dydžio suvokimas priklauso nuo akies tinklainės receptorių (kūgelių ir lazdelių) tankio. Tiriamieji, žiūrėdami viena akimi ir fiksuodami žvilgsnį, dalijo skirtingų ilgių atkarpas – nustatydavo suvokiamą vidurį. Atkarpos dalių santykio nuo atkarpos ilgio funkcija turėjo lūžio tašką (66,7 proc. tiriamiesiems, kai atkarpos ilgis 7 laipsniai, 23,33 proc. – 13 laipsnių, kiti neturėjo). Rezultatai aiškinami skirtingu kūgelių ir lazdelių tankiu akies tinklainėje ir skirtinga kūgelių ir lazdelių įtaka.Pagrindiniai žodžiai: dydžio suvokimas, žievinis didinimo veiksnys, fotoreceptorių tankis.Perceived Size of a Line Depending on Its Projection Place on the RetinaDzekevičiūtė A., Daugirdienė A., Švegžda A., Stanikūnas R., Vaitkevičius H. SummaryIt is known that objects located in the centre of the visual field are perceived as larger than the objects located in the periphery (Пиаже, 1978). The image of an object differs from its perception object. The perceived size of an object depends on the size of its image in the visual cortex. This stems from the so-called cortical magnification factor. It is assumed that the same quantity of receptors sends information to the same area of the cortex. But photoreceptors are different – rods and the cones. It is not clear whether the different type of receptors make a different influence on the above-mentioned distortion of mapping. Also, the image of the object on the retina is perceived differently, depending on its location on the retina. Our goal was to explore how this subjective expansion changes while moving away from the centre of the retina, because there are no data on this, phenomenon.Method. Thirty normal or corrected to normal vision adults participated in the study. Five different length lines (5, 7, 10, 13, 15 degrees) were represented on the computer’s monitor one line at a time. Participants had monoculary bisected lines into two subjectively equal parts fixating sight on a cross located at the given end of the line.Results. The ratio ρ (length of the line near the cross / length of the other part) was calculated. This ratio as a function of the length of the whole line was not monotonic: when the line was short, ρ decreased, but then it began to increase. Three groups of results were formed considering the ratio of the line length (where the function had the extremum point). The largest group (66.67%) had the extremum point when the line length was 7 deg. The second group (23.33%) had the extremum point when the line length was 13 deg. The last group (10%) had not clear extremum point and was excluded from the calculation. Changes of the ρ value cannot be explained by the perceptual instability of the length of the line (Brown, 1953). There could be a correlation between the value of ρ and the density of all receptors in the retina where the line was projected.Conclusions. Humans make a bias while monocular by bisecting a line: the part near the point of fixation is perceived as bigger than the other part. The function of the line size ratio changes not monotonically – it has an extremum point. Most often, the extremum point is observed when the line size is 7 deg. This point is near the point where the density of rods exceeds that of cones. Other subjects show the extremum point when line size is 13 deg., but the reasons for such a point shift remain unclear. Some subjects have no extremum point.Key words: size perception, cortical magnification factor, density of photoreceptors.

Extremal dynamic errors in linear dynamic systems

Extremal dynamic errors in linear dynamic systems Two different analytical methods of determining extremal dynamic errors in linear dynamic systems are presented. The main idea of these methods is based on finding certain additional equations. These additional equations are obtained due to the assumption that an extremal point τ obtained from the necessary condition , is also an extremum point with respect to initial conditions, that is, .