Applied Sciences Research Periodicals

Feedback Functions in Problems Minimax Search

2024-04-26T13:07:47+01:00

This paper considers a method for obtaining a smooth approximation of the maximum function. Some generalizations of this approach are suggested, including formulas for minimax, maximin and their combinations. The resulting error is estimated and ways to reduce it are indicated. The proposed method uses functions that establish feedback links between primary and dual variables of the Lagrange function. These links are similar to the Karush-Kuhn-Tucker theorem, but without conditions of non-negativity or complementary non-rigidity. To illustrate the proposed method, task of searching for global extremum, estimation of the minimax value and an example from game theory are considered.

The Foundation of a Dark Energy Theory

2024-05-03T11:02:58+01:00

Based on the article „Calculation of Dark Energy and Dark Matter“ [1] the article „Commentary about Calculation of Dark energy and Dark Matter“ emerged [2]. The Foundation of a Dark Energy Theory is formulated there.

Foundations of Magnetic Field Definition

2024-05-05T20:14:50+01:00

Any FIELD, by definition, is Force, which is a continuous parameter of space. For the Magnetic Field, this parameter is the Ampere Force, but it was actually neglected. Without fully understanding the ELEMENTARY Lorentz Force, the mystical “Theory” of Magnetism was built - the theory of interaction of Descartes’ “gimlets”, which was used by Maxwell to build General Electrodynamics. This, strictly speaking, led to the uncertainty of the very concept of the Magnetic Field. So in practice, when designing magnets, the “Theory” of Magnetism actually did not work and was used by Kirchhoff’s rules based on empirical parameters. The analysis of the ELEMENTARY Electric Oscillator made it possible to unambiguously connect the IMAGINARY terms of the Complete Solution of the differential equation of the Complex Elementary Oscillator with the IMAGINARY Parameter initially introduced into its equation, which strictly corresponds to the orthogonal Electric Field - Magnetic. And this made it possible to restore the correct picture of the Magnetic Field.

Biotope Distribution of The Common Fox in The Steppe Zone of Ukraine

2024-05-10T20:32:40+01:00

In the steppe zone, foxes use fields, meadows and steppe areas characterised by good visibility during daytime rest. A total of 37.8% of individuals were recorded in these areas, with the highest numbers on the coasts of the Dnipro (48.9%), Azov (43.3%) and Black (29.9%) Seas. In forested areas, foxes rested most often in deciduous (12.5%) and pine plantations (2.8%), while in field areas - in forest belts (6.7%), uncultivated fields (16.2%), and in orchards and vineyards (7.6%). However, the largest number of individuals (32.6%) was found in thickets of southern reeds (Phragmites australis) and other aquatic plants. In the Black Sea region, more than 45% of foxes spent the day in reed beds. This resulted in a high population density (26.6±1.37 individuals/10 ha or 4.4±0.18 per reed bed). The probability of encountering predators in such areas, which usually do not exceed 1-2 ha (49.4%), is very high - out of 231 surveyed sites, animals were absent only in 2. The location of foxes' dwellings, which they create to breed their young, is peculiar: the main number of dens (about 23%) was located on the forest margins, somewhat less - in the treeless valleys of small rivers, as well as on the banks of estuaries. In the Black Sea region, many burrows (18.5%) were found in floodplains of large rivers (Danube, Dniester, Southern Bug and Dnieper), and in the Azov region - on sea spits and islands (14.3%), as well as in numerous forest belts (11.5%). After the dust storms of 1969, many of these sites were covered with high earthen berms made of wind-blown black soil. This improved conditions for dens of all predatory animals, but especially for foxes. Already in the early 20th century in Ukraine, they began to avoid open steppes and fields, although they made holes in haystacks that had been stored for many years and used to feed sheep.