Magic Squares of Cubes Modulo a Prime Number

This work is dedicated to the properties of the 3 × 3 magic squares of cubes modulo a prime number. Its central concept is the number of distinct entries of these squares and the properties associated with this number. We call this number the degree of a magic square. The necessary conditions for the magic square of cubes with degrees 3, 5, 7, and 9 are examined. It was established that there are infinitely many primes for which magic squares of cubes with degrees 3, 5, 7, and 9 exist. I apply n-tuples of consecutive cubic residues to prove that there are infinitely many Magic Squares of Cubes with degree 9. Furthermore I use Brauer’s theorem, that guarantees the existence of a sequence of consecutive integers of any length, to construct Magic Squares of Cubes whose entries are all cubic residues. Such analytic tools as Modular Arithmetic, Legendre symbol, Fermat’s Little Theorem, notions of quadratic and cubic residues were employed in the process of research

Multi-frequency study of relativistic jets in active galactic nuclei

The thesis at hand presents the results of multi-frequency Very Long Baseline Interferometry (VLBI) observations of jets associated with active galactic nuclei. The results are discussed in the context of broad-band jet emission models and used to constrain physical properties of the parsec-scale core -- inner part of the jet which is likely related to the observed high-energy emission. The analysis of the frequency-dependent core position shift supports interpretation of the parsec-core as the integral part of the jet; the observed core position is determined by opacity. Synchrotron self-absorption is found to be the dominating opacity mechanism in the observed sources. A comparison between radio sources possessing jets aligned closely to the line of sight with those aligned at large angles to it supports the idea that the bright extragalactic gamma-ray sources are associated with jets affected by relativistic beaming

Change acidity sifted peat

The results of the reaction medium to neutralize the separated research in peat milling workpiece in “Dokshitsyraygaz”. Peat is taken is characterized as a pine-sphag num (Sphagnum magellansky – 35%, Sphagnum angustifolium – 25%, Scots pine – 25%, vaginal cotton grass – 15%), the degree of decom-position – 18%, ash content – 4.7%, pHKCl – 3.2, 50–60% relative humidity. To change the environment of the reaction as a calcareous material used dolomite flour and chalk. Doze of material is de-signed to skim 1 m3 peat milling blank, which at a relative humidity of 50–60% and the addition of a natural weight of about 250 kg. Studies have shown that the introduction of dolomite chalk and substrate in the reaction medium varies according to the dosage and duration of action of inter-substrate material with lime. The reaction medium in peat substrate is installed after 7-day interaction with chalk and a 10-day interaction with dolomite flour

Geostrophic tripolar vortices in a two-layer fluid : linear stability and nonlinear evolution of equilibria

We investigate equilibrium solutions for tripolar vortices in a two-layer quasi-geostrophic flow. Two of the vortices are like-signed and lie in one layer. An opposite-signed vortex lies in the other layer. The families of equilibria can be spanned by the distance (called separation) between the two like-signed vortices. Two equilibrium configurations are possible when the opposite-signed vortex lies between the two other vortices. In the first configuration (called ordinary roundabout), the opposite signed vortex is equidistant to the two other vortices. In the second configuration (eccentric roundabouts), the distances are unequal. We determine the equilibria numerically and describe their characteristics for various internal deformation radii. The two branches of equilibria can co-exist and intersect for small deformation radii. Then, the eccentric roundabouts are stable while unstable ordinary roundabouts can be found. Indeed, ordinary roundabouts exist at smaller separations than eccentric roundabouts do, thus inducing stronger vortex interactions. However, for larger deformation radii, eccentric roundabouts can also be unstable. Then, the two branches of equilibria do not cross. The branch of eccentric roundabouts only exists for large separations. Near the end of the branch of eccentric roundabouts (at the smallest separation), one of the like-signed vortices exhibits a sharp inner corner where instabilities can be triggered. Finally, we investigate the nonlinear evolution of a few selected cases of tripoles.PostprintPeer reviewe

Problems of socio-geographical assessment of the tourist attractiveness of the region

The article deals with the problems of the study of tourist attractiveness, identifies the main differences of the conceptual apparatus used in tourist studies of the regions, systematizes the criteria for evaluating the tourist attractiveness of the region, analyzes the existing methods and determines the factors of tourist attractiveness, determines the main stages of determining the rating of the tourist rating

Hydroxocomplexes in the system Fe{3+} – Cu {2+} – NO[3]{–} – H[2]O

The hydrolysis processes in the system Fe{3+} – Cu {2+} – NO[3]{–} – H[2]O have been investigated by potentiometric titration and dialysis methods. The experiment data have been obtained under the following conditions: metal ions concentration – 0,01 mol/l, molar ratio Fe{3+}:Cu{2+} = 1 : 1, ionic strength – 0.3 mol/l (NaNO[3]), temperature – (25 ±0.1)°С, pH-range – 1.5–2.4. The distribution of different Fe (III) and Cu (II) forms upon pH value has been calculated upon experimental data. It has been established that Fe (III) and Cu (II) form heteropolynuclear hydroxocomplexes

Growing of oak cultures in floodplain river Pripyat territory of the National park “Pripyat”

The results of the five-year study of cultures of oak, created two sites, located in the left bank of the floodplain. Pripyat in the territory of the National Park “Pripyat”. Object no. 1 is located in the central part of the floodplain on the turf gl eyey and gley sandy soils. Object no . 2 is located in the floodplain of the riverbed on a combination of Nuclear-podzolic sandy and sandy loam soils of various moisture sandy slabozader-nennymi sediments and sma ll areas of turf gley ey sandy loam soil. It is found that in the central part of the height of the flood oak average twice higher than the flood side riverbed. Approximately 50% of the test specimens are characterized by oak-hundredth you within 20–40 cm. Individual oak specimens in riverbed of the flood reached a height of 78 cm and 144 cm in the middle. The first oak growth in height in the extremely arid 2015 in the riverbed of the flood rec-orded in 15% of the trees, and in the central 44%. Included Quantity-tion of trees that have marked the second highest gains, reduced by 3–5 times. It was noted in edanie young oak shoots wild animals and drying it on a high sandy ridges in the riverbed of the floodplain. In the central part of the floodplain survival and preservation of oak is quite high

Modeling the evolution of intrathermocline lenses in the Atlantic Ocean

The existence of a tongue of Mediterranean Water (MW) at the depths of 500–1500 m is a characteristic feature of the hydrological regime in the northeastern part of the Atlantic Ocean. Anticyclonic eddies filled with MW (meddies or lenses) are observed in this region. They are identified via their high temperature and salinity anomalies, which compensate in density, yielding nearly homogeneous meddy cores. The analysis of historical observations has showed that approximately 100 lenses can exist simultaneously in this part of the ocean. High concentration of large water volumes (\u3e4000 km3 each) can be found both in the region of their origin near the Iberian Peninsula and near the Azores Frontal Zone. The latter is precisely the region in which merging of eddies can occur to form larger lenses. The existence of long-living lenses at large distances from the region of their formation is an indirect indication of the fact that merging of lenses occurs (MESOPOLYGON lens, SM1 lens in the SEMAPHORE experiment, and a lens in the Sargasso Sea). Here, we analyze the results of model experiments on interaction between two anticyclonic eddies applying the contour dynamics method (CDM) to a three-layer ocean. In these experiments, the vertical distribution of layerwise density in the layers, the horizontal size of the eddies (assumed to be cylindrical structures), and their depth location correspond to the observed conditions in the Atlantic Ocean. We show that the evolution of intrathermocline eddies and the evolution of barotropic eddies differ significantly. We found the behavior of interacting eddies in the middle layer depends on the Froude number. We determined the critical distances between the lenses when their merger begins and the destruction\u27 criterion for the elliptical intrathermocline eddies