of National Academy of Sciences
of Tajikistan

News of the National Academy of Sciences of Tajikistan.
Department of physical, mathematical, chemical, geological and technical sciences

Известия Национальной академии наук Таджикистана. Отделение физико-математических, химических, геологических и технических наук, №2(183), 2021 г.

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Sharp inequalities of Jackson-Stechkin in terms of τ-modules of continuity in L
For τ modules of smoothness of order the sharp constant in Jackson-Stechkin type inequality were calculated. Also for some classes of functions averaged with given weights of τ modules of smoothness of derivatives which majorized with given functions the sharp upper bounds of the best joint polynomial approximation were found.

Ключевые слова: best polynomial approximation; sharp constants; Jackson type inequality; τ-module of smoothness; approximation characteristic.

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K.V.Kholshevnikov , D.V.Milanov , A.S.Shchepalova
The space of keplerian orbits and a family of its quotient spaces
The research of relationship of meteoroid steams with comets and asteroids as well as the search of streams parent bodies is one of the most interesting problems in astronomy. P. B. Babadzhanov made a significant contribution to the solution of this problem. The key notion in this area of research is a notion of the proximity of orbits of celestial bodies, and the measurement instrument for the proximity is a metric on the five-dimensional space of Keplerian orbits. Several metrics were proposed in last 15 years, which turn various spaces of Keplerian orbits into metric spaces. Quotient spaces of orbits, allowing to disregard the longitude of ascending node or the argument of pericenter or both, play an important role. Those elements evolve secularly under the influence of various perturbations. Here we introduce one more quotient space, where two orbits are considered identical if they differ only in their longitudes of nodes and arguments of pericenters, but have the same sum of these elements (the longitude of pericenter). The function is defined to calculate distance between two equivalence classes of orbits. The algorithm of calculation of value is provided along with corresponding program, written in С language. Unfortunately, is not a full-fledged metric. We proved that it satisfies first two axioms of metric space, but not the third one: the triangle inequality does not hold, at least in the case of large eccentricities. However there are two important particular cases when the triangle axiom is satisfied: one of three orbits is circular, longitudes of pericenters of all three orbits coincide. Perhaps the inequality holds for all elliptic orbits, but this is a matter of future research.

Ключевые слова: keplerian orbit; metric; quotient space of metric space; distance between orbits.

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L.L.Sokolov , I.A.Balyaev , K.S.Kholshevnikov , B.B.Eskin
On the convergence and collisions of asteroids with the planets
Using examples of dangerous asteroids Apophis and 2006 EX5, as well as families of model asteroids, we consider their approach to the Earth on trajectories leading to a collision with it. Such approaches allow detecting a dangerous object in advance, clarifying its orbit from observations, and also provide a potential opportunity to use the effect of a gravitational maneuver to economically prevent an asteroid from colliding with the Earth. It is shown that for real dangerous asteroids and their possible collisions, preliminary approaches are more common than for randomly constructed collision trajectories.

Ключевые слова: asteroids; orbit evolution; convergence; collisions with the planets.

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D.V.Milanov , A.S.Shchepalova
Determination of the mean orbit of a family Keplerian orbits
In problems of identifying meteor showers, searching for their parent bodies and identifying fragments of these bodies the average orbit of the stream plays an important role. This is the Keplerian orbit obtained by averaging the orbits of the bodies that make up the group under study. The averaging operation itself does not have a natural and unambiguous definition, since the systems of orbital elements are diverse, and the transformations between them are nonlinear. We propose to determine the average orbit of the family based on the metric in the orbit space. Following Frechet, we define the mean of the family as an element of the space that minimizes the mean-square distance to family members. It is not an easy task to prove the existence and uniqueness of such an element and find a way to calculate it. Here we accomplish it for three metrics which were introduced by K.V. Kholshevnikov on the space of curvilinear orbits H. Exact formulas are given for calculation of the mean of a family of orbits in the space H and its two quotient spaces, consisting of classes of orbits that differ only in the argument of the pericenter (H / ω) or the argument of the pericenter and the longitude of the ascending node (H / (Ω, ω)). Conditions for the existence and uniqueness of means in these spaces are also given: these conditions are satisfied for all samples, with the exception of a nowhere dense set.

Ключевые слова: keplerian orbit; metric; quotient space of metric space; distance between orbits; mean orbit.

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On the reasons that determine the value of the mass index of meteor bodies
The shapes (slopes) of the meteoroid mass spectra are analyzed. In general, the forms of the mass spectra of meteor bodies that cause sporadic meteor phenomena in differential form are close to dNµMdM (this corresponds to meteoroid massindex s = 2). The appearance of this spectrum can be explained by the random nature of the meteoroid formation process -(sequential) fragmentation of the parent bodies of meteoroids. Deviations from this reflect the influence of factors that dominate further evolution of the meteoroid population.

Ключевые слова: meteor; meteoroid; mass index.

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T.J.Jopek , G.I.Kokhirova , P.Jenniskens , D.Janches , M.Hajdukova , R.Rudawska
IAU meteor data center: the shower database
The IAU Working Group on Meteor Shower Nomenclature was established in 2006 to regulate the nomenclature of meteor showers reported in the scientific literature. One year later the International Astronomical Union Meteor Data Center shower database was implemented (IAU MDC). The database does not contain all information about the meteor showers. Its purpose is to give each new meteoroid stream, published in the scientific literature, a unique name and codes. During the Meteoroids 2019 conference held in Bratislava, the IAU Working Group on Meteor Shower Nomenclature established new rules for the introduction and removal of meteor showers from the MDC. In this paper, we present a concise description of the meteor shower database, its origin, and structure and, in particular, the current requirements for the introduction of new data, and unknown as well as known meteor showers.

Ключевые слова: meteoroid stream; meteor shower; IAU MDC shower database; meteor shower nomenclature rules; new meteor shower submission rules.

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Determination of solar wind velocity by measuring points plasma tail of comet C/2019 Y4 (ATLAS)
The article determined the radial velocity of the solar wind from observations of the plasma tail of comet C/2019 Y4 (ATLAS) for near-comet space and the heliographic latitude of the comet. The effect of the tangential component of the solar wind velocity is proposed as a condition for underestimating the value of the determined velocity relative to the experimentally measured solar wind velocity by the spacecraft.

Ключевые слова: solar wind; comet; heliographic latitude; tangential velocity.

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M.Sh.Kholov , B.Jafari , М.D.Khalikova , Kh.Z.Karambakhshov , Sh.R.Samikhov , P.Langer , S.Sh.Safarov
Palladium cross-coupling reaction of Buchwald-Hartwig for 8-chlora-2-methyl-benzo [4.5] thiazolo [3, 2- a] pyrimidin-4-one
Benzothiazolo [3,2-a] pyrimidine has a wide range of pharmacologically active properties such as antibacterial antitumor antitumor, fungicidal, antitumor, sedative and antifungal. The Buchwald-Hartwig cross-coupling reaction, which is a reaction of the formation of C-N bonds by a palladium cross-coupling reaction between amines and aryl substituted halides, also worked well with different amines and heteryl halides, i.e. 8-chloro-2-methylbenzo [4.5] thiazolo [3,2-a] pyrimidin-4-one. By optimization the reaction of 8-chlorine-2-methylbenzo [4.5] thiazolo [3.2-a]pyrimidine -4-one with morpholine, the best a catalytic condition appeared application as catalyst Pd (dba)x CHCl, (4 mol%) , ligand XPhos (8 mol %) bases NaOtBu, (1.4 экв) and boiling in toluene (2 ml) during 16 h. Under these conditions yield of 8-morfolino-2-methylbenzo [4.5] thiazolo [3.2-a] a pyrimidine -4-one was 85%, for other amines of products of a cross-coupling a percentage of yields were: 52 (8-phenylmethylamino-), 72 (8-fluorphenylamino-), 56 (8-(3-trifluormethylphenylamino)-) and 63 (8-(3.5-dimethoxiphenylamino) - 2-methylbenzo[4.5] thiazole [3.2-a]pyrimidine-4-one, Structural explanation of the synthesized connections are proved by data of NMR H, C and IR-spectroscopy

Ключевые слова: 8-chloro-2-methylbenzo[4,5]thiazolo [3,2-a]pyrimidin-4-one; palladium reaction cross-coupling of Buchwald-Hartwig-amination.

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Kh.M.Nazarov , I.Mirsaidzoda , B.B.Barotov , K.O.Boboev , U.M.Mirsaidov
Possibility assessment of uranium waste processing from Adrasman tailings
The results on the processing of uranium waste from the Adrasman tailing dump are presented in this article. The chemical, granulometric, mineralogical compositions of uranium wastes, as well as their activities, have been determined. The optimal parameters of tailings processing have been found.

Ключевые слова: waste; tailing dump; uranium; activity; Adrasman.

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A.S.Kurbonov , J.Kh.Juraev , A.Р.Tagаev , M.M.Tagoev , U.M.Mirsaidov
Thermodynamic features of processing reactions during decomposition of borosilicate ore with orthophosphoric acid
The paper presents thermodynamic analysis of a number of chemical reactions possibility during the processing of borosilicate ores of Tajikistan with orthophosphoric acid. The analysis showed the reactions feasibility of almost all minerals of the borosilicate ores composition by leaching with orthophosphoric acid in the investigated temperature range.

Ключевые слова: borosilicate ores; decomposition; thermodynamic analysis; enthalpy; entropy; thermal capacity.

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F.N.Hasanov , Yu.F.Bakhodurov , E.J.Goziev , B.K.Rakhmatulloev
Complex formation of copper (ii) with 1-phenyl-2,3-dimethylpyrazoline-5-thione in a medium 3 mol/l HCl
The article investigated the potentiometric method complexing Cu (II) with 1-phenyl-2,3-dimetilpirazolin-5-thione (1-F-2,3-DMT-T-5) in the medium of 3 mol / l HCI. It is shown that four complex particles are formed in the Cu (II) -1-F-2,3-DMP-5-T system. General and stepwise stability constants of 1-phenyl-2,3-dimethylpyrazoline Cu (II) complexes were determined depending on temperature. The thermodynamic functions of complex formation are calculated by the temperature coefficient method. It was found that copper (II) complexes with 1-phenyl-2,3-dimethylpyrazoline-5-thione are enthalpically stabilized. It was found that the temperature factor has an indifferent effect on the dependence of рКi on HCl concentrations for chloro-1-phenyl-2,3-dimethylpyrazoline-5-thionic copper (II) complexes.

Ключевые слова: 1-phenyl-2,3-dimethylpyrazoline-5-thione; complexation; copper (II); stability constant; thermodynamic functions.

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Z.S.Nazarov , H.Safiev
Sluidge field waste recucling of the open joint stock company Tajik aluminum company
Technological parameters of water waste treatment are studied the technological modes of the processes are established: the washing temperature is 25-40C,the mass ratio of sludge and water (t.w.) is 1:5, the duration of the water treatment process is 30 minutes at under these conditions, the degree of recovery of water-soluble waste components reaches 95% and higher, and the optimal parameters are also established decomposition of the solid residue by sulfuric acid after water treatment speca with production of useful components.

Ключевые слова: washed sludge; Industrial waste; part of the water-soluble; water-insoluble part of the sulfuric acid decomposition.

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M.M.Mamadvafoev , D.A.Davlatshoev
Manganese in the rocks of the intrusive complexes of the Kafandara ore field (Central Tajikistan)
The article is the first to consider the probability distribution function of manganese content, its abundance, manganese-iron ratios and correlations and dependences with petrogenic elements in the rocks of the intrusive complexes of Kafandara ore field.

Ключевые слова: manganese; distribution function; abundance in rocks; manganese-iron relationships; correlations; petrogenic elements; rocks; intrusive complexes; Kafandara ore field.

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A.S.Niyozov , A.K.Khodzhiev
The geodynamic evolution of the South Gissar zone as a prerequisit for the development of the ore-bearing volcano-plutonic association
The South Gissar geostructural zone of the Gissar-Alai developed in the Turkestan (O-C) and Gissar (C) oceans, as a borderland active zone. Starting from D, the paleoturkestan paleobasin are decreases and subduction stops. At the end of the Paleozoic, the collision of continental plates continues, and nappes are formed. Intense orogenesis occurs and large plutons are introduced. Magmatism is manifested by powerful outpouring of tholeiitic basalts (Karatag series) and associated gabbro and plagiogranites (Khodjamafrach complex) - the first signs of the final formation of the continental crust of the zone. Subsequent magmatic series manifested themselves in parallel with the absorption of the oceanic crust, the convergence of the Karakum-Tarim (Kazakhstan) and Tajik paleocontinents, which is recorded by the disappearance of carbonate formations and the appearance of flysch (with olistostromes) formations (Muborak formation). The toleiite-basaltic and gabbro-plagiogranitoid series, which form a single volcano-plutonic association, are a derivative of the island-arc stage of development of South Gissar. The ore content of the association, previously estimated without taking into account the syngeneticity of the series, in the light of new plate tectonic studies, seems to be complex and promising.

Ключевые слова: The Gissar-Alai; The South Gissar; geostructural zone; magmatism; toleiitic basalts; gabbro-plagiogranitoids; association; ore-bearing.

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G.N.Petrov , А.S.Kodirov , Kh.M.Akhmedov
On the issue of optimization of the territorial distribution of power plants of medium and low power
The paper considers the issue of optimization of the territorial distribution of power plants of medium and low power in the development of renewable energy sources. The efficiency radius of the power plant as a function of its capacity is used as an optimization criterion to minimize overall costs. Calculations show that in the power range of small power plants up to 2000 kW, the efficiency radius does not exceed 45 km.

Ключевые слова: renewable energy sources; hydropower; annual costs; capital investment; efficiency criterion; energy losses; present value; radius of power plant efficiency.

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L.Sharipov , J.N.Nizomov , A.J.Rahmonzoda , I.S.Muminov , I.Sh.Ashurov
Construction of monolithic reinforced concrete frame-free frame for seisic areas
The article deals with the calculation, design and construction of elements of a monolithic reinforced concrete slab with normal and mixed reinforcement. ABP-basaltoplast is used as composite reinforcement for reinforcing tiled supports. The design, construction, and static and dynamic tests of the slab connection point were performed with the unloaded steel column to its original shape

Ключевые слова: girder-free frame; monolithic reinforced concrete; calculation; composite reinforcement; ABP - basalt plastic reinforcement; joint; node; reinforcing mesh; cantilever part of the slab; construction; welding.

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