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 Академии наук Республики Таджикистан. Отделение физико-математических, химических, геологических и технических наук, №4, 2017 г.

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Mustafokulov R.
About one analogue formula Faa-di-Brun and solutions of the diophantine equation +2+K+=
The paper gives an analogue of the classical Faa-di-Bruno's formula, which is used in the calculation of derivatives of a complex function and, in contrast to the Faa-di-Bruno formula, does not use solutions of the Diophantine equation. Comparison of these formulas makes it possible to determine for any natural all non-negative integer solutions of the Diophantine equation x +2 x +K+ nx = n .

Ключевые слова: формула Фаа-ди-Бруно; дифференцирование сложной функции; диофантово уравнение; the Faa-di-Bruno formula; the differentiation of a complex function; the Diophantine equation.

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Kurbanshoev S.Z., Nusayriev M.A.
The construction of the Green matrix and projectors of systems of difference equations
In the paper, the Greens matrix is used to construct projectors that split the solution of a system of difference equations . Integral manifolds of solutions and projectors for linear, nonlinear and functional systems of difference equatians are constructed.

Ключевые слова: функция Грина; экспоненциальная дихотомия; разностные уравнения; интегральные многообразия; проекторы; Grin function; exponential dichotomy; deference equations; integral manifold; projectors.

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Kurbonov I., Saidaliev Kh.P.
About solubility of the nonlinear marginal problems of electromagnetoelasticity for nonhomogeneous matter
Solutions of bound fields equations of electromagnetoelasticity are studied in the field of . Theorem of existence and unique specified problems, in space with weight is proved. At proof of the theorem of existence characteristics of bound fields and Gronuoll-Bellman inequality are used.

Ключевые слова: магнитоупругость; априорные оценки; неравенство Гронуолла-Беллмана; свойства связанных полей; electromagnetoelasticity; an a priori estimations; Gronuoll-Bellman inequality; a characteristic of bound fieldlds.

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Rahimova M.A.
Polynomial solutions of overdetermined systems of partial differential equations with singular coefficients
In the paper the overdetermined systems of partial differential equations with singular coefficients were investigated. For these systems the problem of solutions defined in the first quarter of the plane and growing at infinity is no faster than the polynom was studied. Sufficient conditions for the existence of these solutions are found. These conditions are written out in terms of the coefficients and the right-hand sides of the system.

Ключевые слова: переопределенная система уравнений в частных производных; сингулярные коэффициенты; полиномиальные решения; пространство локально-интегрируемых функций; overdetermined system of partial differential equations; singular coefficients; polynomial solutions; the space of local-integrable functions.

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Muminov Kh.Kh., Muhamedova Sh.F., Asghari-Larimi M.
Numerical simulation of signal propagation in three-level quantum computer systems within multi-soliton solutions of vector nonlinear equation Shredinger
Modeling of the process of signal propagation between qutrits by use of the vector nonlinear Schrödinger equation with potential 2 ε (| φ |- b )- λ | φ | and condensate boundary conditions is carried out. The possibility of signal propagation in the form of solitary waves - solitons, which are bound excited states with internal dynamics in three-level systems, is shown.

Ключевые слова: n-солитон; кутриты; кудиты; конденсатные граничные условия; векторное нелинейное уравнение Шредингера; бризер; n-soliton; qutrits; qudits; condensate boundary conditions; vector nonlinear Schrödinger equation; breather.

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Normahmedov O.O., Brylev O.A., Kholov A., Muminov Kh.Kh.
Freeze drying synthesis of LiMnNiCoO cathode materials for lithium-ion batteries
For the first time, cathode materials based on LiMnCoNiO were obtained by freeze dried method. The thermal decomposition of freeze drying precursors was carried out at 400-800°С. By using XRD and SEM techniques it was shown that at 400°C, the spinel formation begins, and at 800°С there are signs of breakdown of spinel. Also an increase in the temperature of thermal decomposition from 400 to 800°С leads to an increase in the size of the crystallites from 20-50 to 300-500 nm.

Ключевые слова: криохимический синтез; катодные материалы; литий-ионные аккумуляторы; freeze draying synthesis; cathode materials; Li-ion batteries.

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Kadirov A.L.
Theoretical interpretation of the occurence of EMF at homogeneous heating of isotypic micro-grained silicon
A different physical explanation is given for the occurrence of EMF at ohmic contacts of an isotype semiconductor working medium heated under isothermal conditions. It is shown that the spontaneous generation of electron-hole pairs under uniform heating of isotypic micro-grained powdered polysilicon and technical silicon is due to synergistic process, the impetus to which is the fluctuation difference in the electrical properties of contacts.

Ключевые слова: изотипный вторичный литой поликристаллический кремний (ВЛПК); спонтанная генерация ЭДС; синергетический процесс; бифуркационный параметр; isotype secondary cast polycrystalline silicon; spontaneous EMF generation; synergetic process; bifurcation parameter.

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Khojiev S.K., Nazarov Kh.M., Barotov B.B., Boboyorov M.D., Mirsaidov U.M.
Sulfuric acid leaching of uranium from the ores of «Central Tajikistan» deposit
The sulfuric acid leaching of uranium from the ores of “Central Tajikistan” Deposit is studied. It has been shown that the ore is a uranium silicate, containing more than 30 per cent of SiO and the acid methods of ore decomposition are effective for ore precessing.

Ключевые слова: уран; руда; выщелачивание; Центральный Таджикистан; серная кислота; uranium; ore; leaching; Central Tajikistan; sulfuric acid.

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Akramov M.Yu., Sulaimonshoev Kh.A., Khakimova N.U., Pulatov M.S., Nazarov K.M., Mirsaidov U.M.
Projected synthesis of aluminum hydride and the borohydrides of the rare earth metal
The projected processes of synthesis of aluminum hydride via binary hydrides of alkaline earth metals and aluminum chloride with auto-initiate and model synthesis of rare-earth metal borohydrides Ln(BH) are studied in the article.

Ключевые слова: гидрид алюминия; программированный синтез; редкоземельные металлы; щелочноземельные металлы; хлористый алюминий; aluminum hydride; projected synthesis; rare earth metals; alkaline earth metals.

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Pulatov P.R., Eshov B.B., Ganiev I.N., Norova M.T.
Oxidation of industrial AMg3 alloy with additives of rare earth metals
By gravimetric method oxidation of the alloy AMg3, alloyed with scandium, lanthanum, praseodymium and neodymium in the solid state has been investigated. The dependence of the oxidation of alloys on the composition and temperature is established. Compositions of the oxidation products of alloys are determined.

Ключевые слова: сплав АМг3; редкоземельные металлы; окисление сплавов; энергия активации; скорость окисления; температура и состав сплавов; AMg3 alloy ; rare earth metals; oxidation of alloys; activation energy; oxidation rate; temperature and composition of alloys.

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Tagoev M.M., Barotov A.M., Nazarov Sh.B., Kurbonov A.S., Mirsaidov U.M.
Assessment of the sintering process of borosilicate ores with sodium-containing reagents
The results of the sintering of boron raw concentrate of the Ak-Arkhar field with sodium-containing reagents are presented. Optimal conditions for sintering of borosilicate ore concentrate with NaNO, NaCO and NaSO are determined.

Ключевые слова: спекание; боросиликатная руда; натрийсодержащие реагенты; нитрат натрия; карбонат натрия; сульфат натрия; sintering; borosilicate ore; sodium-containing reagents; sodium nitrate; sodium carbonate; sodium sulfate.

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Ragabov U.R., Sultonov R.A., Yusupov I.Kh., Haydarov K.H.
Synthesis and biological properties of Zincas and It’s investigations by spin label method
Zinc complexes of acetylcysteine (Zincas) with high purity has been synthesized. It is shown that the producing process is technologically distinctive and allows preparing all desired products in quantities, which is necessary for abroad study of biological activity. The concentration dependence of this complex is also studied by the spin-label method, which is inhibited at room temperature with a decrease in the concentration of the complex in the EPR spectrum, the spectral parameters of the rotational diffusion of the mobility of the spin label decrease, i.e., the signal narrows and the mobility of the nitroxide fragment increases. It has been found that in the zinc sulfate compound, when ethanol is added in solution in the presence of a nitroxide radical, it completely restores and affects the chemical stability of the nitroxide fragment, which indicates a strong property of antioxidants.

Ключевые слова: координационные соединения; целевые продукты; цинкацетилцистеин; цинкас; нитроксильный радикал; спектры ЭПР; coordination compound; target product; zincacetylcysteine; zincas; nitroxyl radical EPR spectrа.

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Kariev A.R.
The main milestones and epochs of rock formation in the basins of the tajik region in connection with the aspect of sedimentary ore genesis
Based in a detailed study of the geological structure of the Tajik region lithological and mineral composition of the Phanerozoic rocks the possibility of formation of bauxite ores and high - alumina deposits associated with medium - carbon Border late Permian and Early Triassic intervals of the Paleozoic and mesoroic is established.

Ключевые слова: фанерозой; палеогеография; литология; субстрат; туф; эффузив; пепел; Phanerozoic; paleogeography; lithology; substratum; Tuff; Effusive; ash.

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