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, №1, 2016 г.

Article title and abstractPages
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Tukhliev K.
The exact value of -widths of some classes of functions
The exact meaning of the various n -widths for the classes of functions encountered in accurate estimates of the rate convergence of Fourier-Bessel finding was found.

Ключевые слова: функция Бесселя; наилучшие приближения; обобщённый модуль непрерывности m-го порядка; ряд Фурье-Бесселя; n-поперечники; Bessel function; best approximation; ranks of Fourier-Bessel; generalized modulus of continuity of m-th order; n-widths.

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Akhmadiev M.G., Khasanov Yu.Kh.
Direct methods for solving singulyar integro-differential equations in the diffraction problems
In the article some direct methods for solving singular integro-differential equations erasing in diffraction problems on a segment square-summable functions are given. Convergence velocity of considered methods is corrected depending on structure characteristic properties of the equation’s coefficients.

Ключевые слова: сингулярное интегро-дифференциальное уравнение; задача дифракции; метод коллокации; метод Галеркина; метод наименьших квадратов; скорость сходимости метода; singular integro-differential equation; diffractions problem; collocations method; Galerkin method; least square method; convergence velocity of the method.

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Kurbanshoev S.Z., Yakubov N.S.
Principle information the theory of differential equations in Banach spaces
The article discusses the method of reduction nonlocal character by constructing a special integral manifolds, and sufficient and necessary conditions for the applicability of the principle of information system is sufficiently general form. Indicated substitutions are mixing.

Ключевые слова: метод сведения; интегральные неравенства; интегральное многообразие; метод последовательных приближений; method of information; integral inequality; integral manifold; method of successive approximations.

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Ganiev Ch.T., Yunusi M.K.
Solution of an integro-differential problems of the turbulence population
This work deals with the study and research of the solution of one integro-differential problem describing the population model of turbulence with the time-space distribution and age-related change in the parameters (diffusion coefficient) in a given field of nonlinear equations. A proven theorem on the uniform convergence of Fourier series for a given task.

Ключевые слова: популяция; численность; модель; время; возраст; пространство; турбулентность; model populations; quantity populations; population turbulence; time-age-spatial distribution.

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Nurubloev M.
Boundary value problems for a system of higher order equations of composite type in n-dimensional space
In the paper we investigate solvability of the Dirichlet problem in the half-space for systems of higher order differential equation of composite type. It is proved that problem under consideration have a unique solution.

Ключевые слова: система уравнений составного типа; краевая задача; итерация; характеристическая форма; моногенная функция; system of equations of composite type; boundary value problem; iteration; characteristic form; monogenic function.

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Kosimov A.A.
On a set of the anagrams in poem "Shehnomeh" by A.Firdousi
Thanks to special coding of wordforms, a set of anagrams to "Shehnomeh" by A.Firdousi is exhaustively described. Statistical data on the number of different anagrams with a specified number of items are received. Some anagrams with the highest number of wordforms are presented for discussion.

Ключевые слова: Фирдауси; Шахнаме; словоформа; кодирование; анаграмма; статистика; Firdousi; Shehnomeh; word form; coding; anagram; statistics.

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Rustamov G.Z.
Frequencies of tajik word forms of child and modern literature
Established linear dependence between syntactic word forms and nonlinear dependence between significant word forms of the child and modern literature.

Ключевые слова: таджикский язык; словоформа; служебные; знаменательные; корреляция; Tajik language; word form; syntactic word; significant word; correlation.

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Kokhirova G.I., Rakhimi F., Kryuchkov S.V., Nikolenko I.V., Mullo-Abdolov A.Sh., Khamroev U.Kh., Abdulloev S.H.
New “First Light” of the telescope Zeiss-1000 of the International Astronomical Observatory Sanglokh
The telescope Zeiss-1000 of the International Astronomical Observatory Sanglokh (IAOS) of the Institute of Astrophysics of the Academy of Sciences of the Republic of Tajikistan was out a working state more than 25 years. Taking into account the significant importance of an operating of the telescope for the further development of astronomical investigations in Tajikistan, the excellent astroclimate of the IAOS and existing infrastructure, the reconstruction and modernization of the telescope have started in March 2015. As a result, the new “First light” of the telescope Zeiss-1000 was obtained in April-May 2016, i.e. the digital images of the outer space objects were registered.

Ключевые слова: обсерватория; телескоп; программа; наблюдения; координаты; галактика; observatory; telescope; software; observations; coordinates; galaxy.

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Davlatzoda D., Abdulloev S.Kh., Minikulov N.Kh.
Ambiguous color changes of cepheid V383 Cyg with fadings of light
We analyze the results of BVRI photometric observations of cepheid V383 Cyg and the curve of the brightness of these star is built. The character color changes with the light fading of V383 Cyg on two-color diagrams V- (B-V), V- (V-R), V- (V-I) and V- (R-I) is investigated. It is shown that the star V383 Cyg shows changes in mixed color indices with the weakening of light, which is mainly characterized by young stars with Algol-like fadings of light.

Ключевые слова: переменные звёзды; цефеиды; кривая блеска; двухцветная диаграмма; variable stars; Cepheids; light curve; two-color diagram.

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Amirkhanov I.V., Muminov Kh.Kh., Sarhadov I., Kholov A.
Numerical simulation of oscillations of a gas bubble in a liquid under the influence of acoustic waves
In this paper, numerical simulation of a gas bubble under the influence of acoustic waves in the fluid has been conducted. In the simulation the method of dynamically adapting grids is used, the effectiveness of which has been demonstrated in the model problem. Application of the method of dynamically adapting grids allow to conduct simulation with less number of sampling points and simultaneously increase the speed and precision of calculations.

Ключевые слова: численное моделирование; метод динамических адаптирующих сеток; газовый пузырёк; акустические волны; numerical simulation; method of dynamically adapting grids; gas bubble; acoustic waves.

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Nizomov J.N., Kalandarbekov I., Kalandarbekov I.I.
Calculation of action continuous beams static load by concentrated deformation method
The calculation of two-span continuous beam at static load effect with supple legs is given. Features the formation of the coefficient matrix and the stiffness matrix of the inner intermediate compliant supports were showen. The results are compared with the analytical solution.

Ключевые слова: метод сосредоточенных деформаций; неразрезная балка; матрица внутренней жёсткости; диагональная матрица податливости; коэффициент жёсткости; аналитическое решение; method of lumped strain; continuous beam; internal stiffness matrix; a diagonal matrix ductility; hardness factor; analytic solution.

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Akhmedov Kh.M., Tashbaev G.A., Partoev K., Abdullaev Sh., Abdullaeva S.
The use of the «Duozym» drug at the production of ethyl alcohol from jerusalem artichoke
In this paper, as an alternative feedstock for the production of ethyl alcohol it was used Jerusalem artichoke variety “Interest”. To accelerate the hydrolysis of the enzyme as “Duozym” drug was used. It was found the optimal conditions for hydrolysis of the crushed mass of Jerusalem artichoke under the action of its own raw materials and «Duozym» drug. The use of the enzyme “Duozym” drug and conduction of inulin hydrolysis under milled conditions using own inulase feedstock ordinary bakers yeast in the fermentation yielded clarified word with high fruktozanov of tubers.

Ключевые слова: топинамбур; этиловый спирт; фермент; дрожжи; инулин; гидролиз; сбраживание; фруктоза; Jerusalem artichoke; ethyl alcohol; enzyme; yeast; inulin; hydrolyze; fermentation; fructose.

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Azizov R.O., Saidov M.Kh.
Temperature voltage system "coverage - basis"
The article deals with influencing parameters of the heating and cooling process in the formation of the stress state of the system "coverage - basis".

Ключевые слова: покрытие; основа; напряженное состояние; остаточное напряжени; coverage; base; the state of stress; residual voltage.

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Mamadvafoev M.M., Rachmonov I.Y.
Petrochemistry of magmatic complexes of Loilacul river basin (Hissar ridge)
The article provides the first information about petrochemistry of magmatic complexes of Kafandar river basin (Hissar ridge), presented by granitoids of inversive multiphase intrusion, their vein derivatives, porphyritic sub-volcanic post-inversion and orogenic dikes and alkaline basaltoids dikes of taphrogenic geodynamic regime of development of the region.

Ключевые слова: петрохимия; магматические комплексы; гранитоиды; плутон; эндо- и экзоконтакты; спессартиты; кварцево-латитовые порфиры; щелочные базальтоиды; petrochemistry; magmatic complexes; granitoids; pluton; endo and exocontacts; spessartites; quartz-latite porphyry; alkaline basaltoids.

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Sabirov A.A.
The taxonomy and phylogenesis of the (calcareous foraminifera)
In the article on the basis of analysis of the word literature and author’s research the taxonomy of the genus Salpingothurammina has been worked out and its phylogenetic diagram constructed.

Ключевые слова: фораминиферы; систематика; филогения; палеозой; foraminifera; taxonomy; phylogenesis; Paleozoic.