of National Academy of Sciences
of Tajikistan

Reports of the National Academy of Sciences
of Tajikistan

Доклады Академии наук Республики Таджикистан, том 59, №7-8, 2016 г.

Article title and abstractPages
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Rakhmonov Z.Kh., Rakhmonov F.Z.
Estimation of short cubic exponential sums with prime numbers in minor arcs
A.Dzhuraev Institute of Mathematics, Academy of Sciences of the Republic of Tajikistan When и , ( , - absolute constant) non-trivial estimate is obtained for the short cubic exponential sums of the form

Key words: проблема Варинга-Гольдбаха; короткая тригонометрическая сумма с простыми числами; метод И.М.Виноградова оценок тригонометрических сумм с простыми числами; Waring-Goldbach problem; short exponential sums with prime numbers; the method of I.M.Vinogradov estimates of exponential sums with primes.

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Zamonov B.M.
Estimates of short cubic exponential sums with Möbius function over minor arcs
In this paper for ( , - absolute constant) a non-trivial estimate of short cubic exponential sums with Möbius function of the form over minor arcs for was obtain.

Key words: короткая тригонометрическая сумма; функция Мёбиуса; метод И.М.Виноградова оценок тригонометрических сумм с простыми числами; малые дуги; short exponential sums; I.M.Vinogradov's estimation method for exponential sums over primes; Möbius function; minor arcs.

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Tukhliev K., Malikov A.M.
The approximation of function in the mean at all axes by algebraic polynomials with Chebishov-Ermit's weight
In this article an extremal problem on best approximation of function squared-summable at all axes by algebraic polynomials with Chebishov-Ermit weghts is considered. An exact inequality in the mean of Jackson-Stechkin on the set of functions which colligate the best approximation from above by average values of modulus continuity of m-th order determined by differential operator of second order are received.

Key words: наилучшее приближение; алгебраический полином; коэффиценты Фурье-Эрмита; обобщенный модуль непрерывности; best approximation; algebraic polynomial; coefficients of the Fourier-Hermite; generalized modulus continuity.

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Aligavarov S.A.
About the estimate of error on complicated quadrature formulas for some classes of differentiable functions
In the article error estimates from the above complicated quadrature formulas for sone classes of differentiable functions, which set by the integrated module of smoothness in the L , 1 ≤ p ≤ ∞ . space are found.

Key words: квадратурная формула; погрешность; модуль непрерывности; модуль гладкости; quadrature formula; error; the modulus of continuity; module of smoothness.

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Karimov O.Kh.
Coercive properties and separability nonlinear Helmholtz operator with a matrix potential in the weighted space
In this paper, we investigated the coercive properties of the nonlinear Helmholtz operator with matrix potential in the weight space L ( R ) . The nonlinear operators are not a weak perturbation of linear operators.

Key words: нелинейный оператор Гельмгольца; матричный потенциал; коэрцитивное неравенство; разделимость; весовое пространство; nonlinear Helmholtz operator; matrix potential; coercive inequality; separability; weighted space.

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Mirzoakhmedov F.
Stochastic analog linear programming problems with bifurcation effect
The article presents algorithms effective simplex method for solving the general problem of linear programming, which also used in solving the stochastic version of the problem. We also prove the convergence of the algorithm for solving stochastic version problem with the bifurcation effect and proves to be true of the test example.

Key words: детерминированная и стохастическая задача; ветвление; квазиградиент; алгоритм решения; теорема сходимости; численный эксперимент; deterministic and stochastic problem; kvazigradient algorithm solving; convergence theorem; numerical experiment.

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Kokhirova G.I., Obrubov Yu.V., Vlaykov N.D.
On the influence of differential planetary perturbations on the criteria of orbital closeness
On the base of differential evolution of orbits of comet 2P/Encke, comet 96P/Machholz and asteroid 3200 Phaethon the limits of long-term variations of Tisserand’s constants T , along with Lidov’s constants , and criterion of Southworth and Hawkins, criterion of Drummond, criterion of Jopek and criterion of Valseccki et al. were evaluated. The perturbations from all eight major planets were taken into account. It was shown that D , and criteria have the most significant deviations. Criteria T , , and undergoing much less deviations.

Key words: комета; астероид; орбита; эволюция; планетные возмущения; критерий схожести орбит; comet; asteroid; orbit; evolution; planetary perturbations; criterion of orbital similarity.

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Muminov Kh.Kh., Shokirov F.Sh.
Isospin dynamics of topological vortices
By methods of numerical simulation the isospin dynamics of interacting radially-symmetric topological vortices (solitons) of the Belavin-Polyakov type in (2+1)-dimensional O(3) nonlinear σ-model is studied. The conditions that lead to the elastic interaction, gradual annihilation and long-range interactions of topological vortices are determined.

Key words: топологический вихрь; изоспиновая динамика; нелинейная σ-модель; численное моделирование; topological vortex; isospin dynamics; nonlinear σ-model; numerical simulation.

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Umarov N.N., Yusupov I.Kh., Marupov R.
The study of properties of components wild medicinal plants of L. by EPR spectroscopy
With methods of the EPR spectroscopy the content of free radicals in the stems and leaves of wild Plantago lanceolata L. was investigated. According to the EPR signal of spectral parameters determined that the number of free radicals contained in the biochemical composition of plants depends on the environmental state of habitat.

Key words: ЭПР-спектроскопия; свободные радикалы; подорожник ланцетный; спектры ЭПР; EPR spectroscopy; free radicals; Plantago lanceolata L; EPR spectra.

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Mulloev N.U., Yusupova J., Mahsudov B.I.
H-complexes and spectral characteristics of certain oxygen-containing heterocyclic compounds in solution
The formation of complexes of some N-oxygenated heterocyclic compounds with a methyl alcohol solution is studied. The change in the spectral and energy characteristics of systems associated with the induction of structural fragments influence imposed on the equilibrium position of the electron configuration group 1 of proton accepters is observed. It is concluded that the tested compounds are poor proton accepters.

Key words: гетероциклические соединения; протоноакцепторная способность; производные диоксоланов; индукционное влияние; стерический фактор; heterocyclic compounds; proton-ability; dioxolanes derivatives; inductive influence; the steric factor.

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Saidov R.H.
Temperature dependence of the heat capacity of aluminium, copper, silicon, magnesium and zinc
The results of the study the temperature dependence of the heat capacity of aluminium, copper, silicon, magnesium and zinc with the predictions of the theory were compared.

Key words: алюминий; медь; кремний; магний; цинк; теплоёмкость; aluminum; copper; silicon; magnesium; zinc; heat capacity.

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Safaralikhonov A.B., Khudoyorbekov F.N., Aknazarov O.A.
The influence of the replant UV-irradiation seeds of wheat for its further growth and transpiration intensity of leaves
In this article we brought up the experimental materials on influence of the UV-radiation on growth and transpiration intensity of wheat plant leaves. It shows that UV-radiation in the field of the medium-wave stimulate the growth and relatively increase the intensity of transpiration of wheat plant, but the shot-wave rays inhibit the plant growth processes and comparatively decrease the transpiration of above mentioned sorts of wheat.

Key words: УФ-радиация; пшеница; рост; транспирация; UV-radiation; wheat; growth; transpiration.

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Aliyev K., Mirzorakhimov A.K., Bobokhonov R.S., Ashurov S.Kh., Saburov B.M.
Enzymes of antioxidant system of the cell protection of plants in drought conditions
The results show that sustainable and productive varieties is relatively low the loss of water that characterizes the tolerance of this variety to the stress. Under the influence of water deficiency, the activity of GR and ASCP in genotypes (varieties) changed in different ways. The activity of GR and ASCP in the leaves of Tajikistan potato varieties in the amplification of the drought after 7 and 9 days increased, and the gain was and, conversely, varieties of Picasso as increased drought was observed in the inhibition of the activity of these enzymes.

Key words: антиоксидант; относительное содержание воды; засуха; устойчивость растений; антиоксидантные ферменты; antioxidants; relatively of water contents; drought; resistant; plants; antioxidant enzymes.