# Reports of the National Academy of Sciencesof Tajikistan

## Доклады Академии наук Республики Таджикистан, том 57, №1, 2014 г.

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Usmanov Z.D.
5-8
A generalization of the formula to golden section
For cases when the formula of the golden section is inapplicable as a mathematical model for a satisfactory description of an applied problem we present its modified version, containing two real parameters. The formulas for calculation of the latter on the basis of experimental data are proposed.

Key words: золотое сечение; формула; обобщение; golden section; formula; generalization.

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Ismatov S.N.
9-14
On the distribution of the fractional parts of { }, which argument runs through the primes in a short interval
The problem of the distribution of the fractional parts of argument, which runs through the primes in a short interval is reduced to the evaluation of short sums of exponential sums with prime numbers.

Key words: короткая тригонометрическая сумма; равномерное распределение; распределение дробных частей; простое число; short exponential sum; uniform distribution; distribution of fractional parts; prime.

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Jangibekov G., Chorshanbieva Ch.
15-24
On the noether and the index of a class of two-dimensional singular integral operators
The purpose of this article is to establish an effective necessary and sufficient conditions and Noetherian operator A in L (D) (considered over the field) 1< p <∞ and getting the formula for the calculation of the index.

Key words: нетеровость оператора; индекс оператора; операторная матрица; двумерные сингулярные интегральные операторы; Noetherian; the index of operator; operator matrix; two-dimensional singular integral operators.

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Shakirov I.A., Khasanov Yu.Kh.
25-31
About extreme problem, that is connecting with the asymptotic formula for the Lebesques constant is solved
For the Lébesque’s constant corresponding to the Lagrange interpolation polynomial rather strict bilateral assessment for the first time is received. On this basis then the actual extreme problem, that is connecting with the asymptotic formula for the considered constant is solved.

Key words: тригонометрический полином Лагранжа; интерполяционная характеристика; асимптотическое равенство; верхняя и нижняя оценки константы Лебега; trigonometrically Lagrange polynomial; interpolational characteristic; asymptotic equality.

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Umarov N., Davlatmamadova S.S.H., Shukurov T., Usmanov A., Marupov R.
32-36
Research of molecular properties of leaves medicinal (L.) pall by IR-spectroscopy method
The results of research by IR-spectroscopy method of a herb Melilotus officinalis (L.) Pall, collected from various district Sogd region of the Republic of Tajikistan, showed on formation of molecular structure of leaves Melilotus officinalis (L.) Pall renders essential influence of ecological factors. Character testifies to it between - both intramolecular hydrogen connections and interaction of leaves with СuSO ions.

Key words: донник; лекарственные растения; ИК-спектроскопия; экологические условия места произрастания; энергия межмолекулярного взаимодействия; Leaves Melilotus officinalis (L.) Pall; medicinal plants; IR-spectroscopic; ecological factors of a place of growth; energy of intermolecular interaction.

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Usmanov U.R., Usmanov R., Kukaniev M.A.
37-43
Synthesis of -alkyl-benzo [b] thiophene and their 2,3-dihydro derivatives with long hydrocarbon radicals
In the paper the results of a study on the development of methods to obtain alkyl- benzo[b]thiophene and 2,3- dihydro derivatives containing long hydrocarbon radicals are presents. It is established that under the conditions of synthesis of semi and bicycle aromatic sulfur compounds with short alkyl groups, (C -C ) may be prepared homologues, containing long hydrocarbon radicals.

Key words: алкилирование; ацилирование; 3-втор-алкил-бензо[b]тиофен-2-карбоновые кислоты; алкил-бензо[b]тиофены; 2,3-дигидробензо[b]тиофены; циклизация по Фриделю-Крафтсу; alkylation; acylation; 3-secondary-alkyl-benzo[b]thiophene-2-carboxylic acid; alkyl-benzo[b]thiophene; 2,3-dihydrobenzo[b]thiophenes; cyclization of Frиdelyu-Crafts.

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Shamsara O., Muhidiniv Z.K., Bobokalonov D.T., Usmanova S.R., Liu L.S., Khalikov D.K.
44-50
The comparative study of microcapsule formation processes through interfacial reaction of different low methylated pectins and concentrate of why lactoglobulin, in o/w emulsion systems are presented. It’s shown that the formation of stable emulsion and efficiency of drug encapsulation depends on biopolymers nature, it’s ratio, pectins local charge density and molar mass. Among studied pectins the microcapsules formed from HM-apple pectin has advantageous in particle number, size and drug loading efficiency.

Key words: биополимеры; микрокапсулы; НМ-пектин; лактоглобулины молочной сыворотки; эмульсия; пироксикам; biopolymers; microcapsule; LM-pectin; whey protein concentrate; emulsion; piroxicam.

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Rajabov Sh.Kh., Shoev I.S., Mukhamediev N.P., Ruziev J.R., Safiev A.H., Boboev H.E., Mirpochaev Kh.A., Safiev H.
51-56
Complex processing of floury-, alumina-waste of aluminum production
The results of studies on the establishment of the optimal parameter soda- alkaline processing solution obtained by the sulfuric acid decomposition of floury-, alumina-waste aluminum. Studies have shown that when a solution of sulfate of soda- alkaline treatment can be alumina, fluoride salts and building materials.

Key words: сульфатсодержащий раствор; содо-щелочная обработка; сернокислотное разложение; фтор-, глинозёмсодержащие отходы; фтористые соли; Sulfate-containing solution; soda-alkaline treatment; sulfuric acid decomposition; floury-, alumina-containing waste; fluoride salts.

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Babaev A.M., Liskov L.M.
57-62
To the history of upper part of the vakhsh river’s formation
Geological a geomorphological analysis of the Vakhsh River upstream’s area indicates that the modern river-valley on the site of the Obigarm River’s mouth - Nurek town started be formed since Middle Quaternary time.

Key words: рельеф; террасовидные поверхности; водоток; аллювий; долина; река; relief; bench-like surface; flow; alluvium; valley; river.

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Hisoriev H.H., Mirsaburov Sh., Ebadi A.G.
63-72
Materials for phytogeography of the freshwater algae of the Central Asia
There are about 32 areal types of the freshwater algae of Euglenophyta of the Central Asia region are discussed. During different areal types, species with Eurasia (57 species - 26.27%), azonal (53 -24.4%), and Eurasia - America areal types were dominant.

Key words: фитогеография; пресноводные; водоросли; materials; Phytogeography; freshwater; algae.

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Usmanova O.V., Yakubova M.M., Saidmuradov Sh.D.
73-76
Interaction between natural populations of and their mutants in phytocoenosis model
In this article the results of research on the nature of the interaction between natural populations of Arabidopsis and their mutants grown in pure and binary plant crops are presents. It is shown that the variation of quantitative traits that affect competitiveness between natural populations and their mutants in phytocoenosis model considerably conditioned by coenosis interaction.

Key words: арабидопсис; природные популяции; мутанты; конкурентоспособность; семенная продуктивность; arabidopsis; natural populations; mutants; competitiveness; seed production.

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Mirojov G.K., Dustov A., Sattorova M., Odinaev R.I., Kurbonov B., Radjabova N.I.
77-81
The latent viral infections in chronic diffuse of liver disease
We have found that hepatitis B virus is often present without it's main marker - HBsAg in the peripheral blood, indicating a latent course of the infection. In patients with latent viral infection in peripheral blood revealed antibodies to HBcAg, especially type IgM, which is often correlated with the presence of viral DNA HBV. In patients with chronic hepatitis and liver cirrhosis of unknown cause latent viral infection is found in 16% and 23%, respectively. Laten viral infections are often diagnosed in individuals at high risk of infection, drug addicts (66.3%), pregnant women (4.6%), health care workers (8.9%).

Key words: вирус гепатита В; скрытая инфекция; цирроз печени; virus hepatit B; laten viral infections; cirrhosis.

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Kosimov M.M., Hodjamurodov A.M., Umarova Z.I., Dodkhoeva M.F.
82-86
Treatment and ways of prevention complications of urolithiasis in pregnancy
The paper presents an analysis of the results of observation and treatment of 42 pregnant women suffering from urolithiasis. Therapeutic measures have been taken aimed for temporary or permanent restoration of outflow of urine from the upper urinary tract and relief of the inflammatory process. Minimally invasive palliative surgery and conservative treatment has been performed in 39 (90.62%) pregnant women with a positive effect. Radical surgery performed only in 3 (9.38%) patients.

Key words: мочекаменная болезнь; беременность; почечный стент; паллиативные операции; радикальные операции; медикаментозная экспульсивная терапия; urolitiasis; pregnancy; renal stent; palliative surgery; radical surgery; medical expulsive therapy.