Magtymguly Turkmen State University

This paper presents a numerical study of source identification problems for one-dimensional telegraphparabolic equations subject to Dirichlet and Neumann boundary conditions. In these inverse problems, the unknown source terms are assumed to be space-dependent, which introduces both analytical and computational challenges. The study begins by discretizing the considered problems using the finite difference method – first in space and subsequently in time – resulting in a system of discrete equations. Stability results for the solutions of the resulting finite difference schemes are established to ensure the reliability of the numerical approach. A numerical algorithm is proposed for solving the discrete inverse problems. The algorithm begins by eliminating the unknown source terms, which transforms the original discretized problem into a new nonlocal problem with unknown initial data. To approximate this initial data, an iterative procedure based on fixed-point iterations is constructed. Once the transformed nonlocal problem is solved, the solution of the main finite difference scheme and approximations of the unknown source term are recovered. Numerical results for two test problems are presented to illustrate the proposed method in practice. The findings confirm the accuracy of the approach in solving space-dependent inverse source problems.

The article introduces into scientific circulation and analyses information about the traditions of respecting the older generation in the Turkmen rural community. In large Turkmen villages, the most respected person of the older generation was the main adviser and mentor to all its residents. When making important decisions, he always consulted with other elders of the settlement. For this purpose, the oldest person convened a council. The elder’s opinion was of much significance; the villagers relied on his wisdom, life experience and honesty. The elders did not receive or expect any remuneration, since service to society was considered a sacred duty. All important issues, from naming a newborn to the burial of the deceased, were brought to the attention of representatives of the older generation. People listened to what the elders had to say and acted upon their instructions. As a result of the centuries-old development in the Turkmen rural community, the rules of the people’s council, the principles of managing Turkmen society, based on the knowledge and wisdom of the older generation, were developed.

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Рассматривается ранневенгерский погребальный комплекс Глиное/Водовод 4/1, исследованный в 2016 г. у с. Глиное Слободзейского района, что на левобережье Нижнего Днестра, и ошибочно интерпретированный в 2017 г. как скифское захоронение. Погребение было впущено в скифский курган. В состав инвентаря входили золотая фольга и две позолоченные накладки из серебра. Анализ погребального инвентаря позволил датировать комплекс Глиное/Водовод 4/1 в пределах середины IX — начала X в. С учётом радиоуглеродной даты время захоронения может быть ограничено 850—870-ми гг. Прямые аналогии найденным накладкам в женских погребениях венгров Карпатской котловины позволяют утверждать, что они украшали обувь. Исследованное захоронение не только дополняет список памятников, маркирующих территорию обитания венгерских племен в Северо-Западном Причерноморье перед обретением родины, но и является частью представительной группы венгерских погребений, исследованных у с. Глиное. Это позволяет констатировать присутствие в данном микрорегионе большой семьи либо рода, как это было зафиксировано ранее в Слободзейском могильнике. The article deals with the Early Hungarian grave Glinoe/Vodovod (‘Water distribution system’) 4/1 investigated in 2016 near Glinoe village, Slobodzeya district, on the left bank of the Lower Dniester and erroneously interpreted in 2017 as a Scythian burial; the burial pit, however, was indeed dug through the mound of a Scythian barrow. The grave inventory consisted of golden foil and two gilded plates of silver, the fact which made it possible to set the burial within the time range from the middle of the 9th century until the beginning of the 10th century. Taking into account the radiocarbon dating, the time of the interment can be limited more accurately between the years 850 and 870. Appliqués of gold and silver are basically found in female burials of the Hungarians elsewhere in the Carpathian Basin and are thought to have been footwear adornments. The investigated grave not only supplements the list of sites marking the habitat of the Hungarian tribes in the Northwest Black Sea region before finding their homeland, but is also a part of the representative group of Hungarian burials discovered near Glinoe village. It is argued therefore that some large family or a tribal clan have inhabited the micro-region, just like they most probably did when the burial ground was established in the area around present-day Slobodzeya.

A new two-step route for the preparation of nano-scaled magnetic chitosan particles has been developed, different from reported one-step in situ preparation and two-step preparation method of reversedphase suspension, Triton X-100 reversed-phase water-in-oil microemulsion encapsulation method was employed in coating the pre-prepared Fe3O4 nanoparticles with chitosan. Two model anticancer drugs, Doxorubicin (DOX) and Methotrexate (MTX) were loaded effectively to functionalized MNPs through electrostatic interactions. Our developed UV method was applied for simultaneous determination of DOX and MTX. It was concluded that our findings may open the possibilities for pH-responsive targeted delivery of DOX and MTX to the cancerous tissues.

АннотацияЗолото при наноразмерах показывает необычные физические, химические и биологические свойства.В этой работе, для получения коллоидных наночастиц золота мы восстановили водный раствор золотохлороводородной кислоты (HAuCl 4 ) при помощи цитрата натрия, а также из того же раствора химическим способом осадили нанослой золота на Au-n-GaAs полупроводниковой наноструктуре.Для определения размеров и степени полидисперсности наночастиц мы воспользовались методом динамического рассеяния света.Поверхностную морфологию изготовленных наноструктур и размеры поверхностных наночастиц золота мы проанализировали с помощью атомно-силового и сканирующего электронного микроскопов.Также были определены преимущества и недостатки метода

This paper deals with the behavior of the nonnegative solutions of the problem $$- \Delta u = V(x)u, \left. u \right|\partial \Omega = \varphi (x)$$ in a conical domain Ω ⊂ ℝn, n ≥ 3, where 0 ≤ V (x) ∈ L1(Ω), 0 ≤ ϕ(x) ∈ L1(∂Ω) and ϕ(x) is continuous on the boundary ∂Ω. It is proved that there exists a constant C*(n) = (n − 2)2/4 such that if V0(x) = (c + λ1)|x|−2, then, for 0 ≤ c ≤ C*(n) and V(x) ≤ V0(x) in the domain Ω, this problem has a nonnegative solution for any nonnegative boundary function ϕ(x) ∈ L1(∂Ω); for c > C*(n) and V(x) ≥ V0(x) in Ω, this problem has no nonnegative solutions if ϕ(x) > 0.

A stochastic numerical method is developed for simulation of flows and particle transport in a 2D layer of porous medium. The hydraulic conductivity is assumed to be a random field of a given statistical structure, the flow is modeled in the layer with prescribed boundary conditions. Numerical experiments are carried out by solving the Darcy equation for each sample of the hydraulic conductivity by a direct solver for sparse matrices, and tracking Lagrangian trajectories in the simulated flow. We present and analyze different Eulerian and Lagrangian statistical characteristics of the flow such as transverse and longitudinal velocity correlation functions, longitudinal dispersion coefficient, and the mean displacement of Lagrangian trajectories. We discuss the effect of long-range correlations of the longitudinal velocities which we have found in our numerical simulations. The related anomalous diffusion is also analyzed.

Non-asymptotic exponential upper bounds for the deviation probability for a sum of independent random fields are obtained under Bernstein's condition and assumptions formulated in terms of Kolmogorov's metric entropy. These estimations are constructive in the sense that all the constants involved are given explicitly. In the case of moderately large deviations, the upper bounds have optimal log-asymptotices. The exponential estimations are extended to the local and global continuity modulus for sums of independent samples of a random field. The motivation of the present study comes mainly from the dependence Monte Carlo methods.