Akmaljon Abdujalilovich Abdullayev

Ushbu maqolada qishloq xo'jaligi sektorining resurs salohiyatini baholashning nazariy va metodologik jihatlari chuqur tahlil qilingan. Tadqiqotning maqsadi "resurs salohiyati" toifasining iqtisodiy mohiyatini aniqlash, uning tarkibiy tarkibini asoslash va qisman ko'rsatkichlar tizimiga asoslangan integral baholash metodologiyasini ishlab chiqishdir. Metodologik asos tizimli yondashuv, iqtisodiy tahlil va sintez, qiyosiy tahlil va ilmiy umumlashtirish usullaridan iborat. Tadqiqot qishloq xo'jaligi sektorining resurs salohiyatini alohida resurs turlari bo'yicha emas, balki beshta asosiy komponent - yer, suv, mehnat, moddiy-texnik resurslar va moliyaviy resurslarning o'zaro bog'liqligi orqali baholash zarurligini asoslaydi. 20 ta qisman ko'rsatkichlar tizimi ishlab chiqilgan va og'irlik omillarini aniqlash uchun Analitik ierarxiyani qayta ishlash (AHP) usulidan foydalangan holda integral resurs salohiyati indeksini yaratishga metodologik yondashuv taklif qilingan. Integratsiyalashgan indeksni hisoblashning gipotetik misoli keltirilgan. Va nihoyat, resurslarning sinergiyalari va o'zaro ta'sirini hisobga olgan holda resurs salohiyatini baholash mintaqaviy iqtisodiy rivojlanish uchun juda muhim degan xulosaga kelish mumkin.

Ushbu maqola qishloq xo'jaligi sektorining resurs salohiyatini baholashda ko'rsatkichlarni standartlashtirishdagi metodologik masalalarni o'rganadi. Tadqiqotning maqsadi turli ko'rsatkichlar uchun standartlashtirish usullarini qiyosiy tahlil qilish va keyinchalik integral indeksga agregatsiya qilish uchun optimal usulni tanlashni asoslashdir. Metodologik asos tizimli yondashuv, iqtisodiy tahlil, qiyosiy tahlil va ilmiy umumlashtirishga asoslangan. Tadqiqotda uchta standartlashtirish usulining (chiziqli standartlashtirish, standartlashtirish va nisbiy qiymat usuli) qiyosiy tahlili keltirilgan, chiziqli standartlashtirishni tanlash asoslangan, rag'batlantiruvchi va to'xtatuvchi omillar uchun to'g'ridan-to'g'ri va teskari formulalardan foydalanish holda standartlashtirish protsedurasi ishlab chiqilgan, standartlashtirishning maxsus holatlari (chetga chiqishlar, minimal va maksimal qiymatlarning tengligi, salbiy qiymatlar, foiz ko'rsatkichlari) tavsiflangan, ko'rsatkichlarni ko'p kollinearlik uchun tekshirish tartibi taklif qilingan va to'xtatuvchi omillarni qo'shgan holda standartlashtirishning gipotetik misoli keltirilgan. Xulosa qilib aytganda, ko'rsatkichlarning ta'sir yo'nalishini hisobga olgan holda va ko'p kollinearlikni tekshirish orqali ularni to'g'ri standartlashtirish keyingi agregatsiya va integral resurs salohiyati indeksini shakllantirish uchun zarur shart ekanligi xulosa qilinadi.

The object of research is solvability of a boundary value problem with a nonlocal condition for an equation of elliptic-hyperbolic type of the second kind. Characteristic of boundary value problem is arbitrarily divided into two parts and the Bitsadze–Samarsky condition is given on one part. The second part is freed from the boundary condition and this missing Bitsadze–Samarsky condition is replaced by an analog Frankl conditions on the degeneracy interval. The uniqueness of the solution to the problem is proved, using the extremum principle method. The existence of a solution to the problem is proved, using the theories of singular integral equations and by the Wiener–Hopf equation. As a result, formulated and proved the solvability theorem for the posed problem.

The purpose of the research is to investigate the unique solvability of a nonlocal boundary value problem for a loaded equation of parabolic-hyperbolic type in a special domain. Methods: Using representations of a general regular solution, the existence and uniqueness of the problem posed is proved. Results: A new method for proving the unique solvability of nonlocal boundary value problems for one loaded equation of mixed type in a special domain has been formed and developed. Conclusions: The obtained results make it possible to solve some problems of genetics, immunology, transonic gas dynamics and thermal physics, which are associated with displacement.

Equations of mixed type, the degeneracy line of which is the envelope of a family of characteristics, therefore, is itself also a characteristic, in the literature it is customary to call equations of mixed type of the second kind, which causes additional difficulties in the study of boundary value problems for equations of the second kind. In the present work, a boundary value problem for a homogeneous equation of parabolic-hyperbolic type of the third order of the second kind is investigated. Necessary and sufficient conditions for the existence and uniqueness of a generalized solution of the problem are found. In some special cases, the representation of the solution of the problem under study is written out explicitly.

For a liquid with a nonmonotonic flow curve in the stationary case in the region of the descending branch, setting the velocity at the boundary does not uniquely determine the shear stress, strain rate distribution, and velocity profile that arise since the problem is known to have many unstable solutions. At the same time, the problem of the motion of such fluid under the action of a given pressure difference has no more than three solutions, two of which are stable, and the third is unstable and not reproducible. Which of the two stable solutions is realized depends on the loading history. The problem of determining the velocity profile for a fluid characterized by a nonmonotonic rheological flow curve between parallel planes is considered. The existence of a solution is realized by reducing the problem posed to a singular integral equation of normal type, which is known by the Carleman – Vekua regularization method developed by S.G. Mikhlin and M.M. Smirnov equivalently reduces to the Fredholm integral equation of the second kind, and the solvability of the latter follows from the uniqueness of the solution delivered problem describing of criteria for integro–differential modeling of a plane-parallel flow of a viscous incompressible fluid.

When modeling the flow of groundwater and streams together, two different approaches are used, using hydraulic and hydrological models as channel flow models. The former is based on mathematical equations of water movement in open channels. In contrast, the latter is based on simplified empirical and semi-empirical relationships between the hydraulic characteristics of watercourses. In both cases, the watercourse is an internal boundary for the groundwater flow - otherwise, it is advisable to model it as a body of water. The groundwater model can be a scale model or an electrical model of the state of the groundwater or an aquifer. Groundwater models are used to represent the natural flow of groundwater in an environment. Some groundwater models include aspects of groundwater quality. Such groundwater models attempt to predict the fate and movement of a chemical in natural, urban, or hypothetical scenarios. Groundwater models can be used to predict the impact of hydrological changes on aquifer behavior and are often referred to as groundwater simulation models. Also, groundwater models are currently being used in various water management plans for urban areas. Because calculations in mathematical groundwater models are based on groundwater flow equations, which are differential equations that can often only be solved by approximate methods using numerical analysis, these models are also referred to as mathematical, numerical, or computational groundwater models.

As is known, it is customary in the literature to divide degenerate equations of mixed type into equations of the first and second kind. In the case of an equation of the second kind, in contrast to the first, the degeneracy line is simultaneously the envelope of a family of characteristics, i.e. is itself a characteristic, which causes additional difficulties in the study of boundary value problems for equations of the second kind. In this paper, in order to establish the unique solvability of one nonlocal problem with the Poincaré condition for an elliptic-hyperbolic equation of the second kind developed a new principle extremum, which helps to prove the uniqueness of resolutions as signed problem. The existence of a solution is realized by reducing the problem posed to a singular integral equation of normal type, which known by the Carleman-Vekua regularization method developed by S.G. Mikhlin and M.M. Smirnov equivalently reduces to the Fredholm integral equation of the second kind, and the solvability of the latter follows from the uniqueness of the solution delivered problem.

Modeling the movement of moisture in the soil is of great importance for assessing the impact of agricultural land on surface water bodies and, consequently, on the natural environment and humans. This is because huge volumes of pollutants from the fields (pesticides, mineral fertilizers, nitrates, and nutrients contained in them) are transferred to reservoirs by filtering moisture. Different methods solve all these tasks. The method of natural analogies is based on the analysis of graphs of fluctuations in groundwater level. To apply this method on irrigated lands, it is necessary to have a sufficiently studied irrigated area with similar natural, organizational and economic conditions. The successful application of this method, based on the fundamental theory of physical similarity, mainly depends on the availability of a sufficiently close comparison object, which is quite rare in practice. Physical modeling is often used to construct dams and other hydraulic structures. Previously, the method of electrical modeling was also widely used. It was further found that nonlocal boundary conditions arise in the problems of predicting soil moisture, modeling fluid filtration in porous media, mathematical modeling of laser radiation processes, and plasma physics problems, as well as mathematical biology.

Stationary processes of various physical nature (oscillations, thermal conductivity, diffusion, electrostatics, etc.) are described by equations of elliptic type. In particular, some models, such as hydro and gas dynamics, consider elliptic equations. Modeling the transfer of moisture and salts to predict changes in the state of agricultural land is the most important task in the design of both irrigation and drainage of lands, as well as the construction of hydraulic structures. In this paper, we study a nonlocal boundary value problem with the Poincare condition for an elliptic – hyperbolic equation of the second kind, i.e. for an equation where the line of degeneracy is a characteristic. Due to the mathematical content and the availability of numerous applications in the study of problems of mechanics, physics, engineering and biology, and to modeling the movement of moisture in soil is of great importance for assessing the impact of agricultural land on surface water bodies, and, consequently, on the natural environment and humans. This is due to the fact that huge volumes of pollutants from the fields (pesticides, mineral fertilizers, nitrates, nutrients contained in them) are transferred to reservoirs by filtering moisture. All these tasks are solved by different methods. The method of natural analogies is based on the analysis of graphs of fluctuations in the level of groundwater. To apply this method on irrigated lands, it is necessary to have a sufficiently studied irrigated area with similar natural, organizational and economic conditions. The successful application of this method, based on the fundamental theory of physical similarity, mainly depends on the availability of a sufficiently close comparison object, which is quite rare in practice. Physical modeling is often used in the construction of dams and other hydraulic structures. Previously, the method of electrical modeling was also widely used. It was further found that nonlocal boundary conditions arise in the problems of predicting soil moisture, in modeling fluid filtration in porous media, in mathematical modeling of laser radiation processes and plasma physics problems, as well as mathematical biology.