394 research outputs found
The Tools, Technology and Mathematical Model of Impactive Superficial Plastic Deformation of Metals
The paper shows scientific substantiation and practical confirmation of possibility, application expediency and efficiency of the ultrasonic superficial plastic deformation in zones of welded connections after performance of welding works. For this purpose, a mathematical model to the process of superficial plastic deformation is represented, as the hypercycle of loading consisting of elementary cycles β impacts, we described the standard measurement devices. The technology is intended to use the manufacturing and repair of any metal walls in places of dimensional and structural nonuniformity, such as mechanical defects or a local thinning of a surface owing to corrosion, and the microcracks. The microcracks is influenced by the external forces and become zones of concentration of mechanical tension. Hardening in such places of the pipes walls and tanks working under pressure is effective for pipelines of an oil and gas, water supply systems, and also for caissons and tanks of other appointment. The scopes of technology include the repair of river and sea vessels, objects of oil production. The technology can be applied to improvement of operational characteristics of mechanical engineering and transport details, objects of energetic and construction: surfaces of a rolling motion and sliding of machines and devices, wheels of a rolling stock of railway transport, a metalwork of support of power lines, platforms and bridges for increases in resistance of fatigue at cyclic loadings, wear resistance and corrosion
Sonochemistry of food - area high-energy chemistry which actively is researched now in Russia and Belarus
Simulation control facility for temperature control systems
Π ΡΡΠ°ΡΡΠ΅ ΡΠ°ΡΡΠΌΠΎΡΡΠ΅Π½Π° ΠΈΡΠΏΠΎΠ»Π½ΠΈΡΠ΅Π»ΡΠ½Π°Ρ ΡΠ°ΡΡΡ ΡΡ
Π΅ΠΌΡ ΠΈΠΌΠΈΡΠ°ΡΠΎΡΠ° ΠΎΠ±ΡΠ΅ΠΊΡΠ° ΠΊΠΎΠ½ΡΡΠΎΠ»Ρ Π΄Π»Ρ Π°Π²ΡΠΎΠΌΠ°ΡΠΈΠ·ΠΈΡΠΎΠ²Π°Π½Π½ΡΡ
ΡΠΈΡΡΠ΅ΠΌ ΠΊΠΎΠ½ΡΡΠΎΠ»Ρ ΡΠ΅ΠΌΠΏΠ΅ΡΠ°ΡΡΡΡ, ΠΏΡΠΈΠ²Π΅Π΄Π΅Π½Π° ΡΡ
Π΅ΠΌΠ° ΠΈΡΠΏΠΎΠ»Π½ΠΈΡΠ΅Π»ΡΠ½ΠΎΠΉ ΡΠ°ΡΡΠΈ, ΡΠ°ΠΊ ΠΆΠ΅ ΡΠ°ΡΡΠΌΠΎΡΡΠ΅Π½ ΡΠ°ΡΡΠ΅Ρ ΡΠΎΡΠ½ΠΎΡΡΠΈ ΡΡ
Π΅ΠΌΡ. Π£ΡΡΡΠΎΠΉΡΡΠ²ΠΎ ΠΏΠΎΠ·Π²ΠΎΠ»ΡΠ΅Ρ ΠΏΡΠΎΠ²ΠΎΠ΄ΠΈΡΡ ΠΎΡΠ»Π°Π΄ΠΊΡ ΠΈ ΠΏΡΠΎΠ²Π΅ΡΠΊΡ ΡΠΈΡΡΠ΅ΠΌΡ Π² Π»Π°Π±ΠΎΡΠ°ΡΠΎΡΠ½ΡΡ
ΡΡΠ»ΠΎΠ²ΠΈΡΡ
ΠΈ Π½Π° Π΄Π°Π½Π½ΡΠΉ ΠΌΠΎΠΌΠ΅Π½Ρ ΠΏΡΠΈΠΌΠ΅Π½ΡΠ΅ΡΡΡ Π΄Π»Ρ ΠΏΡΠΎΠ²Π΅ΡΠΊΠΈ Π°Π²ΡΠΎΠΌΠ°ΡΠΈΠ·ΠΈΡΠΎΠ²Π°Π½Π½ΠΎΠΉ ΡΠΈΡΡΠ΅ΠΌΡ ΠΊΠΎΠ½ΡΡΠΎΠ»Ρ ΡΠ΅ΠΌΠΏΠ΅ΡΠ°ΡΡΡΡ Π½Π° ΠΠ Β«ΠΠΠ Π°Π²ΡΠΎΠΌΠ°ΡΠΈΠΊΠΈΒ».The article considers the executive part of the circuit simulator object control for automated temperature control systems, a diagram of the executive, also reviewed the accuracy of the calculation scheme. The device allows you to debug and test systems in the laboratory and is currently used to test the automated system to control the temperature of JSC "NPO Automation"
Scattering of Dirac particles from non-local separable potentials: the eigenchannel approach
An application of the new formulation of the eigenchannel method [R.
Szmytkowski, Ann. Phys. (N.Y.) {\bf 311}, 503 (2004)] to quantum scattering of
Dirac particles from non-local separable potentials is presented. Eigenchannel
vectors, related directly to eigenchannels, are defined as eigenvectors of a
certain weighted eigenvalue problem. Moreover, negative cotangents of
eigenphase-shifts are introduced as eigenvalues of that spectral problem.
Eigenchannel spinor as well as bispinor harmonics are expressed throughout the
eigenchannel vectors. Finally, the expressions for the bispinor as well as
matrix scattering amplitudes and total cross section are derived in terms of
eigenchannels and eigenphase-shifts. An illustrative example is also provided.Comment: Revtex, 9 pages, 4 figures, published versio
Sonochemical Reactor Treating Drinking Water for Pigs
The article deals with the use of activated water for drinking of pigs. Moreover, is described a method sonochemical activation of water. Sonochemical activated water is devoid of own supramolecular structure and has a high solvent power similar to how a boiling water, while remaining virtually the same temperature, which was prior to treatment. It is shown that the water in a thermodynamically nonequilibrium state, in which abideth some time as a result of such treatment, and has bactericidal and bacteriostatic p roperties, which it retains long time. All this suggests that the hydration of biopolymers directly into the esophagus and stomach of animals during their drinking will give tangible effect. Given the description of the mechanisms of cavitational disintegrated of water and described in comparison reactors for water treatment. Said that a regulatory authority in Russia give permission to use sonochemical technologies and devices in the food industry. Described sonochemical reactor, designed specifically for use in drinking of pigs, which have a reduced noise level and power consumption, but with better performance
Proposed Search for Mixing in Polarization Phenomena
The and meson mass difference induces the mixing of the
and resonances, the amplitude of which, between the
and thresholds, is large in magnitude, of the order of , and possesses the
phase sharply varying by about 90. We suggest performing the polarized
target experiments on the reaction at high energy in
which the fact of the existence of mixing can be
unambiguously and very easily established through the presence of a strong jump
in the azimuthal asymmetry of the wave production cross section
near the thresholds. The presented estimates of the polarization
effect to be expected in experiment are to a great extent model independent.Comment: RevTeX, 9 pages, 1 figure. A number of typographical and grammatical
errors correcte
Clustering of Regions Using Basic Agricultural and Economic Criteria
Π Π°Π·Π½ΠΎΠΎΠ±ΡΠ°Π·ΠΈΠ΅ ΠΏΡΠΈΡΠΎΠ΄Π½ΠΎ-ΠΊΠ»ΠΈΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΈ ΡΠΊΠΎΠ½ΠΎΠΌΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΡΠ»ΠΎΠ²ΠΈΠΉ ΡΠΎΡΡΠΈΠΉΡΠΊΠΈΡ
ΡΠ΅Π³ΠΈΠΎΠ½ΠΎΠ² ΠΏΡΠ΅Π΄ΠΏΠΎΠ»Π°Π³Π°Π΅Ρ ΡΠΈΡΠΎΠΊΠΈΠΉ Π΄ΠΈΠ°ΠΏΠ°Π·ΠΎΠ½ ΠΌΠ΅ΡΠΎΠ΄ΠΎΠ»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΏΠΎΠ΄Ρ
ΠΎΠ΄ΠΎΠ² ΠΊ ΠΈΡ
ΠΊΠ»Π°ΡΡΠΈΡΠΈΠΊΠ°ΡΠΈΠΈ. ΠΠ΄Π½ΠΎΠ²ΡΠ΅ΠΌΠ΅Π½Π½ΠΎ ΡΡΠ»ΠΎΠΆΠ½ΡΠ΅ΡΡΡ Π·Π°Π΄Π°ΡΠ° Π°Π±ΡΡΡΠ°Π³ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΡ Π΄Π»Ρ Π»ΡΠ±ΠΎΠΉ ΠΎΡΡΠ°ΡΠ»ΠΈ Π½Π°ΡΠΎΠ΄Π½ΠΎΠ³ΠΎ Ρ
ΠΎΠ·ΡΠΉΡΡΠ²Π°. ΠΡΡΠ΅ΠΊΡΠΈΠ²Π½Π°Ρ ΠΊΠ»Π°ΡΡΠ΅ΡΠΈΠ·Π°ΡΠΈΡ Π²Π°ΠΆΠ½Π° ΡΠ°ΠΊΠΆΠ΅ Π² ΠΏΡΠΎΡΠ΅ΡΡΠ΅ ΡΠΎΡΠΌΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΈ ΡΠ΅Π°Π»ΠΈΠ·Π°ΡΠΈΠΈ Π°Π³ΡΠ°ΡΠ½ΠΎ-ΡΠΊΠΎΠ½ΠΎΠΌΠΈΡΠ΅ΡΠΊΠΎΠΉ ΠΏΠΎΠ»ΠΈΡΠΈΠΊΠΈ. Π ΡΠ°Π±ΠΎΡΠ΅ ΠΈΠ·ΡΡΠ΅Π½Ρ Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΠΎΡΡΠΈ Π±Π°Π·ΠΎΠ²ΠΎΠΉ Π°Π³ΡΠ°ΡΠ½ΠΎ-ΡΠΊΠΎΠ½ΠΎΠΌΠΈΡΠ΅ΡΠΊΠΎΠΉ ΡΠ΅Π³ΠΈΠΎΠ½Π°Π»ΡΠ½ΠΎΠΉ ΠΊΠ»Π°ΡΡΠ΅ΡΠΈΠ·Π°ΡΠΈΠΈ Π½Π° ΠΎΡΠ½ΠΎΠ²Π΅ Π²ΡΠ΅ΠΌΠ΅Π½Π½ΡΡ
ΡΡΠ΄ΠΎΠ² ΠΎΡΠ½ΠΎΠ²Π½ΡΡ
ΡΠΊΠΎΠ½ΠΎΠΌΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΏΠΎΠΊΠ°Π·Π°ΡΠ΅Π»Π΅ΠΉ ΠΈ ΠΏΠΎΠΊΠ°Π·Π°ΡΠ΅Π»Π΅ΠΉ ΡΠ°Π·Π²ΠΈΡΠΈΡ ΡΠ΅Π»ΡΡΠΊΠΎΠ³ΠΎ Ρ
ΠΎΠ·ΡΠΉΡΡΠ²Π°. ΠΠΎΠ²ΠΈΠ·Π½Π° ΠΏΡΠ΅Π΄Π»Π°Π³Π°Π΅ΠΌΠΎΠ³ΠΎ ΠΏΠΎΠ΄Ρ
ΠΎΠ΄Π° Π·Π°ΠΊΠ»ΡΡΠ°Π΅ΡΡΡ Π² ΠΌΠ΅ΡΠΎΠ΄ΠΈΠΊΠ΅ Π΄ΠΈΠ½Π°ΠΌΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΡΠ΅Π³ΠΌΠ΅Π½ΡΠΈΡΠΎΠ²Π°Π½ΠΈΡ, ΠΊΠΎΡΠΎΡΠ°Ρ ΠΏΠΎΠ·Π²ΠΎΠ»ΡΠ΅Ρ Π½Π°Π±Π»ΡΠ΄Π°ΡΡ ΠΈ ΠΏΡΠΎΠ³Π½ΠΎΠ·ΠΈΡΠΎΠ²Π°ΡΡ Π½Π°ΠΏΡΠ°Π²Π»Π΅Π½ΠΈΠ΅ ΠΈΠ·ΠΌΠ΅Π½Π΅Π½ΠΈΠΉ Π² ΠΌΠ΅Π·ΠΎΡΠΊΠΎΠ½ΠΎΠΌΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΏΡΠΎΠΏΠΎΡΡΠΈΡΡ
. ΠΠ° ΠΎΡΠ½ΠΎΠ²Π΅ ΠΎΡΠΈΡΠΈΠ°Π»ΡΠ½ΡΡ
Π΄Π°Π½Π½ΡΡ
Π³ΠΎΡΡΠ΄Π°ΡΡΡΠ²Π΅Π½Π½ΠΎΠΉ ΡΡΠ°ΡΠΈΡΡΠΈΠΊΠΈ ΡΡΠΎΡΠΌΠΈΡΠΎΠ²Π°Π½Ρ Π³ΡΡΠΏΠΏΡ ΠΏΠΎΠΊΠ°Π·Π°ΡΠ΅Π»Π΅ΠΉ ΠΏΠΎ ΠΏΡΠΎΠΈΠ·Π²ΠΎΠ΄ΡΡΠ²Π΅Π½Π½ΠΎΠΌΡ, ΠΏΡΠΎΠΈΠ·Π²ΠΎΠ΄ΡΡΠ²Π΅Π½Π½ΠΎ-ΠΈΠ½ΡΡΠΈΡΡΡΠΈΠΎΠ½Π°Π»ΡΠ½ΠΎΠΌΡ ΠΈ ΠΏΡΠΎΠΈΠ·Π²ΠΎΠ΄ΡΡΠ²Π΅Π½Π½ΠΎ-ΡΡΡΡΠΊΡΡΡΠ½ΠΎΠΌΡ ΠΊΡΠΈΡΠ΅ΡΠΈΡΠΌ. Π ΠΊΠ°ΡΠ΅ΡΡΠ²Π΅ ΠΎΡΠ½ΠΎΠ²Π½ΠΎΠ³ΠΎ ΠΌΠ΅ΡΠΎΠ΄Π° ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΡ Π²ΡΠ±ΡΠ°Π½ ΠΌΠ΅ΡΠΎΠ΄ ΠΊΠ»Π°ΡΡΠ΅ΡΠΈΠ·Π°ΡΠΈΠΈ Β«k-ΡΡΠ΅Π΄Π½Π΅Π΅Β». ΠΠ° ΠΎΡΠ½ΠΎΠ²Π΅ ΡΡΠ΅Ρ
ΡΠΌΠΎΠ΄Π΅Π»ΠΈΡΠΎΠ²Π°Π½Π½ΡΡ
ΡΠ΅Π³ΠΈΠΎΠ½Π°Π»ΡΠ½ΡΡ
ΡΠ΅Π³ΠΌΠ΅Π½ΡΠΎΠ² ΡΠ°ΡΡΡΠΈΡΠ°Π½Ρ ΡΡΠ΅Π΄Π½ΠΈΠ΅ Π·Π½Π°ΡΠ΅Π½ΠΈΡ ΠΏΠΎ ΠΈΡΡ
ΠΎΠ΄Π½ΡΠΌ ΠΏΡΠΈΠ·Π½Π°ΠΊΠ°ΠΌ. Π‘Π΅Π³ΠΌΠ΅Π½ΡΡ ΠΊΠ»Π°ΡΡΠΈΡΠΈΡΠΈΡΠΎΠ²Π°Π½Ρ Ρ ΠΏΠΎΠ·ΠΈΡΠΈΠΉ ΠΏΠΎΠ»ΡΡΠ΅Π½Π½ΡΡ
Ρ
Π°ΡΠ°ΠΊΡΠ΅ΡΠΈΡΡΠΈΠΊ. ΠΡΠ΄Π΅Π»ΡΠ½ΠΎ ΡΠ°ΡΡΠΌΠΎΡΡΠ΅Π½Ρ ΡΡΠ±ΡΠ΅ΠΊΡΡ-Π²ΡΠ±ΡΠΎΡΡ, Π΄Π°Π»Π΅ΠΊΠΎ ΠΎΡΡΡΠΎΡΡΠΈΠ΅ ΠΎΡ ΠΎΡΠ½ΠΎΠ²Π½ΡΡ
ΠΌΠ°ΡΡΠΈΠ²ΠΎΠ² Π΄Π°Π½Π½ΡΡ
. ΠΠΎΠ»ΡΡΠ΅Π½Π½ΡΠ΅ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΡ ΠΏΠΎΠ΄ΡΠ²Π΅ΡΠ΄ΠΈΠ»ΠΈ ΡΠΈΡΠΎΠΊΠΎΠ΅ ΠΏΡΠΎΡΡΡΠ°Π½ΡΡΠ²Π΅Π½Π½ΠΎΠ΅ ΡΠ°ΡΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΠ΅ ΡΠ΅Π³ΠΈΠΎΠ½ΠΎΠ², Π²Ρ
ΠΎΠ΄ΡΡΠΈΡ
Π² ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½Π½ΡΠ΅ Π°Π³ΡΠ°ΡΠ½ΠΎ-ΡΠΊΠΎΠ½ΠΎΠΌΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΡΠ΅Π³ΠΌΠ΅Π½ΡΡ. ΠΠ°Π½Π½Π°Ρ ΠΊΠ»Π°ΡΡΠΈΡΠΈΠΊΠ°ΡΠΈΡ Π±ΡΠ΄Π΅Ρ ΠΏΠΎΠ»Π΅Π·Π½Π° ΠΏΡΠΈ ΠΎΠ±ΠΎΡΠ½ΠΎΠ²Π°Π½ΠΈΠΈ Π½Π°ΠΏΡΠ°Π²Π»Π΅Π½ΠΈΠΉ ΠΈ Π²ΡΠ±ΠΎΡΠ΅ ΠΈΠ½ΡΡΡΡΠΌΠ΅Π½ΡΠΎΠ² Π°Π³ΡΠ°ΡΠ½ΠΎ-ΡΠΊΠΎΠ½ΠΎΠΌΠΈΡΠ΅ΡΠΊΠΎΠΉ ΠΏΠΎΠ»ΠΈΡΠΈΠΊΠΈ, ΡΡΡΠ°ΡΠ΅Π³ΠΈΠΈ ΡΠΎΠ·Π΄Π°Π½ΠΈΡ ΠΏΡΠΎΠΈΠ·Π²ΠΎΠ΄ΡΡΠ²Π΅Π½Π½ΡΡ
ΠΊΠ»Π°ΡΡΠ΅ΡΠΎΠ², Π° ΡΠ°ΠΊΠΆΠ΅ ΠΏΡΠΈ ΠΏΠ»Π°Π½ΠΈΡΠΎΠ²Π°Π½ΠΈΠΈ ΡΠ°Π±ΠΎΡΡ ΡΠ΅Π³ΠΈΠΎΠ½Π°Π»ΡΠ½ΠΎΠ³ΠΎ Π°Π³ΡΠΎΠ±ΠΈΠ·Π½Π΅ΡΠ°, ΡΡΡΡΠ°Π½Π΅Π½ΠΈΠΈ ΡΡΡΠ΅ΡΡΠ²ΡΡΡΠΈΡ
Π΄ΠΈΡΠΏΡΠΎΠΏΠΎΡΡΠΈΠΉ Π² Π΅Π³ΠΎ ΡΠ°Π·Π²ΠΈΡΠΈΠΈ. Π ΠΊΠ°ΡΠ΅ΡΡΠ²Π΅ Π΄Π°Π»ΡΠ½Π΅ΠΉΡΠ΅Π³ΠΎ ΡΠΎΠ²Π΅ΡΡΠ΅Π½ΡΡΠ²ΠΎΠ²Π°Π½ΠΈΡ ΠΌΠ΅ΡΠΎΠ΄ΠΎΠ»ΠΎΠ³ΠΈΠΈ Π°Π³ΡΠ°ΡΠ½ΠΎ-ΡΠΊΠΎΠ½ΠΎΠΌΠΈΡΠ΅ΡΠΊΠΎΠΉ ΡΠ΅Π³ΠΌΠ΅Π½ΡΠ°ΡΠΈΠΈ Π² Π΄ΠΈΠ½Π°ΠΌΠΈΠΊΠ΅ ΠΏΡΠ΅Π΄Π»ΠΎΠΆΠ΅Π½ΠΎ ΡΠ°ΡΡΠΈΡΠΈΡΡ Π°Π½Π°Π»ΠΈΠ· Ρ ΠΏΠΎΠΌΠΎΡΡΡ ΠΈΠ·ΠΌΠ΅Π½Π΅Π½ΠΈΡ ΠΈΠ·ΡΡΠ°Π΅ΠΌΠΎΠ³ΠΎ Π²ΡΠ΅ΠΌΠ΅Π½Π½ΠΎΠ³ΠΎ ΠΈΠ½ΡΠ΅ΡΠ²Π°Π»Π°, ΡΠΎΡΡΠ° ΠΊΠΎΠ»ΠΈΡΠ΅ΡΡΠ²Π° Π²ΠΊΠ»ΡΡΠ°Π΅ΠΌΡΡ
Π² ΠΌΠΎΠ΄Π΅Π»Ρ ΡΠ°ΠΊΡΠΎΡΠΎΠ² ΠΈ ΠΈΡ
Π²Π·Π°ΠΈΠΌΠΎΠ΄Π΅ΠΉΡΡΠ²ΠΈΠΉ, Π²Π²Π΅Π΄Π΅Π½ΠΈΡ Π½ΠΎΠ²ΡΡ
Π°Π»Π³ΠΎΡΠΈΡΠΌΠΎΠ² ΠΊΠ»Π°ΡΡΠ΅ΡΠΈΠ·Π°ΡΠΈΠΈ. ΠΠ°Π½Π½ΡΡ ΠΌΠΎΠ΄Π΅Π»Ρ ΠΌΠΎΠΆΠ½ΠΎ Π΄ΠΎΠΏΠΎΠ»Π½ΠΈΡΠ΅Π»ΡΠ½ΠΎ ΠΏΡΠΈΠΌΠ΅Π½ΡΡΡ Π΄Π»Ρ ΠΏΠΎΠ»ΡΡΠ΅Π½ΠΈΡ ΠΏΡΠΎΠ³Π½ΠΎΠ·ΠΎΠ² ΡΡΡΡΠΊΡΡΡΠ½ΡΡ
ΠΈΠ·ΠΌΠ΅Π½Π΅Π½ΠΈΠΉ ΠΈ Π΄ΠΈΠ½Π°ΠΌΠΈΠΊΠΈ ΠΏΡΠΎΠΈΠ·Π²ΠΎΠ΄ΡΡΠ²Π°.The diversity of natural, climatic, and economic conditions of Russian regions implies a wide range of approaches to their classification. Simultaneously, the task of creating an abstract methodology for any branch of the national economy becomes more complicated. Effective clustering plays an important role in the establishment and implementation of agricultural and economic policies. The paper explores the potential of basic agricultural and economic regional clustering based on time series of main economic and agricultural development indicators. The dynamic segmentation technique was applied in order to monitor and predict the direction of meso-economic changes. Official Russian statistics were analysed to identify groups of indicators on production, production and institutional, and production and structural criteria. The ΠΊ-means clustering algorithm was chosen as the key research method. Based on the three simulated regional segments, baseline average values were calculated. Then, the segments were classified according to the obtained characteristics. The outliers, significantly differing from the main data sets, were considered separately. The findings confirmed a wide spatial distribution of regions included in certain agricultural and economic segments. The presented classification can be applied to justify the directions and choice of instruments of agricultural and economic policy and a strategy for creating production clusters. Moreover, it can be used to plan the activities of regional agri-businesses and reduce their development imbalances. To improve the dynamic segmentation technique in the field of agricultural and economic development, the analysis can be expanded by changing the examined time interval, increasing the number of factors included in the model and their interactions, and introducing new clustering algorithms. Additionally, this model can be used to forecast structural changes and production dynamics
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