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This paper is a short essay about Sergei L'vovich Sobolev (1908–1989), an outstanding mathematician of the 20th century, who made fundamental contributions to the development of the modern theory o...

We study the class of systems of differential equations defined by one class of matrix quasielliptic operators and establish solvability conditions for the systems and boundary value problems on $ {𝕉}^{n}_{+} $ in the special scales of weighted Sobolev spaces $ W^{l}_{p,\sigma} $ . We construct the integral representations of solutions and obtain estimates for the solutions.

The Cauchy problem for one pseudohyperbolic system is considered. The unique solvability of this problem in Sobolev spaces is proved. Systems of this type arise in describing wave dynamics in rods.

Potatoes belong to the most important food crop, are a useful food product and a valuable raw material for food products. The quality of potato tubers depends on the fertilizer’s application and the doses of the active substance. The study about the influence of fertilizer systems (organic, organic-mineral, mineral) on the productivity and quality of potato tubers is relevant. The effect on the quality of potatoes when using fertilizer systems depends on the soil and climatic conditions of the natural cultivation zone, biological characteristics of the variety and other factors. Starch is an indicator of the quality of potato tubers. The starch content in potato tubers increases with the use of mineral fertilizers. The starch content in tubers of early-ripening potato varieties increases their marketability. During heat treatment, the size of starch grains affects the consistency of potato pulp.

1. The new pneumatic system with a measurement limit of 0–600μ provides a high accuracy with a comparatively simple scheme. 2. The distinguishing feature of the new system is the possibility of changing the normal characteristic curve of the “nozzle-gate” system and thus increase the sensitivity for small gaps. The experiments show that the best results are obtained when the value of the coefficientα is approximately equal to 2.5-3 and the value of the coefficients, 2–2.5. 3. The new pneumatic system can find wide use in active automatic checking devices with continuous measurement of the removal of allowances and observation of the course of the process, in automatic checking devices for measuring parts with large allowances, etc.