TASK2 (K2P5. 1, KCNK5) is a two-pore domain K⁺ channel belonging to the TALK subgroup of the K2P family of proteins. TASK2 expression has been reported in a variety of cells and tissues ranging from kidney to immune cells and including specific neurons, its proposed functions spanning from involvement in the regulation of cell volume to control of excitability. The purpose of this study was to determine the tubule location ofthe TASK2 K⁺ channel protein in frog kidney applying polyclonal antibody against the carboxyl terminus of human TASK2 (KCNK5) protein. Immunohistochemical analysis revealed that TASK2 is expressed on distal tubules and proximal epithelial cells. TASK2 is strongly expressed predominantly on the luminal part ofthe proximal epithelial cells and slightly cytoplasmatic staining is expressed. Distal tubules showed diffuse cytoplasmatic staining as well as slight staining on the apical parts ofthe cells. These findings suggest that the TASK2 K⁺ channel has cell-specific roles in renal potassium ion transport.

The vehicle presents a dynamic system performing vibrations under the influence of certain stimulus. Information driver receives from the environment and the vehicle is: macro and micro texture of the road, vibrations and noise of the vehicle's subsystem and so on. The road is usually evaluated according to its macro and micro texture. Microroughness of the roads is of great importance for the study of vehicle's oscillatory movements, reliable computation of vehicle systems, safety etc. Therefore, a special attention must be given to them during the analysis of dynamics, strength and safety of the vehicle. Microroughness that characterize the microprofile of the road in longitudinal and transverse direction have random character and can be established by experimental study of the road with utilization of devices. Accordingly, a variety of devices have been developed for measurement of macro- and micro profiles of the road as well as numerous mathematical and experimental procedures, which with certain approximation satisfy the given requirements, and with the increasing use of computer technology.

In this paper, applying Parseval’s formula, we prove a Gθ – summability analogue of Avadhani’s theorem for the Riesz–summability of the eigenfunction expansion. A crucial step in our proof of this theorem was to find a function g(x) that would lead us to the kernel of the Gθ –summability, which is more complex than the kernel of the Riesz – summability.