Vertically aligned multi-walled carbon nanotubes (VA-MWCNTs) with an average diameter below 80 nm and a thickness of the uniform VA-MWCNT layer of about 16 μm were grown in microwave plasma torch and tested for selected functional properties. IR absorption important for a construction of bolometers was studied by Fourier transform infrared spectroscopy. Basic electrochemical characterization was performed by cyclic voltammetry. Comparing the obtained results with the standard or MWCNT‐modified screen-printed electrodes, the prepared VA-MWCNT electrodes indicated their high potential for the construction of electrochemical sensors. Resistive CNT gas sensor revealed a good sensitivity to ammonia taking into account room temperature operation. Field emission detected from CNTs was suitable for the pressure sensing application based on the measurement of emission current in the diode structure with bending diaphragm. The advantages of microwave plasma torch growth of CNTs, i.e., fast processing and versatility of the process, can be therefore fully exploited for the integration of surface-bound grown CNTs into various sensing structures.

A non-invasive solution for monitoring of the activity and dehydration of organisms is proposed in the work. For this purpose, a wireless standalone chemical sensor platform using two separate measurement techniques has been developed. The first approach for activity monitoring is based on humidity measurement. Our solution uses new humidity sensor based on a nanostructured TiO2 surface for sweat rate monitoring. The second technique is based on monitoring of potassium concentration in urine. High level of potassium concentration denotes clear occurrence of dehydration. Furthermore, a Wireless Body Area Network (WBAN) was developed for this sensor platform to manage data transfer among devices and the internet. The WBAN coordinator controls the sensor devices and collects and stores the measured data. The collected data is particular to individuals and can be shared with physicians, emergency systems or athletes' coaches. Long-time monitoring of activity and potassium concentration in urine can help maintain the appropriate water intake of elderly people or athletes and to send warning signals in the case of near dehydration. The created sensor system was calibrated and tested in laboratory and real conditions as well. The measurement results are discussed.

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Let G be a finite connected graph without loops or multiple edges. A maximal tree subgraph T of G is called a spanning tree of G. Denote by k(G) the number of all trees spanning the graph G. A. Rosa formulated the following problem (private communication): Let x(≠2) be a given positive integer and denote by α(x) the smallest positive integer y having the following property: There exists a graph G on y vertices with x spanning trees. Investigate the behavior of the function α(x).

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Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use. This paper has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital Mathematics Library http://project.dml.cz Časopis pro pěstování matematiky, roč. 94 (1969), Praha

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