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The article concerns the electric techniques of moisture detection that are based on the evaluation of the apparent permittivity of the tested medium. The main goal of the research was to evaluate the non-invasive Time Domain Reflectometry (TDR) sensors’ sensitivity by measuring the span of elements and material moisture. To that aim, two non-invasive sensor designs were investigated for their sensitivity in the evaluation of the apparent permittivity value of aerated concrete. Sensors A and B were characterized by the spacing between the measuring elements equal to 30 mm and 70 mm, respectively. The tested samples differed in moisture, ranging between 0 and 0.3 cm3/cm3 volumetric water content. Within the research, it was stated that in the case of the narrower sensor (A), the range of the sensor equals about 30 mm, and in the case of the wider design (B), it equals about 50 mm. Additionally, it was stated that material moisture influences the range of sensor influence. In the case of the dry and low-saturated material, it was not possible to evaluate the range of sensor sensitivity using the adopted method, whereas the range of sensor signal influence was visible for the moist material.

A subgraph of an edge-colored graph is rainbow if all of its edges have different colors. For a graph H and a positive integer n, the anti-Ramsey number f (n, H) is the maximum number of colors in an edge-coloring of K n with no rainbow copy of H. The rainbow number rb(n, H) is the minimum number of colors such that any edge-coloring of K n with rb(n, H) number of colors contains a rainbow copy of H. Certainly rb(n, H) = f (n, H) + 1. Anti-Ramsey numbers were introduced by Erdös et al. [5] and studied in numerous papers. We show that rb(n, K 1,4 + e) = n + 2 in all nontrivial cases.

The article presents how Wolfram Demonstrations Project platform can support teaching of a great variety of subjects from very basic up to university level. The Wolfram Demonstrations Project is part of the family of free online services from Wolfram Research. General overview of the platform will be presented as well as a particular usage. The application concerns presenting to students certain numerical methods, namely one-step methods for Cauchy problem for ordinary differential equations.