Implicatively implicit extensions of all 27 one-place functions of three-valued logic are characterized. It is found they include both extensions coinciding with known implicatively closed classes and extensions that are not closed with respect to the operation of superposition. It is also shown that any implicatively implicit extension in (P_{k}) contains class (H_{k}) of all homogeneous functions from (P_{k}) for any (kgeqslant 3) .
The problem of an unadvertised agreement between buyers of non-exclusive rights at a spectrum auction for the agreed formation of price bids is considered from the viewpoint of game theory and operations research. Such auction participants are potential freeriders claiming free access to the frequencies being sold, which results in their non-standard behavior. Two ways of organizing an agreement for an auction with pricing according to the Vickrey rule are proposed for the full awareness of the participants about the amount of income of the partners from using the range of frequencies purchased by pooling. It is shown that the lack of information results in an equal distribution of payment between negotiating buyers, and this greatly reduces their competitive advantage in a spectrum auction. The Clarke–Groves mechanism that stimulates the identification of true preferences is analyzed and a modified version of it is developed. Unfortunately, analysis shows it does not make sense for any of them to be applied to this problem. An alternative way of choosing a joint solution based on the Germeyer–Vatel model is discussed.
The author constructs a complete classification of linear codes that are obtained from different types of codimension (1) subcodes of Reed–Muller codes using the Hadamard product operation.
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