On some maximal partial ultraclones on a two-element set

Multifunctions on a two-element set are considered in this paper. Functions from finite set to set of all subsets of this set are called multifunctions. It is obvious that the superposition in the usual sense not appropriate for multifunctions, therefore, we need to expand the standard concept of superposition. Sets of multifunction closed with respect to the operation of "expanded" superposition are called multiclones and partial ultraclones depending on the type of superposition.
In the theory of discrete functions the classical problem is description of lattice of clones. Because of difficulty of this problem lattice fragments are studied, for example, the minimum and maximum elements, different intervals. In particular, we note that the descriptions of all maximal clones are known for $k$-valued logic functions, partial functions on $k$-element sets, the descriptions of all maximal hyperclones and ultraclones on a two-element set, multiclones on a two-element set are known. In this work the problem of description of of some maximal ultraclones on a two-element set is considered.