The He matrix, put forward by He and He in 1989, is designed as a means for uniquely representing the structure of a hexagonal system (= benzenoid graph). Observing that the He matrix is just the adjacency matrix of a pertinently weighted inner dual of the respective hexagonal system, we establish a number of its spectral properties. Afterwards, we discuss the number of eigenvalues equal to zero of the He matrix of a hexagonal system. Moreover, we obtain a relation between the number of triangles and the eigenvalues of the He matrix of a hexagonal system. Finally, we present an upper bound on the He energy of hexagonal systems.
In the frame of the formal-semantic level description of the language system, complex sentence with paratactic subordinate clauses is delimited on the complex-sentence element level. In this type of complex sentence, subordinate clauses of the same complex-sentence element role are connected by a paratactic (from the formal-semantic point of view) connective (special paratactic connectives are found in apposition). A classifikacion of complex sentences with paratactic subordinate clauses is presented as a hierarchized complex-sentence system. In the first phase of the classification, a given complex sentence containing three or more clauses is classified according to the semantic-syntactic relationships (coordination, restricted coordination, determination, restricted determination, apposition). In the second phase, in coordination (or restricted coordination) and apposition, either the hypotactic connective is repeated, or the individual subordinate clauses are introduced by different connectives; coordination display also ellipsis of the hypotactic connective in the second clause. In the third phase of classification, semantic relationships among the subordinate clauses (copulative, escalating, adversative, disjunctive) are identified in coordination; in the various hypotactic connectives, their word-class role is noticed.