This text presents Egon Bondy’s political thought at the turn of the 1940s and 1950s, with special focus on his texts “The Dictatorship of the Proletariat” and “2000” (both written in 1949/1950), which represent one of the first expressions of Marxist criticism of Soviet-type society after 1948 in Czechoslovakia. The introductory study analyses Bondy’s evaluation of the Soviet Union as “fascism in its most advanced form”, and the implications of the fusion of economic and political power. It also points to the continuity of this type of Marxist criticism with earlier critiques written by Josef Guttmann and Záviš Kalandra in the 1930s and 1940s, while also pointing out how these texts by Bondy in some ways anticipated his later analyses from the 1960s, in which he understood Eastern Bloc regimes as examples of state capitalism. Following this introduction, we print a revised and annotated edition of Bondy’s “Dictatorship of the Proletariat.” and Petr Kužel (ed.),
The eigenproblem of a circulant matrix in max-min algebra is investigated. Complete characterization of the eigenspace structure of a circulant matrix is given by describing all possible types of eigenvectors in detail.
Eigenvectors of a fuzzy matrix correspond to stable states of a complex discrete-events system, characterized by a given transition matrix and fuzzy state vectors. Description of the eigenspace (set of all eigenvectors) for matrices in max-min or max-drast fuzzy algebra was presented in previous papers. In this paper the eigenspace of a three-dimensional fuzzy matrix in max-Łukasiewicz algebra is investigated. Necessary and sufficient conditions are shown under which the eigenspace restricted to increasing eigenvectors of a given matrix is non-empty, and the structure of the increasing eigenspace is described. Complete characterization of the general eigenspace structure for arbitrary three-dimensional fuzzy matrix, using simultaneous row and column permutations of the matrix, is presented in Sections 4 and 5, with numerical examples in Section 6.
In this paper, the eigenvalue distribution of complex matrices with certain ray patterns is investigated. Cyclically real ray patterns and ray patterns that are signature similar to real sign patterns are characterized, and their eigenvalue distribution is discussed. Among other results, the following classes of ray patterns are characterized: ray patterns that require eigenvalues along a fixed line in the complex plane, ray patterns that require eigenvalues symmetric about a fixed line, and ray patterns that require eigenvalues to be in a half-plane. Finally, some generalizations and open questions related to eigenvalue distribution are mentioned.