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In this paper, we deal with one of the basic problems of the theory of autonomous superposition operators acting in the spaces of functions of bounded variation, namely the problem concerning their continuity. We basically consider autonomous superposition operators generated by analytic functions or functions of C 1 -class. We also investigate the problem of compactness of some classical linear and nonlinear operators acting in the space of functions of bounded variation in the sense of Jordan. We apply our results to the examination of the existence and the topological properties of solutions to nonlinear equations in those spaces. Keywords

This review synthesizes knowledge on epigenetic regulation of leaf senescence and discusses the possibility of using this knowledge to improve crop quality. This control level is implemented by different but interacting epigenetic mechanisms, including DNA methylation, covalent histone modifications, and non-covalent chromatin remodeling. The genetic and epigenetic changes may act alone or together and regulate the gene expression, which may result in heritable (stress memory) changes and may lead to crop survival. In the review, the question also arises whether the mitotically stable epigenetic information can be used for crop improvement. The barley crop model for early and late events of dark-induced leaf senescence (DILS), where the point of no return was defined, revealed differences in DNA and RNA modifications active in DILS compared to developmental leaf senescence. This suggests the possibility of a yet-to-be-discovered epigenetic-based switch between cell survival and cell death. Conclusions from the analyzed research contributed to the hypothesis that chromatin-remodeling mechanisms play a role in the control of induced leaf senescence. Understanding this mechanism in crops might provide a tool for further exploitation toward sustainable agriculture: so-called epibreeding.

The main goal of this paper is to give an answer to the main problem of the theory of nonautonomous superposition operators acting in the space of functions of bounded variation in the sense of Jordan. Namely, we give necessary and sufficient conditions which guarantee that nonautonomous superposition operators map that space into itself and are locally bounded. Moreover, special attention is drawn to nonautonomous superposition operators generated by locally bounded mappings as well as to superposition operators generated by functions with separable variables.