In this paper a nonmonotone limited memory BFGS (NLBFGS) method is applied for approximately solving optimal control problems (OCPs) governed by one-dimensional parabolic partial differential equations. A discretized optimal control problem is obtained by using piecewise linear finite element and well-known backward Euler methods. Afterwards, regarding the implicit function theorem, the optimal control problem is transformed into an unconstrained nonlinear optimization problem (UNOP). Finally the obtained UNOP is solved by utilizing the NLBFGS method. In comparison to other existing methods, the NLBFGS method shows a significant improvement especially for nonlinear and ill-posed control problems.
The article deals with little researched subject from the history of Czech music in the 20th century – public music life at the time of the Nazi Protectorate of Bohemia and Moravia (1939–1945). Based on research in Czech music journals of the time, which are listed in the article, it informs on important concerts and theatre performances, music festivals and festivities, taking place in Prague and other places in the Protectorate territory. It also follows the ways in which the press wrote about period music life, and tries – even if only in a preliminary way – to answer a difficult question – how much these activities corresponded with the official cultural politics of the Protectorate regime, and on the other hand, to what extent they manifested patriotic feelings and resistence against the enemy occupying power.
In the present paper we deal with generalized $MV$-algebras ($GMV$-algebras, in short) in the sense of Galatos and Tsinakis. According to a result of the mentioned authors, $GMV$-algebras can be obtained by a truncation construction from lattice ordered groups. We investigate direct summands and retract mappings of $GMV$-algebras. The relations between $GMV$-algebras and lattice ordered groups are essential for this investigation.