On the “bang-bang” principle for a class of Riemann-Liouville fractional semilinear evolution inclusions

In this paper, we research the existence of solutions for a class of Riemann-Liouville fractional evolution inclusions with nonconvex right hand side. Our main results obtain the existence of the extreme solution and the relationship of the solution sets between the original problem and the convexified problem. In the end, we give an example to illustrate the applications of the abstract results.

On the ‘bang-bang’ principle for a class of fractional semilinear evolution inclusions

In this paper, we study the problem of the existence of solutions for a class of fractional semilinear evolution inclusions with non-convex right-hand side. We mainly focus on the existence of the extreme solution and the relationship of the solution sets between the original problem and the convexified problem. An example is provided to illustrate the application of the obtained theory.

Arthur Benjamin and the Problem of Popularity. A Critical Appreciation

The strongest single cause of the present-day cleft between composer and listener has been the increasingly swift raising of the norm of dissonance: if indeed “norm” is still the word: from modern music as a whole it is quite impossible to extract anything like generally valid harmonic formulae. It is true that with the increased availability of art to the inartistic the problem of popularity would in any case have arisen; but the dynamic development and—in 12-tone technique—dethronement of harmony has left the majority of listeners so far behind that most talents trying to be popular fall between the proletarian and the musical stools. It is in fact the Marxist musicians' bad luck that they have to attempt their extreme solution of the question how to be popular at the very time when the history of harmony and tonality makes their task extremely unsolvable. Thus they have come to demand more than the maximal musical conservatism, and to consider the atonalists right-wing. Meanwhile the right wing, while condemning Moscow's artistic approach, regards the atonalists as left wing, and an unhappy time is had by all. The paradox is easily solved: a political revolution needs the mass; an artistic revolution revolts against it.