Let F be a distribution inD′ and let f be a locally summable function. The composition F f x of F and f is said to exist and be equal to the distribution h x if the limit of the sequence {Fn f x } is equal to h x , where Fn x F x ∗ δn x for n 1, 2, . . . and {δn x } is a certain regular sequence converging to the Dirac delta function. In the ordinary sense, the composition δ s sinh−1x r does no...

The main contribution of the present paper is to train efficient neural networks for seismic design of double layer grids subject to multiple-earthquake loading. As the seismic analysis and design of such large scale structures require high computational efforts, employing neural network techniques substantially decreases the computational burden. Square-on-square double layer grids with the va...

The investigation of boundary breather states of the sinh-Gordon model restricted to a half-line is revisited. Properties of the classical boundary breathers for the twoparameter family of integrable boundary conditions are reviewed and extended. The energy spectrum of the quantized boundary states is computed, firstly by using a bootstrap technique and, subsequently using a WKB approximation. ...