1.1 Shocks and the Rankine-Hugoniot condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 Hopf’s treatment of Burgers equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3 Two basic examples of Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.4 Entropies and Admissibility Criteria . . . . ...

It is shown that the right shift semigroup on L(R+) does not satisfy the weighted Weiss conjecture for α ∈ (0, 1). In other words, αadmissibility of scalar valued observation operators cannot always be characterised by a simple resolvent growth condition. This result is in contrast to the unweighted case, where 0-admissibility can be characterised by a simple growth bound. The result is proved ...

Abstract This paper presents an investigation of the approximation property of neural networks with unbounded activation functions, such as the rectified linear unit (ReLU), which is the new de-facto standard of deep learning. The ReLU network can be analyzed by the ridgelet transform with respect to Lizorkin distributions. By showing three reconstruction formulas by using the Fourier slice the...

The main goal of the paper is to define and use a condition sufficient choose unique solution conservation law systems with singular measure in initial data. Different approximations can lead solutions different distributional limits. new notion called backward energy then single out proper approximation definition based on maximal dissipation defined Dafermos (J Differ Equ 14:202–212, 1973). S...

This paper is pertained with the problem of admissibility analysis of uncertain discrete-time nonlinear singular systems by adopting the state-space Takagi-Sugeno fuzzy model with time-delays and norm-bounded parameter uncertainties. Lyapunov Krasovskii functionals are constructed to obtain delay-dependent stability condition in terms of linear matrix inequalities, which is dependent on the low...

Abstract In this work, a new common fixed point result by generalized contractive functions fulfilling the type of admissibility condition in Hausdorff Branciari metric space with support C -functions, was obtained.

We study the admissibility and network capacity of imperfect power-controlled Code-Division Multiple Access (CDMA) systems with linear receivers in fading environments. In a CDMA system, a set of users is admissible if their simultaneous transmission does not result in violation of any of their Quality-of-Service (QoS) requirements; the network capacity is the maximum number of admissible users...

Finding optimal representations of signals in higher dimensions, in particular directional representations, is currently the subject of intensive research. Since it might be difficult to obtain directional information by means of wavelets, several new representation systems were proposed in the past, including ridgelets, curvelets and, more recently, shearlets. In this paper we study and visual...

Cyclotomic Birman–Wenzl–Murakami (BMW) algebras are BMW analogues of cyclotomic Hecke algebras [2, 1]. They were defined by Häring–Oldenburg in [7] and have recently been studied by three groups of mathematicians: Goodman and Hauschild–Mosley [4, 5, 6, 3], Rui, Xu, and Si [9, 8], andWilcox and Yu [10, 11, 12, 13]. A peculiar feature of these algebras is that it is necessary to impose “admissibi...