In this paper, the connection between Menger probabilistic norms and H"{o}hle probabilistic norms is discussed. In addition, the correspondence between probabilistic norms and Wu-Fang fuzzy (semi-) norms is established. It is shown that a probabilistic norm (with triangular norm $min$) can generate a Wu-Fang fuzzy semi-norm and conversely, a Wu-Fang fuzzy norm can generate a probabilistic norm.

The solving of linear systems provides a rich area to investigate the use nearer-term, noisy, intermediate-scale quantum computers. In this work, we discuss hybrid quantum-classical algorithms for skewed over-determined and under-determined cases. Our input model is such that columns or rows matrix defining system are given via circuits poly-logarithmic depth number much smaller than their Hilb...

Abstract We study distinguished objects in the category $\mathcal{B}\mathcal{L}$ of Banach lattices and lattice homomorphisms. The free construction introduced by de Pagter Wickstead [ 8] generates push-outs, combining this with an old result Kellerer 17] on marginal measures, amalgamation property is established. This will be key tool to prove that $L_1([0,1]^{\mathfrak{c}})$ separably $\mathc...