A number of global optimisation algorithms rely on the value of the Lipschitz constant of the objective function. In this paper we present a stochastic method for estimating the Lipschitz constant. We show that the largest slope in a fixed size sample of slopes has an approximate Reverse Weibull distribution. Such a distribution is fitted to the largest slopes and the location parameter used as...

in this paper, the problem of decentralized model reference adaptive control (mrac) for a class of large scale systems with time varying delay in interconnected term and input and state delays is studied. to compensate the effect of input delay indirectly, a smith predictor built on. to handle the effects of the time delays in input, the adaptive controller part includes two auxiliary dynamic f...

We prove that allKK-homology classes of the stable (and unstable) Ruelle algebra a Smale space have explicit Fredholm module representatives ...

let $mathfrak{l}$ be the virasoro-like algebra and $mathfrak{g}$ itsderived algebra, respectively. we investigate the structure of the lie triplederivation algebra of $mathfrak{l}$ and $mathfrak{g}$. we provethat they are both isomorphic to $mathfrak{l}$, which provides twoexamples of invariance under triple derivation.

We show that there is an operator space notion of Lipschitz embeddability between spaces which strictly weaker than its linear counterpart but still strong enough to impose restrictions on structures. This shows a nontrivial theory nonlinear geometry for and it answers question in Braga et al. (Proc Am Math Soc 149(3):1139–1149, 2021). For that, we introduce the version Lipschitz-free Banach pr...

in this paper, we show that every surjective $n$-homomorphism ($n$-anti-homomorphism) from a banach algebra $a$ into a semisimple banach algebra $b$ is continuous.

A manifold with a “Lie structure at infinity” is a non-compact manifold M0 whose geometry is described by a compactification to a manifold with corners M and a Lie algebra V of vector fields on M subject to constraints only on M rM0. This definition recovers several classes of non-compact manifolds that were studied before: manifolds with cylindrical ends, manifolds that are Euclidean at infini...

This paper sheds new light on regularity of multifunctions through various characterizations of directional Hölder/Lipschitz metric regularity, which are based on the concepts of slope and coderivative. By using these characterizations, we show that directional Hölder/Lipschitz metric regularity is stable, when the multifunction under consideration is perturbed suitably. Applications of directi...

Lipschitz condition is a natural notion of function regularity in this context, and the norm dual to the mixed Lipschitz space is a natural distance between measures. In this paper, we consider the tensor product of spaces equipped with tree metrics and give effective formulas for the mixed Lipschitz norm and its dual. We also show that these norms behave well when approximating an arbitrary me...