One of the tools for building new fixed-point results is use symmetry in distance functions. The symmetric property metrics particularly useful constructing contractive inequalities analyzing different models practical consequences. A lot important invariant point crisp mappings have been improved by using metrics. However, more than a handful theorems spaces are yet to be investigated fuzzy ve...

We consider elliptic systems generated by variational integrals of linear growth satisfying the condition \(\mu\)-ellipticity for some exponent \(\mu >1\) and prove that stationary points \(u\colon\mathbb{R}^2\to\mathbb{R}^N\) with property
 \(\limsup_{|x|\to \infty} \frac{|u(x)|}{|x|} < \infty\)
 must be affine functions. The latter can dropped in scalar case together appropria...

Machine learning can extrapolate beyond tipping points and predict the long-term behavior of non-stationary systems like climate change.

New, full-dimensional potential energy surface for acetylacetone allows description of H-tunneling dynamics and characterization stationary points.

We prove the existence of at least two timelike non self-intersecting periodic geodesics in compact stationary Lorentzian manifolds and we discuss some properties of the topology of such manifolds. In particular, we show that a compact manifold M admits a stationary Lorentzian metric if and only if M admits a smooth circle action without fixed points.

There are three “starting” points for the development of intelligent robots: Conventional, stationary industrial robots; mobile, unintelligent platforms (robots) and walking machines. Stationary industrial robots equipped with external sensors are used today for assembly and disassembly operations, fluelling cars, cleaning of buildings and airplanes, humanitarian demining ... and have been the ...

1 Stationary Points of the Log-Likelihood In this section, we briefly explain why the log-likelihood in Luce's model has a unique stationary point, that at the ML estimate. Recall that we assume that the comparison graph G D is strongly connected. The log-likelihood is given by