For the family of exponential maps Eκ(z) = exp(z)+κ, we prove an analog of Böttcher’s theorem by showing that any two exponential maps Eκ1 and Eκ2 are conjugate on suitable subsets of their escaping sets, and this conjugacy is quasiconformal. Furthermore, we prove that any two attracting and parabolic exponential maps are conjugate on their sets of escaping points; in fact, we construct an anal...

We show that the fast escaping set A(f) of a transcendental entire function f has a structure known as a spider’s web whenever the maximum modulus of f grows below a certain rate. We give examples of entire functions for which the fast escaping set is not a spider’s web which show that this growth rate is best possible. By our earlier results, these are the first examples for which the escaping...

Abstract In this article, I argue that Benedictine stability might provide a rational modulation for some people to not only cope with but also flourish during the pandemic vis-à-vis stay-at-home (SHO) order. will those who obey SHO are more than don’t or vice versa . Instead, end up following SHO, whether voluntarily involuntarily, can rationalize by learning from vow of stability. First, in p...

Molecular chaperones reside in nearly every organelle within a eukaryotic cell, and in each of these compartments, they ensure that protein homeostasis (or proteostasis) is maintained. In this issue, Wiseman and colleagues find that an ER lumenal chaperone escapes this compartment when a specific stress pathway is activated. The chaperone, an Hsp40 homolog known as ERdj3, transits through the s...

The system of electrons in a metastable well near a helium surface is an ideal system to test our understanding of the escape process from a metastable well with many body correlations due to Coulomb interaction. A number of experiments have been performed on the escaping of electrons from a helium surface. Recent theoretical studies have mainly concentrated on how the static correlations affec...

The paper researches the fire sources and programs escaping path using mobile robots for intelligent building, and presents the movement scenario in the experimental platform. The mobile robot has the shape of cylinder and its diameter, height and weight is 10cm, 18cm and 1.5kg. The controller of the mobile robot is MCS-51 microchip, and acquires the detection signals from flame sensor and refl...