Solutions for the p-order Feigenbaum's functional equation h(g(x))=g^p(h(x))

Abstract

This work deals with Feigenbaum's functional equationwhere p ≥ 2 is an integer, g p is the p-fold iteration of g, and h is a strictly monotone odd continuous function on [−1, 1] with h(0) = 0 and |h(x)| < |x| (x ∈ [−1, 1], x = 0). Using a constructive method, we discuss the existence of continuous unimodal even solutions of the above equation.

An Organoselective Zirconium‐Based Metal–Organic‐Framework UiO‐66 Membrane for Pervaporation

“…This indicates that water adsorption was inhibited by the competitive adsorption of ethanol. Indeed, UiO‐66 could be applied to selective organic adsorption from water owing to its hydrophobicity , . Therefore, the ethanol selectivity of UiO‐66 membrane can be attributed to the preferential adsorption of ethanol rather than water.…”

Manipulation of pH induced sensitivity of a fluorescent probe in presence of silver nanoparticles

“…This can be attributed to the formation of aggregates in the polymeric matrix and formation of larger structures with different size and shape. This kind of aggregate formation has been reported earlier[33].These structures distribute disorderly in the metal-dielectric composites and their surface plasmon can be excited in a broad spectral range between 350-510 nm. Therefore, the observed 2.65 unit shift in the pKa can be attributed to the plasmon absorption of Ag nanoparticles.…”

Hybrid Coordination Networks Constructed from ɛ‐Keggin‐Type Polyoxometalates and Rigid Imidazole‐Based Bridging Ligands as New Carriers for Noble‐Metal Catalysts

“…[17][18][19] In at ypical catalytic reaction, as olution of NaBH 4 (1 mL, 2.3 mg mL À1 )w as dispersed in ice-cold distilledw ater and added into as olution of 4-NP (2 mL, 0.12 mmol L À1 ). [17][18][19] In at ypical catalytic reaction, as olution of NaBH 4 (1 mL, 2.3 mg mL À1 )w as dispersed in ice-cold distilledw ater and added into as olution of 4-NP (2 mL, 0.12 mmol L À1 ).…”