Amphiphilic porphyrin assembly as a highly selective chemosensor for organic mercury in water

Homogeneously sized nanoparticles were successfully constructed based on amphiphilic porphyrin-cholesterol arrays, showing unique spectral and colourimetric response to organic mercury in water, even in the presence of Hg(2+).     

Chiral Iridium Spiro Aminophosphine Complexes: Asymmetric Hydrogenation of Simple Ketones,Structure, and Plausible Mechanism

The iridium complexes of chiral spiro aminophophine ligands, especially the ligand with 3,5‐di‐tert‐butylphenyl groups on the P atom ( 1c ) were demonstrated to be highly efficient catalysts for the asymmetric hydrogenation of alkyl aryl ketones. In the presence of KOtBu as a base and under mild reaction conditions, a series of chiral alcohols were synthesized in up to 97 % ee with high turnover number (TON up to 10 000) and high turnover frequency (TOF up to 3.7×10⁴ h⁻¹). Investigation on the structures of the iridium complexes of ligands (R)‐ 1a and 1c by X‐ray analyses disclosed that the 3,5‐di‐tert‐butyl groups on the P‐phenyl rings of the ligand are the key factor for achieving high activity and enantioselectivity of the catalyst. Study of the catalysts generated from the Ir‐(R)‐ 1c complex and H₂ by means of ESI‐MS and NMR spectroscopy indicated that the early formed iridium dihydride complex with one (R)‐ 1c ligand was the active species, which was slowly transformed into an inactive iridium dihydride complex with two (R)‐ 1c ligands. A plausible mechanism for the reaction was also suggested to explain the observations of the hydrogenation reactions.     

Higher order log-concavity in Euler’s difference table

For 0≤k≤n, let be the entries in Euler’s difference table and let . Dumont and Randrianarivony showed equals the number of permutations on [n] whose fixed points are contained in {1,2,…,k}. Rakotondrajao found a combinatorial interpretation of the number in terms of k-fixed-points-permutations of [n]. We show that for any n≥1, the sequence is essentially 2-log-concave and reverse ultra log-concave.     

Chaos,feedback control and synchronization of a fractional-order modified Autonomous Van der Pol–Duffing circuit

In this work, stability analysis of the fractional-order modified Autonomous Van der Pol–Duffing (MAVPD) circuit is studied using the fractional Routh–Hurwitz criteria. A necessary condition for this system to remain chaotic is obtained. It is found that chaos exists in this system with order less than 3. Furthermore, the fractional Routh–Hurwitz conditions are used to control chaos in the proposed fractional-order system to its equilibria. Based on the fractional Routh–Hurwitz conditions and using specific choice of linear controllers, it is shown that the fractional-order MAVPD system is controlled to its equilibrium points; however, its integer-order counterpart is not controlled. Moreover, chaos synchronization of MAVPD system is found only in the fractional-order case when using a specific choice of nonlinear control functions. This shows the effect of fractional order on chaos control and synchronization. Synchronization is also achieved using the unidirectional linear error feedback coupling approach. Numerical results show the effectiveness of the theoretical analysis.     

How to recognize nonexpansive mappings and isometric mappings

In two real Banach spaces, we shall present two conditions, under one of which each nonexpansive mapping must be an isometry.     

Sharp Hölder continuity of the Lyapunov exponent of finitely differentiable quasi-periodic cocycles

Mathematische Zeitschrift - We show that if the base frequency is Diophantine, then the Lyapunov exponent of a $$C^{k}$$ quasi-periodic $$SL(2,{\mathbb {R}})$$ cocycle is...     

Isometric Extension Problem Between Strictly Convex Two-dimensional Normed Spaces

In this paper, based on the smooth point of the unit ball and its support linear functional,we show two equivalent formulations of the isometric extension problem between the unit spheres of strictly convex two-dimensional normed spaces. We prove that these equivalent formulations have a positive answer in a special case.