Catalytic Asymmetric Reductive Condensation of N–H Imines: Synthesis of C2‐Symmetric Secondary Amines

A highly diastereoselective and enantioselective Brønsted acid catalyzed reductive condensation of N?H imines was developed. This reaction is catalyzed by a chiral disulfonimide (DSI), uses Hantzsch esters as a hydrogen source, and delivers useful C₂‐symmetric secondary amines.     

Synthesis of a pH‐Sensitive Hetero[4]Rotaxane Molecular Machine that Combines [c2]Daisy and [2]Rotaxane Arrangements

The synthesis of a novel pH‐sensitive hetero[4]rotaxane molecular machine through a self‐sorting strategy is reported. The original tetra‐interlocked molecular architecture combines a [c2]daisy chain scaffold linked to two [2]rotaxane units. Actuation of the system through pH variation is possible thanks to the specific interactions of the dibenzo‐24‐crown‐8 (DB24C8) macrocycles for ammonium, anilinium, and triazolium molecular stations. Selective deprotonation of the anilinium moieties triggers shuttling of the unsubstituted DB24C8 along the [2]rotaxane units.     

Unprecedented Efficient Structure Controlled Phosphorescence of Silver(I) Clusters Stabilized by Carba‐closo‐dodecaboranylethynyl Ligands

{Ag₂(12‐C≡C‐closo‐1‐CB₁₁H₁₁)}_n and selected pyridine ligands have been used for the synthesis of photostable Ag^I clusters that, with one exception, exhibit for Ag^I compounds unusual room‐temperature phosphorescence. Extraordinarily intense phosphorescence was observed for a distorted pentagonal bipyramidal Ag^I₇ cluster that shows an unprecedented quantum yield of Φ=0.76 for Ag^I clusters. The luminescence properties correlate with the structures of the central Ag^I_n motifs as shown by comparison of the emission properties of the clusters with different numbers of Ag^I ions, different charges, and electronically different pyridine ligands.     

Stabilized nodal‐based finite element methods for the magnetic induction problem

We consider the time‐dependent magnetic induction model as a step towards the resistive magnetohydrodynamics model in incompressible media. Conforming nodal‐based finite element approximations of the induction model with inf‐sup stable finite elements for the magnetic field and the magnetic pseudo‐pressure are investigated. Based on a residual‐based stabilization technique proposed by Badia and Codina, SIAM J. Numer. Anal. 50 (2012), pp. 398–417, we consider a stabilized nodal‐based finite element method for the numerical solution. Error estimates are given for the semi‐discrete model in space. Finally, we present some examples, for example, for the magnetic flux expulsion problem, Shercliff's test case and singular solutions of the Maxwell problem. Copyright © 2015 John Wiley & Sons, Ltd.     

On a question of Külshammer for representations of finite groups in reductive groups

Let G be a simple algebraic group of type G₂ over an algebraically closed field of characteristic 2. We give an example of a finite group Γ with Sylow 2-subgroup Γ₂ and an infinite family of pairwise non-conjugate homomorphisms ρ: Γ → G whose restrictions to Γ₂ are all conjugate. This answers a question of Burkhard Külshammer from 1995. We also give an action of Γ on a connected unipotent group V such that the map of 1-cohomologies H¹(Γ, V) → H¹(Γ_p, V) induced by restriction of 1-cocycles has an infinite fibre.     

Mean‐Field Evolution of Fermionic Mixed States

In this paper we study the dynamics of fermionic mixed states in the mean‐field regime. We consider initial states that are close to quasi‐free states and prove that, under suitable assumptions on the initial data and on the many‐body interaction, the quantum evolution of such initial data is well approximated by a suitable quasi‐free state. In particular, we prove that the evolution of the reduced one‐particle density matrix converges, as the number of particles goes to infinity, to the solution of the time‐dependent Hartree‐Fock equation. Our result holds for all times and gives effective estimates on the rate of convergence of the many‐body dynamics towards the Hartree‐Fock evolution.© 2015 Wiley Periodicals, Inc.     

Perfect state transfer in Laplacian quantum walk

For a graph G and a related symmetric matrix M, the continuous-time quantum walk on G relative to M is defined as the unitary matrix \(U(t) = \exp (-itM)\), where t varies over the reals. Perfect state transfer occurs between vertices u and v at time \(\tau \) if the (u, v)-entry of \(U(\tau )\) has unit magnitude. This paper studies quantum walks relative to graph Laplacians. Some main observations include the following closure properties for perfect state transfer. If an n-vertex graph has perfect state transfer at time \(\tau \) relative to the Laplacian, then so does its complement if \(n\tau \in 2\pi {\mathbb {Z}}\). As a corollary, the join of \(\overline{K}_{2}\) with any m-vertex graph has perfect state transfer relative to the Laplacian if and only if \(m \equiv 2\pmod {4}\). This was previously known for the join of \(\overline{K}_{2}\) with a clique (Bose et al. in Int J Quant Inf 7:713–723, 2009). If a graph G has perfect state transfer at time \(\tau \) relative to the normalized Laplacian, then so does the weak product \(G \times H\) if for any normalized Laplacian eigenvalues \(\lambda \) of G and \(\mu \) of H, we have \(\mu (\lambda -1)\tau \in 2\pi {\mathbb {Z}}\). As a corollary, a weak product of \(P_{3}\) with an even clique or an odd cube has perfect state transfer relative to the normalized Laplacian. It was known earlier that a weak product of a circulant with odd integer eigenvalues and an even cube or a Cartesian power of \(P_{3}\) has perfect state transfer relative to the adjacency matrix. As for negative results, no path with four vertices or more has antipodal perfect state transfer relative to the normalized Laplacian. This almost matches the state of affairs under the adjacency matrix (Godsil in Discret Math 312(1):129–147, 2011).