Abelian varieties with finite abelian group action

An automorphism of an abelian variety induces a decomposition of the variety up to isogeny. There are two such results, namely the isotypical decomposition and Roan’s decomposition theorem. We show that they are essentially the same. Moreover, we generalize in a sense this result to abelian varieties with action of an arbitrary finite abelian group. An early version of this article was inadvertently published before all the revisions had been completed and then retracted [https://doi.org/10.1007/s00013-018-1244-3]. This article is the final peer reviewed version.

     

Partial control of delay-coordinate maps

Nonlinear Dynamics - Delay-coordinate maps have been widely used recently to study nonlinear dynamical systems, where there is only access to the time series of one of their variables. Here, we...     

Role of the Bridge in Photoinduced Electron Transfer in Porphyrin–Fullerene Dyads

The role of π‐conjugated molecular bridges in through‐space and through‐bond electron transfer is studied by comparing two porphyrin–fullerene donor–acceptor (D–A) dyads. One dyad, ZnP–Ph–C₆₀ (ZnP=zinc porphyrin), incorporates a phenyl bridge between D and A and behaves very similarly to analogous dyads studied previously. The second dyad, ZnP–EDOTV–C₆₀, introduces an additional 3,4‐ethylenedioxythienylvinylene (EDOTV) unit into the conjugated bridge, which increases the distance between D and A, but, at the same time, provides increased electronic communication between them. Two essential outcomes that result from the introduction of the EDOTV unit in the bridge are as follows: 1) faster charge recombination, which indicates enhanced electronic coupling between the charge‐separated and ground electronic states; and 2) the disappearance of the intramolecular exciplex, which mediates photoinduced charge separation in the ZnP–Ph–C₆₀ dyad. The latter can be interpreted as a gradual decrease in electronic coupling between locally excited singlet states of D and A when introducing the EDOTV unit into the D–A bridge.     

Strengthened splitting methods for computing resolvents

Computational Optimization and Applications - In this work, we develop a systematic framework for computing the resolvent of the sum of two or more monotone operators which only activates each...     

Zinc‐Catalyzed Functionalization of SiH Bonds with 2‐Furyl Carbenoids through Three‐Component Coupling

A three‐component coupling of alk‐2‐ynals, 1,3‐dicarbonyls and silanes is reported. ZnCl₂ serves as an inexpensive and low‐toxic catalyst for the overall transformation, which involves Knoevenagel condensation, cyclization, and carbene Si?H bond insertion. The process takes place with high atom economy in the absence of organic solvents and shows a broad scope. This reaction is also applicable to the functionalization of oligomeric siloxanes.     

Direct On‐Surface Patterning of a Crystalline Laminar Covalent Organic Framework Synthesized at Room Temperature

We report herein an efficient, fast, and simple synthesis of an imine‐based covalent organic framework (COF) at room temperature (hereafter, RT‐COF‐1 ). RT‐COF‐1 shows a layered hexagonal structure exhibiting channels, is robust, and is porous to N₂ and CO₂. The room‐temperature synthesis has enabled us to fabricate and position low‐cost micro‐ and submicropatterns of RT‐COF‐1 on several surfaces, including solid SiO₂ substrates and flexible acetate paper, by using lithographically controlled wetting and conventional ink‐jet printing.     

Comprehensive Characterization of the Self-Folding Cavitand Dynamics

The conformational equilibria and guest exchange process of a resorcin[4]arene derived self-folding cavitand receptor have been characterized in detail by molecular dynamics simulations (MD) and ¹H EXSY NMR experiments. A multi-timescale strategy for exploring the fluxional behaviour of this system has been constructed, exploiting conventional MD and accelerated MD (aMD) techniques. The use of aMD allows the reconstruction of the folding/unfolding process of the receptor by sampling high-energy barrier processes unattainable by conventional MD simulations. We obtained MD trajectories sampling events occurring at different timescales from ns to s: 1) rearrangement of the directional hydrogen bond seam stabilizing the receptor, 2) folding/unfolding of the structure transiting partially open intermediates, and 3) guest departure from different folding stages. Most remarkably, reweighing of the biased aMD simulations provided kinetic barriers that are in very good agreement with those determined experimentally by ¹H NMR. These results constitute the first comprehensive characterization of the complex dynamic features of cavitand receptors. Our approach emerges as a valuable rational design tool for synthetic host-guest systems     

Some classes of operators with symbol on the Lipschitz space of a tree

In this paper, we expand the study of the multiplication operators on the Lipschitz space of a tree begun in Colonna and Easley (Integral Equ Oper Theory 68:391–411, 2010) by focusing on their adjoint acting on a certain separable subspace of the Lipschitz space whose dual is isometrically isomorphic to \(\mathbf L^1\). We then study the properties of two useful operators \(\nabla \) and \(\Delta \) and use them (along with the multiplicative symbol \(\psi \)) to define the Toeplitz operator \(T_\psi \) on the space \(\mathbf L^p\) for \(1\le p \le \infty \). We give conditions for its boundedness and study its point spectrum.