On‐Surface Synthesis and Characterization of Triply Fused Porphyrin–Graphene Nanoribbon Hybrids

On‐surface synthesis offers a versatile approach to prepare novel carbon‐based nanostructures that cannot be obtained by conventional solution chemistry. Graphene nanoribbons (GNRs) have potential for a variety of applications. A key issue for their application in molecular electronics is in the fine‐tuning of their electronic properties through structural modifications, such as heteroatom doping or the incorporation of non‐benzenoid rings. In this context, the covalent fusion of GNRs and porphyrins (Pors) is a highly appealing strategy. Herein we present the selective on‐surface synthesis of a Por–GNR hybrid, which consists of two Pors connected by a short GNR segment. The atomically precise structure of the Por–GNR hybrid has been characterized by bond‐resolved scanning tunneling microscopy (STM) and noncontact atomic force microscopy (nc‐AFM). The electronic properties have been investigated by scanning tunneling spectroscopy (STS), in combination with DFT calculations, which reveals a low electronic gap of 0.4 eV.     

Collective All‐Carbon Magnetism in Triangulene Dimers

Triangular zigzag nanographenes, such as triangulene and its π‐extended homologues, have received widespread attention as organic nanomagnets for molecular spintronics, and may serve as building blocks for high‐spin networks with long‐range magnetic order, which are of immense fundamental and technological relevance. As a first step towards these lines, we present the on‐surface synthesis and a proof‐of‐principle experimental study of magnetism in covalently bonded triangulene dimers. On‐surface reactions of rationally designed precursor molecules on Au(111) lead to the selective formation of triangulene dimers in which the triangulene units are either directly connected through their minority sublattice atoms, or are separated via a 1,4‐phenylene spacer. The chemical structures of the dimers have been characterized by bond‐resolved scanning tunneling microscopy. Scanning tunneling spectroscopy and inelastic electron tunneling spectroscopy measurements reveal collective singlet–triplet spin excitations in the dimers, demonstrating efficient intertriangulene magnetic coupling.     

Picolinamides as Effective Ligands for Copper‐Catalysed Aryl Ether Formation: Structure–Activity Relationships,Substrate Scope and Mechanistic Investigations

The use of picolinic acid amide derivatives as an effective family of bidentate ligands for copper‐catalysed aryl ether synthesis is reported. A fluorine‐substituted ligand gave good results in the synthesis of a wide range of aryl ethers. Even bulky phenols, known to be very challenging substrates, were shown to react with aryl iodides with excellent yields using these ligands. At the end of the reaction, the first examples of end‐of‐life Cu species were isolated and identified as Cu^II complexes with several of the anionic ligands tested. A preliminary mechanistic investigation is reported that suggests that the substituents on the ligands might have a crucial role in determining the redox properties of the metal centre and, consequently, its efficacy in the coupling process. An understanding of these effects is important for the development of new efficient and tunable ligands for copper‐based chemistry.     

Shuffles of copulas

We show that every copula that is a shuffle of Min is a special push-forward of the doubly stochastic measure induced by the copula M. This fact allows to generalize the notion of shuffle by replacing the measure induced by M with an arbitrary doubly stochastic measure, and, hence, the copula M by any copula C.     

Notes on local o‐minimality

We introduce and study some local versions of o‐minimality, requiring that every definable set decomposes as the union of finitely many isolated points and intervals in a suitable neighbourhood of every point. Motivating examples are the expansions of the ordered reals by sine, cosine and other periodic functions (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the convergence toward nonequilibrium stationary states in thermostatted kinetic models

A differential equation‐based framework is suitable for the modeling of nonequilibrium complex systems if its solution is able to reach, as time goes to infinity, the related nonequilibrium steady states. The thermostatted kinetic theory framework has been recently proposed for the modeling of complex systems subjected to an external force field. The present paper is devoted to the mathematical proof of the convergence of the solutions of the thermostatted kinetic framework towards the related nonequilibrium stationary states. The proof of the main result is gained by employing the Fourier transform and distribution theory arguments.     

A matrix-less and parallel interpolation–extrapolation algorithm for computing the eigenvalues of preconditioned banded symmetric Toeplitz matrices

Numerical Algorithms - In the past few years, Bogoya, Böttcher, Grudsky, and Maximenko obtained the precise asymptotic expansion for the eigenvalues of a Toeplitz matrix Tn(f), under suitable...     

Multicategory classification via discrete support vector machines

Discrete support vector machines (DSVM), originally proposed for binary classification problems, have been shown to outperform other competing approaches on well-known benchmark datasets. Here we address their extension to multicategory classification, by developing three different methods. Two of them are based respectively on one-against-all and round-robin classification schemes, in which a number of binary discrimination problems are solved by means of a variant of DSVM. The third method directly addresses the multicategory classification task, by building a decision tree in which an optimal split to separate classes is derived at each node by a new extended formulation of DSVM. Computational tests on publicly available datasets are then conducted to compare the three multicategory classifiers based on DSVM with other methods, indicating that the proposed techniques achieve significantly higher accuracies. This research was partially supported by PRIN grant 2004132117.