A new look at the John–Nirenberg and John–Strömberg theorems for BMO

We develop some techniques for studying various versions of the function space BMO. Special cases of one of our results give alternative proofs of the celebrated John–Nirenberg inequality and of related inequalities due to John and to Wik. Our approach enables us to pose a simply formulated “geometric” question, for which an affirmative answer would lead to a version of the John–Nirenberg inequality with dimension free constants.     

Electronic properties of Si surfaces and side reactions during electrochemical grafting of phenyl layers

The electrochemical grafting process of 4-nitrobenzene and 4-methoxybenzene (anisole) from diazonium salt solutions has been investigated in situ by monitoring the current density, the band bending, and the nonradiative surface recombination during grafting at different potentials and different concentrations of the diazonium salt in the solution. Ex situ infrared spectroscopic ellipsometry has been used to inspect the Si surface species before and after the grafting process. The band bending decreases with either increasing concentration of diazonium salt or when the redox potential of the diazonium compound (anisole) is nearer to the competing H+/H2 couple. The surface recombination increases at more cathodic potentials if an electron donor group is present at the phenyl ring (nitrobenzene) and vice versa for the electron acceptor group (anisole). The influence of side reactions can be reduced by use of moderate concentration and moderate or strong cathodic potential, depending on the redox potential of the diazonium compound.     

Empirical extraction of mechanisms underlying real world network generation

The generation mechanisms of real world networks have been described using multiple models. The mathematical features of these models are usually extrapolated from statistical properties of a snapshot of these networks. We here propose an alternative method based on direct measurement of a sequence of consecutive snapshots to uncover the dynamics underlying real world generation. We assume that the probability of adding a node or an edge depends only on local features surrounding the newly added node/edge, and directly measure the contribution of these features to the node/edge addition probability. These measurements are performed using newly defined N-node local structures. Each N-node local structure represents the configuration of edges surrounding a newly added edge. The N-node local structure measurements reproduce for some networks the now classical addition of edges between high degree node mechanisms. It also provides quantitative estimates of more complex mechanisms driving other networks’ evolution, such as the effect of common first and second neighbors. This new methodology reveals the relative importance of different generation mechanisms. We show, for example, that the main mechanism driving hyperlink addition between two websites is the existence of a third website linking to both the source and the target of the new hyperlink.     

The complete infinite series solution of systems governed by the wave equation with boundary damping

A common method of solving initial boundary value problems is separation of variables, denoted as modal analysis in the field of flexible structures. For systems with undamped boundary conditions the method is well-established, but for systems with boundary damping it does not provide closed form solutions. In this paper the exact modal series solution for second order systems with damped boundaries is derived with explicit expressions for the series coefficients. Knowledge of these coefficients enables practical applications of the solution, such as finite dimension approximation. The key element of the derivation is a new orthogonality condition for the damped eigenfunctions. The modal series is also transformed into a traveling wave form. The solution, which is the extension of the classical D’Alembert formula, is represented by a single equivalent propagating wave. A component of the solution, denoted by “end waves”, is identified to provide the continuity of the systems displacement response.     

Kinetic Stabilities and Exchange Dynamics of Water-Soluble Bis-Formamide Caviplexes Studied Using Diffusion-Ordered NMR Spectroscopy (DOSY)

A deep cavitand binds long-chain trans,trans- and trans,cis-bis-formamide isomers in water solution giving a pair of caviplexes in a ca. 60:40 ratio. Both caviplexes display in/out guest exchange dynamics that are slow on the ¹H NMR chemical shift timescale, but fast on the EXSY timescale. We apply diffusion-ordered NMR spectroscopy (DOSY) to characterize the caviplexes. On the diffusion timescale, the guest in/out exchange processes feature intermediate dynamics allowing the assessment of their kinetic stabilities. We found that the trans,cis-bis-formamide isomers form kinetically more stable caviplexes than the trans,trans-counterparts. We also show that the kinetic stabilities of the bis-formamide caviplexes relate well with their relative thermodynamic stabilities. Fortunately, the tuning of the DOSY parameters allowed the observation of the exchange dynamics as slow processes on the experiment timescale.     

pH‐Responsive Pillar[6]arene‐based Water‐Soluble Supramolecular Hexagonal Boxes

We describe the preparation of the first water‐soluble pH‐responsive supramolecular hexagonal boxes (SHBs) based on multiple charge‐assisted hydrogen bonds between peramino‐pillar[6]arenes 2 with the molecular “lid” mellitic acid ( 1 a ). The interaction between 2 and 1 a , as well as the other “lids” pyromellitic and trimesic acids ( 1 b and 1 c , respecively) were studied by a combination of experimental and computational methods. Interestingly, the addition of 1 a to the complexes of the protonated form of pillar[6]arene 2 , that is, 3 , with bis‐sulfonate 4 a or 4 b , immediately led to guest escape along with the formation of closed 1 a₂2 supramolecular boxes. Moreover, the process of the openning and closing of the supramolecular boxes along with threading and escaping of the guests, respectively, was found to be reversible and pH‐responsive. This study paves the way for the easy and modular preparation of different SHBs that may have myriad applications.     

Effect of molecule-metal electronic coupling on through-bond hole tunneling across metal-organic monolayer-semiconductor junctions

Using Hg/alkyl-chain-monolayer/p-Si devices we find that the type of contact between the chains and the electrodes (chemical bonding or not) is of critical importance for electronic transport across the junctions. As the semiconductor is p-type, the transport is that of holes. In agreement with theory we find that holes tunnel more efficiently through alkyl chains than do electrons.