On the Strongly Supermedian Functions and Kernels

We answer to a question of P.J. Fitzsimmons and R.K. Getoor concerning the characterization of a strongly supermedian function by the property of being universally supermedian. Based on the Revuz correspondence we also prove (alternatively to the probabilistic approach of Fitzsimmons and Getoor) that the Radon–Nikodym derivative between the Revuz measures of a semiregular excessive kernel and the regular strongly supermedian kernel generating it, does not depend on the kernel. Mathematics Subject Classifications (2000) Primary 60J45, 31D05; Secondary 60J35, 60J40.     

Irreducible recurrence,ergodicity, and extremality of invariant measures for resolvents

We analyze the transience, recurrence, and irreducibility properties of general sub-Markovian resolvents of kernels and their duals, with respect to a fixed sub-invariant measure $m$. We give a unifying characterization of the invariant functions, revealing the fact that an $L^p$-integrable function is harmonic if and only if it is harmonic with respect to the weak dual resolvent. Our approach is based on potential theoretical techniques for resolvents in weak duality. We prove the equivalence between the $m$-irreducible recurrence of the resolvent and the extremality of $m$ in the set of all invariant measures, and we apply this result to the extremality of Gibbs states. We also show that our results can be applied to non-symmetric Dirichlet forms, in general and in concrete situations. A second application is the extension of the so called Fukushima ergodic theorem for symmetric Dirichlet forms to the case of sub-Markovian resolvents of kernels.     

A Connectedness Theorem for Products of Weighted Projective Spaces

We prove a connectedness result for products of weighted projective spaces.     

Survival of the Dirac points in rippled graphene

We study the effects of the rippling of a graphene sheet on quasiparticle dispersion. This is achieved using a generalization to the honeycomb lattice of the momentum average approximation, which is accurate for all coupling strengths and at all energies. We show that even though the position of the Dirac points may move and the Fermi speed can be renormalized significantly, quasiparticles with very long lifetimes survive near the Dirac points even for very strong couplings.     

Collapse of the electron gas to two dimensions in density functional theory

Local and semilocal density functional approximations for the exchange-correlation energy fail badly in the zero-thickness limit of a quasi-two-dimensional electron gas, where the density variation is rapid almost everywhere. Here we show that a fully nonlocal fifth-rung functional, the inhomogeneous Singwi-Tosi-Land-Sj?lander (STLS) approach, which employs both occupied and unoccupied Kohn-Sham orbitals, recovers the true two-dimensional STLS limit and appears to be remarkably accurate for any thickness of the slab (and thus for the dimensional crossover). We also show that this good behavior is only partly due to the use of the full exact exchange energy.     

High-level correlated approach to the jellium surface energy, without uniform-gas input

We resolve the long-standing controversy over the metal surface energy: Density-functional methods that require uniform-electron-gas input agree with each other, but not with high-level correlated calculations such as Fermi hypernetted chain and diffusion Monte Carlo calculations that predict the uniform-gas correlation energy. Here we apply the inhomogeneous Singwi-Tosi-Land-Sj?lander method, and find that the density functionals are indeed reliable (because the surface energy is bulklike). Our work also vindicates the use of uniform-gas-based nonlocal kernels in time-dependent density-functional theory.     

An Approach to Paracyclophane-Based Tetrathiafulvalenes: Synthesis and Characterization of a Pseudo-Geminal [2.2]Paracyclophane 1,3-Dithia-2-Thione

The synthesis of paracyclophane-based tetrathiafulvalene precursors is described in the context of the importance of these compounds in the field of material chemistry. Pseudo-geminal bis(1,3-dithia-2-thione) was synthesized via the corresponding 1,3-dithiol-2-ylium salt. The latter was obtained by a synthetic procedure that involves 4,15-bis(acetyl)[2.2]paracyclophane, a new compound of interest for many researchers.     

Synthesis and structural characterization of amino-functionalized polysaccharides

A variety of carbohydrates, in particular polysaccharides can be subjected to chemical modification to obtain derivatives with amphiphilic properties, which enable biochemical or biological reactions at the polymer surface. In the present work, a polydisperse maltodextrin mixture of average molecular weight 3000 was coupled with 1,6-hexamethylenediamine (HMD) via reductive amination reaction. Resulting products were characterized by thermal analysis and positive nanoelectrospray quadrupole time-of-flight (Q-TOF) mass spectrometry (MS) and tandem mass spectrometry (MS/MS). Both thermal analysis and MS screening confirmed the formation of the HMD-polysaccharide coupling products. Moreover, HMD-linked polysaccharide chains containing 2 to 26 glucose building blocks were identified by nanoESI Q-TOF MS. MS/MS fragmentation using collision-induced dissociation (CID) at low ion acceleration energies provided strong evidence for HMD-maltodextrin linkage formation and the set of sequence ions diagnostic for the composition and structure of a HMD-linked chain containing 18 glucose residues.