Graph-theoretical analysis of the bonding topology in polyhedral organic cations

It is shown that in several cases where planar delocalisation in organic cations would result in the formation of an anti-aromatic system, polyhedral delocalisation is the form of bonding actually preferred. This explains, for instance, why organic cations in such cases adopt cage-like structures. A full graph-theoretical analysis, similar to one previously published¹² for polyhedral boranes, carboranes and metal clusters, indicates that the nido structure for (CH)₅⁺ may readily be accounted for. Moreover, in the case of the dication (CH)₆²⁺ the fact that its energy minimum also corresponds to a nido structure is explained. In fact, no closo- or arachno-type structures appear to be possible for organic cations. A number of structural predictions concerning these species are given in the conclusion.     

Markov processes conditioned on their location at large exponential times

Suppose that ${\left(X_t\right)}_{t\ge 0}$ is a one-dimensional Brownian motion with negative drift $?\mu$. It is possible to make sense of conditioning this process to be in the state 0 at an independent exponential random time and if we kill the conditioned process at the exponential time the resulting process is Markov. If we let the rate parameter of the random time go to 0, then the limit of the killed Markov process evolves like $X$ conditioned to hit 0, after which time it behaves as $X$ killed at the last time $X$ visits 0. Equivalently, the limit process has the dynamics of the killed “bang–bang” Brownian motion that evolves like Brownian motion with positive drift $+\mu$ when it is negative, like Brownian motion with negative drift $?\mu$ when it is positive, and is killed according to the local time spent at 0.An extension of this result holds in great generality for a Borel right process conditioned to be in some state $a$ at an exponential random time, at which time it is killed. Our proofs involve understanding the Campbell measures associated with local times, the use of excursion theory, and the development of a suitable analogue of the “bang–bang” construction for a general Markov process.As examples, we consider the special case when the transient Borel right process is a one-dimensional diffusion. Characterizing the limiting conditioned and killed process via its infinitesimal generator leads to an investigation of the $h$-transforms of transient one-dimensional diffusion processes that goes beyond what is known and is of independent interest.     

Quasistationary distributions for one-dimensional diffusions with singular boundary points

In the present work we characterize the existence of quasistationary distributions for diffusions on $(0,\infty )$ allowing singular behavior at 0 and $\infty$. If absorption at 0 is certain, we show that there exists a quasistationary distribution as soon as the spectrum of the generator is strictly positive. This complements results of Cattiaux et al. (2009) and Kolb and Steinsaltz (2012) for 0 being a regular boundary point and extends results by Cattiaux et al. (2009) on singular diffusions.     

Diamond hydrocarbons revisited: partitioned formula tables of diamondoids

Isomeric diamondoids with the same number $n$ of adamantane units (or cells), which share the same molecular formula $\text{ C}_\mathrm{Q}(\text{ CH})_\mathrm{T}(\text{ CH}_{2})_\mathrm{S}$ , can be divided into valence isomers by partitioning the number $C $ of their carbon atoms according to whether they are Quaternary, Tertiary, or Secondary: $C =Q +T +S$ . Each [ $n$ ]diamondoid has a dualist (or inner dual) with $n$ vertices (situated at centers of adamantane units), and edges connecting vertices of adjacent adamantane units sharing a chair-shaped hexagon of carbon atoms. Such a dualist is characterized by a quadruplet of indices (denoted as p, s, t, q for primary, secondary, tertiary, or quaternary) specifying again the connectivity of each vertex by assimilating it with a virtual carbon atom. The diamond lattice is self-dual. Dualists help in classifying diamondoids as catamantanes with acyclic dualists, perimantanes with dualists having chair-shaped six-membered rings, or coronamantanes with dualists having only higher-membered rings. In turn, catamantanes can be either regular when they have formulas $\text{ C}_{4n+6}\text{ H}_{4n+12}$ , or irregular when the numbers of carbon and hydrogen atoms are lower than the above values for the given numbers $n$ of adamantane units. Regular catamantanes can have branched or non-branched dualists and they are isomeric when having the same $n$ . Partitioned formulas reflect the branching patterns, encoded in their dualists. Partition formulas and codes are presented for all possible diamondoids with up to 7 adamantane units. A remarkable symmetry is observed for the table of partition periodic table of regular catamantanes with up to 7 adamantane units. Isomeric irregular catamantanes with six or more adamantane units may be valence-isomeric (or homomeric, sharing both the molecular and the partitioned formulas), or heteromeric when they have different partitioned formulas.     

Magnetic dimer motion effects in a rotating magnetic field (A qualitative model of magnetoviscosity and permittivity in magnetorheological suspensions)

The motion of a pair of uniform interacting spherical mesoscopic particles situated in a viscous fluid under the influence of a rotating magnetic field was studied. The coupling interactions between the particles were chosen as a superposition of steric and dipolar pair potentials (for the dipoles parallel to the external field). The model dynamics consisting of particular rotation and vibration modes is the result of the interplay of viscous and interaction forces. The transition from the synchronous to the asynchronous regime of dimer rotation has been found. The results were discussed from a synergetic point of view. A qualitative picture of behaviour of the effective magnetoviscosity and permittivity for dimerized magnetorheological suspension has been given.     

Stable isotope geochemistry of calcrete nodules and septarian concretions in a Quaternary 'red clay' paleovertisol from Hungary

Calcrete nodules and concretions in unusually large amounts are embedded in the Quaternary clay-rich (Vertisol-type) 'red clay' soil-sedimentary complex at the pediment of the Mátra Mountains (Hungary). Stable isotope signatures were studied in nodules and septarian concretions, uncommon due to their several millimeter sized calcite crystals filling voids and fractures, to reveal their origin. The isotope composition of calcrete covers a wide range: delta18O=-5.9 to-10.4 per thousand and delta13C=-8.9 to-12.3 per thousand (vs. V-PDB). Isotope compositions support pedogenic (sensu stricto) and/or shallow groundwater origin for the calcrete nodules and concretions, the role of 'evolved' (isotopically modified) groundwaters in the formation of secondary carbonate was possibly subordinate. Late-stage, large, Mn-rich euhedral calcite crystals in concretions have the lowest delta13C values, which are interpreted as a result of larger contribution of isotopically light organic carbon due to decomposition of organic matter under reducing conditions. Precipitation of late calcite crystals in concretions occurred in early diagenetic environment after shallow burial of the 'red clay' paleovertisol.     

Synthesis and electron paramagnetic resonance study of a nitroxide free radical covalently bonded on aminopropyl-silica gel

A solid spin-labeled material was obtained starting from 2-chloro-3,5-dinitro-N-(4-(2,2,6,6-tetramethyl-piperidine-1-oxyl)-benzamide) and aminopropyl-silica gel. Stability tests showed that even after several months the spin-labeled material had the same properties as immediately after synthesis. EPR properties of the TEMPO-derivatized silica were studied as a function of solvent polarity and temperature. Rotational correlation times were calculated from EPR spectra and correlated with solvent characteristics and temperature. Polar solvents induce a fast motion of the spin-label, clearly seen in the EPR spectra by the apparition of the well-known TEMPO radical triplet. The solid spin-labeled (dry) sample showed a high interspin interaction, which can be disrupted not only by different (liquid) solvents, but also by absorption of different solids, like cyclodextrins, dendrimers or polyethyleneglycols. Also, changes induced by the temperature were studied in the case of toluene wet sample. From 150 to 370 K, the spectrum is changing from a slow motion spectrum type to a fast motion regime. The preparative procedures to obtain the spin-labeled silica as well as some of its parameters are described.     

On pyrylium cations,molecular graphs,topological indices for QSAR,and various other structural problems

In this autobiographical sketch, I will present my contributions in two areas of chemistry: experimental organic and theoretical chemistries.

     

Convergence rates for sparse chaos approximations of elliptic problems with stochastic coefficients

^** Email: todor{at}math.ethz.ch^*** Corresponding author. Email: schwab{at}math.ethz.ch A scalar, elliptic boundary-value problem in divergence formwith stochastic diffusion coefficient a(x, ) in a bounded domainD ^d is reformulated as a deterministic, infinite-dimensional,parametric problem by separation of deterministic (x D) andstochastic ( ) variables in a(x, ) via Karhúnen–Loèveor Legendre expansions of the diffusion coefficient. Deterministic,approximate solvers are obtained by projection of this probleminto a product probability space of finite dimension M and sparsediscretizations of the resulting M-dimensional parametric problem.Both Galerkin and collocation approximations are considered.Under regularity assumptions on the fluctuation of a(x, ) inthe deterministic variable x, the convergence rate of the deterministicsolution algorithm is analysed in terms of the number N of deterministicproblems to be solved as both the chaos dimension M and themultiresolution level of the sparse discretization resp. thepolynomial degree of the chaos expansion increase simultaneously.