Reconfiguration graphs of shortest paths

For a graph $G$ and$a,b\in V\left(G\right)$, the shortest path reconfiguration graph of $G$ with respect to $a$ and$b$ is denoted by $S(G,a,b)$. The vertex set of $S(G,a,b)$ is the set of all shortest paths between $a$ and$b$ in $G$. Two vertices in $V\left(S(G,a,b)\right)$ are adjacent, if their corresponding paths in $G$ differ by exactly one vertex. This paper examines the properties of shortest path graphs. Results include establishing classes of graphs that appear as shortest path graphs, decompositions and sums involving shortest path graphs, and the complete classification of shortest path graphs with girth 5 or greater. We include an infinite family of well structured examples, showing that the shortest path graph of a grid graph is an induced subgraph of a lattice.     

Inequalities for mixed p-affine surface area

We prove new Alexandrov-Fenchel type inequalities and new affine isoperimetric inequalities for mixed p-affine surface areas. We introduce a new class of bodies, the illumination surface bodies, and establish some of their properties. We show, for instance, that they are not necessarily convex. We give geometric interpretations of L _p affine surface areas, mixed p-affine surface areas and other functionals via these bodies. The surprising new element is that not necessarily convex bodies provide the tool for these interpretations.     

A first principles study on the structure of ice-VI: static distortion, molecular geometry, and proton ordering

We have studied the structure of ice-VI by examining all ice-rule-allowed structures in its primary unit cell of 10 water molecules with first principles methods. A significant amount of static distortions in the oxygen positions away from their crystallographic positions are found, which is in good agreements with significant higher-order terms in the atomic displacement parameters obtained from X-ray and neutron diffraction data. Structural anomalies (such as exceptionally short OH bonds and small H-O-H angles) noted in conventional crystal structure refinements were not seen in our ab initio calculations, and it is evident that these structural anomalies arose from oversimplified models in which static distortions are not properly accounted for. Our results also show that the molecular geometry of water in ice-VI is similar to but richer than those in ice-Ih and ice-VII. Larger distortions in bond lengths/angles and correlation between the molecular geometry and the neighboring environments were found. Different proton-ordering schemes proposed in the literature were examined, and our calculations provide evidence in favor of a ferroelectric phase of the proton-ordered counterpart of ice-VI at about 80 K.     

Propensity for the air/water interface and ion pairing in magnesium acetate vs magnesium nitrate solutions: molecular dynamics simulations and surface tension measurements

Molecular dynamics simulations in slab geometry and surface tension measurements were performed for aqueous solutions of magnesium acetate and magnesium nitrate at various concentrations. The simulations reveal a strong affinity of acetate anions for the surface, while nitrate exhibits only a very weak surface propensity, and magnesium is per se strongly repelled from the air/water interface. CH3COO- also exhibits a much stronger tendency than NO3- for ion pairing with Mg2+ in the bulk and particularly in the interfacial layer. The different interfacial behavior of the two anions is reflected by the opposite concentration dependence (beyond 0.5 M) of surface tension of the corresponding magnesium salts. Measurements, supported by simulations, show that the surface tension of Mg(NO3)2(aq) increases with concentration as for other inorganic salts. However, in the case of Mg(OAc)2(aq) the surface tension isotherm exhibits a turnover around 0.5 M, after which it starts to decrease, indicating a positive net solute excess in the interfacial layer at higher concentrations.     

Formation of a regular fullerene nanochain lattice

A vicinal Au(11 12 12) surface, naturally patterned into a rectangular superlattice, has been used as a template to prepare C60 nanostructures with long-range order and uniform size. At a coverage of 0.1 monolayer and at room temperature, a two-dimensional long-range ordered superlattice of molecular nanochains is achieved, which perfectly replicates the periodicity of the template surface. The fullerene nanochains are found to be located exclusively on the face-centered cubic stacking domains at the lower step edges. Our experiments demonstrate that highly periodic molecular nanochains can be fabricated through a site-selective anchoring method.     

Universally programmable quantum cellular automaton

We discuss the role of classical control in the context of reversible quantum cellular automata. Employing the structure theorem for quantum cellular automata, we give a general construction scheme to turn an arbitrary cellular automaton with external classical control into an autonomous one, thereby proving the computational equivalence of these two models. We use this technique to construct a universally programmable cellular automaton on a one-dimensional lattice with single cell dimension 12.     

A general ultrasound-assisted access to room-temperature ionic liquids

The replacement of common organic solvents by room-temperature ionic liquids (RTILs) is a topical subject in both academia and industry. In the last decades, the number of applications for RTILs has followed an exponential curve and spilled over the boundaries of chemistry. Still, one of the main drawbacks of these compounds is their difficult access. The present ultrasound-assisted method affords a general and easy access to a large variety of room-temperature ionic liquids.     

The inverse syzygy problem in algebraic systems theory

We present a constructive solution of the inverse syzygy problem over arbitrary coherent rings and show how it can be used to compute certain extension groups. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Electron spectroscopy of liquid mercury under impact of metastable He(23 S) atoms

We have performed electron spectroscopy of a liquid mercury surface under impact of HeI photons and of metastable He(2³ S) atoms. The latter data are interpreted in terms of Auger neutralization. This process involves two electrons from the metal surface and thereby yields information about the mutual interaction between two metal electrons. Evaluation of our data shows that the interaction is specific to the band from which the electrons come and whether they originate from the same or from different bands. Further, we find no support for the suggestion that a few per cent of the surface sites of liquid surface are occupied by nonmetallic mercury atoms.     

A novel methodological approach for δ18O analysis of sugars using gas chromatography-pyrolysis-isotope ratio mass spectrometry

Although the instrumental coupling of gas chromatography-pyrolysis-isotope ratio mass spectrometry (GC-Py-IRMS) for compound-specific δ¹⁸O analysis has been commercially available for more than a decade, this method has been hardly applied so far. Here we present the first GC-Py-IRMS δ¹⁸O results for trimethylsilyl-derivatives of plant sap-relevant sugars and a polyalcohol (glucose, fructose, sucrose, raffinose and pinitol). Particularly, we focus on sucrose, which is assimilated in leaves and which is the most important transport sugar in plants and hence of utmost relevance in plant physiology and paleoclimate studies. Replication measurements of sucrose standards and concentration series indicate that the GC-Py-IRMS δ¹⁸O measurements are not stable over time and that they are amount (area) dependent. We, therefore, suggest running sample batch replication measurements in alternation with standard concentration series of reference material. This allows for carrying out (i) a drift correction, (ii) a calibration against reference material and (iii) an amount (area) correction. Tests with ¹⁸O-enriched water do not provide any evidence for oxygen isotope exchange reactions affecting sucrose and raffinose. We present the first application of GC-Py-IRMS δ¹⁸O analysis for sucrose from needle extract (soluble carbohydrate) samples. The obtained δ¹⁸O_{sucrose/ Vienna Standard Mean Ocean Water (VSMOW)} values are more positive and vary in a wider range (32.1–40.1 ‰) than the δ¹⁸O_{bulk/ VSMOW} values (24.6–27.2 ‰). Furthermore, they are shown to depend on the climate parameters maximum day temperature, relative air humidity and cloud cover. These findings suggest that δ¹⁸O_sucrose of the investigated needles very sensitively reflects the climatically controlled evaporative ¹⁸O enrichment of leaf water and thus highlights the great potential of GC-Py-IRMS δ¹⁸O_sucrose analysis for plant physiology and paleoclimate studies.