A Note on the Cops and Robber Game on Graphs Embedded in Non-Orientable Surfaces

We consider the two-player, complete information game of Cops and Robber played on undirected, finite, reflexive graphs. A number of cops and one robber are positioned on vertices and take turns in sliding along edges. The cops win if, after a move, a cop and the robber are on the same vertex. The minimum number of cops needed to catch the robber on a graph is called the cop number of that graph. Let c(g) be the supremum over all cop numbers of graphs embeddable in a closed orientable surface of genus g, and likewise ${\tilde c(g)}$ for non-orientable surfaces. It is known (Andreae, 1986) that, for a fixed surface, the maximum over all cop numbers of graphs embeddable in this surface is finite. More precisely, Quilliot (1985) showed that c(g) ≤ 2g + 3, and Schröder (2001) sharpened this to ${c(g)\le \frac32g + 3}$ . In his paper, Andreae gave the bound ${\tilde c(g) \in O(g)}$ with a weak constant, and posed the question whether a stronger bound can be obtained. Nowakowski & Schröder (1997) obtained ${\tilde c(g) \le 2g+1}$ . In this short note, we show ${\tilde c(g) \leq c(g-1)}$ , for any g ≥ 1. As a corollary, using Schröder’s results, we obtain the following: the maximum cop number of graphs embeddable in the projective plane is 3, the maximum cop number of graphs embeddable in the Klein Bottle is at most 4, ${\tilde c(3) \le 5}$ , and ${\tilde c(g) \le \frac32g + 3/2}$ for all other g.     

Differences in porous characteristics of styrenic monoliths prepared by controlled thermal polymerization in molds of varying dimensions

Nitroxide‐mediated polymerization was used as a model system for preparing styrenic monolithic materials with significant mesopore contents in different mold formats, with the aim of assessing the validity of pore characterization of capillary monoliths by analysis of parallel bulk polymerized precursor solution. Capillary monoliths were prepared in 250 μm id fused silica tubes (quadruplicate samples, in total 17 m), and the batch polymerizations were carried out in parallel in 100 μL microvials and regular 2 mL glass vials, both in quintuplicate. The monoliths recovered from the molds were characterized for their meso‐ and macroporous properties by nitrogen sorptiometry (three repeated runs on each sample), followed by a single analysis by mercury intrusion porosimetry. A total of 14 monolith samples were thus analyzed. A Grubbs' test identified one regular vial sample as an outlier in the sorptiometric surface area measurements, and data from this sample were consequently excluded from the pore size calculations, which are based on the same nitrogen sorption data, and also from the mercury intrusion data set. The remaining data were subjected to single factor analyses of variance analyses to test if the porous properties of the capillary monoliths were different from those of the bulk monoliths prepared in parallel. Significant differences were found between all three formats both in their meso‐ and macroporous properties. When the dimension was shrunk from conventional vial to capillary size, the specific surface area decreased from 52.2±4.7 to 34.6±1.7 m²/g. This decrease in specific surface area was accompanied by a significant shift in median diameter of the through‐pores, from 310±3.9 to 544±13 nm. None of these differences were obvious from the scanning electron micrographs that were acquired for each sample type. The common practice of determining the mesopore characteristics from analysis of samples prepared by parallel bulk polymerization and looking for changes in the macropore structure by visual assessment of SEMs are therefore both rather questionable, at least for monoliths of the kind used in this study.     

The First Synthesis of a Ribo-Hexos-5-Ulose: the L-Enantiomer

ABSTRACT

The title compound, previously unreported in either enantioform, and its 2,6-di-O-benzyl derivative have been synthesized through a stereocontrolled epimerization at C-2 of 6-O-protected methyl 3,4-O-isopropylidene-5-C-methoxy-β-D-galactopyranosides. The epimerization, performed through a high yielding sequence of oxidation-reduction owing to the cooperative role of the equatorial C-1 aglycon and the steric hindrance of the isopropylidene group, turned out to be completely diastereoselective. Whereas the unprotected L-ribo-hexos-5-ulose exists, as proved by NMR in D₂O, in five main tautomeric forms in a ratio of about 4:2:2:1:1, only two anomeric 1,4-furanosic forms are present at equilibrium in its 2,6-di-O-benzyl derivative, in ratios ranging from 10:1 to 7:3, depending on the prevalence of D₂O or CD₃CN in the solvent mixture.     

On the angular shape of van der Waals dimers of small polar molecules

Ab initio calculations on twenty van der Waals dimers of small polar molecules at the experimentally observed intermolecular separation R, using Hartree-Fock molecular moments, show that the minima in the electrostatic interaction expanded up to R⁻⁶ converges to angular structures which are close to those observed experimentally for such complexes.     

Limit on monopole flux in the Mont Blanc NUSEX experiment

Summary A trigger dedicated to the search of superheavy monopoles operates since about two years in the NUSEX apparatus, installed in the Mont Blanc tunnel. Monopoles are identified by time of flight and visualization of the pulses involved in a trigger. The present upper limit on monopole flux is 2.3·10⁻¹³ cm⁻² s⁻¹ sr⁻¹ (90% c.l.).

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Riassunto Da circa due anni è operativo sull'apparato NUSEX, installato nel tunnel del Monte Bianco, un trigger dedicato alla ricerca dei monopoli previsti dalle teorie di grande unificazione. L'identificazione dei monopoli è basata sul tempo di volo e sulla localizzazione nello spazio degli impulsi coinvolti nel trigger. Il limite superiore fino ad oggi raggiunto per il flusso di monopoli è 2.3·10⁻¹³ cm⁻²s⁻¹ sr⁻¹ (90% c.l.).

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Резюме Триггерная схема, предназначенная для поиска сверхтяжелых монополей, действует в течение почти двух лет в установке NUSEX, расположенной в туннеле под Мон Бланом. Идентификация монополей основана на времени пролета, а локализация в пространстве осуществляется с помощью импульсов в триггерной схеме. Настоящий верхний предел на поток монополей составляет 2.3· ·10⁻¹³ см⁻² с⁻¹ ср⁻¹ (к 90% вероятностью).

     

Synthesis, spectroscopic characterization, DFT studies and biological assays of a novel gold(I) complex with 2-mercaptothiazoline

A new gold(I) complex with 2-mercaptothiazoline (MTZ) with the coordination formula [AuCN(C₃H₅NS₂)] was synthesized and characterized by chemical and spectroscopic measurements, DFT studies and biological assays. Infrared (IR) and ¹H, ¹³C and ¹⁵N nuclear magnetic resonance (NMR) spectroscopic measurements indicate coordination of the ligand to gold(I) through the nitrogen atom. Studies based on DFT confirmed nitrogen coordination to gold(I) as a minimum of the potential energy surface with calculations of the hessians showing no imaginary frequencies. Thermal decomposition starts at temperatures near 160 °C, leading to the formation of Au⁰ as the final residue at 1000 °C. The gold(I) complex with 2-mercaptothiazoline (Au-MTZ) is soluble in dimethyl sulfoxide (DMSO), and is insoluble in water, methanol, ethanol, acetonitrile and hexane. The antibacterial activities of the Au-MTZ complex were evaluated by an antibiogram assay using the disc diffusion method. The compound showed an effective antibacterial activity against Staphylococcus aureus (Gram-positive) and Escherichia coli and Pseudomonas aeruginosa (Gram-negative) bacterial cells. Biological analysis for evaluation of the cytotoxic effect of the Au-MTZ complex was performed using HeLa cells derived from human cervical adenocarcinoma. The complex presented a potent cytotoxic activity, inducing 85% of cell death at a concentration of 2.0 μmol L⁻¹.     

A theoretical description of elastic pillar substrates in biophysical experiments.

Arrays of elastic pillars are used in biophysical experiments as sensors for traction forces. The evaluation of the forces can be complicated if they are coupled to the pillar displacements over large distances. This is the case if many of the pillars are interconnected by elastic linkages as, for example, in fiber networks that are grown on top of pillars. To calculate the traction forces in such a network, we developed a set of nonlinear inhomogeneous equations relating the forces in the linking elements to the resulting pillar deflections. We chose a homogeneous, activated two-dimensional network of cytoskeletal actin filaments to illustrate that a pillar substrate is generally not a force sensor but a force-gradient sensor. In homogeneous networks the forces acting along the filaments can be approximated by analyzing only pillar deflections in the edge zones of the substrate and by integration over the corresponding force gradients.     

A cryogenic underground observatory for rare events: CUORE, an update

CUORE is a proposed tightly packed array of 1000 TeO₂ bolometers, each being a cube 5 cm on a side with a mass of 750 g. The array consists of 25 vertical towers, arranged in a square of 5 towers by 5 towers, each containing ten layers of four crystals. The design of the detector is optimized for ultralow-background searches for neutrinoless double beta decay of ¹³⁰Te (33.8% abundance), cold dark matter, solar axions, and rare nuclear decays. A preliminary experiment involving 20 crystals of various sizes (MIBETA) has been completed, and a single CUORE tower is being constructed as a smaller scale experiment called CUORICINO. The expected performance and sensitivity, based on Monte Carlo simulations and extrapolations of present results, are reported.