A Reconfigurations Analogue of Brooks' Theorem and Its Consequences

Let G be a simple undirected connected graph on n vertices with maximum degree Δ. Brooks' Theorem states that G has a proper Δ‐coloring unless G is a complete graph, or a cycle with an odd number of vertices. To recolor G is to obtain a new proper coloring by changing the color of one vertex. We show an analogue of Brooks' Theorem by proving that from any k‐coloring, , a Δ‐coloring of G can be obtained by a sequence of recolorings using only the original k colors unless

• – G is a complete graph or a cycle with an odd number of vertices, or
• – , G is Δ‐regular and, for each vertex v in G, no two neighbors of v are colored alike.

We use this result to study the reconfiguration graph of the k‐colorings of G. The vertex set of is the set of all possible k‐colorings of G and two colorings are adjacent if they differ on exactly one vertex. We prove that for , consists of isolated vertices and at most one further component that has diameter . This result enables us to complete both a structural and an algorithmic characterization for reconfigurations of colorings of graphs of bounded maximum degree.     

Localized Mixed‐Valence and Redox Activity within a Triazole‐Bridged Dinucleating Ligand upon Coordination to Palladium

The new dinucleating redox‐active ligand ( L^H4 ), bearing two redox‐active NNO‐binding pockets linked by a 1,2,3‐triazole unit, is synthetically readily accessible. Coordination to two equivalents of Pd^II resulted in the formation of paramagnetic (S= ) dinuclear Pd complexes with a κ²‐N,N′‐bridging triazole and a single bridging chlorido or azido ligand. A combined spectroscopic, spectroelectrochemical, and computational study confirmed Robin–Day Class II mixed‐valence within the redox‐active ligand, with little influence of the secondary bridging anionic ligand. Intervalence charge transfer was observed between the two ligand binding pockets. Selective one‐electron oxidation allowed for isolation of the corresponding cationic ligand‐based diradical species. SQUID (super‐conducting quantum interference device) measurements of these compounds revealed weak anti‐ferromagnetic spin coupling between the two ligand‐centered radicals and an overall singlet ground state in the solid state, which is supported by DFT calculations. The rigid and conjugated dinucleating redox‐active ligand framework thus allows for efficient electronic communication between the two binding pockets.     

Exploring fundamental differences between red- and blue-shifted intramolecular hydrogen bonds using FAMSEC,FALDI, IQA and QTAIM

We have discovered, using developed by us recently FALDI and FAMSEC computational techniques, fundamentally distinct mechanisms of intramolecular red- and blue-shifted H-bond formation that occurred in different conformers of the same molecule (amino-acid β-alanine) involving the same heteroatoms (O–H???N and N–H???O). Quantitative topological, geometric and energetic data of both H-bonds obtained with well-known QTAIM and IQA methodologies agree with what is known regarding H-bonding in general. However, the FALDI charge and decomposition scheme for calculating in real space 3D conformational deformation densities provided clear evidence that the process of electron density redistribution taking place on the formation of the stronger red-shifted H-bond is fundamentally distinct from the weaker blue-shifted H-bond. Contributions made by atoms of the X–H???Y–Z fragment (IUPAC notation) as well as distinct atoms on the H-bond formation were fully explored. The FAMSEC energy decomposition approach showed that the atoms involved in formation of the red-shifted H-bond interact in a fundamentally different fashion, both locally and with the remainder of the molecule, as compared with those of the blue-shifted H-bond. Excellent correlations of trends obtained with QTAIM, IQA, FAMSEC and FALDI techniques were obtained. Commentary regarding IUPAC recommended definition of an H-bond and validity of observed AILs (or bond paths) of the two H-bond kinds is also discussed.     

Parallel imaging for first-pass myocardial perfusion

Two parallel imaging methods used for first-pass myocardial perfusion imaging were compared in terms of signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR) and image artifacts. One used adaptive Time-adaptive SENSitivity Encoding (TSENSE) and the other used GeneRalized Autocalibrating Partially Parallel Acquisition (GRAPPA), which are both applied to a gradient-echo sequence. Both methods were tested on 12 patients with coronary artery disease. The order of perfusion sequences was inverted in every other patient. Image acquisition was started during the administration of a contrast bolus followed by a 20-ml saline flush (3 ml/s), and the next perfusion was started at least 15 min thereafter using an identical bolus. An acceleration rate of 2 was used in both methods, and acquisition was performed during breath-holding. Significantly higher SNR, CNR and image quality were obtained with GRAPPA images than with TSENSE images. GRAPPA, however, did not yield a higher CNR when applied after the second bolus. GRAPPA perfusion imaging produced larger differences between subjects than did TSENSE. Compared to TSENSE, GRAPPA produced significantly better CNR on the first bolus. More consistent SNR and CNR were obtained from TSENSE images than from GRAPPA images, indicating that the diagnostic value of TSENSE may be better.     

Accurate determination of plutonium by Controlled Potential Coulometry: uncertainty evaluation by the Monte Carlo Method approach

Journal of Radioanalytical and Nuclear Chemistry - The accurate determination of plutonium (Pu) mass fraction in nuclear materials is essential to nuclear matter accountancy and international...     

Hydrogen induced changes in the crystal structure and magnetic properties of UCoGe

Hydrogen pressure of 0.5-140 bar has been applied to synthesize hydrides of UCoGe. Besides an α hydride crystallizing in the structure type of the parent compound, which loses the weak ferromagnetism found in pure UCoGe, two distinctly different β hydrides were identified. The almost pure β hydride (UCoGeH(1.7)) is a ferromagnet below T(C) = 50 K. The highest H(2) pressures (> 130 bar) produce admixture of another hydride called β' hydride, with less H/f.u. and T(C) = 8 K, obtained presumably as a decay product of a full hydride UCoGeH(2.0) unstable at ambient conditions. The value of the Sommerfeld coefficient of electronic specific heat γ increases over 100 mJ mol(-1) K(-2) for the magnetic hydrides.     

Influence of the structure of polyfluorinated alcohols on Brønsted acidity/hydrogen-bond donor ability and consequences on the promoter effect

The influence of substituents on the properties of tri- and hexafluorinated alcohols derived from 2,2,2-trifluoroethanol (TFE) and 1,1,1,3,3,3-hexafluoro-2-propanol (HFIP) was examined. Measurements of specific solvent-solute interactions revealed that H-bond donation (HBD) of fluorinated alcohols is sensitive to the steric hindrance of the OH group, whereas their Br?nsted acidity is dependent only on the number of fluorine atoms. For hexafluorinated alcohols (HFAs), their association with amines characterized by X-ray diffraction showed that the balance between HBD and acidity is influenced by their structure. Moreover, the ability of HFAs to donate H-bonds is exerted in synclinal (sc), synperiplanar (sp), and also antiperiplanar (ap) conformations along the C-O bond. Comparison of the effects of fluorinated alcohols as promoting solvents in three reactions is reported. The positive correlation between rate constants and H-bonding donation ability for sulfide oxidation and imino Diels-Alder reaction brings to light the role of this property, while acidity might have a minor influence. In the third reaction, epoxide opening by piperidine, none of these properties can clearly be put forward at this stage.     

Enthalpy and entropy of nanoparticle association from temperature-dependent cryo-TEM

Quantum dots form equilibrium structures in liquid dispersions, due to thermodynamic forces that are often hard to quantify. Analysis of these structures, visualized using cryogenic electron microscopy, yields their formation free energy. Here we show that the nanoparticle interaction free energy can be further separated into the enthalpic and entropic contributions, using the temperature dependence of the assembled structures. Monodisperse oleic acid-capped PbSe nanoparticles dispersed in decalin were used as a model system, and the temperature-dependent equilibrium structures were imaged by cryo-TEM, after quenching from different initial temperatures. The interaction enthalpy and entropy follow from van 't Hoff's exact equation for the temperature dependence of thermodynamic equilibria, now applied to associating nanoparticles. The enthalpic component gives the magnitude of the contact interaction, which is crucial information in understanding the energetics of the self-assembly of nanoparticles into ordered structures.     

Influence of shape variation on capacitance matrices

We theoretically determine the per-unit-of-length N × N capacitance matrix of a set of N conductors w.r.t. a reference conductor, obtained when expanding the cross-section of one or more of these conductors w.r.t. some nominal configuration. It is shown that certain relationships between the individual matrix elements of the nominal and of the expanded configuration exist. For the N ≤ 2 case, the expansion leads to the increase of the absolute value of all matrix elements. For N > 2 no such general conclusion is shown to exist. The results remain valid in three dimensions. A number of numerical examples illustrate the theory.     

Students’ emergent articulations of uncertainty while making informal statistical inferences

Research on informal statistical inference has so far paid little attention to the development of students?? expressions of uncertainty in reasoning from samples. This paper studies students?? articulations of uncertainty when engaged in informal inferential reasoning. Using data from a design experiment in Israeli Grade 5 (aged 10?C11) inquiry-based classrooms, we focus on two groups of students working with TinkerPlots on investigations with growing sample size. From our analysis, it appears that this design, especially prediction tasks, helped in promoting the students?? probabilistic language. Initially, the students oscillated between certainty-only (deterministic) and uncertainty-only (relativistic) statements. As they engaged further in their inquiries, they came to talk in more sophisticated ways with increasing awareness of what is at stake, using what can be seen as buds of probabilistic language. Attending to students?? emerging articulations of uncertainty in making judgments about patterns and trends in data may provide an opportunity to develop more sophisticated understandings of statistical inference.