Coulomb interaction symmetries and the Mayer series in the two-dimensional dipole gas

We study the Mayer series of the two-dimensional dipole gas in the high-temperature, low-density regime. Without performing any multiscale analysis, we obtain bounds showing that the Mayer coefficients are finite in the thermodynamic limit. These bounds are obtained by exploiting a particular partial symmetry of the interaction (which we nameO-symmetry), already used in some problems related to the two-dimensional Coulomb gas. By direct bounds on some Mayer graphs we also conjecture that any technique based uniquely on theO-symmetry will not be sufficient to prove analyticity of the series.     

Scars of the Wigner Function

We propose a picture of Wigner function scars as a sequence of concentric rings along a two-dimensional surface inside a periodic orbit. This is verified for a two-dimensional plane that contains a classical hyperbolic orbit of a Hamiltonian system with 2 degrees of freedom. The stationary wave functions are the familiar mixture of scarred and random waves, but the spectral average of the Wigner functions in part of the plane is nearly that of a harmonic oscillator and individual states are also remarkably regular. These results are interpreted in terms of the semiclassical picture of chords and centers.     

M?ssbauer analysis of high-energy mechanical-milled sand fraction of a magnetic soil developing on basalt

A sample of the coarse sand fraction from the soil material of the A-horizon (0?C0.2 m from the soil surface) of a dusky red magnetic Oxisol was submitted to high-energy mechanical milling for different times. This assay aimed mainly at (a) monitoring the individualization of strongly aggregated mineral particles, and (b) measuring the effect of the milling pressure on the mineralogy changes of the material. These data are also intended to experimentally subside any physical model describing the mechanical behavior of the superficial soil layer that is subjected to intensive machine management, in agriculture fields. Powder X-ray data reveal that some mineralogical phases, notably gibbsite, disappear soon after the first few hours milling. The 298 K-transmission Mössbauer spectrum for the non-milled sand sample shows a qualitatively typical pattern for the sand fraction of basalt derived soils, with magnetically ordered sextets, assignable mainly to hematite and maghemite, and an intense central (super)paramagnetic Fe^3?+? doublet. For the milled samples, spectra revealed progressive spectral reduction of the magnetic hyperfine structure, with concomitant increase of relative subspectral areas due to (super)paramagnetic phases, as the milling time increased. This result is consistent with the reduction of measured saturation magnetization, from 4.96(8) J T^???1 kg^???1, for the non-milled sample, to 3.26(7) J T^???1 kg^???1, for the sample milled for 8 hours.     

Metal Organic Framework-235 (MOF-235) Modified Carbon Paste Electrode for Catechol Determination in Water

MOF-235 is presented as an orange powder, with crystals of the octahedral formation. It was already used as adsorbent to remove different compounds from water; however, no attempts have been published about the exploration of the MOF-235 application as electrochemical sensor for organic compounds yet. MOF-235 was synthetized and after that, it was characterized by SEM, XRD and FTIR. Graphite electrodes (GEs) were modified with different MOF-235 ratio (5 %, 7 %, 10 %, 12 % and 14 %) and these modified GEs were characterized by cyclic voltammetry (CV) measurements in order to determine the effect of MOF-235 concentration on the current response. Results indicated that, a significant improvement on the current response was attained at MOF-235(10 %)/GE respect to unmodified GE. This behavior is related to the pore structure and multiple active sites on the MOF surface. The performance of the MOF-235(10 %)/GE as electrochemical sensor for detecting catechol was assessed by differential pulse voltammetry (DPV). Catechol detection response of MOF-based sensor provided a detection limit of about 12.79 μmol L⁻¹ with a correlation coefficient (R²) of about 0.9928 ranging from 12 to 514 μmol L⁻¹. Finally, MOF-235(10 %)/GE was used to determine catechol in real water matrixes.     

Water Docking Bias in [4]Helicene

We report on the one‐ and two‐water clusters of [4]helicene, the smallest polycyclic aromatic hydrocarbon with a helical sense, which were captured in the gas phase using high‐resolution rotational spectroscopy. The structures of the complexes are unambiguously revealed using microwave spectra of isotopically enriched species. In the one‐water cluster, the apparent splitting pattern is consistent with a tunneling motion that encompasses an exchange of strongly and weakly bonded water hydrogens. This motion is “locked” in the two‐water cluster. The relevant intermolecular contacts, symmetry, and aromaticity effects are unveiled for the microsolvated chiral topologies. These observations entail the first glance at the structures and internal dynamics of the water binding motifs of a chiral polycyclic aromatic hydrocarbon.     

Coordination of 2,2'-bipyridyl and 1,10-phenanthroline to yttrium and lanthanum complexes based on a scorpionate ligand

Reaction of yttrium and lanthanum trichloride with 1 equiv of sodium or potassium hydrotris(3,5-dimethylpyrazolyl)borate and 1 equiv of 2,2'-bipyridine gives good yields of the complexes [MCl(2)(Tp(Me2))(C(10)H(8)N(2))] (M = Y (1), La (2)). The analogous compounds with 1,10-phenanthroline, [MCl(2)(Tp(Me2))(C(12)H(8)N(2))] (M = Y (3), La (4)), have been obtained by a similar procedure. The solid-state structures of 2-4 were determined by single-crystal X-ray diffraction and revealed that the compounds are all seven-coordinate with capped octahedral geometry. In contrast, reaction of yttrium trichloride with 1 equiv of sodium hydrotris(3,5-dimethylpyrazolyl)borate in the presence of 1 equiv of neocuproine affords [YCl(3)(Tp(Me2))][Na(neoc)(3))] (5). Compounds 1 and 2 provide an entry for the synthesis of complexes containing the bipyridyl ligand in a radical anionic form or in a dianionic form. Reaction of 1 and 2 with an excess of sodium amalgam gives [Y(Tp(Me2))(bipy)(THF)(2)] (6) and [La(Tp(Me2))(2)(bipy)] (7), respectively. The structures of both compounds have been determined by X-ray crystallography. Compound 7 can be oxidized with iodine to give [La(Tp(Me2))(2)(bipy)]I (8).     

On induced Ramsey numbers for k‐uniform hypergraphs

Let denote the complete k‐uniform k‐partite hypergraph with classes of size t and the complete k‐uniform hypergraph of order s. One can show that the Ramsey number for and satisfies when t = s^o(1) as s →∞. The main part of this paper gives an analogous result for induced Ramsey numbers: Let be an arbitrary k‐partite k‐uniform hypergraph with classes of size t and an arbitrary k‐graph of order s. We use the probabilistic method to show that the induced Ramsey number (i.e. the smallest n for which there exists a hypergraph such that any red/blue coloring of yields either an induced red copy of or an induced blue copy of ) satisfies . © 2015 Wiley Periodicals, Inc. Random Struct. Alg., 48, 5–20, 2016     

Eigenvalue Asymptotics of the Stokes Operator for Fractal Domains

The leading asymptotic term for the function that counts theeigenvalues of the Stokes operator is determined for fairlygeneral underlying bounded domains. Moreover, the remainderis estimated in terms of the fractality of the boundary of thedomain. The results obtained resemble corresponding ones forthe Dirichlet Laplacian. 1991 Mathematics Subject Classification:35P20.     

Relations between (κ, τ)-regular sets and star complements

Let G be a finite graph with an eigenvalue µ of multiplicity m. A set X of m vertices in G is called a star set for µ in G if µ is not an eigenvalue of the star complement G\X which is the subgraph of G induced by vertices not in X. A vertex subset of a graph is (κ, τ)-regular if it induces a κ-regular subgraph and every vertex not in the subset has τ neighbors in it. We investigate the graphs having a (κ, τ)-regular set which induces a star complement for some eigenvalue. A survey of known results is provided and new properties for these graphs are deduced. Several particular graphs where these properties stand out are presented as examples.