The critical probability for Voronoi percolation in the hyperbolic plane tends to 1/2

We consider percolation on the Voronoi tessellation generated by a homogeneous Poisson point process on the hyperbolic plane. We show that the critical probability for the existence of an infinite cluster tends to 1/2 as the intensity of the Poisson process tends to infinity. This confirms a conjecture of Benjamini and Schramm [5].     

Metastable decay rates,asymptotic expansions,and analytic continuation of thermodynamic functions

The grand potentialP(z)/kT of the cluster model at fugacityz, neglecting interactions between clusters, is defined by a power series _n Q _n z ⁿ , whereQ _n , which depends on the temperatureT, is the partition function of a cluster of sizen. At low temperatures this series has a finite radius of convergencez _s . Some theorems are proved showing that ifQ _n , considered as a function ofn, is the Laplace transform of a function with suitable properties, thenP(z) can be analytically continued into the complexz plane cut along the real axis fromz _s to + and that (a) the imaginary part ofP(z) on the cut is (apart from a relatively unimportant prefactor) equal to the rate of nucleation of the corresponding metastable state, as given by Becker-Döring theory, and (b) the real part ofP(z) on the cut is approximately equal to the metastable grand potential as calculated by truncating the divergent power series at its smallest term.     

Characterization of the organization in shear layers via the Proper Orthogonal Decomposition

Experiments are performed in an incompressible plane turbulent mixing layer, using various hot wire rake configurations. From these experiments, the Proper Orthogonal Decomposition is applied for kernels where the space-time correlation tensor is evaluated over different spatial meshes and velocity components configurations. The resulting decompositions are then discussed in terms of characterization of the organization of the flow for various scalar or vectorial approaches of the POD. An incrtial range law is evidenced. The instantaneous contribution of the first modes of the POD to the organization of the flow is analyzed. A dynamical behavior for the organization of the flow is observed from the correlation between the first two modes contribution.     

On two--block--factor sequences and one--dependence

The distributions of two--block--factors arising from i.i.d. sequences are observed to coincide with the distributions of the superdiagonals of jointly exchangeable and dissociated arrays . An inequality for superdiagonal probabilities of the arrays is presented. It provides, together with the observation, a simple proof of the fact that a special one--dependent Markov sequence of Aaronson, Gilat and Keane (1992) is not a two--block factor.

     

Sensitivity in Supramolecular Architectures of Polyaromatic Salts Containing Two Singly‐Pimerized Bipyridines

Three novel supramolecular arrays of zigzag polyaromatic salts are reported. Both the conformation and disposition of the dications are subjected to various noncovalent interactions. Thus, the presence or absence of the π‐π interacting enclathrated molecules, the efficient packing and the involved hydrogen bonding interactions of anions, as well as the increased hydrophobic property of the dications themselves exert influence.     

Simultaneous multichannel mass-specific detection for high-performance liquid chromatography using an array detector sector-field mass spectrometer

The use of a separation step, such as liquid chromatography, prior to inductively coupled plasma mass spectrometry (ICP–MS) has become a common tool for highly selective and sensitive analyses. This type of coupling has several benefits including the ability to perform speciation analysis or to remove isobaric interferences. Several limitations of conventional instruments result from the necessity to scan or pulse the mass spectrometer to obtain a complete mass spectrum. When the instrument is operated in such a non-continuous manner, duty cycle is reduced, resulting in poorer absolute limits of detection. Additionally, with scanning instruments, spectral skew can be introduced into the measurement, limiting quantitation accuracy. To address these shortcomings, a high-performance liquid chromatograph has been coupled to an ICP–MS capable of continuous sample introduction and simultaneous multimass detection. These features have been realized with a novel detector array, the focal plane camera. Instrument performance has been tested for both speciation analysis and for the elimination of isobaric interferences. Absolute limits of detection in the sub picogram to tens of picograms regime are obtainable, while the added mass dimension introduced by simultaneous detection dramatically increases chromatographic peak capacity.     

Solution of periodic Poisson's equation and the Hartree–Fock approach for solids with extended electron states: Application to linear augmented plane wave method

We formulate a Hartree–Fock‐LAPW method for electronic band structure calculations. The method is based on the Hartree–Fock–Roothaan approach for solids with extended electron states and closed core shells where the basis functions of itinerant electrons are linear augmented plane waves. All interactions within the restricted Hartree–Fock approach are analyzed and in principle can be taken into account. In particular, we obtained the matrix elements for the exchange interactions of extended states and the crystal electric field effects. To calculate the matrix elements of exchange for extended states, we first introduce an auxiliary potential and then integrate it with an effective charge density corresponding to the electron exchange transition under consideration. The problem of finding the auxiliary potential is solved by using the strategy of the full potential LAPW approach, which is based on the general solution of periodic Poisson's equation. Here, we use an original technique for the general solution of periodic Poisson's equation and multipole expansions of electron densities. We apply the technique to obtain periodic potentials of the face‐centered cubic lattice and discuss its accuracy and convergence in comparison with other methods. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Cyclic Voltammograms of Ferrocene on Multi‐Walled Carbon Nanotubes (MWCNTs)‐Modified Edge Plane Pyrolytic Graphite (EPPG) Electrode in Room Temperature Ionic Liquids (RTILs) of 1‐Ethyl‐3‐Methylimidazolium Tetrafluoroborate (EMIBF4)

In this work, the electrochemical behavior of ferrocene (Fc) was investigated by cyclic voltammetry (CV) in room temperature ionic liquids (RTILs) of 1‐ethyl‐3‐methylimidazolium tetrafluoroborate (EMIBF₄) on glass carbon (GC), edge plane pyrolytic graphite (EPPG) and multi‐walled carbon nanotube (MWCNTs)‐modified EPPG electrodes, respectively. The results demonstrated that on GC electrode, pairs of well‐defined reversible peaks were observed, while for the electrode of EPPG, the peak potential separation (ΔE_p) is obviously larger than the theoretical value of 59 mV, hinting that the electrode of EPPG is distinguished from the commonly used electrode, consistent with the previous proposition that EPPG has many “defects”. To obtain an improved electrochemical response, multi‐walled carbon nanotubes (MWCNTs) were modified on the electrode of EPPG; the increased peak current and promoted peak potential separation not only proved the existence of “defects” in MWCNTs, but also supported that “creating active points” on an electrode is the main contribution of MWCNTs. Initiating the electrochemical research of Fc on the MWCNTs‐modified EPPG electrode in RTILs and verifying the presence of “defects” on both EPPG and MWCNTs using cyclic voltammograms (CVs) of Fc obtained in RTILs of EMIBF₄, is the main contribution of this preliminary work.     

Kristallstruktur und Pseudosymmetrie einer neuen Modifikation von Kaliumhexachloroniobat(V), KNbCl6. Anmerkungen zur kubischen Phase

Crystal Structure and Pseudosymmetry of a New Modification of Potassium Hexachloroniobate(V), KNbCl₆. Comments on the Cubic Phase Long needles of KNbCl₆ – invariably twinned around [100] – are obtained if the material is crystallized from SOCl₂ solution. The structure has been determined from X-ray data collected with a single-crystal diffractometer at room temperature [space group P2₁/n, Z = 16, a = 6.894(1), b = 22.073(4), c = 23.337(3) Å, β = 91.00(1)°, R = 0.032 for 2 909 unique reflexions, 290 structural parameters]. Distorted NbCl₆^? octahedra and ?interstitial’? K⁺ ions are found to form similar arrangements, each of them corresponding to a closest packing of spheres with the layer sequence ACAB (stacking symbol hc). The resulting asymmetry in coordination by potassium is coupled with a strong off-centre displacement of the Nb atoms in any of the four independent chlorine polyhedra (0.14 Å on average). A pronounced pseudosymmetry accounts for the twinning. Since P2₁/m2₁/n2₁/b (no. 62) is already a good approximation of the real structure, only one formal step of symmetry reduction (index t2) is needed to create both, the observed twin law and the actual space group P1 2₁/n1. Above 180°C a reconstructive phase transition leads to the ‘face-centred cubic’ modification with ～ 10% lower density.     

Synthesis and Crystal Structure of Isonicotinic Acid [1-（3,5-Dibromo-2- hydroxyphenyl）methylidene]hydrazide Methanol

A new Schiff base compound, C13H9Br2N3O2·CH3OH, isonicotinic acid [1-(3,5- dibromo-2-hydroxyphenyl)methylidene]hydrazide methanol, has been synthesized and characterized by elemental analysis, IR spectra, and single-crystal X-ray diffraction. The compound comprises a Schiff base moiety isonicotinic acid [1-(3,5-dibromo-2-hydroxyphenyl) methylidene]hydrazide and a methanol molecule. The crystal belongs to the triclinic system, space group P1 with a = 8.464(1), b = 9.511(2), c = 10.901(2) , α = 92.940(2), β = 110.456(2), γ = 96.040(2)o, Z = 2, V = 814.0(2) 3, Dc = 1.759 g/cm3, Mr = 431.09, λ(MoKα) = 0.71073 , μ = 4.994 mm-1, F(000) = 424, R = 0.0440 and wR = 0.1061. A total of 3284 unique reflections were collected, of which 2197 with I > 2σ(I) were observed. The molecule adopts a trans configuration about the C=N double bond. The dihedral angle between the benzene and pyridine rings is 22.0(4)o. The crystal structure is stabilized by intermolecular O-H···N and C-H···O hydrogen bonds, forming layers parallel to the ac plane. The preliminary biological tests show that the compound has potential antibacterial activities.