Sparsest cut in planar graphs,maximum concurrent flows and their connections with the max-cut problem

We study the sparsest cut problem when the “capacity-demand” graph is planar, and give a combinatorial polynomial algorithm. In this type of graphs there is an edge for each positive capacity and also an edge for each positive demand. We extend this result to graphs with no \(K_5\) minor. We also show how to find a maximum concurrent flow in these two cases. We also prove that the sparsest cut problem is NP-hard if we only impose that the “capacity-demand” graph has no \(K_6\) minor. We use ideas that had been developed for the max-cut problem, and show how to exploit the connections among these problems.     

Preparative free‐flow electrophoretic offline ESI‐Fourier transform ion cyclotron resonance/MS analysis of Suwannee River fulvic acid

Free‐flow electrophoresis (FFE), a preparative free zone electrophoretic method, was used offline in conjunction with ultrahigh‐resolution FT/ion cyclotron resonance ‐MS to resolve the complexity of Suwannee River fulvic acid (SRFA). Before MS, the FFE separation conditions and the compatibility with ESI were optimized. The constituents in SRFA were effectively separated based on their charge states and sizes. The obtained mass spectra were compared by means of van Krevelen diagrams and the calculated aromaticity indices of the individual constituents were used to describe the distribution of aromatic/unsaturated structures across the FFE‐fractionated samples. The consolidated number of ions observed within the individual SRFA fractions were much higher than those of the bulk samples alone, demonstrating extensive ion suppression effects in bulk SRFA likely also operating in the analysis of complex biogeochemical mixtures in flow injection mode. The FFE approach allows for producing sizable amounts of sample from dilute solutions, which can be easily fractionated into dozens of individual samples with the possibility of further in‐depth characterization.     

A -analogue of the Whittaker-Shannon-Kotel'nikov sampling theorem

The Whittaker-Shannon-Kotel'nikov (WSK) sampling theorem plays an important role not only in harmonic analysis and approximation theory, but also in communication engineering since it enables engineers to reconstruct analog signals from their samples at a discrete set of data points. The main aim of this paper is to derive a -analogue of the Whittaker-Shannon-Kotel'nikov sampling theorem. The proof uses recent results in the theory of -orthogonal polynomials and basic hypergeometric functions, in particular, new results on the addition theorems for -exponential functions.

     

Pedicelloside,nouveau phtalide isole de gentiana pedicellata wall.

The title compound, isolated from $\text{Gentiana pedicellata}$ leaves, is a new alkyl-3-phthalide characterized by an acylated side chain. It has been identified by spectral analysis as [3-(1-β-D-glucosyloxy)-2-hydroxy]benzoyl 3-(3-phthalidyl)-propyl ester.     

The iron phosphate NaZnFe2(PO4)3

Crystals of sodium zinc diiron(III) triphosphate, NaZnFe₂(PO₄)₃, have been synthesized and structurally characterized by single‐crystal X‐ray diffraction. The compound features a new structural type built up from ZnO₆ octahedra, FeO₆ octahedra and FeO₄ tetrahedra, linked together via the corners and edges of PO₄ tetrahedra to form a three‐dimensional framework, with tunnels running along [100]. Within these tunnels, Na⁺ cations occupy a highly distorted cubic site.     

Condensations aryniques d'enolates de cetones—VII: Synthese generale de benzocyclenones non substituees; Mecanisme de condensation du benzyne sur les enolates de cetones

Some 1,2-benzocyclene-3 ones, so far, unknown have been prepared easily by condensation of the benzyne on the enolates of cyclanones. The general mechanism of the condensation of the benzyne on the enolates of alicyclic ketones in aprotic medium is proposed.     

Self‐Assembled Triple‐Stranded Lanthanide Dimetallic Helicates with a Ditopic Ligand Derived from Bis(benzimidazole)pyridine and Featuring an (4‐Isothiocyanatophenyl)ethynyl Substituent

Bis(2‐{6‐(diethylcarbamoyl)‐4‐[(4‐isothiocyanatophenyl)ethynyl]pyridin‐2′‐yl}‐1‐ethylbenzimidazol‐5‐yl)methane ( L ^G ) reacts with trivalent lanthanide ions in acetonitrile to yield triple‐stranded dimetallic helicates [Ln₂( L ^G )₃]⁶⁺. ¹H‐NMR Data point to the helicates being the only species formed under stoichiometric conditions and having a time‐averaged D₃ symmetry on the NMR time scale. The photophysical properties of L ^G and its helicates are discussed with respect to the closely related ligands L ^B , L ^E , and their complexes, two ligands devoid of the isothiocyanatophenylethynyl substituent. The quantum yield of the ligand fluorescence is three times smaller compared to L ^E , while that of the Eu^III‐centered luminescence (1.1%) is three times larger. On the other hand, the luminescence of Tb^III is not sensitized by L ^G . This is explained in terms of energy differences between the singlet and triplet states on one hand, and between the 0‐phonon transition of the triplet state and the excited metal ion states on the other. This work demonstrates that bulky substituents in the 4‐position of the pyridine ring do not prevent the formation of triple‐stranded helicates, opening the way for luminescent probes that can easily be coupled to biological materials.     

First Use of Benzyl Phosphites in the Michaelis-Arbuzov Reaction synthesis of mono-, Di-, and triphosphate analogs

Benzyl phosphites were used in the Micaelis-Arbuzov reaction. Special experimental conditions allowed preparation of a set of phosphonate analogs of mono-, di-, and triphosphate. Furthermore, regioselective monodeprotection makes these molecules useful building blocks for the synthesis of analogs of polyphosphorylated compounds of biological interest (e.g. nucleotides), after removal of all phosphonate benzyl ester groups under very mild conditions and high yields.     

Linear connections on the quantum plane

A general definition has been proposed recently of a linear connection and a metric in noncommutative geometry. It is shown that to within normalization there is a unique linear connection on the quantum plane and there is no metric.     

Hartmann wave-front measurement at 13.4 nm with lambdaEUV/120 accuracy

We report, for the first time to our knowledge, experimental demonstration of wave-front analysis via the Hartmann technique in the extreme ultraviolet range. The reference wave front needed to calibrate the sensor was generated by spatially filtering a focused undulator beam with 1.7- and 0.6-microm-diameter pinholes. To fully characterize the sensor, accuracy and sensitivity measurements were performed. The incident beam's wavelength was varied from 7 to 25 nm. Measurements of accuracy better than lambdaEUV/120 (0.11 nm) were obtained at lambdaEUV = 13.4 nm. The aberrations introduced by an additional thin mirror, as well as wave front of the spatially unfiltered incident beam, were also measured.