Modular design of icosahedral metal clusters

The concept of crystalline module, that is, an unambiguously isolated, repeated quasi-molecular element, is introduced. This concept is more general than the concept of crystal lattice. The generalized modular approach allows extension of the methods and principles of crystallography to quasi-crystals, clusters, amorphous solids, and periodic biological structures. Principles of construction of aperiodic, nonequilibrium regular modular structures are formulated. Limitations on the size of icosahedral clusters are due to the presence of spherical shells with non-Euclidean tetrahedral tiling in their structure. A parametric relationship between the structures of icosahedral fullerenes and metal clusters of the Chini series was found.     

Synthesis and Electrospray Ionization Mass Spectra of N-（1,3, 2-Dioxaphosphorinan-2-ylmethyl）thiophosphoramidates

N-（1,3,2-Dioxaphosphorinan-2-ylmethyl）thiophosphoramidates were synthesized and determined by NMR spectra and positive ion electrospray ionization mass spectrometry （ESI-MS） in conjunction with tandem mass spectrometry （MS/MS）. The fragmentation pathways were investigated. The results show that these characteristic ions in ESI mass spectra are useful in the structural determination of N-（1,3,2-dioxaphosphorinan-2-ylmethyl）- thiophosphoramidates.     

Synthesis,Crystal Structures and Properties of Two Novel Co（Ⅱ） and Cd（Ⅱ） Complexes of N-AcetyI-L-glutamic Acid and Imidazole Ligands

Two novel complexes {[Co（A-glu）（Im）2]·0.5H2O}n （1） and [Cd（A-glu）（Im）3]n （2） （H2A-glu=N-acetyl-L-glutamic acid, Im=imidazole） have been synthesized from the reaction of H2A-glu with Co（CH3COO）2·4H2O or Cd（CH3COO）2·2H2O in the presence of Im. Both of the complexes display different coordination environment and similar one-dimensional chain structure. The magnetic susceptibility measurements for 1 show a weak antiferromagnetic interaction between two cobalt（Ⅱ） ions bridged by A-glu ligand. The complex 2 exhibits an intense fluorescent emission in solid state at room temperature.     

Analysis of uniform binary subdivision schemes for curve design

The paper analyses the convergence of sequences of control polygons produced by a binary subdivision scheme of the form

Cocycles d'Euler et de Maslov

Conclusion Nous espérons avoir convaincu le lecteur qu'il peut être utile de considérer la classe de Maslov comme une classe bornée. Dans [Gh], nous avons montré que la classe d'Euler bornée pour un groupe d'homéomorphismes directs du cercle rend compte de la dynamique topologique de ce groupe. Existe-t-il un résultat analogue pour Sp(2n,)? En d'autres termes, soit un groupe discret et ₁, ₂ deux représentations de dans Sp(2n,). On suppose que les cocycles ₁ ^* et ₂ ^* définissent la même classe bornée. Que peut-on en conclure sur ₁ et ₂?Par ailleurs, l'article [At l] traite aussi d'invariants sur SL(2,) différents de ceux que nous avons considérés, comme par exemple les fonctionsL de Shimizu. Est-il possible de les faire rentrer naturellement dans notre cadre?

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The number of edges of many faces in a line segment arrangement

We show that the maximum number of edges boundingm faces in an arrangement ofn line segments in the plane isO(m ^2/3 n ^2/3+n(n)+nlogm). This improves a previous upper bound of Edelsbrunner et al. [5] and almost matches the best known lower bound which is (m ^2/3 n ^2/3+n(n)). In addition, we show that the number of edges bounding anym faces in an arrangement ofn line segments with a total oft intersecting pairs isO(m ^2/3 t ^1/3+n(t/n)+nmin{logm,logt/n}), almost matching the lower bound of (m ^2/3 t ^1/3+n(t/n)) demonstrated in this paper.Work on this paper by the first and fourth authors has been partially supported by Office of Naval Research Grant N00014-87-K-0129, by National Science Foundation Grants DCR-83-20085 and CCR-89-01484. Work by the first author has also been supported by an AT&T Bell Laboratories Ph.D. scholarship at New York University and by DIMACS (Center for Discrete Mathematics and Theoretical Computer Science), a National Science Foundation Science and Technology Center (NSF-STC88-09648). Work by the second author has been supported by NSF under Grants CCR-87-14565 and CCR-89-21421. Work by the fourth author has additionally been supported by grants from the U.S.-Israeli Binational Science Foundation, the NCRD (the Israeli National Council for Research and Development) and the Fund for Basic Research in Electronics, Computers and Communication, administered by the Israeli National Academy of Sciences.     

Convex hull of powers of a complex number,trinomial equations and the Farey sequence

The color of a complex number is defined as the number of vertices of the convex hull of powers of that number. This induces a coloring of the unit disk. The structure of the set of points where the color changes is investigated here. It is observed that there is a connection between this fractal set and some family of trinomial equations. Three algorithms for coloring the unit disk are described, the last one (related to the Farey sequence) arising out of a conjecture. This conjecture is formulated and proved in this presentation.     

Molecular structure and conformation of 2,3-dichloro-1-propene as determined by gas-phase electron diffraction

The molecular structure and conformation of 2,3-dichloro-1-propene have been determined by gas-phase electron diffraction at nozzle temperatures of 24, 90 and 273°C. The molecules exist as a mixture of two conformers with the chlorine atoms anti (torsion angle ∠φ = 0°) or gauche (∠φ = 109°) to each other and with the anti form the more stable. The composition (mole fraction) of the vapor with uncertainties estimated at 2σ was found to be 0.55 (0.08), 0.49 (0.08) and 0.41 (0.10) at 24, 90 and 273°, respectively. These values correspond to an energy difference with estimated standard deviation ΔE° = E°_g-E°_a = 0.7 ± 0.3 kcal mol^?1 and an entropy difference ΔS° = S°_g-S°_a = 0.6 ± 0.9 cal mol^?1 K^?1. Some of the diffraction results, together with spectroscopic observations, permit the evaluation of an approximate torsional potential function of the form 2V = V₁ (1 - cos φ) + V₂ (1 - cos 2φ) + V₃ (1 - cos 3φ); the results are V₁ = 4.4 ± 0.5, V₂ = ?2.9 ± 0.5 and V₃ = 4.8 ± 0.2, all in kcal mol^?1. The results at 24°C for the distance (r_a) and angle (∠_α) parameters, with estimated uncertainties of 2σ, are: r(C_sp²-H) = 1.098(0.020)Å, r(C_sp³-H) = 1.103(0.020)Å, r(CC) = 1.334(0.009)Å, r(C-C) = 1.504(0.013)Å, r(C_sp²-Cl) = 1.752(0.021)Å, r(C_sp³-Cl) = 1.776(0.020)Å, ∠C-CC = 127.6(1.1)°, ∠C_sp³-C_sp²-Cl = 110.2(1.0), ∠C_sp²-C_sp³-Cl = 113.1(1.2)°, ∠H-C_sp³-H = 109.5° (assumed), ∠CC-H = 120.0° (assumed) and ∠φ = 108.9(3.4)°.     

The coulometric titration of bromate with cuprous copper

A coulometric procedure has been developed by which 18 to 240 μg quantities of bromate may be determined to within 0.3 μg. The bromate is allowed to react with bromide in an acid solution and electrolytically generated cuprous copper is used for the titration. A dual platinum electrode indicator system is used in an amperometric end-point procedure     

Wavelength-modulated,continuum-source excited atomic fluorescence spectrometric system for wear metals in jet engine lubricating oils using electrothermal atomization

A system for measuring atomic fluorescence of atoms produced via an electrically-heated graphite filament in a flame (acetylene/air or acetylene/nitrous oxide) and excited with a 300-W Eimac xenon are lamp is described. The experimental system also included wavelength modulation for background emission/fluorescence/scatter correction and an optically-triggered electronic integrator for efficient monitoring of the analyte fluorescence signal. Copper, aluminum and molybdenum were determined in jet engine lubricating oil samples (1 μl) with no pretreatment. The determinations are evaluated with respect to the accuracy and repeatability criteria of the U.S. Joint Oil Analysis Program.