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.     

U型管换热器管束固有频率研究

本文充分考虑了各种影响因素，采用理论分析和实验研究相结合的方法，得到了Ｕ型管管束固有频率的计算公式。实验结果表明，该公式的误差，一般在±８％以内，满足工程设计要求。另外，本文提供了相应图表，使工程设计简单方便。     

Alternating-current losses in two-layer superconducting cables consisting of second-generation superconductors coated by U-shaped ferromagnetic materials

Alternating-current losses in a two-layer superconducting cable, each layer being composed of 15 closely-spaced rectangular wires made up of second-generation superconductors when the ends of wires are coated by either a non-magnetic or strong ferromagnetic material having a U profile is numerically investigated. Computations are carried out through the finite-element method. The alternating-current losses do not increase significantly if the relative permeability of the coating is increased three orders of magnitude, provided that the current amplitude is less than half of the critical current in a superconducting wire. However, the losses are much higher for ferromagnetic coating if the amplitude of the applied current oscillating at 50 Hz is close to the critical current. The ferromagnetic coating is seen to accumulate the magnetic field lines normally on its surfaces, while the field lines are parallel to the long axes of the wires, leading to more significant flux penetration in the coated regions. This facilitates a uniform low-loss current flow in the uncoated regions of the wires. In contrast, coating with a non-magnetic material gives rise to a considerably smaller current flow in the uncoated regions, whereas the low-loss flow is maintained in the coated regions. Moreover, the current flows in opposite directions in the coated and uncoated regions, where the direction in each region is converse for the two materials.     

Stripping Voltammetric Determination of Uranium Traces in Sea Water Samples: Effect of Surfactants on the Measurements

The variables affecting determination of ultra trace levels of uranium (VI) in aqueous samples by differential pulse cathodic stripping voltammetry using chloranilic acid as the complexing agent have been examined in detail. Effect of organic surfactants on the voltammetric behavior has been studied. Electrochemical impedance measurements reveal the effect of adsorption of different surfactants on the adsorption pre-concentration step of uranium-chloranilic acid complex. Additionally, to better understand the analytical feature of the method, physicochemical aspects of the preconcentration process has been studied. Adsorption of uranium-chloranilic acid complex follows the Langmuir adsorption isotherm. Analysis results on sea water samples from India are reported.     

Exhaled breath condensate: Determination of non-volatile compounds and their potential for clinical diagnosis and monitoring. A review

Exhaled breath condensate is a promising, non-invasive, diagnostic sample obtained by condensation of exhaled breath. Starting from a historical perspective of early attempts of breath testing towards the contemporary state-of-the-art breath analysis, this review article focuses mainly on the progress in determination of non-volatile compounds in exhaled breath condensate. The mechanisms by which the aerosols/droplets of non-volatile compounds are formed in the airways are discussed with methodological consequences for sampling. Dilution of respiratory droplets is a major problem for correct clinical interpretation of the measured data and there is an urgent need for standardization of EBC. This applies also for collection instrumentation and therefore various commercial and in-house built devices are described and compared with regard to their design, function and collection parameters. The analytical techniques and methods for determination of non-volatile compounds as potential markers of oxidative stress and lung inflammation are scrutinized with an emphasis on method suitability, sensitivity and appropriateness. The relevance of clinical findings for each group of possible non-volatile markers of selected pulmonary diseases and methodological recommendations with emphasis on interdisciplinary collaboration that is essential for future development into a fully validated clinical diagnostic tool are given.     

采空区埋管抽放技术在U型通风系统工作面上隅角瓦斯治理应用研究

本文以山西晋煤集团岳城矿1302(下)综采工作面为例,探讨了U型通风系统工作面采空区瓦斯涌出规律及其治理原则,研究结果表明,通过在回风巷敷设两趟采空区管路,一趟插入上隅角进行抽放,另一趟埋入采空区进行埋管抽放,通过进行两趟管路抽放,可有效地遏制采空区瓦斯涌出,消除工作面上隅角瓦斯积聚现象,确保工作面安全生产。