Inverse scattering problem for Sturm–Liouville operator with nonlinear dependence on the spectral parameter in the boundary condition

The inverse problem of the scattering theory for Sturm–Liouville operator on the half line with boundary condition depending quadratic on the spectral parameter is considered. Scattering data are defined, some properties of the scattering data are examined, the main equation is obtained, solvability of the integral equation is proved and uniqueness of algorithm to the potential with given scattering data is studied. Copyright © 2010 John Wiley & Sons, Ltd.     

矩形毛细微槽中三角形区域接触线特性的研究

利用CCD和宽视场体视显微镜相结合的技术,拍摄了矩形毛细微槽内液体工质在三角形区域的润湿图像,并进行了图像处理,研究结果表明:随着热流密度的增加,三角形区域内的三相接触线向微槽底角收缩,导致三相接触线的长度减小,液膜厚度减小;随着微槽深度的增加,三角形区域的接触线长度减小;随着微槽宽度和倾斜角度的增加,三角形区域内的接触线长度增加,液膜厚度增加.     

Gradient‐based solvent suppression methods on a benchtop spectrometer

Benchtop NMR emerges as an appealing alternative to widely extend the scope of NMR spectroscopy in harsh environments and for on‐line monitoring. Obviously, the use of low‐field magnets induces a dramatic reduction of the spectral resolution leading to frequent peak overlaps. This issue is even more serious because applications such as chemical process monitoring involve the use of non‐deuterated solvents, leading to intense and broad peaks overlapping with the signals of interest. In this article, we highlight the need for efficient suppression methods compatible with flowing samples, which is not the case of the common pre‐saturation approaches. Thanks to a gradient coil included in our benchtop spectrometer, we were able to implement modern and efficient solvent suppression blocks such as WET or excitation sculpting to deliver quantitative spectra in the conditions of the on‐line monitoring. While these methods are commonly used at high field, this is the first time that they are investigated on a benchtop setting. Their analytical performance is evaluated and compared under static and on‐flow conditions. The results demonstrate the superiority of gradient‐based methods, thus highlighting the relevance of implementing this device on benchtop spectrometers. The comparison of major solvent suppression methods reveals an optimum performance for the WET‐180‐NOESY experiment, both under static and on‐flow conditions. Copyright © 2016 John Wiley & Sons, Ltd.     

Influence of pressure on the relative population of the two lowest vibrational levels of the C <Superscript>3</Superscript> Π<Subscript>u</Subscript> state of nitrogen for electron beam excitation

Continuous and pulsed 12 keV electron beams were used to excite nitrogen within a gas cell at pressures ranging from 10 to 1400 hPa. The pressure dependence of the ratio of photon fluxes for emission from vibrational levels v'=0 and 1 of the C ³Π _u state has been studied. The results confirm the presence of a collisional excitation mechanism populating v'=0, 1 in addition to electron impact excitation. Rate constants of (1.27 ±0.04)×10^-11 cm³s^-1 [ v'=0] and (2.68 ±0.08)×10^-11 cm³s^-1 [ v'=1] were measured for C ³Π _u quenching by ground state nitrogen. For electron beam conditions relative excitation efficiencies of 1:0.59:0.22 for vibrational levels 0, 1 and 2 were calculated. The recorded flux ratios are compared with the predictions given by a vibrational relaxation model.     

Design of the low energy beam transport line for the China spallation neutron source

The design of the China Spallation Neutron Source (CSNS) low-energy beam transport (LEBT) line, which locates between the ion source and the radio-frequency quadrupole (RFQ), has been completed with the TRACE3D code. The design aims at perfect matching, primary chopping, a small emittance growth and sufficient space for beam diagnostics. The line consists of three solenoids, three vacuum chambers, two steering magnets and a pre-chopper. The total length of LEBT is about 1.74 m. This LEBT is designed to transfer 20 mA of H-pulsed beam from the ion source to the RFQ. An induction cavity is adopted as the pre-chopper.The electrostatic octupole steerer is discussed as a candidate. A four-quadrant aperture for beam scraping and beam position monitoring is designed.     

Line Intensities of the Phosphine Dyad at 10 μm

Over 1000 measured line intensities of phosphine (PH₃) are reported for the region 830 to 1310 cm⁻¹, which contains the two lowest fundamentals in Coriolis interaction. These measurements are fitted to 1.5% for ν₂ at 992.13 cm⁻¹ and 2.1% for ν₄ at 1118.31 cm⁻¹, respectively, using five intensity parameters that include three Herman-Wallis type terms. In addition, some 60 intensities of the 2ν₂-ν₂ hot band are modeled. The corresponding assignments and line positions of the dyad from previous work [L. Fusina and G. Di Lonardo, J. Mol. Struct.517-518, 67-78 (2000)] are combined with the present intensity study to provide an improved PH₃ database for planetary studies. The total integrated intensity for the dyad is 156.(4) cm⁻² atm⁻¹ at 296 K.     

On Analogs of the Tits Alternative for Groups of Homeomorphisms of the Circle and of the Line

In [1] G. Margulis proved Ghys's conjecture stating the validity of the following analog of the Tits alternative: either the group of homeomorphisms of the circle possesses a free subgroup with two generators or there is an invariant probabilistic measure on S ¹ . In the present paper, we prove the following strengthening of Margulis's statement: an invariant probabilistic measure for a group exists if and only if the quotient group does not contain a free subgroup with two generators (here is some specific subgroup of G defined in a canonical way). We also formulate and prove analogs of the Tits alternative for groups of homeomorphisms of the line.     

Derivation of a new class of distributions for the microcanonical ensemble

A new class of distributions for the microcanonical ensemble, which are shown to be stable laws, are derived by applying the central limit theorem to the canonical ensemble. This opens up a whole new host of phenomena that can be treated from a unified thermodynamic point of view. Pressure broadening of line shapes is used as an illustration.1. Work supported, in part, by contributions from the Consiglio Nazionale di Ricerche and the Ministero dell'Università e della Ricerca Scientifica e Tecnologica.2. The interaction parameterC is proportional to the mean square dipole moment. As an order of magnitude of the dipole moment, we can take it as the product of the electric charge and a typical atomic radius for a moderately excited state, which is several times the Bohr radius. Multiplication by the fine structure constant converts the Bohr radius into the Compton wavelength, thereby reducing the magnitude of the interaction by 1/137.