一类线图的泛圈性

本文的主要结果是:设G是n≥3阶简单图,ε≥2,且不含3度的边,若GC_4,C_5及C_4∪K_1且对任意无公共顶点的两边e_1和e_2,有d(e_1) d(e_2)≥2n-3,则G的线圈L(G)是泛圈图。     

Line integrals and Green's formula on time scales

In this paper we study curves parametrized by a time scale parameter, introduce line delta and nabla integrals along time scale curves, and obtain an analog of Green's formula in the time scale setting.     

Geometrical aberrations of self-imaged line gratings

We analyze the properties of a self-imaging system from the point of view of aberration theory. We examine analytically and numerically the geometrical aberrations that are observed in the self-image of a parallel-line grating. We first derive the raytracing equations for determining the optical path of a self-imaging ray with the order of diffraction l. We then obtain the third- and fifth-order contributions to ray aberrations which arise from the difference between the optical paths of a self-imaging ray and of an actual ray. We show that the overall ray aberrations are entirely undercorrected. The ray aberrations approach zero as the ratio of the grating constant to the wavelength of light becomes large enough. In a case of unit magnification, no curvatures are observed in the self-imaged lines. If the magnification is bigger than unity, the light rays passing through the point in a positive or negative domain of the aperture variable contribute to the formation of the curved images. The image evaluation technique discussed here can be useful in the various applications related to the self-image formation of a parallel-line grating and it can also provide insight into the self-imaging of other periodic objects.     

The first measured Ag I, Ag II and Ag III Stark broadening parameters

The Stark widths (W) and shifts (d) of two neutral (520.908 and 546.550 nm), eleven singly (211.382, 224.643, 224.874, 232.029, 232.468, 233.140, 241.141, 241.323, 243.781, 244.793 and 276.754 nm) and three doubly (216.189, 231.004 and 239.569 nm) ionized silver (Ag I, Ag II and Ag III, respectively) spectral lines have been measured in nitrogen plasma at about 18,000 K electron temperature and electron density ranged between 0.65 × 10²³ and 1.15 × 10²³ m^− 3. They are the first measured W and d values while those of the Ag II and Ag III lines are the first published data in these spectra. The modified version of the linear, low-pressure, pulsed arc was used as a plasma source operated in nitrogen with silver atoms, as impurities, evaporated from silver cylindrical plates located in the homogeneous part of the discharge. No theoretical predictions exist for W and d values of above mentioned spectral lines. Besides, we have checked the transition probability ratio of two investigated Ag I lines. An agreement with theoretical predictions was found.     

Multispectrum fitting of line parameters for C2H2 in the 3.8-μm spectral region

Using FT spectra (Bruker IFS 120, unapodized FWHM resolution ≈ 0.001 cm⁻¹) of acetylene ¹²C₂H₂, absolute positions and intensities have been measured for about 250 lines between 2600 and 2800 cm⁻¹ in the and cold bands, and in the and hot bands. These measurements improve the accuracy of wavenumbers previously available and lead to individual line intensities for the first time in this spectral region. A multispectrum fitting procedure has been used to retrieve line parameters from five experimental spectra recorded at different pressures. The frequencies of the ν₃ band of ¹²C¹⁶O₂ allowed to perform an absolute wavenumber calibration. The accuracy of the amount of ¹²C₂H₂ in the sample has been checked using the cold band around 2100 cm⁻¹, and has been estimated to be around ±2%. The average absolute accuracy of the line parameters obtained in this work has then been estimated to be ±0.0002 cm⁻¹ for line positions, and ±5% for line intensities. For each studied band, the vibrational transition dipole moment squared value has been determined, as also empirical Herman-Wallis coefficients. A complete line list containing positions and intensities for the five strongest bands around 3.8 μm has been set up for atmospheric applications.     

A connection between linear normal modes and lines of curvature on the potential surface

For the N-degree-of-freedom of linear conservative vibratory systems, the corresponding potential functions can be viewed as N-hypersurfaces in (N + 1)-dimensional space. In this paper, a connection between the geometrical properties (principal curvatures, curvature lines) of potential surfaces and the vibratory characteristics (natural frequencies, linear modes) of the system is built. It is proved that the linear normal modes are exactly the projections of the lines of curvature on the potential surface onto the configuration space with metric m_ij (the mass-matrix); and that the squared natural frequencies are exactly the principal curvatures, at the origin of the configuration space, of the potential surface.     

Location-domination in line graphs

A set $D$ of vertices of a graph $G$ is locating if every two distinct vertices outside $D$ have distinct neighbors in $D$; that is, for distinct vertices $u$ and $v$ outside $D$, $N\left(u\right)\cap D\ne N\left(v\right)\cap D$, where $N\left(u\right)$ denotes the open neighborhood of $u$. If $D$ is also a dominating set (total dominating set), it is called a locating-dominating set (respectively, locating-total dominating set) of $G$. A graph $G$ is twin-free if every two distinct vertices of $G$ have distinct open and closed neighborhoods. It is conjectured (Garijo et al., 2014 [15]) and (Foucaud and Henning, 2016 [12]) respectively, that any twin-free graph $G$ without isolated vertices has a locating-dominating set of size at most one-half its order and a locating-total dominating set of size at most two-thirds its order. In this paper, we prove these two conjectures for the class of line graphs. Both bounds are tight for this class, in the sense that there are infinitely many connected line graphs for which equality holds in the bounds.     

A note on line forces in gradient elasticity

The theory of gradient elasticity is applied to line forces. Line forces acting on a point within the body and a concentrated normal force (Flamant problem) which acts on a half plane are studied. Closed analytical solutions which have a simple form are obtained for displacement fields of these forces. The gradient elasticity solutions are free from undesirable displacement singularities predicted by classical elasticity.     

Heat transfer from a line source located in the periodic laminar near wake of a circular cylinder

This experimental study is devoted to the diffusion of a passive scalar downstream a line source located in a Bénard–von Kármán street. Measurements of velocity and temperature have been performed using LDA and cold wire thermometer with a phase reference. Information on the initial evolution of mean, fluctuating velocity and temperature and associated shear-stresses and heat fluxes fields are presented for two locations of the source: ( and 1). The results show that the velocity field in the wake is strongly related to the geometric structure of vortices while the temperature field is controlled by both the time scale of rotation of the vortices and the location of the heated fluid within the vortex street.     

The distance-regular graphs such that all of its second largest local eigenvalues are at most one

In this paper, we classify distance regular graphs such that all of its second largest local eigenvalues are at most one. Also we discuss the consequences for the smallest eigenvalue of a distance-regular graph. These extend a result by the first author, who classified the distance-regular graphs with smallest eigenvalue .