Thermal expansion of a rig

Summary We have estimated and measured the daily thermal expansion of an oceanographic platform. This has been found negligible as far as the calibration of a satellite altimeter is concerned.     

Letter: Differential Invariants of the Kerr Vacuum

The norms associated with the gradients of the two non-differential invariants of the Kerr vacuum are examined. Whereas both locally single out the horizons, their global behavior is more interesting. Both reflect the background angular momentum as the volume of space allowing a timelike gradient decreases with increasing angular momentum becoming zero in the degenerate and naked cases. These results extend directly to the Kerr-Newman geometry.     

The polarization property and irradiance distribution of incoherent and coherent Gaussian beam combinations

Based on the beam coherence-polarization (BCP) matrix, the polarization property of coherent and incoherent Gaussian beam combinations is studied in detail. The general expressions for the degree of polarization P of the resulting beam in case of incoherent and coherent combinations are derived. It is shown that P is dependent on the incoherent or coherent combination, propagation distance, separation, azimuth of the polarization plane and numbers of beamlets in general. The irradiance distribution of the resulting beam for the coherent cases depends on the azimuth of the polarization plane of beamlets. However, for the incoherent case it does not.     

Minimum Distance Between the Faces of Two Convex Polyhedra: A Sufficient Condition

The problem of finding the Euclidean distance between two convex polyhedra can be reduced to the combinatorial optimization problem of finding the minimum distance between their faces. This paper presents a global optimality criterion for this problem. An algorithm (QLDPA) for the fast computation of the distance between convex and bounded polyhedra is proposed as an application of it. Computer experiments show its fast performance, especially when the total number of vertices is large.     

A Semiconductor Laser of the Visible Range as an Exciting Source of Raman Scattering

A possibility of application of semiconductor lasers of the visible range as exciting sources for Raman spectroscopy is studied. An experimental set-up for measuring Raman spectra of polycrystalline dielectrics and broad-gap semiconductors excited by a semiconductor laser with a wavelength of 640 nm was created. The conditions under which the spectral width of the lasing line of a semiconductor laser was within 10^-3 cm^-1 in the continuous mode with a power of 10 mW are realized. The characteristics of various types of exciting sources used in Raman spectroscopy are compared. The results of studies of the characteristic Raman spectra excited with a semiconductor laser in polycrystalline sulfur are presented.     

Self-bonding in an amorphous polymer below the glass transition: A T-peel test investigation

Films of amorphous polystyrene (PS) with a weight-average molecular weight (M_w) of 225 × 10³ g/mol were bonded in a T-peel test geometry, and the fracture energy (G) of a PS/PS interface was measured at the ambient temperature as a function of the healing time (t_h) and healing temperature (T_h). G was found to develop with (t_h)^1/2 at T_h = T_g-bulk − 33 °C (where T_g-bulk is the glass-transition temperature of the bulk sample), and log G was found to develop with 1/T_h at T_g-bulk − 43 °C ≤ T_h ≤ T_g-bulk − 23 °C. The smallest measured value of G = 1.4 J/m² was at least one order of magnitude larger than the work of adhesion required to reversibly separate the PS surfaces. These three observations indicated that the development of G at the PS/PS interface in the temperature range investigated (<T_g-bulk) was controlled by the diffusion of chain segments feasible above the glass-transition temperature of the interfacial layer, in agreement with our previous findings for fracture stress development at several polymer/polymer interfaces well below T_g-bulk. Close values of G = 8–9 J/m² were measured for the symmetric interfaces of polydisperse PS [M_w = 225 × 10³, weight-average molecular weight/number-average molecular weight (M_w/M_n) = 3] and monodisperse PS (M_w = 200 × 10³, M_w/M_n = 1.04) after healing at T_h = T_g-bulk − 33 °C for 24 h. This implies that the self-bonding of high-molecular-weight PS at such relatively low temperatures is not governed by polydispersity. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1861–1867, 2004     

Second-order Nonlinear Optical Properties of a Series of Azulene Derivatives

The first hyperpolarizabilities of a series of novel azulenic-barbituric acid chromophores have been studied by using 12 excitation wavelengths, ranging from 900 to 1907 nm. The dispersion relation of the first hyperpolarizabilities of chromophores holds the same tendency as the experimental results. In addition, the static first hyperpolarizability β0 of molecules was calculated by means of the Sum-Over-States (SOS) expression and the two-level formula respectively. The results show that these molecules possess large static first hyperpolarizabilities and the, β0 value increases as the donor or acceptor strength enhances; the distorted degree of molecules has also an important influence on the β0 value.     

The canonical solution operator of $ {\bar \partial } $ on weighted spaces with holomorphic coefficients

On weighted spaces with strictly plurisubharmonic weightfunctions the canonical solution operator of and the ‐Neumann operator are bounded. In this paper we find a class of strictly plurisubharmonic weightfunctions with certain growth conditions, so that they are Hilbert‐Schmidt operators between weighted spaces with different weightfunctions, if they are restricted to forms with holomorphic coefficients. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

3-正则图的分割问题是NP-完全问题

证明了3-正则图的最小平分问题和最小α-分割问题都是NP-完全问题.