简易弧高计的误差分析

本文介绍了使用简易弧高计测量球面弧高时的误差公式，并用实例说明了此类弧高计在一般光学元件件加工测量中的可靠性。     

A half-moment model for radiative transfer in a 3D gray medium and its reduction to a moment model for hot, opaque sources

We present in this paper a new 3D half-moment model for radiative transfer in a gray medium, called the height="25" border="0" style="vertical-align:bottom" width="39" alt="View the MathML source" title="View the MathML source" src="http://ars.els-cdn.com/content/image/1-s2.0-S0022407304003954-si67.gif"> model, which uses maximum entropy closure. This model is a generalization to 3D of the 1D version recently proposed in (J. Comp. Phys. 180 (2002) 584). The direction space Ω is divided into two pieces, Ω⁺ and Ω^-, in a dynamical way by the plane perpendicular to the total radiative flux, and the half moments are defined from these subspaces. The model closure and the integrations of the radiative transfer equation performed on the moving Ω^± spaces are detailed. 1D planar results, which have motivated the extension of the model of (J. Comp. Phys. 180 (2002) 584) to multi-dimensions, are shown. These results are very good. The model is thereafter derived for 3D spherically symmetric geometry, where the correctness of the non-trivial border terms can be checked. Two 3D spherically symmetric problems are numerically solved in order to show the accuracy of the closure and the role of the border terms. Once again, compared to the solution obtained with a ray tracing solver, results are very good. From the 3D half-moment model, a new moment model, called height="21" border="0" style="vertical-align:bottom" width="35" alt="View the MathML source" title="View the MathML source" src="http://ars.els-cdn.com/content/image/1-s2.0-S0022407304003954-si72.gif">, is derived for the particular case of a 3D hot and opaque source radiating into a cold medium, for applications such as simulations of stellar atmospheres and fires. Two-dimensional numerical results are presented and compared to those obtained solving the RTE and with other moment models. They demonstrate the very good accuracy of the height="21" border="0" style="vertical-align:bottom" width="29" alt="View the MathML source" title="View the MathML source" src="http://ars.els-cdn.com/content/image/1-s2.0-S0022407304003954-si73.gif"> model, its good convergence properties, and better prediction compared to all other existing moment models in its domain of applicability.     

High-power continuous-wave operation of a diode-pumped laser at

The continuous-wave laser properties of an efficient diode-pumped Nd:GdVO₄ crystal operating at height=16 width="52"/> formed with a simple plane-concave cavity have been studied. With the incident pump power of 21 W, an output power of 6.9 W was obtained, giving an optical conversion efficiency of 32.8% and a slope efficiency of 35.3%. The laser characterization of two different Nd³⁺-doped concentration of Nd:GdVO₄ crystals were studied.     

Remarks on the formula for γ-interior

The paper presents a formula for the γ-interior of a set under special conditions for height="15" border="0" style="vertical-align:bottom" width="133" alt="View the MathML source" title="View the MathML source" src="http://ars.els-cdn.com/content/image/1-s2.0-S0022247X04002252-si1.gif">, more general than those in the previous paper [Acta Math. Hungar. 80 (1998) 89-93]. There are also some applications.     

On the horospherical ridges of submanifolds of codimension 2 in Hyperbolic <Emphasis Type="Italic">n</Emphasis>-space

We introduce the notion of horospherical ridges for submanifolds of codimension 2 in hyperbolic n-space, and study some of their properties.*Work partially supported by DGCYT grant no. BFM2003-02037.     

Iterated monoidal categories

We develop a notion of an n-fold monoidal category and show that it corresponds in a precise way to the notion of an n-fold loop space. Specifically, the group completion of the nerve of such a category is an n-fold loop space, and free n-fold monoidal categories give rise to a finite simplicial operad of the same homotopy type as the classical little cubes operad used to parametrize the higher H-space structure of an n-fold loop space. We also show directly that this operad has the same homotopy type as the n-th Smith filtration of the Barratt-Eccles operad and the n-th filtration of Berger's complete graph operad. Moreover, this operad contains an equivalent preoperad which gives rise to Milgram's small model for height="14" border="0" style="vertical-align:bottom" width="56" alt="View the MathML source" title="View the MathML source" src="http://ars.els-cdn.com/content/image/1-s2.0-S0001870803000653-si1.gif"> when n=2 and is very closely related to Milgram's model of height="12" border="0" style="vertical-align:bottom" width="62" alt="View the MathML source" title="View the MathML source" src="http://ars.els-cdn.com/content/image/1-s2.0-S0001870803000653-si2.gif"> for n>2.     

On the commutator of the Marcinkiewicz integral

height="17" border="0" style="vertical-align:bottom" width="49" alt="View the MathML source" title="View the MathML source" src="http://ars.els-cdn.com/content/image/1-s2.0-S0022247X02004985-si1.gif"> boundedness is considered for the commutator of higher-dimensional Marcinkiewicz integral. Some conditions implying the height="19" border="0" style="vertical-align:bottom" width="49" alt="View the MathML source" title="View the MathML source" src="http://ars.els-cdn.com/content/image/1-s2.0-S0022247X02004985-si2.gif"> and the height="17" border="0" style="vertical-align:bottom" width="49" alt="View the MathML source" title="View the MathML source" src="http://ars.els-cdn.com/content/image/1-s2.0-S0022247X02004985-si3.gif"> boundedness for the commutator of the Marcinkiewicz integral are obtained.     

Unusual Corrections to Scaling in the 3-State Potts Antiferromagnet on a Square Lattice

At zero temperature, the 3-state antiferromagnetic Potts model on a square lattice maps exactly onto a point of the 6-vertex model whose long-distance behavior is equivalent to that of a free scalar boson. We point out that at nonzero temperature there are two distinct types of excitation: vortices, which are relevant with renormalization-group eigenvalue 1/2 and non-vortex unsatisfied bonds, which are strictly marginal and serve only to renormalize the stiffness coefficient of the underlying free boson. Together these excitations lead to an unusual form for the corrections to scaling: for example, the correlation length diverges as J/kT according to Ae ² (1+be ^– +···), where b is a nonuniversal constant that may nevertheless be determined independently. A similar result holds for the staggered susceptibility. These results are shown to be consistent with the anomalous behavior found in the Monte Carlo simulations of Ferreira and Sokal.     

Estimates in surfaces with positive constant Gauss curvature

We give optimal bounds of the height, curvature, area and volume of -surfaces in bounding a planar curve. The spherical caps are characterized as the unique -surfaces achieving these bounds.

     

Spatial Carrier Bi-frequency Fourier Transform Profilometry for the 3-D Shape Measurement of Object with Discontinuous Height Steps

1 IntroductionProjecting a single frequency lfringe pattern upon an Object and observing itsdeformation from a different view angle has been a common method for various threedimensional shape measurement techniques. An autpmatic analysis of the fringepatterns is normally carried out either by the FOurier transform method[IJ or by phasestepping['] of the fringe patterns. HOWever, these techniques have a disadvantage ofprincipal importance, the so-called indetedrinaCy tO a factor Of Zap, or …