Development of a Comprehensive Network for Scientific and Technical Information in Japan

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Stereographical visualization of a polarization state using weak measurements with an optical-vortex beam

We propose a stereographical-visualization scheme for a polarization state by two-dimensional imaging of a weak value with a single setup. The key idea is to employ Laguerre-Gaussian modes or an optical vortex beam for a probe state in weak measurement. Our scheme has the advantage that we can extract information on the polarization state from the single image in which the zero-intensity point of the optical vortex beam corresponds to a stereographic projection point of the Poincare sphere. We experimentally perform single-setup weak measurement to validate the stereographical relationship between the polarization state on the Poincare sphere and the location of the zero-intensity point.Comment: 6 pages, 4 figure

Stable extendibility of vector bundles over RPn and the stable splitting problem

AbstractLet F be the real number field R or the complex number field C, and let RPn denote the real projective n-space. In this paper, we study the conditions for a given F-vector bundle over RPn to be stably extendible to RPm for every m>n, and establish the formulas on the power ζr=ζ⊗⋯⊗ζ (r-fold) of an F-vector bundle ζ over RPn. Our results are improvements of the previous papers [T. Kobayashi, H. Yamasaki, T. Yoshida, The power of the tangent bundle of the real projective space, its complexification and extendibility, Proc. Amer. Math. Soc. 134 (2005) 303–310] and [Y. Hemmi, T. Kobayashi, Min Lwin Oo, The power of the normal bundle associated to an immersion of RPn, its complexification and extendibility, Hiroshima Math. J. 37 (2007) 101–109]. Furthermore, we answer the stable splitting problem for F-vector bundles over RPn by means of arithmetic conditions

Cosmic R-string, R-tube and Vacuum Instability

We show that a cosmic string associated with spontaneous $U(1)_R$ symmetry breaking gives a constraint for supersymmetric model building. In some models, the string can be viewed as a tube-like domain wall with a winding number interpolating a false vacuum and a true vacuum. Such string causes inhomogeneous decay of the false vacuum to the true vacuum via rapid expansion of the radius of the tube and hence its formation would be inconsistent with the present Universe. However, we demonstrate that there exist metastable solutions which do not expand rapidly. Furthermore, when the true vacua are degenerate, the structure inside the tube becomes involved. As an example, we show a "bamboo"-like solution, which suggests a possibility observing an information of true vacua from outside of the tube through the shape and the tension of the tube.Comment: 28 pages, 17 figures, v2: references added, improved arguments in sec 3.5.

The Practice of Computer-Assisted Planning and Navigation for Hip Arthroscopy

Despite significant developments in hip arthroscopic surgery in recent years, precise preoperative planning and accurate performance remain challenging. Preoperative planning is particularly important in cases of osteochondroplasty for cam-type femoroacetabular impingement (FAI), and can be aided by several computer-assisted tools, including three-dimensional imaging analysis or kinematic analysis. Initially, the exact point of the bony impingement is identified using simulation analysis; then, virtual osteochondroplasty is performed. Improvements in the range of motion can then be evaluated using computer simulation again. In this way, the required area and depth of bone resection can be assessed preoperatively. In addition, computed tomography-based navigation assistance can be used to complete the osteochondroplasty in accordance with the preoperative planning. After surgery, postoperative evaluation provides valuable feedback to improve future planning and procedures. In this chapter, we describe the practice of computer-assisted planning and navigation for hip arthroscopy