Narrow Results

The detection efficiency of the submilli-PIXE camera was improved by installing a new X-ray detector with a smaller distance from specimens. The distortion of elemental images caused by position dependent detection efficiency was corrected by estimating the detection efficiency based on the geometrical configuration of the detection system. The detection efficiency of characteristic X-rays from heavy elements such as iron and bromine became from 11 to 23 times higher than the previous system. The signal to noise ratios was improved from 1.8 to 2.5 times higher and detection limit was also decreased from 1/8 to 1/6 compared to the previous system. The in-air submilli-PIXE camera with improved detection system can be useful to biological applications.

With the advent of modern synchrotron radiation facilities, fluorescence-detected X-ray absorption spectroscopy (XAS) has proven its capability as a highly sensitive local structural tool. Previous applications have been limited to dilute systems and thin films where the absorption of incoming incidence X-ray and outgoing fluorescence X-ray can be neglected. In this chapter we describe unconventional applications beyond this criterion, which are made possible by improving detection efficiency by orders of magnitude combining a high flux insertion devices and highly efficient detectors. In the first application, the non-equilibrium local structure of photo-induced phase of Fe(II) spin crossover complex, [Fe(2-pic)₃]Cl₂EtOH (2-pic=2-aminomethyl pyridine), was investigated under laser illumination. The results indicated no symmetry breaking of FeN₆ clusters upon spin-state switching, establishing the origin of new Raman lines as unrelaxed “frozen-in” distorted outer ligand molecules. Secondly, we demonstrate that polarization-dependent XAS is obtained with a high quality for high temperature superconducting (HTSC) single crystals. The results of temperature-dependent local lattice study on high-quality single crystal of LaSr- CuO revealed doping-induced local lattice distortion $T_d^{\max }$ that maximizes at the superconducting critical temperature $T_c^{\max }$, indicating the strong intimacy of HTSC with local lattice, casting doubts to the purely electronic pairing mechanisms that ignore the contribution of lattice. Lastly, we describe that, combining a microfluidic cell with a fluorescence detection, position-dependent XAS provides time-dependent XAS for dilute systems. The application to CdSe nanocrystal formation demonstrated that such an approach would allow in situ studies on the structural evolution of intermediate state of nanocluster formation known as puzzling state, i.e. “monomers”, in association with molecular orbital calculations. Because of a limited space, unconventional applications are briefly described in this chapter but it could be sufficient to expect more outputs from the 4^th generation synchrotron facilities that would allow higher brilliance and a smaller focus size because the methodology described here is strongly dependent on synchrotron instrumentation.

In these lectures we present for the first time a mathematical reconstruction of what might have been Gauss' own derivation of the linking number of 1833, and we provide also an alternative, explicit proof of its modern interpretation in terms of degree, signed crossings and intersection number. The reconstruction offered here is entirely based on an accurate study of Gauss' own work on terrestrial magnetism and it is complemented by the independent analysis and discussion made by Maxwell in 1867. Since the linking number interpretations in terms of degree, signed crossings and intersection index play such an important rôle in modern mathematical physics, we offer a direct proof of their equivalence, and we provide some examples of linking number computation based on oriented area information. The material presented in these lectures forms an integral part of a paper that will appear in the Journal of Knot Theory and Its Ramifications.

This paper is an introduction to virtual knot theory and an exposition of new ideas and constructions, including the parity bracket polynomial, the arrow polynomial, the parity arrow polynomial and categorifications of the arrow polynomial.

We will discuss how to evaluate the area Ω surrounded by great circles and/or small circles on a unit sphere. Formally, Ω is given as , where θ and φ are usual spherical coordinates and S is the region of which area we want to evaluate. We will show the method that employs an Aharanov-Anandan geometrical phase.