Optical Computed Tomography Imaging of Absorbers in a Highly Scattering Medium by Detection of Photons Preserving Initial Polarization

A method utilizing light polarization was applied to take the projection data of absorbers in a highly scattering medium. The floor level of the projection data due to diffused light was significantly suppressed by detection of photons which preserved initial polarization. An optical computed tomgraphy image was reconstructed from the projection data taken by this method and exhibited higher spatial resolution than the image reconstructed from the projection data by conventional method.     

A quantum dual pair \mathfraks\mathfrakl2 ,\mathfrakon \mathfrak{s}\mathfrak{l}_2 ,\mathfrak{o}_n and the associated Capelli identity

A quantum analogue of the dual pair is introduced in terms of the oscillator representation of U _q . Its commutant and the associated identity of Capelli type are discussed.     

Size-selective formation of C78 fullerene from a three-dimensional polyyne precursor

Multicyclic cagelike cyclophanes 2 a and 2 b containing cyclobutene rings have been prepared as precursors of three-dimensional polyynes C78H18 (1a) and C78H12Cl6 (1b), respectively. Laser irradiation of 2a and 2b induced expulsion of the aromatic fragment, indane, to give the three-dimensional polyyne anions C78H18- and C78H12Cl6-, respectively. Whereas the former anion lost only four hydrogen atoms to form C78H14-, complete loss of all hydrogen and chlorine atoms was observed from the latter anion, to yield a C78- ion that has a fullerene structure which was proven by its characteristic fragmentation pattern.     

Mean Curvature Flow Closes Open Ends of Noncompact Surfaces of Rotation

We discuss the motion of noncompact axisymmetric hypersurfaces Γ _t evolved by mean curvature flow. Our study provides a class of hypersurfaces that share the same quenching time with the shrinking cylinder evolved by the flow and prove that they tend to a smooth hypersurface having no pinching neck and having closed ends at infinity of the axis of rotation as the quenching time is approached. Moreover, they are completely characterized by a condition on initial hypersurface.     

On Central Elements in the Universal Enveloping Algebras of the Orthogonal Lie Algebras

We present an analogy of the famous formula that the square of the Pfaffian is equal to the determinant for an alternating matrix for the case where the entries are the generators of the orthogonal Lie algebras. This identity clarifies the relation between the two sets of central elements in the enveloping algebra of the orthogonal Lie algebras. We employ systematically the exterior calculus for the proof.