On a numerical solution of the Cauchy problem for the Laplace equation by the fundamental solutions method

We discuss a numerical method to solve a Cauchy problem for the Laplace equation in the two-dimensional annular domain. We consider the case that the Cauchy data is given on an arc. We develop an approximation method based of the fundamental solutions method using the least squares method with Tikhonov regularization. The effectiveness of our method is examined by a numerical experiment. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Recent Progress on Cyclic Nitrenoid Precursors in Transition-Metal-Catalyzed Nitrene-Transfer Reactions

Nitrene-transfer reactions are powerful synthetic tools for the direct incorporation of nitrogen atoms into organic molecules. The discovery of novel nitrene-transfer reactions has been dominantly supported not only by improvements in transition-metal catalysts but also by the employment of novel precursors of nitrenoids. Since pioneering work involving the use of organic azides and iminoiodinanes as practical synthetic tools for nitrogen-containing compounds was reported, a new approach using various N-heterocycles containing strain energy or a weak bond has emerged. In this review, we briefly summarize the history of nitrene-transfer chemistry from the viewpoint of its precursors. In particular, the use of N-heterocycles such as 2H-azirines, 1,4,2-dioxazol-5-ones, 1,2,4-oxadiazol-5-ones, isoxazol-5(4H)-ones, and isoxazoles is comprehensively described, showing the recent remarkable progress in this chemistry.     

π-Conjugated Macrocycles Bearing Angle-Strained Alkynes

Angle-strained alkyne-containing π-conjugated macrocycles are attractive compounds both in functional materials chemistry and biochemistry. Their interesting reactivity as well as photophysical and supramolecular properties have been revealed in the past three decades. This review highlights the recent advances in angle-strained alkyne-containing π-conjugated macrocycles, especially their synthetic methods, the bond angles of alkynes (∠_sp at C≡C−C), and their functions. The theoretical and experimental research on cyclo[n]carbons and para-cyclophynes consisting of ethynylenes and para-phenylenes are mainly summarized. Related macrocycles bearing other linkers, such as ortho-phenylenes, meta-phenylenes, heteroaromatics, biphenyls, extended aromatics, are also overviewed. Bond angles of strained alkynes in π-conjugated macrocycles, which are generable, detectable, and isolable, are summarized at the end of this review.     

Field-Like spin-transfer torque in a chiral helimagnet

Based on the microscopic model of sd coupling between free electrons and local moments, we present a quantum calculation of a nonadiabatic spin-transfer torque in a chiral helimagnet.     

pH-Responsive Cy5 dyes having nucleophilic substituents for molecular imaging

pH-Responsive fluorescent pentamethine cyanine (Cy5) derivatives having nucleophilic substituents were synthesized. Cy5 derivatives 1-O having mercaptopropyl, hydroxypropyl, and aminopropyl groups on an indole nitrogen atom showed pH-dependent equilibria between a fluorescent open-ring structure (1-O) and a non-fluorescent closed-ring structure (1-C) in pH ranges 3–7, 6–7.5, and 8–9, respectively. pH-Responsive dyes 1a-C having a 1,3-thiazinane structure were easily internalized into A549 cells and converted to open-ring structure 1a-O in response to the relatively low pH of acidic compartments in the cells.     

In-focus Fourier-domain Optical Coherence Tomography by Complex Numerical Method

We introduce a numerical in-focus Fourier-domain optical coherence tomography(in-focus FD-OCT) which can measure cross-sectional images of samples with the high lateral resolution comparable with the resolution in the focal plane in overall range of measurement. In this method, the lateral resolution is enhanced by lateral signal processing of a complex OCT image obtained with FD-OCT. Quantitative evaluation of this method and application to measurement of a porcine eyeball are presented.