Total synthesis of apoptolidin: construction of enantiomerically pure fragments

A general strategy for the total synthesis of the antitumor agent apoptolidin (1) is proposed, and the chemical synthesis of the defined key building blocks (4, 5, 6, 8, and 9) in their enantiomerically pure forms is described. The projected total synthesis calls for a dithiane coupling reaction to construct the C(20)-C(21) bond, a Stille coupling reaction to form the C(11)-C(12) bond, and a Yamaguchi macrolactonization to assemble the macrolide ring, as well as two glycosidation reactions to fuse the carbohydrate units onto the molecule. First and second generation syntheses to the required fragments for apoptolidin (1) are described.     

Spectral decomposition of path space in solvable lattice model

We give thespectral decomposition of the path space of the vertex model with respect to the local energy functions. The result suggests the hidden Yangian module structure on the levell integrable modules, which is consistent with the earlier work [1] in the level one case. Also we prove the fermionic character formula of the levell integrable representations in consequence.     

Aggregation of a Cationic Cyanine Dye Intercalated in the Interlayer Space of a Layered Titanate Na2Ti3O7

Abstract

A cationic cyanine dye. 1,1′-diethyl-2,2′-cyanine (PIC), was successfully intercalated into Na₂Ti₃O₇ by a guest-exchange method using a propylamine/Ti₃O₇ intercalation compound as the intermediate. Based on the XRD and chemical analytical results, it was presumed that PIC was densely packed in the interlayer space with the short axis of its quinoline-ring almost perpendicular to the host layer. Spectroscopic results revealed that the PIC formed J-aggre-gates even in the restricted space between the titanate layers.     

A novel phenyl–bromine ligand exchange reaction on germanium by boron tribromide

A novel phenyl–bromine ligand exchange reaction by BBr₃ on germanium was investigated that proceeds without breaking Ge CH₂Ar bond. Typically, the reaction between (PhCH₂)₃PhGe and BBr₃ resulted exclusively in the formation of (PhCH₂)₃GeBr. Copyright © 2005 John Wiley & Sons, Ltd.     

Grazing-induced crises in hybrid dynamical systems

In hybrid dynamical systems including both continuous and discrete components, an interplay between a continuous trajectory and a discontinuity boundary can trigger a sudden qualitative change in the system dynamics. Grazing phenomena, which occur when a continuous trajectory hits a boundary tangentially, are well known as a representative of such phenomena. We demonstrate that a grazing phenomenon of a chaotic attractor can result in its sudden disappearance and initiate chaotic transients. The mechanism of this grazing-induced crisis is revealed in an illustrative example. Furthermore, we derive a formula to obtain the critical exponent of the power law on the mean duration of chaotic transients.     

Stability of twistor lifts for surfaces in four-dimensional manifolds as harmonic sections

We prove that the twistor lifts of certain twistor holomorphic surfaces in four-dimensional manifolds are weakly stable harmonic sections. As a corollary, if ambient spaces are self-dual Einstein manifolds with nonnegative scalar curvature, then the twistor lifts of twistor holomorphic surfaces are weakly stable. Moreover, for certain surfaces in four-dimensional hyperkähler manifolds, we show that the surfaces are twistor holomorphic if their twistor lifts are weakly stable harmonic sections. In particular, we characterize twistor holomorphic surfaces in four-dimensional Euclidean space by weak stability of the twistor lifts.     

X‐ray fluorescent CT imaging of cerebral uptake of stable‐iodine perfusion agent iodoamphetamine analog IMP in mice

Using X‐ray fluorescent computed tomography (XFCT), the in vivo and ex vivo cerebral distribution of a stable‐iodine‐labeled cerebral perfusion agent, iodoamphetamine analog (¹²⁷I‐IMP), has been recorded in the brains of mice. In vivo cerebral perfusion in the cortex, hippocampus and thalamus was depicted at 0.5 mm in‐plane spatial resolution. Ex vivo XFCT images at 0.25 mm in‐plane spatial resolution allowed the visualisation of the detailed structures of these regions. The quality of the XFCT image of the hippocampus was comparable with the ¹²⁵I‐IMP autoradiogram. These results highlight the sensitivity of XFCT and its considerable potential to evaluate cerebral perfusion in small animals without using radioactive agents.     

Chaotic Motion of the N-Vortex Problem on a Sphere: I. Saddle-Centers in Two-Degree-of-Freedom Hamiltonians

We study the motion of N point vortices with N∈ℕ on a sphere in the presence of fixed pole vortices, which are governed by a Hamiltonian dynamical system with N degrees of freedom. Special attention is paid to the evolution of their polygonal ring configuration called the N -ring, in which they are equally spaced along a line of latitude of the sphere. When the number of the point vortices is N=5n or 6n with n∈ℕ, the system is reduced to a two-degree-of-freedom Hamiltonian with some saddle-center equilibria, one of which corresponds to the unstable N-ring. Using a Melnikov-type method applicable to two-degree-of-freedom Hamiltonian systems with saddle-center equilibria and a numerical method to compute stable and unstable manifolds, we show numerically that there exist transverse homoclinic orbits to unstable periodic orbits in the neighborhood of the saddle-centers and hence chaotic motions occur. Especially, the evolution of the unstable N-ring is shown to be chaotic.      

Expansion ratio dependence of lattice vibration of GaN using ab initio molecular dynamics calculations

Temperature dependence of Raman shift wavenumbers are important for the measurements of heat distribution of high-power GaN devices. In this study, calculated results of vibrational modes of ground state structure and some expanded structures of wurtzite type gallium nitride were presented using ab initio molecular dynamic (AIMD) simulations. Frequency analyses have been done for these calculated results and compared with the experimental results of temperature dependence of Raman spectra. Good agreement was achieved between the calculated and the experimental results quantitatively. AIMD would be a useful tool for the prediction of vibrating analysis for III-N systems.