The first bowl-shaped stable neutral radical with a corannulene system: synthesis and characterization of the electronic structure

[structure: see text] A bowl-shaped neutral radical with a corannulene system has been designed and synthesized for the first time as a stable solid in air. An unequivocal characterization of the electronic properties of the radical shows that an appreciable amount of spin delocalization extends onto the corannulene unit's curved surface.     

Optimal Control Problem Associated with Jump Processes

An optimal portfolio/control problem is considered for a two-dimen\-sional model in finance. A pair consisting of the wealth process and cumulutative consumption process driven by a geometric Lévy process is controlled by adapted processes. The value function appears and turns out to be a viscosity solution to some integro-differential equation, by using the Bellman principle.     

Canceling branch points and cusps on projections of knotted surfaces in -space

For a knotted surface in -space, its generic projection into -space has branch points as its singularities, and its successive projection into -space has fold points and cusps as its singularities. In this paper, we show that for non-orientable knotted surfaces, the numbers of branch points and cusps can be minimized by isotopy.

     

Computation of multiple eigenvalues of infinite tridiagonal matrices

In this paper, it is first given as a necessary and sufficient condition that infinite matrices of a certain type have double eigenvalues. The computation of such double eigenvalues is enabled by the Newton method of two variables. The three-term recurrence relations obtained from its eigenvalue problem (EVP) subsume the well-known relations of (A) the zeros of ; (B) the zeros of ; (C) the EVP of the Mathieu differential equation; and (D) the EVP of the spheroidal wave equation. The results of experiments are shown for the three cases (A)-(C) for the computation of their ``double pairs'.

     

Back-to-back correlations of high-p(T) hadrons in relativistic heavy-ion collisions

We investigate the suppression factor and the azimuthal correlation function for high p(T) hadrons in central Au+Au collisions at sqrt[s(NN)]=200 GeV by using a dynamical model in which hydrodynamics is combined with explicitly traveling jets. We study the effects of parton energy loss in a hot medium, intrinsic k(T) of partons in a nucleus, and p (perpendicular) broadening of jets on the back-to-back correlations of high p(T) hadrons. Parton energy loss is found to be a dominant effect on the reduction of the awayside peaks in the correlation function.     

Diastereoselective photochromism of a bisbenzothienylethene governed by steric as well as electronic interactions

Introduction of an asymmetric center to C-2 of one of the benzothiophene rings of bisbenzothienylperfluorocyclopentene results in a highly diastereoselective photochromic system. The stereogenic center bears a hydrogen atom, a methyl group, and a methoxymethoxy group. The steric as well as the electronic repulsions gave an 87-88% diastereomer excess in various solvents at room temperature with 80-85% conversion to the colored form. The enantioselective synthesis was also carried out. Upon photoirradiation in hexane, a change in optical rotation at 820 nm, where neither the open form nor the colored form absorbs light, was observed repeatedly.     

Fourth-order perturbation theory for the half-filled Hubbard model in infinite dimensions

We calculate the zero-temperature self-energy to fourth-order perturbation theory in the Hubbard interaction U for the half-filled Hubbard model in infinite dimensions. For the Bethe lattice with bare bandwidth W, we compare our perturbative results for the self-energy, the single-particle density of states, and the momentum distribution to those from approximate analytical and numerical studies of the model. Results for the density of states from perturbation theory at U/W = 0.4 agree very well with those from the Dynamical Mean-Field Theory treated with the Fixed-Energy Exact Diagonalization and with the Dynamical Density-Matrix Renormalization Group. In contrast, our results reveal the limited resolution of the Numerical Renormalization Group approach in treating the Hubbard bands. The momentum distributions from all approximate studies of the model are very similar in the regime where perturbation theory is applicable, . Iterated Perturbation Theory overestimates the quasiparticle weight above such moderate interaction strengths.Received: 9 September 2003, Published online: 30 January 2004PACS: 71.10.Fd Lattice fermion models (Hubbard model, etc.) - 71.27. + a Strongly correlated electron systems; heavy fermions - 71.30. + h Metal-insulator transitions and other electronic transitions     

Measurement Accuracy in Phase-Shifting Point Diffraction Interferometer with Two Optical Fibers

A phase-shifting point diffraction interferometer (PS/PDI) with point sources of two single mode optical fibers has been developed, which will be appropriate for the surface figure measurement of large aperture optics on a sub-nanometer scale. To reduce the measurement error factors, a fiber optic plate (FOP) is used as a projection plane for interference pattern. Errors caused by imperfection of optical alignment, such as position of point sources and tilt of FOP, are minimized by analyzing the measured phase data with an original method. Measurement accuracy in the PS/ PDI is estimated with the interference pattern produced by the two optical fiber sources. If inhomogeneity of the FOP and a systematic error of the PS/PDI are eliminated, the measurement accuracy of the present system is estimated to be less than 4nm P-V and 0.7nm rms, respectively, at a measurement wavelength of 632.8 nm.     

Selectively degradable alternating copolymers of isobutyl vinyl ether and plant‐derived aldehydes with acyclic side chains: Effects of side group structures on copolymerization behaviors

Side group structures of aldehydes were demonstrated to have decisive effects on cationic copolymerizations with alkyl vinyl ether (VE). Alternating copolymerizations of isobutyl VE (IBVE) and plant‐derived aldehydes with acyclic side chains such as trans‐2,cis‐6‐nonadienal, trans‐2‐nonenal, and citral proceeded under appropriate reaction conditions with the EtSO₃H/GaCl₃ initiating system. In addition, some aldehydes copolymerized in a well‐controlled fashion to yield alternating copolymers with controlled molecular weights and narrow molecular weight distributions. Quantitative and selective acid hydrolysis of the resulting alternating copolymers, based on the acetal structures in the main chains, was also achieved to give other conjugated aldehydes as nearly sole degradation products. Copolymerization results of IBVE and various plant‐derived aldehydes with acyclic or cyclic side groups suggested that electron‐donating ability and bulkiness of the side groups were most likely responsible for the alternating and/or controlled copolymerization behaviors. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013 , 51, 4684–4693