Transient resonance Raman and density functional theory investigation of the 2-fluorenylnitrenium ion.

We report a transient resonance Raman spectrum for the 2-fluorenylnitrenium ion obtained after photolysis of 2-azidofluorene. The 10 experimental Raman band frequencies of the transient spectrum show very good agreement with the computed frequencies from BPW91/cc-PVDZ density functional theory calculations for the 2-fluorenylnitrenium ion. Our results confirm the assignment of the approximately 460 nm transient absorption band formed after photolysis of 2-azidofluorene in water/acetonitrile or water solution to the singlet ground electronic state 2-fluorenylnitrenium ion. Our study indicates the 2-fluorenylnitrenium has a large degree of iminocyclohexadienyl cation character with significant delocalization of the charge over both phenyl rings of the fluorene moiety. We compare our results for the 2-fluoreneylnitrenium ion to those previously reported for several other arylnitrenium ions.     

Self‐organized micropatterns of high aspect ratio polymer nanofibers by wetting of nanopores

The self‐organized micropatterns of high aspect ratio polymer nanofibers were prepared via a facile nanoporous wetting strategy. Various micropatterns with labyrinth‐like or honeycomb‐like topography can be formed in a controllable manner by adjusting the nanoporous template's nanochannel characteristic (deep‐hole or through‐hole), the size of nanopores, and the wetting time. The honeycomb‐like micropattern shows a little higher hydrophobicity than labyrinth‐like micropattern when the diameters of their nanofibers are similar. The formation of various self‐organized micropatterns is mainly dependant on the dilation stress and interaction between nanofibers during the template's removal and solvent evaporation process. The confining or free conditions of unreleased nanofibers' tips in nanopores determine the topography of the resultant self‐organized micropattern, i.e., labyrinth‐like or honeycomb‐like. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 1280–1289, 2008     

Vanishing Sums ofmth Roots of Unity in Finite Fields

In an earlier work, the authors determined all possible weightsnfor which there exists a vanishing sum ζ₁+ · · · + ζ_n= 0 ofmth roots of unity ζ_iin characteristic 0. In this paper, the same problem is studied in finite fields of characteristicp. For givenmandp, results are obtained on integersn₀such that all integersn≥n₀are in the “weight set”W_p(m). The main result in this paper guarantees, under suitable conditions, the existence of solutions ofx^d1 + · · · +x^d_n= 0with all coordinates not equal to zeroover a finite field.     

On the topology of a compact submanifold of a sphere with bounded second fundamental form

Leth be the second fundamental form of a compact submanifold of a unit sphere. We show that if ‖h(u, u)‖²<1/3 holds for any unit tangent vectoru at any point on the submanifold then it is a homotopy sphere.     

Singlet-triplet splittings in free and self-trapped excitons

We discuss the available experimental data for the singlet-triplet splitting of free and self-trapped excitons in alkali halides. These data are analysed quantitatively using the pseudopotential method of Bartram, Stoneham and Gash. The predictions confirm the trend emerging from the observed data, namely that the splittings are systematically lower for the self-trapped systems. This difference comes principally from the spread of the self-trapped hole onto two ions, and would not be expected, for example, if the hole were localised on a single site.     

A perturbation method for computing the simplest normal forms of dynamical systems

A previously developed perturbation method is generalized for computing the simplest normal form (at each level of computation, the minimum number of terms are retained) of general n-dimensional differential equations. This “direct” approach, combining the normal form theory with center manifold theory in one unified procedure, can be used to systematically compute the simplest (or unique) normal form. Two particular singularities of the Jacobian of the system are considered in this paper: the first one is associated with one pair of purely imaginary eigenvalues (Hopf-type singularity), and the other corresponds to a simple zero and a pair of purely imaginary eigenvalues (Hopf-zero-type singularity). The approach can be easily formulated and implemented using a computer algebra system. Maple programs have been developed in this paper which can be “automatically” executed by a user without the knowledge of computer algebra. A physical oscillator model is studied in detail to show the computational efficiency of the “direct” method, and the advantage of using the simplest normal form, which greatly simplifies the analysis on dynamical systems, in particular, for bifurcations and stability.     

Symplectic Structures on Gauge Theory

We study certain natural differential forms and their equivariant extensions on the space of connections. These forms are defined using the family local index theorem. When the base manifold is symplectic, they define a family of symplectic forms on the space of connections. We will explain their relationships with the Einstein metric and the stability of vector bundles. These forms also determine primary and secondary characteristic forms (and their higher level generalizations). Received: 27 February 1996 / Accepted: 7 July 1997     

Stochastic integrals of empirical-type processes with applications to censored regression

Motivated by the analysis of linear rank estimators and the Buckley-James nonparametric EM estimator in censored regression models, we study herein the asymptotic properties of stochastic integrals of certain two-parameter empirical processes. Applications of these results on empirical processes and their stochastic integrals to the asymptotic analysis of censored regression estimators are also given.