Enhanced surface-plasmon resonance absorption in metal-dielectric-metal layered microspheres

We present a theoretical study of the dispersion relation of surface-plasmon resonances of mesoscopic metal-dielectric-metal microspheres. By analyzing the solutions to Maxwell's equations, we obtain a simple geometric condition for which the system exhibits a band of surface-plasmon modes whose resonant frequencies are weakly dependent on the multipole number. Using a modified Mie calculation, we find that a large number of modes belonging to this flat-dispersion band can be excited simultaneously by a plane wave, thus enhancing the absorption cross section. We demonstrate that the enhanced absorption peak of the sphere is geometrically tunable over the entire visible range.     

Slow convergence of sequences of linear operators II: Arbitrarily slow convergence

We study the rate of convergence of a sequence of linear operators that converges pointwise to a linear operator. Our main interest is in characterizing the slowest type of pointwise convergence possible. This is a continuation of the paper Deutsch and Hundal (2010) [14]. The main result is a “lethargy” theorem (Theorem 3.3) which gives useful conditions that guarantee arbitrarily slow convergence. In the particular case when the sequence of linear operators is generated by the powers of a single linear operator, we obtain a “dichotomy” theorem, which states the surprising result that either there is linear (fast) convergence or arbitrarily slow convergence; no other type of convergence is possible. The dichotomy theorem is applied to generalize and sharpen: (1) the von Neumann–Halperin cyclic projections theorem, (2) the rate of convergence for intermittently (i.e., “almost” randomly) ordered projections, and (3) a theorem of Xu and Zikatanov.     

Benchmark policies for utility-carrying queues with impatience

Queueing Systems - Men and jobs alike are characterized by a single trait, which may take on categorical values according to given population frequencies. Men arrive to the system following a...     

Fenchel Duality and the Strong Conical Hull Intersection Property

We study a special dual form of a convex minimization problem in a Hilbert space, which is formally suggested by Fenchel dualityand is useful for the Dykstra algorithm. For this special duality problem, we prove that strong duality holds if and only if the collection of underlying constraint sets {C ₁,...,C _m} has the strong conical hull intersection property. That is,

Comparison of the mass spectra of 6-thiotheophyllines and 6-sulfinytheophyllines

Under electron impact, 6-thiotheophyllines eliminate various fragments from the pyrimidine moiety. In a retro Diels-Alder reaction, they lose the fragment X?C?NCH₃ from positions 1 and 2 of the pyrimidine ring. In 6-sulfinyltheophyllines, the sulfinyl group is the main target for fragmentation; it can lose either oxygen or sulfur, and the abundance of [M—16]⁺ and [M—32]⁺ is much higher than the abundance of the molecular ion. Elimination of the sulfur atom of the 6-sulfinyl substituent, with retention of its oxygen, may be explained by intermediate formation of a ring. All further fragmentations of the 6-sulfinyl derivatives proceed by a primary loss of oxygen or sulfur, followed by elimination of fragments from the pyrimidine moiety, similar to the primary processes, observed in the mass spectra of the 6-thiotheophyllines.     

The NMR spectral characteristics of some meso-Ionic s-triazoles

The hetero-ring proton of anhydro-1,4-diphenyl-3-mercapto-s-triazolium hydroxide (I) is more highly deshielded than its 3-hydroxy analog (II). The chemical shifts of the hetero-ring proton for compounds I and II were found to be solvent dependent due to hydrogen bond formation. Two series of anhydro-1,4-diaryl-3-hydroxy-s-triazolium hydroxides have been synthesized and their NMR spectra determined. The chemical shift of the hetero-ring proton of these compounds was found to correlate with the Hammett sigma constants of the meta- and para- substituents in the aryl groups.     

Calculation of absolute electron-impact ionization cross-sections of dimers and trimers

We report calculations of the electron-impact ionization cross-sections of selected dimers (homonuclear diatomic molecules) and trimers (homonuclear triatomic molecules) using a method which relies only on macroscopic quantities in conjunction with a “defect concept”. The empirically determined defect describes the deviation of the cluster (dimer, trimer) cross-sections from a simple linear dependence on the cluster size. We compare the calculated cross-sections to experimental data for the dimers S₂ and F₂ and the trimer O₃ and we present predictions for the ionization cross-sections of Br₂, I₂, C₂ and C₃ for which no experimental data are available. Lastly, we extend the method to the calculation of ionization cross-sections for the fullerenes C₆₀ and C₇₀. Received 6 December 1999 and Received in final form 10 April 2000