Optimal dividends in the dual model

The optimal dividend problem proposed by de Finetti [de Finetti, B., 1957. Su un’impostazione alternativa della teoria collettiva del rischio. In: Transactions of the XVth International Congress of Actuaries, vol. 2. pp. 433-443] is to find the dividend-payment strategy that maximizes the expected discounted value of dividends which are paid to the shareholders until the company is ruined or bankrupt. In this paper, it is assumed that the surplus or shareholders’ equity is a Lévy process which is skip-free downwards; such a model might be appropriate for a company that specializes in inventions and discoveries. In this model, the optimal strategy is a barrier strategy. Hence the problem is to determine b^∗, the optimal level of the dividend barrier. A key tool is the method of Laplace transforms. A variety of numerical examples are provided. It is also shown that if the initial surplus is b^∗, the expectation of the discounted dividends until ruin is the present value of a perpetuity with the payment rate being the drift of the surplus process.     

Super-edge-graceful Labelings of Some Cubic Graphs

The notion of super-edge-graceful graphs was introduced by Mitchem and Simoson in 1994.However, few examples except trees are known. In this paper, we exhibit two classes of infinitely many cubic graphs which are super-edge-graceful. A conjecture is proposed.     

Residue races

Given a prime p and distinct non-zero integers a₁, a₂,..., a_k (mod p), we investigate the number N = N(a₁, a₂,..., a_k; p) of residues n (mod p) for which (na₁)_p < (na₂)_p < ... < (na_k)_p, where (b)_p is the least non-negative residue of b (mod p). We give complete solutions to the problem when k = 2,3,4, and establish some general results corresponding to k≥5. The first author is a Presidential Faculty Fellow. He is also supported, in part, by the National Science Foundation. 2000 Mathematics Subject Classification Primary—11A07; Secondary—11F20     

A transient absorption study of allophycocyanin

Transient dynamics of allophycocyanin trimers and monomers are observed by using the pump-probe, transient absorption technique. The origin of spectral components of the transient absorption spectra is discussed in terms of both kinetics and spectroscopy. We find that the energy gap between the ground and excited states of the unexcited subunit of allophycocyanin monomer decreases via an interaction with another excited subunit. For allophycocyanin trimer, we find that the fast dynamics results from the fast internal conversion and the first excited state is the only one electronic state which can trap the final population.     

Plasmonic Zener tunneling in metal-dielectric waveguide arrays

We elucidate in this Letter plasmonic Zener tunneling (PZT) in metal-dielectric waveguide arrays (MDWAs) by using numerical simulations and theoretical analyses. PZT in MDWAs occurs at the waveguide entrance and wherever the beam completes Bloch oscillations, because the bandgap between the first and second bands is minimal at the center of the first Brillouin zone. This feature significantly differs from that of optical Zener tunneling in dielectric waveguide arrays. The dependence of the simulated tunneling rate on the gradient of the relative permittivity of the dielectric layers correlates with the tunneling theory, thus confirming the occurrence of PZT in MDWAs.     

Growth of Co clusters on thin films Al2O3NiAl(100)

We present a scanning tunnel microscopy study of Co clusters grown through vapor deposition on Al(2)O(3) thin films over NiAl(100) at different coverages and temperatures. Formation of Co clusters was observed at 90, 300, 450, and 570 K. At the three lower temperatures, we find narrow cluster size distributions and the mean sizes (with a diameter of 2.6 nm and a height of 0.7 nm) do not change significantly with the coverage and temperature, until the clusters start to coalesce. Even on 3-4-nm-wide crystalline Al(2)O(3) strips where the deposited Co atoms are confined, the same features sustain. Only at 570 K the normal growth mode where the cluster size increases with the deposition coverage is observed, although the data are less conclusive. A simple modeling of kinetic surface processes on a strip confirms the normal growth mode, but fails to show a favored size unless additional energetic constraints are applied on the cluster sizes. Increasing Co coverages to cluster coalescence, a larger preferable size (mean diameter of 3.5 nm and height of 1.4 nm) appears for growth at 450 K. These two sizes are corroborated by morphology evolution of high Co coverages deposited at 300 K and annealed to 750 K, in which the coalescence is eliminated and the two preferable geometries appear and coexist.     

Synthesis,structures, and properties of iridium(III) bis-cyclometallated complexes containing three-atom chelates

Heating of [Ir(η²-ppy)₂(MeCN)₂]NO₃ (1, ppy = 2-phenylpyridine) in MeCN under reflux afforded [Ir(η²-ppy)₂(η²-NO₃)] (2). Treatment of 1 with 2-mercaptopyridine (Hmp), 6-methyl-2-hydroxypyridine (Hmhp), 6-chloro-2-hydroxypyridine (Hchp), trimethylacetic acid (Htma), benzoic acid (Hbz), 2-methylacrylic acid (Hma), and acetic acid (Hac) in the presence of excess Et₃N produced [Ir(η²-ppy)₂(η²-XZY)] (XZY^? = mp^? (3), mhp^? (4), chp^? (5), ac^? (6), bz^? (7), ma^? (8), tma^? (9)). Crystal structures of 2, 3, 7, 8, and 9 have been characterized by X-ray diffraction. The inherent strain contained in the four-member rings, {Ir(η²-XZY)}, is apparently reflected in the long Ir–X and Ir–Y distances. The absorption and emission properties of nearly all the new complexes except 2 show small variations.     

A complete characterization for <Emphasis Type="Italic">k</Emphasis>-resonant Klein-bottle polyhexes

A hexagonal tessellation K(p, q, t) on Klein bottle, a non-orientable surface with cross-cap number 2, is a finite-sized elemental benzenoid which can be produced from a p × q-parallelogram of hexagonal lattice with usual identifications of sides and with torsion t. Unlike torus, Klein bottle polyhex K(p, q, t) is not transitive except for some degenerated cases. We shall show, however, that K(p, q, t) does not depend on t. Accordingly, criteria for K(p, q, t) to be k-resonant for every positive integer k will be given. Moreover, we shall show that K(3, q, t) of 3-resonance are fully-benzenoid.      

Imaging the reaction dynamics of OH + CD4. 2. Translational energy dependencies

The reaction of OH + CD4 is investigated in a crossed-beam experiment over the collisional energies ranging from reaction threshold of about 5 to 16 kcal/mol. Exploiting a time-sliced ion velocity imaging detection scheme, the coincident information on the two polyatomic product pairs, HOD and CD3, is revealed in a state-correlated manner. The recently discovered vibrational mode-correlation between the two products is found to persist over the full range of collision energies of this study. In addition, the energy dependencies of the correlated cross section, state distribution, and angular distribution are elucidated, providing an unprecedented insight into this important reaction.