Algorithms for Unconstrained Optimization Problems via Control Theory

Existing algorithms for solving unconstrained optimization problems are generally only optimal in the short term. It is desirable to have algorithms which are long-term optimal. To achieve this, the problem of computing the minimum point of an unconstrained function is formulated as a sequence of optimal control problems. Some qualitative results are obtained from the optimal control analysis. These qualitative results are then used to construct a theoretical iterative method and a new continuous-time method for computing the minimum point of a nonlinear unconstrained function. New iterative algorithms which approximate the theoretical iterative method and the proposed continuous-time method are then established. For convergence analysis, it is useful to note that the numerical solution of an unconstrained optimization problem is none other than an inverse Lyapunov function problem. Convergence conditions for the proposed continuous-time method and iterative algorithms are established by using the Lyapunov function theorem.     

Passively mode-locked lasers with 17.2-GHz fundamental-mode repetition rate pulsed by carbon nanotubes

17.2 GHz, the highest fundamental-mode repetition rate to our knowledge, of a carbon nanotube-based passively mode-locked laser is realized at 1570 nm by employing purified single-walled carbon nanotubes as saturable absorbers. The ultrashort linear laser cavity configured with a approximately 9 mm length is designed and demonstrated with our extremely miniaturized nanotube mode locker and a mirror-coated semiconductor optical amplifier as gain medium. The demonstrated pulsed laser has the inferred temporal pulse width of 14 ps and a 3 dB spectral bandwidth of 0.73 nm.     

Total Synthesis of (+)‐Rubriflordilactone A

Two enantioselective total syntheses of the nortriterpenoid natural product rubriflordilactone A are described, which use palladium‐ or cobalt‐catalyzed cyclizations to form the CDE rings, and converge on a late‐stage synthetic intermediate. These key processes are set up through the convergent coupling of a common diyne component with appropriate AB‐ring aldehydes, a strategy that sets the stage for the synthetic exploration of other members of this family of natural products.     

Synthesis of novel 7-substituted 5,6-dihydroindol-2-ones via a Suzuki-Miyaura cross-coupling strategy

A versatile method for the synthesis of new 7-substituted 5,6-dihydroindol-2-ones is described. The synthetic strategy proceeds through the use of the established palladium-catalyzed Suzuki-Miyaura cross-coupling reaction of halogenated indol-2-ones and arylboronic acids/esters.     

Miscibility and interactions in blends of two proton‐donating polymers: Poly(acrylic acid)/poly(p‐vinylphenol) blends

Blends of poly(acrylic acid) (PAA) and poly(p‐vinylphenol) (PVPh) were prepared from N,N‐dimethylformamide (DMF) and ethanol solutions. The DMF‐cast blends exhibited single T_g's, as shown by modulated differential scanning calorimetry, whereas the ethanol‐cast blends had double T_g's. Fourier transform infrared spectroscopy showed that there was a specific interaction between PAA and PVPh in the DMF‐cast blends. The single‐T_g blends cast from DMF showed single‐exponential decay behavior for the proton spin–lattice relaxation in both the laboratory frame and the rotating frame, indicating that the two polymers mixed intimately on a scale of 2–3 nm. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 789–796, 2003     

Scale-free random graphs and Potts model

We introduce a simple algorithm that constructs scale-free random graphs efficiently: each vertexi has a prescribed weight P_i ∝ i^-μ (0 < μ< 1) and an edge can connect verticesi andj with rateP _i P _j . Corresponding equilibrium ensemble is identified and the problem is solved by theq → 1 limit of the q-state Potts model with inhomogeneous interactions for all pairs of spins. The number of loops as well as the giant cluster size and the mean cluster size are obtained in the thermodynamic limit as a function of the edge density. Various critical exponents associated with the percolation transition are also obtained together with finite-size scaling forms. The process of forming the giant cluster is qualitatively different between the cases of λ > 3 and 2 < λ < 3, whereλ = 1 +μ ^-1 is the degree distribution exponent. While for the former, the giant cluster forms abruptly at the percolation transition, for the latter, however, the formation of the giant cluster is gradual and the mean cluster size for finiteN shows double peaks.     

Iodine-catalyzed allylation of 1,3-dicarbonyl compounds with allylic alcohols at room temperature

A highly efficient iodine-catalyzed allylation of 1,3-dicarbonyl compounds with a wide variety of allylic alcohols has been developed. The reaction is operationally straightforward and proceeds under very mild conditions at room temperature in good to excellent yields (up to 99%) and regioselectivity.