Risk-Sensitive Ergodic Control of Continuous Time Markov Processes With Denumerable State Space

In this article, we study risk-sensitive control problem with controlled continuous time Markov chain state dynamics. Using multiplicative dynamic programming principle along with the atomic structure of the state dynamics, we prove the existence and a characterization of optimal risk-sensitive control under geometric ergodicity of the state dynamics along with a smallness condition on the running cost.     

Parallelization of heterogeneous reactor calculations on a graphics processing unit

Parallelization is applied to the neutron calculations performed by the heterogeneous method on a graphics processing unit. The parallel algorithm of the modified TREC code is described. The efficiency of the parallel algorithm is evaluated.     

Synthesis and characterization of low bandgap copolymers based on indenofluorene and thiophene derivative

A series of low band gap, highly soluble alternating conjugated copolymers, comprised of 11,11,12,12‐tetrahexylindenofluorene and thiophene derivatives ( P1‐P4 ), were synthesized via Pd‐catalyzed Suzuki coupling reaction with very good yields. Described here are the synthesis, thermal, optical, and electrochemical properties of these new copolymers as potential new active materials for electronic and optoelectronic device applications. P1 and P2 have electron donating non‐π‐substituents with ethylenedioxy and propylenedioxy bridging the 3,3 positions of the cyclopentadithiophene groups; whereas P3 and P4 have electron withdrawing π‐substituents (carbonyl and pyrazine groups on P3 and P4 , respectively). For the main absorptions in UV‐vis spectrum, P1 and P2 displayed more red absorptions in comparison with P3 and P4 . Nevertheless, much suppressed quantum yields are exhibited by P3 and P4 . The behaviors of P3 can be attributed to the significant charge transfer interactions between the π‐substituents and the conjugated polymer backbone that leads to a less allowed optical transition between the ground and the lowest excited state. For P4 , the weak fluoresence might associate with energy transfer from indenofluorene to the low band gap thiophene‐pyrazinethiophene‐thiophene (T‐PT‐T) unit. In comparison with the corresponding polymers containing fluorene instead of indenofluorene, the use of indenofluorene exhibited mixed effects on the optical properties and improved solubility. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 5044–5056, 2009     

Convergence rates for rank-based models with applications to portfolio theory

We determine rates of convergence of rank-based interacting diffusions and semimartingale reflecting Brownian motions to equilibrium. Bounds on fluctuations of additive functionals are obtained using Transportation Cost-Information inequalities for Markov processes. We work out various applications to the rank-based abstract equity markets used in Stochastic Portfolio Theory. For example, we produce quantitative bounds, including constants, for fluctuations of market weights and occupation times of various ranks for individual coordinates. Another important application is the comparison of performance between symmetric functionally generated portfolios and the market portfolio. This produces estimates of probabilities of “beating the market”.