The Heun equation and the Calogero-Moser-Sutherland system V: generalized Darboux transformations

We obtain isomonodromic transformations for Heun's equation by generalizing Darboux transformation, and we find pairs and triplets of Heun's equation which have the same monodromy structure. By composing generalized Darboux transformations, we establish a new construction of the commuting operator which ensures finite-gap property. As an application, we prove conjectures in part III.Comment: 24 page

Comparative study of macroscopic quantum tunneling in Bi_2Sr_2CaCu_2O_y intrinsic Josephson junctions with different device structures

We investigated macroscopic quantum tunneling (MQT) of Bi$_2$Sr$_2$CaCu$_2$O$_y$ intrinsic Josephson junctions (IJJs) with two device structures. One is a nanometer-thick small mesa structure with only two or three IJJs and the other is a stack of a few hundreds of IJJs on a narrow bridge structure. Experimental results of switching current distribution for the first switching events from zero-voltage state showed a good agreement with the conventional theory for a single Josephson junction, indicating that a crossover temperature from thermal activation to MQT regime for the former device structure was as high as that for the latter device structure. Together with the observation of multiphoton transitions between quantized energy levels in MQT regime, these results strongly suggest that the observed MQT behavior is intrinsic to a single IJJ in high-$T_c$ cuprates, independent of device structures. The switching current distribution for the second switching events from the first resistive state, which were carefully distinguished from the first switchings, was also compared between two device structures. In spite of the difference in the heat transfer environment, the second switching events for both devices were found to show a similar temperature-independent behavior up to a much higher temperature than the crossover temperature for the first switching. We argue that it cannot be explained in terms of the self-heating owing to dissipative currents after the first switching. As possible candidates, the MQT process for the second switching and the effective increase of electronic temperature due to quasiparticle injection are discussed.Comment: 10pages, 7figures, submitted to Phys. Rev.

Capital process and optimality properties of a Bayesian Skeptic in coin-tossing games

We study capital process behavior in the fair-coin game and biased-coin games in the framework of the game-theoretic probability of Shafer and Vovk (2001). We show that if Skeptic uses a Bayesian strategy with a beta prior, the capital process is lucidly expressed in terms of the past average of Reality's moves. From this it is proved that the Skeptic's Bayesian strategy weakly forces the strong law of large numbers (SLLN) with the convergence rate of O(\sqrt{\log n/n})$ and if Reality violates SLLN then the exponential growth rate of the capital process is very accurately described in terms of the Kullback divergence between the average of Reality's moves when she violates SLLN and the average when she observes SLLN. We also investigate optimality properties associated with Bayesian strategy

Heun's equation, generalized hypergeometric function and exceptional Jacobi polynomial

We study Heun's differential equation in the case that one of the singularities is apparent. In particular we conjecture a relationship with generalized hypergeometric differential equation and establish it in some cases. We apply our results to exceptional Jacobi polynomials.Comment: 15 pages; validity of the conjecture was extende

A study of uncertainties in the sulfate distribution and its radiative forcing associated with sulfur chemistry in a global aerosol model

The direct radiative forcing by sulfate aerosols is still uncertain, mainly because the uncertainties are largely derived from differences in sulfate column burdens and its vertical distributions among global aerosol models. One possible reason for the large difference in the computed values is that the radiative forcing delicately depends on various simplifications of the sulfur processes made in the models. In this study, therefore, we investigated impacts of different parts of the sulfur chemistry module in a global aerosol model, SPRINTARS, on the sulfate distribution and its radiative forcing. Important studies were effects of simplified and more physical-based sulfur processes in terms of treatment of sulfur chemistry, oxidant chemistry, and dry deposition process of sulfur components. The results showed that the difference in the aqueous-phase sulfur chemistry among these treatments has the largest impact on the sulfate distribution. Introduction of all the improvements mentioned above brought the model values noticeably closer to in-situ measurements than those in the simplified methods used in the original SPRINTARS model. At the same time, these improvements also brought the computed sulfate column burdens and its vertical distributions into good agreement with other AEROCOM model values. The global annual mean radiative forcing due to the direct effect of anthropogenic sulfate aerosol was thus estimated to be −0.26 W m<sup>−2</sup> (−0.30 W m<sup>−2</sup> with a different SO<sub>2</sub> inventory), whereas the original SPRINTARS model showed −0.18 W m<sup>−2</sup> (−0.21 W m<sup>−2</sup> with a different SO<sub>2</sub> inventory). The magnitude of the difference between original and improved methods was approximately 50% of the uncertainty among estimates by the world's global aerosol models reported by the IPCC-AR4 assessment report. Findings in the present study, therefore, may suggest that the model differences in the simplifications of the sulfur processes are still a part of the large uncertainty in their simulated radiative forcings