Large Deviations, Guerra’s and A.S.S. Schemes, and the Parisi Hypothesis

We investigate the problem of computing $$\lim_{N \to \infty}\frac{1}{aN}\log EZ_N^a$$ for any value of a, where Z _N is the partition function of the celebrated Sherrington-Kirkpatrick (SK) model, or of some of its natural generalizations. This is a natural “large deviation” problem. Its study helps to get a fresh look at some of the recent ideas introduced in the area, and raises a number of natural questions. We provide a complete solution for a ≥ 0.     

Analysis on Mural Structures and Components of the Tombs in Liao Dynasty (A.D. 907–A.D. 1125)

The compositions of plaster, pigments, and binding medium were identified using micro-Raman spectroscopy, scanning electron microscopy coupled with energy-dispersive X-ray, and gas chromatograph-mass spectrometer. The results show that the plaster was calcium carbonate; the red color was ascribed to hematite; the blue pigment was ultramarine; the black pigment was carbon; and the yellow pigment was litharge. Animal glue as the binding medium was mixed in the pigments. Dissolved salt (mirabilite) was confirmed on the tomb passage. The mural detachment was detected with portable infrared thermal imager, and this damage resulted from the soil layer. This will serve as the basis for repairing the murals and reliable methods for identifying ancient murals.     

Transport and relaxation properties of isotopomeric hydrogen–helium binary mixtures. II. HD,D2, T2–He mixtures

The comprehensive comparison between calculated bulk non-equilibrium properties of hydrogen–helium isotopomeric mixtures and experiment that has previously been carried out for H₂–helium mixtures [2004, Molec. Phys., submitted] has been extended to mixtures of HD, D₂ and T₂ with ³He and ⁴He. For HD–⁴He mixtures, comparison is also made, where possible, with previous calculations of Köhler and Schaefer [1983, Physica A, 120, 185]. The phenomena examined herein include low temperature interaction second virial coefficients, binary diffusion and thermal conductivity coefficients, rotational relaxation, transport property field effects and flow birefringence. Scattering calculations have been carried out for the HD–He PES of Schaefer and Köhler [1985, Physica A, 129, 469], and for both the Köhler–Schaefer and Tao [1994, J. chem. Phys., 100, 4947] potential surfaces for the D₂–He and T₂–He interactions. Comparisons between calculated and experimental results for HD, D₂, T₂–He mixtures confirm the conclusion, reached earlier from the H₂–He comparisons, that these potential surfaces are very close to the correct one for the hydrogen–helium interaction, and that the small differences between them cannot be distinguished readily by measurements of bulk gas phenomena unless the attendant experimental uncertainties are better than ±0.3%.