The São Paulo School of Advanced Sciences (ESPCA) on Recent Developments in Synchrotron Radiation

The São Paulo School of Advanced Sciences (ESPCA) on Recent Developments in Synchrotron Radiation was held July 13–24, 2015, at the Brazilian Synchrotron Light Laboratory (LNLS) in Campinas, Brazil. The school was attended by 96 students, 48 from Brazil and 48 from 17 different countries. A total of 27 different nationalities were represented in this 12-day school. In addition, 22 lecturers presented 34 talks.     

The additivity of the η-invariant. The case of a singular tangential operator

We prove the decomposition formula for the -invariant of the compatible Dirac operator on a closed manifoldM which is a sum of two submanifolds with common boundary.Research partially supported by NSF     

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.     

Origin of the E.S.R. hyperfine anisotropy and the cos2 θ rule of the β-fluorine couplings

The origin of the hyperfine couplings of β-fluorine nuclei in free radicals has been studied using the hyperfine tensors determined for and in single crystals. The direction of the maximum principal element of the β-fluorine coupling tensor in was found to be very close to the direction of the maximum overlap of the fluorine 2p π orbital with the half-filled carbon 2p π orbital. This means that the spin density in the fluorine 2p π orbital is mainly due to the direct overlap with the carbon 2p π orbital and the contributions from the hyperconjugation and the spin polarization mechanisms are less important. The cos²θ rule, B ₀ + B cos²θ, for the β-fluorine coupling tensor was also derived from the conformational dependence of the overlap integral. Using the ratio of B/B ₀ calculated from the overlap integral together with the observed hyperfine tensor for , the absolute values of B ₂ and B were determined and results were applied to the β-fluorine coupling tensor of the rotating CF₃ group in . The calculated tensor is in very good agreement with the one observed.     

The mass of the isodoublet of the 2^1S0 meson nonet revisited

In the qq quark model, the states π（1300）, η（1295） and η（1475） are assigned as the 2^1S0 meson nonet. The mass of the isodoublet remains interesting and needs further confirmation in experiments. This paper employs the phenomenological trajectory on the （N, M^2）-plot and meson meson mixing methods to calculate the mass of this state, the calculated results are 1341 MeV and 1311.58 ± 59 MeV respectively. These predictions can be compared with experiments in the future.[第一段]     

The K-Orbits, Identities, and Classification of Four-Dimensional Homogeneous Spaces with the Group of Poincaré and de Sitter Transforms

The method of orbits traditionally applied to geometric quantization problems is used to study homogeneous spaces. Based on the proposed classification of the orbits of co-adjoint representation (K-orbits), a classification of homogeneous spaces is constructed. This classification allows one, in particular, to point out the explicit form of identities – functional relations between the transform-group generators – which are of great importance in applied problems (e.g., in the theory of separation of variables). All four-dimensional homogeneous spaces with the group of Poincaré and de Sitter transforms are classified and all independent identities on these spaces are given in explicit form.     

The molecular systems composed of the charmed mesons in the H\bar{S}+h.c. doublet

We study the possible heavy molecular states composed of a pair of charm mesons in the H and S doublets. Since the P-wave charm-strange mesons D _s0(2317) and D _s1(2460) are extremely narrow, the future experimental observation of the possible heavy molecular states composed of $D_{s}/D_{s}^{\ast}$ and D _s0(2317)/D _s1(2460) may be feasible if they really exist. Especially the possible J ^PC =1^?? states may be searched for via the initial state radiation technique.     

‘Factors of ignorance’ and the rationalized M.K.S.A. system of units

An attempt is made, by means of an allusive (rather than a systematic) historical account of the development of the subject, to exhibit the essentially unique character of the rationalized M.K.S.A. system of units. The establishment of this system involved one arbitrary decision—the determination to retain unaltered the size of the previously accepted unit of current. Thereafter, any choice of derived units, other than the choice actually made, would have destroyed the basic symmetry of the formulation.     

Large field renormalization. I. The basic step of the ℝ operation

We construct the renormalization operation of the expressions connected with the large field regions. This operation, denoted by , removes the main obstacle to prove the ultraviolet stability of four-dimensional gauge field theories. The proof will be completed in the second part of this paper.Research supported in part by the National Science Foundation under Grant DMS-86 02207