Computations of cuspidal cohomology of congruence subgroups of SL(3, Z)

Algorithms are presented which find a basis of the vector space of cuspidal cohomology of certain congruence subgroups of SL(3, $\text{Z}$) and which determine the action of the Hecke operators on this space. These algorithms were implemented on a computer. Four pairs of cuspidal classes were found with prime level less than 100. Tables are given of the eigenvalues of the first few Hecke operators on these classes.     

A Conjecture Concerning the Spectrum of a Sentence

We give a plausible-sounding conjecture involving the number of n-equivalence classes of structures of size m which would imply that the complement of a spectrum is also a spectrum. Mathematics Subject Classification : 03B10, 03D15, 68Q15.     

The shape of axisymmetric rotating fluid

The equations for axisymmetric self-gravitating rotating fluid have been studied extensively since Poincaré. The model derives its primary interest from celestial mechanics, where it can be used to study the geometry of stars and planets. Existence of a solution for both the compressible and the incompressible cases is known. The smoothness of the boundary of the fluid is studied, and, in particular, it is proved that the rotating fluid has at most a finite number of rings.     

Separating chemical shift and quadrupolar anisotropies via multiple-quantum NMR spectroscopy

Chemical shift anisotropy (CSA) has been an invaluable probe of structure and dynamics for a variety of systems in NMR spectroscopy. Unfortunately, the presence of strong quadrupolar couplings has severely limited the ability to measure CSA in nuclei with spins I > 1/2. Here we show that these two interactions can be refocused at different times in a 2D multiple-quantum NMR experiment on polycrystalline samples. Combining this experiment with appropriate affine transformations allows these interactions to be cleanly separated into orthogonal dimensions. The 1D projection onto each axis can be fit to extract the respective principal tensor components. These components can then be used to fit the 2D spectrum for the relative orientation between the CSA and quadrupolar-coupling tensors. The necessary affine transformation parameters are given for all possible I values. Illustrative examples of spectra and analyses are given for 63Cu in K3[Cu(CN)4], 59Co in K3[Co(CN)6], and 87Rb in RbCrO4.     

Direct Sums of Mod p Characters of Gal and the Homology of GL(n, ℤ)

The paper classifies multilincnr algebras, known as comlrans algebras, that are determined by pairs of matrices and have dimensions which are less than or equal to two. The comtrans algebras are isomophic if and only if the corresponding pairs of matrices arc multiplicatively cogredient by a matrix M.     

Exploring the low-Z shore of the island of inversion at n=19

The technique of invariant mass spectroscopy has been used to measure, for the first time, the ground state energy of neutron-unbound (28)F, determined to be a resonance in the (27)F+n continuum at 220(50) keV. States in (28)F were populated by the reactions of a 62 MeV/u (29)Ne beam impinging on a 288 mg/cm(2) beryllium target. The measured (28)F ground state energy is in good agreement with USDA/USDB shell model predictions, indicating that pf shell intruder configurations play only a small role in the ground state structure of (28)F and establishing a low-Z boundary of the island of inversion for N=19 isotones.