As generalizations of the seniority model, four Hamiltonians are considered to investigate some of the physics associated with the pairing of parafermions of order p = 2. 2-particle and 4-particle states are explicitly constructed for HA ≡ −G A†A with A† ≡ 1 2 ∑ m>0 c † mc † −m and the distinct HC ≡ −G C†C with C† ≡ 1 2 ∑ m>0 c † −mc † m, and for the time-reversal invariant H(−) ≡ −G (A† − C†)(...

Precise definitions for different degrees of controllability for quantum systems are given, and necessary and sufficient conditions for each type of controllability are discussed. The results are applied to determine the degree of controllability for various atomic systems with degenerate energy levels and transition frequencies. Degrees of controllability for quantum systems and application to...

We show that in the worst case, Q(nd) sidedness queries are required to determine whether a set of n points in Rd is affinely degenerate, i .e . , whether it contains d + 1 points on a common hyperplane. This matches known upper bounds. We give a straightforward adversary argument, based on the explicit construction of a point set containing Q(nd) “collapsible” simplices, any one of which can b...

Before it becomes a sensitive probe of the Epoch of Reionization, the Dark Ages, and fundamental physics, 21 cm tomography must successfully contend with the issue of foreground contamination. Broadband foreground sources are expected to be roughly four orders of magnitude larger than any cosmological signals, so precise foreground models will be necessary. Such foreground models often contain ...

We present deep optical observations of the gravitational lens system CLASS B0218+357 from which we derive an estimate for the Hubble Constant (H0) Extensive radio observations using the VLA, MERLIN, the VLBA and VLBI have reduced the degeneracies between H0 and the mass model parameters in this lens to one involving only the position of the radioquiet lensing galaxy with respect to the lensed ...

The spectra of a particular class of PT symmetric eigenvalue problems has previously been studied, and found to have an extremely rich structure. In this paper we present an explanation for these spectral properties in terms of quantisation conditions obtained from the complex WKB method. In particular, we consider the relation of the quantisation conditions to the reality and positivity proper...

The distance-3 cyclic lowest-density MDS array code (called the C-Code) is a good candidate for RAID 6 because of its optimal storage efficiency, optimal update complexity, optimal length, and cyclic symmetry. In this paper, the underlying connections between C-Codes (or quasi-C-Codes) and starters in group theory are revealed. It is shown that each C-Code (or quasi-C-Code) of length 2n can be ...

In this paper, we propose a pair of shape features for shape-similarity search of 3D polygonal-mesh models. The shape features are extension of the D2 shape functions proposed by Osada et al. [Osada01, Osada02]. Our proposed shape features are tolerant of topological variations and geometrical degeneracies. Our shape feature is also invariant to similarity transformation. Experiments showed tha...

We prove sharp L estimates for oscillatory integral and Fourier integral operators for which the associated canonical relation C ⊂ T ∗ΩL × T ∗ΩR projects to T ∗ΩL and to T ∗ΩR with corank one singularities of type ≤ 2. This includes two-sided cusp singularities. Applications are given to operators with one-sided swallowtail singularities such as restricted X-ray transforms for well-curved line ...

Variable-temperature NMR spectroscopy is probably the most convenient and sensitive technique to monitor changes in molecular structure in solution. Rearrangements that are rapid on the NMR time-scale exhibit simplified spectra, whereby non-equivalent nuclear environments yield time-averaged resonances. At lower temperatures, when the rate of exchange is sufficiently reduced, these degeneracies...