Microscopic Description of Band Structure at Very Extended Shapes in the A ~ 110 Mass Region

Recent experiments have confirmed the existence of rotational bands in the A \~ 110 mass region with very extended shapes lying between super- and hyper-deformation. Using the projected shell model, we make a first attempt to describe quantitatively such a band structure in 108Cd. Excellent agreement is achieved in the dynamic moment of inertia J(2) calculation. This allows us to suggest the spin values for the energy levels, which are experimentally unknown. It is found that at this large deformation, the sharply down-sloping orbitals in the proton i_{13/2} subshell are responsible for the irregularity in the experimental J(2), and the wave functions of the observed states have a dominant component of two-quasiparticles from these orbitals. Measurement of transition quadrupole moments and g-factors will test these findings, and thus can provide a deeper understanding of the band structure at very extended shapes.Comment: 4 pages, 3 eps figures, final version accepted by Phys. Rev. C as a Rapid Communicatio

Coronal magnetic topology and the production of solar impulsive energetic electrons

We investigate two candidate solar sources or active regions (ARs) in association with a solar impulsive energetic electron (SIEE) event on 2002 October 20. The solar particle release (SPR) times of SIEEs are derived by using their velocity dispersion with consideration of the instrumental effect. It is found that there are double electron injections at the Sun. The low-energy (<13 keV) electron injection coincides with a C6.6 flare in AR10154 and is accompanied with prominent type III radio bursts rather than a stronger M1.8 flare in AR10160. The M1.8 flare produces, however, faint type III radio bursts. Whereas electrons of 25 to 300 keV are released 9 min later when a jet-like CME travels to 2.6 solar radii. We further examine the coronal magnetic configurations above the two ARs based on the potential field source surface (PFSS) model. It is found that open field lines, rooted in AR10154 and well connected to the Earth, provide escaping channels for energetic electrons. Only a small portion of magnetic fields are opened above AR10160, being responsible for the faint type III radio bursts. These lines are, however, not well connected, making it impossible for SIEEs detection by near-Earth spacecraft. The results appear to establish a physical link between coronal magnetic topology, formation of type III radio bursts, and production of SIEEs.Comment: A&A Letters, accepte

Melham's Conjecture on Odd Power Sums of Fibonacci Numbers

Ozeki and Prodinger showed that the odd power sum of the first several consecutive Fibonacci numbers of even order is equal to a polynomial evaluated at certain Fibonacci number of odd order. We prove that this polynomial and its derivative both vanish at $1$, and will be an integer polynomial after multiplying it by a product of the first consecutive Lucas numbers of odd order. This presents an affirmative answer to a conjecture of Melham.Comment: 15page

Enumeration of Corners in Tree-like Tableaux

In this paper, we confirm conjectures of Laborde-Zubieta on the enumeration of corners in tree-like tableaux and in symmetric tree-like tableaux. In the process, we also enumerate corners in (type $B$) permutation tableaux and (symmetric) alternative tableaux. The proof is based on Corteel and Nadeau's bijection between permutation tableaux and permutations. It allows us to interpret the number of corners as a statistic over permutations that is easier to count. The type $B$ case uses the bijection of Corteel and Kim between type $B$ permutation tableaux and signed permutations. Moreover, we give a bijection between corners and runs of size 1 in permutations, which gives an alternative proof of the enumeration of corners. Finally, we introduce conjectural polynomial analogues of these enumerations, and explain the implications on the PASEP.Comment: 26 pages, 11 figures. This is the final version for publicatio