Changes in the size distribution of U.S. banks: 1960-2005

Banks and banking

New limits on the β+\beta^{+}EC and ECEC processes in 120^{120}Te

New limits on the double beta processes for $^{120}$Te have been obtained using a 400 cm$^3$ HPGe detector and a source consisting of natural Te0$_2$ powder. At a confidence level of 90% the limits are $0.19\times 10^{18}$ y for the $\beta^+$EC$(0\nu + 2\nu)$ transition to the ground state, $0.75\times 10^{18}$ y for the ECEC$(0\nu + 2\nu)$ transition to the first 2$^+$ excited state of $^{120}$Sn (1171.26 keV) and $(0.19-0.6)\times 10^{18}$ y for different ECEC($0\nu$) captures to the ground state of $^{120}$Sn.Comment: 9 pages, 4 figures; v2: minor change

Rational invariants of even ternary forms under the orthogonal group

In this article we determine a generating set of rational invariants of minimal cardinality for the action of the orthogonal group $\mathrm{O}_3$ on the space $\mathbb{R}[x,y,z]_{2d}$ of ternary forms of even degree $2d$. The construction relies on two key ingredients: On one hand, the Slice Lemma allows us to reduce the problem to dermining the invariants for the action on a subspace of the finite subgroup $\mathrm{B}_3$ of signed permutations. On the other hand, our construction relies in a fundamental way on specific bases of harmonic polynomials. These bases provide maps with prescribed $\mathrm{B}_3$-equivariance properties. Our explicit construction of these bases should be relevant well beyond the scope of this paper. The expression of the $\mathrm{B}_3$-invariants can then be given in a compact form as the composition of two equivariant maps. Instead of providing (cumbersome) explicit expressions for the $\mathrm{O}_3$-invariants, we provide efficient algorithms for their evaluation and rewriting. We also use the constructed $\mathrm{B}_3$-invariants to determine the $\mathrm{O}_3$-orbit locus and provide an algorithm for the inverse problem of finding an element in $\mathbb{R}[x,y,z]_{2d}$ with prescribed values for its invariants. These are the computational issues relevant in brain imaging.Comment: v3 Changes: Reworked presentation of Neuroimaging application, refinement of Definition 3.1. To appear in "Foundations of Computational Mathematics

Optimization of nanostructured permalloy electrodes for a lateral hybrid spin-valve structure

Ferromagnetic electrodes of a lateral semiconductor-based spin-valve structure are designed to provide a maximum of spin-polarized injection current. A single-domain state in remanence is a prerequisite obtained by nanostructuring Permalloy thin film electrodes. Three regimes of aspect ratios $m$ are identified by room temperature magnetic force microscopy: (i) high-aspect ratios of $m \ge 20$ provide the favored remanent single-domain magnetization states, (ii) medium-aspect ratios $m \sim 3$ to $m \sim 20$ yield highly remanent states with closure domains and (iii) low-aspect ratios of $m \le 3$ lead to multi-domain structures. Lateral kinks, introduced to bridge the gap between micro- and macroscale, disturb the uniform magnetization of electrodes with high- and medium-aspect ratios. However, vertical flanks help to maintain a uniformly magnetized state at the ferromagnet-semiconcuctor contact by domain wall pinning.Comment: revised version, major structural changes, figures reorganized,6 pages, 8 figures, revte

Resonant and antiresonant bouncing droplets

When placed onto a vibrating liquid bath, a droplet may adopt a permanent bouncing behavior, depending on both the forcing frequency and the forcing amplitude. The relationship between the droplet deformations and the bouncing mechanism is studied experimentally and theoretically through an asymmetric and dissipative bouncing spring model. Antiresonance effects are evidenced. Experiments and theoretical predictions show that both resonance at specific frequencies and antiresonance at Rayleigh frequencies play crucial roles in the bouncing mechanism. In particular, we show that they can be exploited for droplet size selection.Comment: 4 pages, 4 figures and 1 vide

Complexity and growth for polygonal billiards

We establish a relationship between the word complexity and the number of generalized diagonals for a polygonal billiard. We conclude that in the rational case the complexity function has cubic upper and lower bounds. In the tiling case the complexity has cubic asymptotic growth.Comment: 12 pages, 4 figure