A 2-chain can interlock with an open 10-chain

It is an open problem, posed in \cite{SoCG}, to determine the minimal $k$ such that an open flexible $k$-chain can interlock with a flexible 2-chain. It was first established in \cite{GLOSZ} that there is an open 16-chain in a trapezoid frame that achieves interlocking. This was subsequently improved in \cite{GLOZ} to establish interlocking between a 2-chain and an open 11-chain. Here we improve that result once more, establishing interlocking between a 2-chain and a 10-chain. We present arguments that indicate that 10 is likely the minimum.Comment: 9 pages, 6 figure

Good Lamps Are the Best Police: Darkness Increases Dishonesty and Self-Interested Behavior

Darkness can conceal identity and encourage moral transgressions; it may also induce a psychological feeling of illusory anonymity that disinhibits dishonest and self-interested behavior regardless of actual anonymity. Three experiments provided empirical evidence supporting this prediction. In Experiment 1, participants in a room with slightly dimmed lighting cheated more and thus earned more undeserved money than those in a well-lit room. In Experiment 2, participants wearing sunglasses behaved more selfishly than those wearing clear glasses. Finally, in Experiment 3, an illusory sense of anonymity mediated the relationship between darkness and self-interested behaviors. Across all three experiments, darkness had no bearing on actual anonymity, yet it still increased morally questionable behaviors. We suggest that the experience of darkness, even when subtle, may induce a sense of anonymity that is not proportionate to actual anonymity in a given situation

On the propagation of plane waves above an impedance surface

The propagation of grazing incidence plane waves along a finite impedance boundary is investigated. A solution of the semi-infinite problem, where a harmonic motion, parallel to the boundary, is imposed along a line perpendicular to the boundary, is obtained. This solution consists of quasiplane waves, waves moving parallel to the boundary with amplitude and phase variations perpendicular to the boundary. Several approximations to the full solution are considered

Exploration of Resonant Continuum and Giant Resonance in the Relativistic Approach

Single-particle resonant-states in the continuum are determined by solving scattering states of the Dirac equation with proper asymptotic conditions in the relativistic mean field theory (RMF). The regular and irregular solutions of the Dirac equation at a large radius where the nuclear potentials vanish are relativistic Coulomb wave functions, which are calculated numerically. Energies, widths and wave functions of single-particle resonance states in the continuum for ^{120}Sn are studied in the RMF with the parameter set of NL3. The isoscalar giant octupole resonance of ^{120}Sn is investigated in a fully consistent relativistic random phase approximation. Comparing the results with including full continuum states and only those single-particle resonances we find that the contributions from those resonant-states dominate in the nuclear giant resonant processes.Comment: 16 pages, 2 figure