The Magnus–Derek game

AbstractWe introduce a new combinatorial game between two players: Magnus and Derek. Initially, a token is placed at position 0 on a round table with n positions. In each round of the game Magnus chooses the number of positions for the token to move, and Derek decides in which direction, + (clockwise) or − (counterclockwise), the token will be moved. Magnus aims to maximize the total number of positions visited during the course of the game, while Derek aims to minimize this quantity.We define f∗(n) to be the eventual size of the set of visited positions when both players play optimally. We prove a closed form expression for f∗(n) in terms of the prime factorization of n, and provide algorithmic strategies for Magnus and Derek to meet this bound.We note the relevance of the game for a mobile agent exploring a ring network with faulty sense of direction, and we pose variants of the game for future study

AN URGENT TRACHEOTOMIA

No abstrac

Detailed comparison of the pp -> \pi^+pn and pp -> \pi^+d reactions at 951 MeV

The positively charged pions produced in proton-proton collisions at a beam momentum of 1640 MeV/c were measured in the forward direction with a high resolution magnetic spectrograph. The missing mass distribution shows the bound state (deuteron) clearly separated from the $pn$ continuum. Despite the very good resolution, there is no evidence for any significant production of the $pn$ system in the spin-singlet state. However, the $\sigma(pp\to \pi^+pn)/\sigma(pp\to \pi^+d)$ cross section ratio is about twice as large as that predicted from $S$-wave final-state-interaction theory and it is suggested that this is due to $D$-state effects in the $pn$ system.Comment: 8 pages, 3 figure

Recoil Polarization Measurements of the Proton Electromagnetic Form Factor Ratio to Q^2 = 8.5 GeV^2

Among the most fundamental observables of nucleon structure, electromagnetic form factors are a crucial benchmark for modern calculations describing the strong interaction dynamics of the nucleon's quark constituents; indeed, recent proton data have attracted intense theoretical interest. In this letter, we report new measurements of the proton electromagnetic form factor ratio using the recoil polarization method, at momentum transfers Q2=5.2, 6.7, and 8.5 GeV2. By extending the range of Q2 for which GEp is accurately determined by more than 50%, these measurements will provide significant constraints on models of nucleon structure in the non-perturbative regime

Fast optoelectric printing of plasmonic nanoparticles into tailored circuits

Plasmonic nanoparticles are able to control light at nanometre-scale by coupling electromagnetic fields to the oscillations of free electrons in metals. Deposition of such nanoparticles onto substrates with tailored patterns is essential, for example, in fabricating plasmonic structures for enhanced sensing. This work presents an innovative micro-patterning technique, based on optoelectic printing, for fast and straightforward fabrication of curve-shaped circuits of plasmonic nanoparticles deposited onto a transparent electrode often used in optoelectronics, liquid crystal displays, touch screens, etc. We experimentally demonstrate that this kind of plasmonic structure, printed by using silver nanoparticles of 40 nm, works as a plasmonic enhanced optical device allowing for polarized-color-tunable light scattering in the visible. These findings have potential applications in biosensing and fabrication of future optoelectronic devices combining the benefits of plasmonic sensing and the functionality of transparent electrodes

Consonance and Cantor set-selectors

It is shown that every metrizable consonant space is a Cantor set-selector. Some applications are derived from this fact, also the relationship is discussed in the framework of hyperspaces and Prohorov spaces.peer-reviewe

Search for η\eta-mesic nuclei in recoil-free transfer reaction

We have studied the reaction $p+{^{27}Al}\to {^3{He}}+p+\pi^-+X$ at recoil-free kinematics. An $\eta$ meson possibly produced in this reaction would be thus almost at rest in the laboratory system and could therefore be bound with high probability, if nuclear $\eta$ states exist. The decay of such a state through the $N^*(1535)$ resonance would lead to a proton-$\pi^-$ pair emitted in opposite directions. For these conditions we find some indication of such a bound state. An upper limit of $\approx$ 0.5 nb is found.Comment: 3 figure