Geometrical extensions of Wythoff’s game

In 1905 Bouton gave the complete theory of a two-player combinatorial game: the game of Nim. Two years later, Wythoff defined his game as “a modification” of the game of Nim. In this paper, we give the sets of the losing positions of geometrical extensions of Wythoff’s game, where allowed moves are considered according to a set of vectors (v₁,…,v_n). When n=3, we present algorithms and algebraic characterizations to determine the losing positions of such games. In the last part, we investigate a bounded version of Wythoff’s game, and give a polynomial way to decide whether a game position is losing or not.     

Current-induced two-level fluctuations in pseudo-spin-valve (Co/Cu/Co) nanostructures

Two-level fluctuations of the magnetization state of pseudo-spin-valve pillars Co(10 nm)/Cu(10 nm)/Co(30 nm) embedded in electrodeposited nanowires ( approximately 40 nm in diameter, 6000 nm in length) are triggered by spin-polarized currents of 10(7) A/cm(2) at room temperature. The statistical properties of the residence times in the parallel and antiparallel magnetization states reveal two effects with qualitatively different dependences on current intensity. The current appears to have the effect of a field determined as the bias field required to equalize these times. The bias field changes sign when the current polarity is reversed. At this field, the effect of a current density of 10(7) A/cm(2) is to lower the mean time for switching down to the microsecond range. This effect is independent of the sign of the current and is interpreted in terms of an effective temperature for the magnetization.     

Graphs whose choice number is equal to their chromatic number

A graph G is k-choosable if it admits a vertex-coloring whenever the colors allowed at each vertex are restricted to a list of length k. If χ denotes the usual chromatic number of G, we are interested in which kind of G is χ-choosable. This question contains a famous conjecture, which states that every line-graph is χ-choosable. We present some other classes of graphs that are χ-choosable; all these classes are related to claw-free graphs. © 1998 John Wiley & Sons, Inc. J Graph Theory 27: 87–97, 1998     

On Nordhaus–Gaddum type inequalities for the game chromatic and game coloring numbers

A seminal result by Nordhaus and Gaddum states that $2\sqrt{n}\le \chi \left(G\right)+\chi \left(\overline{G}\right)\le n+1$ for every graph $G$ of order $n$, where $\overline{G}$ is the complement of $G$ and $\chi$ is the chromatic number. We study similar inequalities for ${\chi }_g\left(G\right)$ and $co{l}_g\left(G\right)$, which denote, respectively, the game chromatic number and the game coloring number of $G$. Those graph invariants give the score for, respectively, the coloring and marking games on $G$ when both players use their best strategies.     

Absorption optique du niobium en couches minces entre 0,32 ET 5,5 eV. interpretation par la theorie des bandes d'energie

Niobium optical conductivity has been determined from reflexion and transmission data measured, at room temperature, on polycrystalline thin films in the 0.32–5.50 eV spectral range. The films have been deposited in ultra high vacuum and the measurements carried out in situ. Structures are observed at -.55, 2.3, 3.0 and 4.4 eV and tentatively identified with interband transitions in fairly good agreement with the band structure calculated by Mattheiss. In addition, we compare our results with recent experiments on niobium.     

Optimal impulsive transfers between real planetary orbits

This study presents the derivation of the equations necessary to establish a practical method for computing optimal transfers in the real case. It makes it possible to compute and use actual optimal transfers for advanced planning of preliminary mission analysis in place of the standard Hohmann transfers. This realizable solution includes the effects of the inclination and eccentricity of the orbits of the planets. It applies directly to cases in which a two-impulse transfer is the optimal solution and presents the results as functions of the corresponding idealized Hohmann transfers.     

The gyrokinetic water-bag modeling in toroidal geometry

The present paper addresses the gyrokinetic water-bag model in toroidal geometry. The previous works were focused on the water-bag concept in magnetized cylindrical plasmas. Here we report on the possibility to improve the water-bag model by taking into account the curvature and gradient drifts. After a presentation of the model, a local linear analysis with some approximations is performed. Interchange and ion temperature gradient instabilities are examined with this new gyro-water-bag model in order to show its ability and its theoretical interest in describing kinetic instabilities in toroidal geometry.