Sets of permutations that generate the symmetric group pairwise

The paper contains proofs of the following results. For all sufficiently large odd integers n, there exists a set of ²n−1 permutations that pairwise generate the symmetric group Sn. There is no set of ²n−1+1 permutations having this property. For all sufficiently large integers n with n≡2mod4, there exists a set of ²n−2 even permutations that pairwise generate the alternating group An. There is no set of ²n−2+1 permutations having this property.     

Connectedness of the Isospectral Manifold for One-Dimensional Half-Line Schrödinger Operators

Journal of Statistical Physics - Let V 0be a real-valued function on [0,∞) and V∈L 1([0,R]) for all R&;gt;0 so that H(V 0)=? $\frac{{d^2 }}{{dx^2 }}$ +V 0in L 2([0,∞))...     

The existence of equilibria in certain games,separation for families of convex functions and a theorem of Borsuk-Ulam type

The existence of a Nash equilibrium in the undiscounted repeated two-person game of incomplete information on one side is established. The proof depends on a new topological result resembling in some respect the Borsuk-Ulam theorem.     

A Hilbert Space Approach to Bounded Analytic Interpolation

We generalize several results on bounded analytic interpolation of Fitzgerald and Horn, which work by majorization by positive definite kernels, to the cases of several complex variables and operator-valued interpolation. Using a lemma of Kolmogorov, we complement a simplification due to Szafraniec in the proofs of the theorems. Received: November 21, 2006. Accepted: August 03, 2007.     

Size of the interpolated cation and hole carrier density: two key parameters for the optimisation of colossal magnetoresistive properties of Pr-based manganites

The exploration of the magnetic and transport properties of four series of manganese perovskites, Pr_0.7Ca_0.34−xA_xMnO_3−δ (A=Sr, Ba), Pr_0.7−xLa_xCa_0.3 MnO_3−δ and Pr_0.66Ca_0.34−x Sr_xMnO_3−δ has allowed four phases with colossal magnetoresistive (CMR) properties to be isolated: Pr_0.7Ca_0.25Sr_0.025MnO_3−δ and Pr_0.66Ca_0.26Sr_0.08MnO_3−δ that exhibit a variation of resistance of 2.5. 10⁷% and 10⁹% at μ₀ H=5 T for T=88 K and 50 K respectively, Pr_0.58La_0.12Ca_0.3 MnO_3−δ that exhibits a variation of 6.10⁶% for μ₀ H=5 T at T=80 K and Pr_0.7Ba_0.025Ca_0.275MnO_3−δ for which a resistance variation of 5.10⁹%, at T=50 K, for μ₀ H=5 T is evidenced. for each compound of this series except the barium phase, one observes that the temperature T_max, which corresponds to the resistance maximum on the R(T) curves in zero magnetic field, increases dramatically as the mean size of the interpolated cations increases, and that the CMR effect correlatively decreases dramatically. The comparison of the two series Pr_0.7Ca_0.3−xSr_xMnO_3−δ and Pr_0.66Ca_0.34−xSr_xMnO_3−δ shows also the crucial role of the hole carrier density: for a same mean ionic radius of the interpolated cation T_max is decreased of about 50 K by introducing 0.034 hole per Mn mole.     

Investigation of the photothermally modulated ferromagnetic resonance signal from magnetostatic modes in yttrium iron garnet films

The conventional and photothermally modulated (PM) ferromagnetic resonance (FMR) of magnetostatic modes (MSM) in yttrium iron garnet (YIG) films have been investigated as a function of temperature. Approaching the ferrimagnetic transition at T _c=560 K a strong enhancement of the PM-FMR signal amplitude is observed which is accompanied by a change of the signal shape. The observations are discussed in the framework of a model that takes into account the temperature derivatives of those quantities that contribute to the high-frequency susceptibility. At temperatures still below T _c a paramagnetic line emerges. The MSM disappear in a state of finite magnetization which is explained on the basis of damping of the MSM being important in the vicinity of the magnetic phase transition. Additionally, frequency and power dependent measurements are presented and the imaging ability of PM-FMR is demonstrated.