Non-local symmetries of first-order equations

It is shown how one can transform scalar first-order ordinarydifferential equations which admit non-local symmetries of theexponential type to integrable equations admitting canonicalexponential non-local symmetries. As examples we invoke theAbel equation of the second kind, the Riccati equation and naturalgeneralizations of these. Moreover, our method describes howa double reduction of order for a second-order ordinary differentialequation which admits a two-dimensional Lie algebra of generatorsof point symmetries can be affected if the second-order equationis first reduced in order once by a symmetry which does notspan an ideal of the two-dimensional Lie algebra.     

Magnon excitation by spin injection in thin Fe/Cr/Fe films

The technique of Brillouin light scattering is used to observe strong excitation of magnons in antiferromagnetically coupled trilayers of Fe/Cr/Fe at room temperature. The magnons are driven out of equilibrium by a microwave current applied in the trilayer through point contacts. The magnitude of the scattering intensity is investigated as a function of the magnon wave number and applied magnetic field. Confirming recent theoretical predictions, the observations provide strong evidence of electronic spin injection in the rf driving field.     

STATISTICAL ASPECTS OF SAMPLING POPULATIONS OF FOREST ELEPHANTS

ABSTRACT. Statistical issues relating to a number of sampling methods which can be used to obtain estimates of the number, or density, of forest elephants are discussed. The most widely used method, distance sampling, is briefly described. A recently proposed method, recce sampling, that reduces sampling effort is described and discussed. Adaptive sampling, often used when populations are sparse, patchy or clustered, is described and proposed as an alternative. Model‐based and design‐based inferences are compared and their use in sampling forest elephant populations is discussed. Further considerations that are required to estimate or monitor changes in elephant populations over time are outlined.