The compositional inverse of a class of permutation polynomials over a finite field

A new class of bilinear permutation polynomials was recently identified. In this note we determine the class of permutation polynomials which represents the functional inverse of the bilinear class.

Air target detection via bistatic radar based on LEOS communication signals

The paper discusses the bistatic radar parameters for the case when the transmitter is a satellite emitting communication signals. The model utilises signals from an Iridium-like low earth orbiting satellite system. The maximum detection range, when thermal noise-limited, is discussed at the theoretical level and these results are compared with experimentation. Satellite-radar signal levels and the power of ground reflections are evaluated.

Twisting and planarization in push-pull ethylenes

As determined by X-ray crystallography, Meldrum's acid derivatives 8–19 feature dihedral angles around the central CC double bonds between 3 and 83°. Hydrogen bonds between substituents RHN and the carbonyl groups favour near-planarity. Sterically demanding substituents favour large dihedral angles and zwitterionic structures as in formula 20. AM1 calculations of the structures are in excellent agreement with the experimental X-ray data, provided a dielectric field is incorporated (?= 40). This can be ascribed to the highly polar (zwitterionic) nature of the molecules. It is further predicted that all these molecules, including those that are stabilised in a planar form by intramolecular hydrogen bonds, undergo rapid rotation about the central CC bonds at room temperature. DFT calculations incorporating a dielectric field model (PCM) are in excellent agreement with the near-perpendicular arrangement of the alkene moiety in 19.

Mating behavior of Trissolcus basalis (Wollaston) (Hymenoptera : Scelionidae): Potential for outbreeding in a predominantly inbreeding species

The mating behavior of the quasi-gregarious egg parasitoid Trissolcus basalis (Wollaston) was investigated under field conditions. Trissolcus basalis has female-biased sex ratios and is a protandrous species, with males emerging 1-2 days before females. Males competed aggressively for control of the egg mass, with one male assuming dominance and control of the egg mass, although changes in dominance occurred at least once on each egg mass observed. Typical mating behavior involved the dominant male mating his sisters immediately upon their emergence from the egg mass. These behaviors are characteristic of an inbreeding species that manifests local mate competition. However, several aspects of the mating behavior of T. basalis are inconsistent with that of an inbreeding species. Over 18% of emerging females were not mated by the dominant male upon emergence, 13% of females were not observed to be mated at all and may have left their natal site as virgins, 25% of females were mated multiple times and sometimes by multiple males, females remained near the natal site for up to several hours after emergence before emigrating, and males dispersed away from the natal site during female emergence. Trissolcus basalis may be a predominantly inbreeding species but its emergence and mating behavior suggest that low-frequency outbreeding is also likely to occur.

Magnetic-field-induced superconductivity in layered organic molecular crystals with localized magnetic moments

l-(BETS)2FeCl4 undergoes transitions from an antiferromagnetic insulator to a metal and then to a superconductor as a magnetic field is increased. We use a Hubbard-Kondo model to clarify the role of the Fe31 magnetic ions in these phase transitions. In the high-field regime, the magnetic field acting on the electron spins is compensated by the exchange field He due to the magnetic ions. We show how He can be extracted from the observed splitting of the Shubnikov–de Haas frequencies. We predict the field range for field-induced superconductivity in other materials.