Boundedness and Dissipativity of Truncated Rotations on Uniform Planar Lattices

The finiteness of computer arithmetic can lead to some dramatic differences between the behaviour of a continuous dynamical system and a computer simulation. A thorough rigorous theoretical analysis of what may or what does happen is usually extremely difficult and to date little has been done even in relatively simple contexts. The comparative behaviour of a rotation mapping in the plane and on a uniform lattice in the plane is one such example. Simulations show that the rounding operator applied to a planar rotation mapping more or less preserves the qualitative behaviour of the original mapping, whereas the application of the truncation operator to a planar rotation can lead to quite different dynamical features. In this paper a theoretical justification of the properties of the planar rotation mappings under truncation to a, uniform integer lattice is provided, in particular properties of boundedness and dissipativity are investigated.     

Reflection of light by a slab containing electrically small dielectric spheres

Theoriginal and theenhanced Maxwell-Garnett estimates for the permittivity of a particulate medium are applied to the reflection of light by a composite dielectric slab. The reflection coefficients for incident s and p polarizations are calculated and some curves are plotted and discussed.     

Synthesis of some dibenzodiazepinone derivatives as potent and m2-selective antimuscarinic compounds

Two series of 5-[[4-[4-(dialkylamino)butyl]-l-cyclohexyl]acetyl], and 5-[(dialkylamino)acyl]-10,11-dihydro-5H- dibenzo[b,e][1,4]diazepin-11-ones were synthesized as potential m2-selective ligands 1,2. Their affinity and selectivity for the muscarinic cholinergic receptor m-AChR subtypes were determined. Replacing a nitrogen with CH in the piperidine ring of 5-[[4-[4-(dialkylamino)butyl]-l-piperidinyl]acetyl]-10,11-dihydro-5H-dibenzo-[b,e][1,4]diazepin-11-ones 3 significantly altered the affinity and selectivity to the muscarinic receptor subtypes.