Representations of finite groups are much simpler than those of larger ones, but they offer a model for the general theory and for that reason are very valuable as an introduction to the subject. The challenge is to present the material in such a way as to give some idea of techniques that might generalize, rather than use tricks that definitely work only for finite groups. Pursuing this goal s...

A study has been made on the parametric excitation of a nonlinear system with hardening springs. I n the parametric excitation of linear systems, the only subharmonic predicted i s a subharmonic of order 1/2. However, i n the parametric excitation of nonlinear systems, i t i s shown th I ? higher order subharmonics can exist, depending both on the amplitude and frequency of the parametric excit...

Under 5 years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 5.7 5 to 9 years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 5.7 10 to 14 years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 4.7 15 to 19 years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 11.3 20 to 24 years . . . . . . . . . . . . . . . . . . . . . . ...

In most bird species timing of breeding affects reproductive success whereby early breeding is favoured. In migratory species migration time, especially arrival at the breeding grounds, and breeding time are expected to be correlated. Consequently, migration time should also have fitness consequences. However, in contrast to breeding time, evidence for fitness consequences of migration time is ...

This summary of the state of the knowledge related to nutrient effects on spring ecosystems and biota draws from the proceeding seven chapters of this report. It represents a synthesis of the most important findings; greater details can be found within each of the chapters. This synthesis chapter is organized into three parts: 1) a summary of the “knowns” regarding nutrient effects on springs a...

We consider the spatiotemporal fluctuation of slip-link positions via the implementation of elastic slip-links. The level of description is similar to our previously proposed slip-link model, wherein we use the entanglement position in space as dynamic variables, and the number of Kuhn steps between entanglements. However, since it is a mean-field, single-chain description it has some relevance...

The relaxation in a spin transition compound is modeled on the basis of molecules interacting by the way of connecting springs and situated in a bidimensional open boundary hexagonal lattice. The switch of individual molecules is randomly checked using a standard Monte Carlo procedure. The switching probability depends on the energy gap between the two states in the absence of interactions and ...

The square and kagome lattices with nearest-neighbor springs of spring constant k are isostatic with a number of zero-frequency modes that scale with their perimeter. We analytically study the approach to this isostatic limit as the spring constant k' for next-nearest-neighbor bonds vanishes. We identify a characteristic frequency omega* approximately square root of k' and length l* approximate...

We consider a one-dimensional elastic string as a set of massless beads interacting through springs characterized by anisotropic elastic constants. The string, driven by an external force, moves in a medium with quenched disorder. We find that longitudinal fluctuations lead to nonlinear behavior in the equation of motion that is kinematically generated by the motion of the string. The strength ...

We consider a physical system constituted by a finite chain of point masses consecutively linked by linear springs and dashpots. At one of the end points acts an external control force aligned with the chain and the system is observable by the position of the other end point. We show that, whatever is the number of the point masses, if the sequence of the elastic constants is proportional to th...