Various interpretations of the notion of a trend in the context of global warming are discussed, contrasting the difference between viewing a trend as the deterministic response to an external forcing and viewing it as a slow variation which can be separated from the background spectral continuum of long-range persistent climate noise. The emphasis in this paper is on the latter notion, and a ...

We use a mathematical model to show that if symmetric stem cell division is regulated by differentiated cells, then changes in the population dynamics of the differentiated cells can lead to changes in the population dynamics of the stem cells. More precisely, the relative fitness of the stem cells can be affected by modifying the death rate of the differentiated cells. This result is interesting ...

A stochastic theory for the toppling activity in sandpile models is developed, based on a simple mean-field assumption about the toppling process. The theory describes the process as an anti-persistent Gaussian walk, where the diffusion coefficient is proportional to the activity. It is formulated as a generalization of the Itˆo stochastic differential equation with an anti-persistent fractional ...

In this paper, we investigate the learning experiences, beliefs and motivations of students in classes where the mathematics teachers have received support for using inquiry-based learning activities. Data were collected from 248 students in the age-range 11–16 using electronic questionnaires. Our results show that key features of inquiry-based mathematics were only moderately reflected in these ...

The mass balance of Antarctica is one of the crucial factors for determining sea-level change in a warming climate. The marginal zones of the continent, namely the ice shelves, are most sensitive to climate change. During the 2009/10 austral summer an extensive glaciological field campaign was carried out on Fimbulisen, an ice shelf in East Antarctica, to investigate its recent surface mass balance. ...

An ideal of polynomials is symmetric if it is closed under permutations of variables. We relate general symmetric ideals to the so called Specht ideals generated by all Specht polynomials of a given shape. We show a connection between the leading monomials of polynomials in the ideal and the Specht polynomials contained in the ideal. This provides applications in several contexts. Most notably, this ...

Symmetries and the corresponding fields of differential invariants of the inviscid flows on a curve are given. Their dependence on thermodynamic states of media is studied, and a classification of thermodynamic states is given.

Many methods for reducing and simplifying differential equations are known. They provide various generalizations of the original symmetry approach of Sophus Lie. Plenty of relations between them have been noticed and in this note a unifying approach will be discussed. It is rather close to the differential constraint method, but we make this rigorous basing on recent advances in compatibility ...

The maximal contact symmetry dimensions for scalar ODEs of order ≥ 4 and vector ODEs of order ≥ 3 are well known. Using a Cartan-geometric approach, we determine for these ODEs the next largest realizable (submaximal) symmetry dimension. Moreover, finer curvature-constrained submaximal symmetry dimensions are also classified.

The arithmetic mean/geometric mean inequality (AM/GM inequality) facilitates classes of nonnegativity certificates and of relaxation techniques for polynomials and, more generally, for exponential sums. Here, we present a first systematic study of the AM/GM-based techniques in the presence of symmetries under the linear action of a finite group. We prove a symmetry-adapted representation theorem and ...