Assessing publically financed metrology expenditure against economic parameters

The objective of this paper is to provide an economic perspective to those involved in public financing of the national metrology infrastructure. Whereas justifications for subsidising the national metrological activities are often historically biased, we raise the importance of economic considerations, which could be used during prioritisation. The expenditure in measurement and metrology infrastructure of European countries are compared to economic indicators for quality of life. Various proxies are used, such as measuring instruments sale (for measurement infrastructure) and data from the BIPM’s KCDB (as a proxy for national standards). As the EU Internal Market also holds for the provision of metrological services, the paper exposes possible trends regarding public financing to the sector.

UV-radiation-induced electron emission by hormones. Hypothesis for specific communication mechanisms

The highlights of recently observed electron emission from electronically excited sexual hormones (17β-estradiol, progesterone, testosterone) and the phytohormone genistein in polar media are briefly reviewed. The electron yield, Q(e_aq⁻), dependence from substrate concentration, hormone structure, polarity of solvent, absorbed energy and temperature are discussed. The hormones reactivity with e_aq⁻ and efficiency in electron transfer ensure them the ability to communicate with other biological systems in an organism. A hypothesis is presented for the explanation of the mechanisms of the distinct recognition of signals transmitted by electrons, originating from different types of hormones to receiving centres. Biological consequences of the electron emission in respect to cancer are mentioned.     

Random holomorphic iterations and degenerate subdomains of the unit disk

Given a random sequence of holomorphic maps of the unit disk to a subdomain , we consider the compositions

The sequence is called the iterated function system coming from the sequence We prove that a sufficient condition on the domain for all limit functions of any to be constant is also necessary. We prove that the condition is a quasiconformal invariant. Finally, we address the question of uniqueness of limit functions.

     

Markov interlacing property for exponential polynomials

Let Un be an extended Tchebycheff system on the real line. Given a point , where x₁<?<xn, we denote by the polynomial from Un, which has zeros x₁,…,xn. (It is uniquely determined up to multiplication by a constant.) The system Un has the Markov interlacing property (M) if the assumption that and interlace implies that the zeros of and interlace strictly, unless . We formulate a general condition which ensures the validity of the property (M) for polynomials from Un. We also prove that the condition is satisfied for some known systems, including exponential polynomials and . As a corollary we obtain that property (M) holds true for Müntz polynomials , too.     

Mixed-mode oscillations in a three time-scale model for the dopaminergic neuron

Mixed-mode dynamics is a complex type of dynamical behavior that has been observed both numerically and experimentally in numerous prototypical systems in the natural sciences. The compartmental Wilson-Callaway model for the dopaminergic neuron is an example of a system that exhibits a wide variety of mixed-mode patterns upon variation of a control parameter. One characteristic feature of this system is the presence of multiple time scales. In this article, we study the Wilson-Callaway model from a geometric point of view. We show that the observed mixed-mode dynamics is caused by a slowly varying canard structure. By appropriately transforming the model equations, we reduce them to an underlying three-dimensional canonical form that can be analyzed via a slight adaptation of the approach developed by M. Krupa, N. Popovic, and N. Kopell (unpublished).     

A geometric analysis of front propagation in a family of degenerate reaction-diffusion equations with cutoff

We investigate the effects of a Heaviside cutoff on the dynamics of traveling fronts in a family of scalar reaction-diffusion equations with degenerate polynomial potential that includes the classical Zeldovich equation. We prove the existence and uniqueness of front solutions in the presence of the cutoff, and we derive the leading-order asymptotics of the corresponding propagation speed in terms of the cutoff parameter. For the Zeldovich equation, an explicit solution to the equation without cutoff is known, which allows us to calculate higher-order terms in the resulting expansion for the front speed; in particular, we prove the occurrence of logarithmic (switchback) terms in that case. Our analysis relies on geometric methods from dynamical systems theory and, in particular, on the desingularization technique known as ‘blow-up.’     

Stability properties of autonomous homogeneous polynomial differential systems

A geometrical approach is used to derive a generalized characteristic value problem for dynamic systems described by homogeneous polynomials. It is shown that a nonlinear homogeneous polynomial system possesses eigenvectors and eigenvalues, quantities normally associated with a linear system. These quantities are then employed in studying stability properties. The necessary and sufficient conditions for all forms of stabilities characteristic of a two-dimensional system are provided. This result, together with the classical theorem of Frommer, completes a stability analysis for a two-dimensional homogeneous polynomial system.