Achieving or exceeding maximum available feedback

A feedback system for control or electronics should have high loop gain, so that its output is close to its desired state, and the effects of changes in the system and of disturbances are minimised. Bode proposed a method for single loop feedback systems to obtain the maximum available feedback, defined as the largest possible loop gain over a bandwidth pertinent to the system, with appropriate gain and phase margins. The method uses asymptotic approximations, and this paper describes some novel adjustments to the asymptotes, so that the final system often exceeds the maximum available feedback. The implementation of the method requires the cascading of a series of lead-lag element. This paper describes a new way to determine how many elements should be used.

Maximum induced subgraph of a recursive circulant

The recursive circulant RC(2(n), 4) enjoys several attractive topological properties. Let max_epsilon(G) (m) denote the maximum number of edges in a subgraph of graph G induced by m nodes. In this paper, we show that max_epsilon(RC(2n,4))(m) = Sigma(i)(r)=(0)(p(i)/2 + i)2(Pi), where p(0) > p(1) > ... > p(r) are nonnegative integers defined by m = Sigma(i)(r)=(0)2(Pi). We then apply this formula to find the bisection width of RC(2(n), 4). The conclusion shows that, as n-dimensional cube, RC(2(n), 4) enjoys a linear bisection width. (c) 2005 Elsevier B.V. All rights reserved.

Principles and calibration of solid phase microextraction fibre (passive sampler) for measurements of airflow and air infiltration in dwellings

Tracer gas techniques have been the most appropriate experimental method of determining airflows and ventilation rates in houses. However, current trends to reduce greenhouse gas effects have prompted the need for alternative techniques, such as passive sampling. In this research passive sampling techniques have been used to demonstrate the potential to fulfil these requirements by using solutions of volatile organic compounds (VOCs) and solid phase microextraction (SPME) fibres. These passive sampling techniques have been calibrated against tracer gas decay techniques and measurements from a standard orifice plate. Two constant sources of volatile organic compounds were diffused into two sections of a humidity chamber and sampled using SPME fibres. From a total of four SPME fibres (two in each section), reproducible results were obtained. Emission rates and air movement from one section to the other were predicted using developed algorithms. Comparison of the SPME fibre technique with that of the tracer gas technique and measurements from an orifice plate showed similar results with good precision and accuracy. With these fibres, infiltration rates can be measured over grab samples in a time weighted averaged period lasting from 10 minutes up to several days. Key words: passive samplers, solid phase microextraction fibre, tracer gas techniques, airflow, air infiltration, houses.

The evolution of maximum body size of terrestrial mammals

The extinction of dinosaurs at the Cretaceous/Paleogene (K/Pg) boundary was the seminal event that opened the door for the subsequent diversification of terrestrial mammals. Our compilation of maximum body size at the ordinal level by sub-epoch shows a near-exponential increase after the K/Pg. On each continent, the maximum size of mammals leveled off after 40 million years ago and thereafter remained approximately constant. There was remarkable congruence in the rate, trajectory, and upper limit across continents, orders, and trophic guilds, despite differences in geological and climatic history, turnover of lineages, and ecological variation. Our analysis suggests that although the primary driver for the evolution of giant mammals was diversification to fill ecological niches, environmental temperature and land area may have ultimately constrained the maximum size achieved.