Norms on Free Topological Groups

A norm on a group G is a function N mapping G into the set ofnon-negative real numbers such that for each x and y in G, N(xy^–1) N(x)+N(y) and N(e) = 0, where e is the identity element ofG. It is shown here that if F(X) is the free topological groupon any completely regular Hausdorff space X and H is a subgroupof F(X) generated by a finite subset of X, then any norm onH can be extended to a continuous norm on F(X).     

Step functions from the half-open unit interval into a topological space

The set of continuous-from-the-right step functions from the half-open unit interval[0, 1[into a topological space X is denoted by X¹. Elsewhere a topology has been defined which makes X¹ a contractible, locally contractible space with the subspace of constant functions being homeomorphic to X. When X has a bounded metric ?, the topology of X¹ may be described by the metric $\text{d>(f,g)=}\text{∫}\text{0}\text{1}\text{ρ(f(t),g(t))dt}$.It is shown here that if X is separable, then X¹ is separable and if X satisfies the first (or second) axiom of countability, then X¹ satisfies it too. In contrast, it is shown that properties such as normality do not extend from X to X¹. This follows from the main result: X¹ is homeomorphic to its square, and thus contains a copy of X×X (which is closed when X is Hausdorff). The final theorem states that if X has at least two points then X¹ is not complete metrizable.     

Effects of formalin preservation on stable carbon and nitrogen isotope signatures in Calanoid copepods: implications for the use of Continuous Plankton Recorder Survey samples in stable isotope analyses

Preserved and archived organic material offers huge potential for the conduct of retrospective and long-term historical ecosystem reconstructions using stable isotope analyses, but because of isotopic exchange with preservatives the obtained values require validation. The Continuous Plankton Recorder (CPR) Survey is the most extensive long-term monitoring program for plankton communities worldwide and has utilised ships of opportunity to collect samples since 1931. To keep the samples intact for subsequent analysis, they are collected and preserved in formalin; however, previous studies have found that this may alter stable carbon and nitrogen isotope ratios in zooplankton. A maximum ~0.9‰ increase of δ(15) N and a time dependent maximum ~1.0‰ decrease of δ(13) C were observed when the copepod, Calanus helgolandicus, was experimentally exposed to two formalin preservatives for 12 months. Applying specific correction factors to δ(15) N and δ(13) C values for similarly preserved Calanoid species collected by the CPR Survey within 12 months of analysis may be appropriate to enable their use in stable isotope studies. The isotope values of samples stored frozen did not differ significantly from those of controls. Although the impact of formalin preservation was relatively small in this and other studies of marine zooplankton, changes in isotope signatures are not consistent across taxa, especially for δ(15) N, indicating that species-specific studies may be required.     

Fully-connected networks with local connections

Fully-connected mesh networks with local connections are described. Each connector links only nearest neighbors of the node lattice and carries enough passive pass-through vias to provide direct one-to-one links between all the nodes. If the nodes form a one-dimensional ring, then each connector must contain at least N(N−1)/2 physical channels. However, if the nodes are arranged in a d-dimensional hyper-torus, the number of channels per connector drops to N(N ^1/d −1)/2, which scales much more favorably at large N. Such arrangements can provide fully-meshed connectivity when parts of the network are physically inaccessible or when the network needs to be scaled up in a modular fashion.     

Study of burning behavior of small scale wood crib with cone calorimeter

Burning behavior of small-scale wood crib was studied by a serial of cone calorimeter tests. The heat release rate curves of these small wood cribs were different due to porosity factor and this shows that the control condition switches from one to another. The burning of some crib with small porosity factors was self-extinguished in fixed flow rate of air supply in cone calorimeter. These results were compared with Gross’s studies. The switch point of porosity-controlled and surface area controlled burning regime is different from Gross’s result.     

Index proposal and basic estimator study for quantification of oscillation of the secondary flow pattern in tortuous vessels

The development of atherosclerosis has been shown to correlate with regions of low wall shear stress and seemingly reduced mass transport. The local tortuosity of the arteries and local secondary flow oscillation also seem to be negatively correlated with the local occurrence of the disease. However there is currently no tool or physiological parameter that can be measured non-invasively to assess the local oscillation of the flow. Standard Colour Doppler imaging of secondary flow patterns during the blood pulse is studied and illustrated, and the local oscillation of the secondary flow pattern is proposed as an index, which could be an indicator of the likelihood of future disease development. Preliminary results are presented using a basic estimator developed for the proof of concept in the case of swirling flow, and based on colour-coded video signals collected in different configurations. In vitro results show that there is a correspondence between the Doppler patterns and the secondary flow patterns, the repeatability of the measures, and that the proposed index and its estimator reflect a joint influence of the local oscillation of the secondary flow pattern and of the flow rate. On another hand, while in vivo results still suffer from instabilities, noise and from scanners and processing limitations, they demonstrate that it is possible to use Colour Doppler imaging to image and characterize in vivo the secondary flow patterns and their oscillations non-invasively, and that it is possible for a trained clinician to perform manually such Doppler measurements for processing.     

Compensation of beam walk-off in hollow metal waveguides

Hollow metal waveguides feature well collimated beams and small losses across air gaps. This enables introduction of multiple optical beam splitters, or taps, along the waveguide to multicast signals from a source to multiple receivers. The splitters need to be of sufficient thickness to provide mechanical integrity and ease of handling. As a result, passing through the thickness leads to a beam walk-off. Walk-off dependence on the splitter thickness and its effect on the system optical efficiency are investigated. Two methods to compensate the walk-off are described: by offsetting the outgoing waveguide, and by introducing an additional symmetric optical element to shift the beam back to the original optical path. Both methods have been shown to effectively mitigate the walk-off effects.