A Caratheodory theorem for the bidisk via Hilbert space methods

If \ph is an analytic function bounded by 1 on the bidisk \D^2 and \tau\in\tb is a point at which \ph has an angular gradient \nabla\ph(\tau) then \nabla\ph(\la) \to \nabla\ph(\tau) as \la\to\tau nontangentially in \D^2. This is an analog for the bidisk of a classical theorem of Carath\'eodory for the disk. For \ph as above, if \tau\in\tb is such that the $\liminf$ of (1-|\ph(\la)|)/(1-\|\la\|) as \la\to\tau is finite then the directional derivative D_{-\de}\ph(\tau) exists for all appropriate directions \de\in\C^2. Moreover, one can associate with \ph and $\tau$ an analytic function $h$ in the Pick class such that the value of the directional derivative can be expressed in terms of $h$

Facial behaviour of analytic functions on the bidisk

We prove that if $\phi$ is an analytic function bounded by 1 on the bidisk and $\tau$ is a point in a face of the bidisk at which $\phi$ satisfies Caratheodory's condition then both $\phi$ and the angular gradient $\nabla\phi$ exist and are constant on the face. Moreover, the class of all $\phi$ with prescribed $\phi(\tau)$ and $\nabla\phi(\tau)$ can be parametrized in terms of a function in the two-variable Pick class. As an application we solve an interpolation problem with nodes that lie on faces of the bidisk.Comment: 18 pages. We have replaced an erroneous proof of Theorem 5.4(1) by a valid proo

Operator monotone functions and L\"owner functions of several variables

We prove generalizations of L\"owner's results on matrix monotone functions to several variables. We give a characterization of when a function of $d$ variables is locally monotone on $d$-tuples of commuting self-adjoint $n$-by-$n$ matrices. We prove a generalization to several variables of Nevanlinna's theorem describing analytic functions that map the upper half-plane to itself and satisfy a growth condition. We use this to characterize all rational functions of two variables that are operator monotone

The PAS domain-containing histidine kinase RpfS is a second sensor for the diffusible signal factor of <em>Xanthomonas campestris</em>

Summary: A cell-cell signalling system mediated by the fatty acid signal DSF controls the virulence of Xanthomonas campestris pv. campestris (Xcc) to plants. The synthesis and recognition of the DSF signal depends upon different Rpf proteins. DSF signal generation requires RpfF whereas signal perception and transduction depends upon the sensor RpfC and regulator RpfG. Detailed analyses of the regulatory roles of different Rpf proteins have suggested the occurrence of further sensors for DSF. Here we have used a mutagenesis approach coupled with high-resolution transcriptional analysis to identify XC_2579 (RpfS) as a second sensor for DSF in Xcc. RpfS is a complex sensor kinase predicted to have multiple Per/Arnt/Sim (PAS) domains, a histidine kinase domain and a C-terminal receiver (REC) domain. Isothermal calorimetry showed that DSF bound to the isolated N-terminal PAS domain with a Kd of 1.4μM. RpfS controlled expression of a sub-set of genes distinct from those controlled by RpfC to include genes involved in type IV secretion and chemotaxis. Mutation of XC_2579 was associated with a reduction in virulence of Xcc to Chinese Radish when assayed by leaf spraying but not by leaf inoculation, suggesting a role for RpfS-controlled factors in the epiphytic phase of the disease cycle.</p

Fluttering energy harvesters in the wind: A review

The growing area of harvesting energy by aerodynamically induced flutter in a fluid stream is reviewed. Numerous approaches were found to understand, demonstrate and [sometimes] optimise harvester performance based on Movement-Induced or Extraneously Induced Excitation. Almost all research was conducted in smooth, unidirectional flow domains; either experimental or computational. The power outputs were found to be very low when compared to conventional wind turbines, but potential advantages could be lower noise levels. A consideration of the likely outdoor environment for fluttering harvesters revealed that the flow would be highly turbulent and having a mean flow angle in the horizontal plane that could approach a harvester from any direction. Whilst some multiple harvester systems in smooth, well-aligned flow found enhanced efficiency (due to beneficial wake interaction) this would require an invariant flow approach angle. It was concluded that further work needs to be performed to find a universally accepted metric for efficiency and to understand the effects of the realities of the outdoors, including the highly variable and turbulent flow conditions likely to be experienced

The experience of enchantment in human-computer interaction

Improving user experience is becoming something of a rallying call in human–computer interaction but experience is not a unitary thing. There are varieties of experiences, good and bad, and we need to characterise these varieties if we are to improve user experience. In this paper we argue that enchantment is a useful concept to facilitate closer relationships between people and technology. But enchantment is a complex concept in need of some clarification. So we explore how enchantment has been used in the discussions of technology and examine experiences of film and cell phones to see how enchantment with technology is possible. Based on these cases, we identify the sensibilities that help designers design for enchantment, including the specific sensuousness of a thing, senses of play, paradox and openness, and the potential for transformation. We use these to analyse digital jewellery in order to suggest how it can be made more enchanting. We conclude by relating enchantment to varieties of experience.</p

The climatic impact of food consumption in a representative sample of Irish adults and implications for food and nutrition policy

peer-reviewedTo evaluate the greenhouse gas emissions (GHGE) associated with the diet of Irish adults. GHGE were estimated by applying conversion factors to habitual food consumption data taken from the National Adult Nutrition Survey, which was representative of the population. Descriptive analyses were undertaken for GHGE for the total population, as well as accounting for energy misreporting and across categories of sociodemographic and socio-economic factors and tertiles of emissions. Republic of Ireland. Adults aged 18–87 years (n 1500). The GHGE derived from daily dietary intakes was estimated as 6·5 kg of CO2 equivalents (CO2eq) per person. Males, younger consumers, those with secondary education and student employment status were associated with significantly higher GHGE. Red meat was the highest contributor to GHGE with 1646 g CO2eq arising from a mean intake of 47 g/d. Dairy and starchy staples were the next largest dietary GHGE sources, with mean daily emissions of 732 g CO2eq and 647 g CO2eq, respectively. The lowest emissions were associated with consumption of vegetables, fruits and legumes/pulses/nuts. Based on profiling using actual food consumption data, it is evident that one single measure is not sufficient and a range of evidence-based mitigation measures with potential to lower emissions throughout the food chain should be considered. The research contributes towards an improved understanding of the climatic impact of the dietary intakes of Irish adults and can serve to inform a sustainability framework to guide action in food and nutrition policyThis study was funded by the Department of Agriculture Food and the Marine through the Food Institutional Research Measure (FIRM)funding instrument (grant number 13/F/527)

Forever Young: High Chromospheric Activity in M subdwarfs

We present spectroscopic observations of two halo M subdwarfs which have H alpha emission lines. We show that in both cases close companions are the most likely cause of the chromospheric activity in these old, metal-poor stars. We argue that Gl 781 A's unseen companion is most likely a cool helium white dwarf. Gl 455 is a near-equal-mass M subdwarf (sdM) system. Gl 781 A is rapidly rotating with v sin i = 30 km/s. The properties of the chromospheres and X-ray coronae of these systems are compared to M dwarfs with emission (dMe). The X-ray hardness ratios and optical chromospheric lines emission ratios are consistent with those seen in dMe stars. Comparison to active near-solar metallicity stars indicates that despite their low metallicity ([m/H] = -1/2), the sdMe stars are roughly as active in both X-rays and chromospheric emission. Measured by L_X/L_bol, the activity level of Gl 781 A is no more than a factor of 2.5 subluminous with respect to near-solar metallicity stars.Comment: 16 pages including 1 figure, AASTeX, to appear in May 1998 A.