Integrating control systems defined on the frame bundles of the space forms

This paper considers left-invariant control systems defined on the orthonormal frame bundles of simply connected manifolds of constant sectional curvature, namely the space forms Euclidean space E-3, the sphere S-3 and Hyperboloid H-3 with the corresponding frame bundles equal to the Euclidean group of motions SE(3), the rotation group SO(4) and the Lorentz group SO(1, 3). Orthonormal frame bundles of space forms coincide with their isometry groups and therefore the focus shifts to left-invariant control systems defined on Lie groups. In this paper a method for integrating these systems is given where the controls are time-independent. In the Euclidean case the elements of the Lie algebra se(3) are often referred to as twists. For constant twist motions, the corresponding curves g(t) is an element of SE(3) are known as screw motions, given in closed form by using the well known Rodrigues' formula. However, this formula is only applicable to the Euclidean case. This paper gives a method for computing the non-Euclidean screw motions in closed form. This involves decoupling the system into two lower dimensional systems using the double cover properties of Lie groups, then the lower dimensional systems are solved explicitly in closed form.

Operator Theory and Its Applications: In Memory of V. B. Lidskii (1924-2008)

This book is a collection of articles devoted to the theory of linear operators in Hilbert spaces and its applications. The subjects covered range from the abstract theory of Toeplitz operators to the analysis of very specific differential operators arising in quantum mechanics, electromagnetism, and the theory of elasticity; the stability of numerical methods is also discussed. Many of the articles deal with spectral problems for not necessarily selfadjoint operators. Some of the articles are surveys outlining the current state of the subject and presenting open problems.

Filtering techniques in self-tuning

In the last few years a state-space formulation has been introduced into self-tuning control. This has not only allowed for a wider choice of possible control actions, but has also provided an insight into the theory underlying—and hidden by—that used in the polynomial description. This paper considers many of the self-tuning algorithms, both state-space and polynomial, presently in use, and by starting from first principles develops the observers which are, effectively, used in each case. At any specific time instant the state estimator can be regarded as taking one of two forms. In the first case the most recently available output measurement is excluded, and here an optimal and conditionally stable observer is obtained. In the second case the present output signal is included, and here it is shown that although the observer is once again conditionally stable, it is no longer optimal. This result is of significance, as many of the popular self-tuning controllers lie in the second, rather than first, category.

Adobe Devanagari typeface

Typeface design: collaborative work commissioned by Adobe Inc. Published but unreleased. The Adobe Devanagari typefaces were commissioned from Tiro Typeworks and collaboratively designed by Tim Holloway, Fiona Ross and John Hudson, beginning in 2005. The types were officially released in 2009. The design brief was to produce a typeface for modern business communications in Hindi and other languages, to be legible both in print and on screen. Adobe Devanagari was designed to be highly readable in a range of situations including quite small sizes in spreadsheets and in continuous text setting, as well as at display sizes, where the full character of the typeface reveals itself. The construction of the letters is based on traditional penmanship but possesses less stroke contrast than many Devanagari types, in order to maintain strong, legible forms at smaller sizes. To achieve a dynamic, fluid style the design features a rounded treatment of distinguishing terminals and stroke reversals, open counters that also aid legibility at smaller sizes, and delicately flaring strokes. Together, these details reveal an original hand and provide a contemporary approach that is clean, clear and comfortable to read whether in short or long passages of text. This new approach to a traditional script is intended to counter the dominance of rigid, staccato-like effects of straight verticals and horizontals in earlier types and many existing fonts. OpenType Layout features in the fonts provide both automated and discretionary access to an extensive glyph set, enabling sophisticated typography. Many conjuncts preferred in classical literary texts and particularly in some North Indian languages are included; these literary conjuncts may be substituted by specially designed alternative linear forms and fitted half forms. The length of the ikars—ि and ी—varies automatically according to adjacent letter or conjunct width. Regional variants of characters and numerals (e.g. Marathi forms) are included as alternates. Careful attention has been given to the placements of all vowel signs and modifiers. The fonts include both proportional and tabular numerals in Indian and European styles. Extensive kerning covers several thousand possible combinations of half forms and full forms to anticipate arbitrary conjuncts in foreign loan words. _____

Optimal piecewise locally linear modeling

Associative memory networks such as Radial Basis Functions, Neurofuzzy and Fuzzy Logic used for modelling nonlinear processes suffer from the curse of dimensionality (COD), in that as the input dimension increases the parameterization, computation cost, training data requirements, etc. increase exponentially. Here a new algorithm is introduced for the construction of a Delaunay input space partitioned optimal piecewise locally linear models to overcome the COD as well as generate locally linear models directly amenable to linear control and estimation algorithms. The training of the model is configured as a new mixture of experts network with a new fast decision rule derived using convex set theory. A very fast simulated reannealing (VFSR) algorithm is utilized to search a global optimal solution of the Delaunay input space partition. A benchmark non-linear time series is used to demonstrate the new approach.

Sustainable food? Teikei, co-operatives and food citizenship in Japan and the UK

This paper explores in particular how Teikei groups, as forms of Community Supported Agriculture (CSA), operate in Japan, focussing on one particular group. The paper links the Teikei approach to debates around social capital and consumer-citizenship, arguing that pre-existing consumer/citizen institutions may usefully be engaged in developing food citizenship and CSA operations. The discussion is linked to CSA and various other alternative food networks (AFNs) that have grown up in various forms in Japan, the US, the UK and elsewhere in Europe over the past thirty years or so. CSA in similar fashion to Teikei involves bringing producers and consumers closer together in terms of reconnecting the agricultural producer and consumer to aid food traceability and quality (including organic). CSA also exhibits elements of new assemblies of agricultural governance based on enhanced consumer-citizenship where consumers, to varying degrees, have a say in what and how produce is grown and how the land is managed.

Determination of the degradation kinetics of anthocyanins in a model juice system using isothermal and non-isothermal methods

The effect of temperature on the degradation of blackcurrant anthocyanins in a model juice system was determined over a temperature range of 4–140 °C. The thermal degradation of anthocyanins followed pseudo first-order kinetics. From 4–100 °C an isothermal method was used to determine the kinetic parameters. In order to mimic the temperature profile in retort systems, a non-isothermal method was applied to determine the kinetic parameters in the model juice over the temperature range 110–140 °C. The results from both isothermal and non-isothermal methods fit well together, indicating that the non-isothermal procedure is a reliable mathematical method to determine the kinetics of anthocyanin degradation. The reaction rate constant (k) increased from 0.16 (±0.01) × 10−3 to 9.954 (±0.004) h−1 at 4 and 140 °C, respectively. The temperature dependence of the rate of anthocyanin degradation was modelled by an extension of the Arrhenius equation, which showed a linear increase in the activation energy with temperature.

Elevated atmospheric CO2 changes phosphorus fractions in soils under a short rotation poplar plantation (EuroFACE)

Future high levels of atmospheric carbon dioxide (CO2) may increase biomass production of terrestrial plants and hence plant requirements for soil mineral nutrients to sustain a greater biomass production. Phosphorus (P), an element essential for plant growth, is found in soils both in inorganic and in organic forms. In this work, three genotypes of Populus were grown under ambient and elevated atmospheric CO2 concentrations (FACE) for 5 years. An N fertilisation treatment was added in years 4 and 5 after planting. Using a fractionation scheme, total P was sequentially extracted using H2O, NaOH, HCl and HNO3, and P determined as both molybdate (Mo) reactive and total P. Molybdate-reactive P is defined as mainly inorganic but also some labile organic P which is determined by Vanado-molybdophosphoric acid colorimetric methods. Organic P was also measured to assess all plant available and weatherable P pools. We tested the hypotheses that higher P demand due to increased growth is met by a depletion of easily weatherable soil P pools, and that increased biomass inputs increases the amount of organic P in the soil. The concentration of organic P increased under FACE, but was associated with a decrease in total soil organic matter. The greatest increase in the soil P due to elevated CO2 was found in the HCl-extractable P fraction in the non-fertilised treatment. In the NaOH-extractable fraction the Mo-reactive P increased under FACE, but total P did not differ between ambient and FACE. The increase in both the NaOH- and HCl-extractable fractions was smaller after N addition. The results showed that elevated atmospheric CO2 has a positive effect on soil P availability rather than leading to depletion.We suggest that the increase in the NaOH- and HCl-extractable fractions is biologically driven by organic matter mineralization, weathering and mycorrhizal hyphal turnover.

The role of the log transformation in forecasting economic variables

For forecasting and economic analysis many variables are used in logarithms (logs). In time series analysis, this transformation is often considered to stabilize the variance of a series. We investigate under which conditions taking logs is beneficial for forecasting. Forecasts based on the original series are compared to forecasts based on logs. For a range of economic variables, substantial forecasting improvements from taking logs are found if the log transformation actually stabilizes the variance of the underlying series. Using logs can be damaging for the forecast precision if a stable variance is not achieved.

WAXS studies of global molecular orientation induced in nematic liquid crystals by simple shear flow

Global molecular orientation function coefficients for the nematic liquid crystal 4-cyano 4'-nn -pentylbiphenyl (5CB) in shear flow are presented, being extracted from 2-dimensional Wide-Angle X-ray Scattering data. A linear increase in orientation parameter P2 is observed with a logarithmic increase in shear rate. It is proposed that this arises from an increased number of LC directors aligning to the shear axis. Upon cessation of shear flow, the anisotropy is seen to relax away completely, over a time scale which is inversely proportional to the previously applied shear rate.

On instabilities in data assimilation algorithms

Data assimilation algorithms are a crucial part of operational systems in numerical weather prediction, hydrology and climate science, but are also important for dynamical reconstruction in medical applications and quality control for manufacturing processes. Usually, a variety of diverse measurement data are employed to determine the state of the atmosphere or to a wider system including land and oceans. Modern data assimilation systems use more and more remote sensing data, in particular radiances measured by satellites, radar data and integrated water vapor measurements via GPS/GNSS signals. The inversion of some of these measurements are ill-posed in the classical sense, i.e. the inverse of the operator H which maps the state onto the data is unbounded. In this case, the use of such data can lead to significant instabilities of data assimilation algorithms. The goal of this work is to provide a rigorous mathematical analysis of the instability of well-known data assimilation methods. Here, we will restrict our attention to particular linear systems, in which the instability can be explicitly analyzed. We investigate the three-dimensional variational assimilation and four-dimensional variational assimilation. A theory for the instability is developed using the classical theory of ill-posed problems in a Banach space framework. Further, we demonstrate by numerical examples that instabilities can and will occur, including an example from dynamic magnetic tomography.

Incremental effect of a calcium salt of cis-monounsaturated fatty acids supplement on milk fatty acid composition in cows fed maize silage-based diets

In most Western countries, saturated fatty acid (SFA) intake exceeds recommended levels, which is considered a risk factor for cardiovascular disease (CVD). As milk and dairy products are major contributors to SFA intake in many countries, recent research has focused on sustainable methods of producing milk with a lower saturated fat concentration by altering dairy cow diets. Human intervention studies have shown that CVD risk can be reduced by consuming dairy products with reduced SFA and increased cis-monounsaturated fatty acid (MUFA) concentrations. This milk fatty acid profile can be achieved by supplementing dairy cow diets with cis-MUFA-rich unsaturated oils. However, rumen exposure of unsaturated oils also leads to enhanced milk trans fatty acid (TFA) concentrations. Because of concerns about the effects of TFA consumption on CVD, feeding strategies that increase MUFA concentrations in milk without concomitant increases in TFA concentration are preferred by milk processors. In an attempt to limit TFA production and increase the replacement of SFA by cis-MUFA, a preparation of rumen-protected unsaturated oils was developed using saponification with calcium salts. Four multiparous Holstein-Friesian cows in mid-late lactation were used in a 4 × 4 Latin square design with 21-d periods to investigate the effect of incremental dietary inclusion of a calcium salt of cis-MUFA product (Ca-MUFA; 20, 40, and 60 g/kg of dry matter of a maize silage-based diet), on milk production, composition, and fatty acid concentration. Increasing Ca-MUFA inclusion reduced dry matter intake linearly, but no change was observed in estimated ME intake. No change in milk yield was noted, but milk fat and protein concentrations were linearly reduced. Supplementation with Ca-MUFA resulted in a linear reduction in total SFA (from 71 to 52 g/100 g of fatty acids for control and 60 g/kg of dry matter diets, respectively). In addition, concentrations of both cis- and trans-MUFA were increased with Ca-MUFA inclusion, and increases in other biohydrogenation intermediates in milk fat were also observed. The Ca-MUFA supplement was very effective at reducing milk SFA concentration and increasing cis-MUFA concentrations without incurring any negative effects on milk and milk component yields. However, reduced milk fat and protein concentrations, together with increases in milk TFA concentrations, suggest partial dissociation of the calcium salts in the rumen