39 resultados para Difference Equations with Maxima

em QUB Research Portal - Research Directory and Institutional Repository for Queen's University Belfast


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Background & aims: Little is known about energy requirements in brain injured (TBI) patients, despite evidence suggesting adequate nutritional support can improve clinical outcomes. The study aim was to compare predicted energy requirements with measured resting energy expenditure (REE) values, in patients recovering from TBI.

Methods: Indirect calorimetry (IC) was used to measure REE in 45 patients with TBI. Predicted energy requirements were determined using FAO/WHO/UNU and Harris–Benedict (HB) equations. Bland– Altman and regression analysis were used for analysis.

Results: One-hundred and sixty-seven successful measurements were recorded in patients with TBI. At an individual level, both equations predicted REE poorly. The mean of the differences of standardised areas of measured REE and FAO/WHO/UNU was near zero (9 kcal) but the variation in both directions was substantial (range 591 to þ573 kcal). Similarly, the differences of areas of measured REE and HB demonstrated a mean of 1.9 kcal and range 568 to þ571 kcal. Glasgow coma score, patient status, weight and body temperature were signi?cant predictors of measured REE (p < 0.001; R2= 0.47).

Conclusions: Clinical equations are poor predictors of measured REE in patients with TBI. The variability in REE is substantial. Clinicians should be aware of the limitations of prediction equations when estimating energy requirements in TBI patients.

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Using the Rapid Oscillation in the Solar Atmosphere (ROSA) instrument at the Dunn Solar Telescope we have found that the spectra of fluctuations of the G-band (cadence 1.05 s) and Ca II K-line (cadence 4.2 s) intensities show correlated fluctuations above white noise out to frequencies beyond 300 mHz and up to 70 mHz, respectively. The noise-corrected G-band spectrum presents a scaling range (Ultra High Frequency “UHF”) for f = 25-100 mHz, with an exponent consistent with the presence of turbulent motions. The UHF power, is concentrated at the locations of magnetic bright points in the intergranular lanes, it is highly intermittent in time and characterized by a positive kurtosis κ. Combining values of G-band and K-line intensities, the UHF power, and κ, reveals two distinct “states” of the internetwork solar atmosphere. State 1, with κ ≍ 6, which includes almost all the data, is characterized by low intensities and low UHF power. State 2, with κ ≍ 3, including a very small fraction of the data, is characterized by high intensities and high UHF power. Superposed epoch analysis shows that for State 1, the K-line intensity presents 3.5 min chromospheric oscillations with maxima occurring 21 s after G-band intensity maxima implying a 150-210 km effective height difference. For State 2, the G-band and K-line intensity maxima are simultaneous, suggesting that in the highly magnetized environment sites of G-band and K-line emission may be spatially close together. Analysis of observations obtained with Hinode/SOT confirm a scaling range in the G-band spectrum up to 53 mHz also consistent with turbulent motions as well as the identification of two distinct states in terms of the H-line intensity and G-band power as functions of G-band intensity.

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The harsh environment presented by engines, particularly in the exhaust systems, often necessitates the use of robust and therefore low bandwidth temperature sensors. Consequently, high frequencies are attenuated in the output. One technique for addressing this problem involves measuring the gas temperature using two sensors with different time-constants and mathematically reconstructing the true gas temperature from the resulting signals. Such a technique has been applied in gas turbine, rocket motor and combustion research. A new reconstruction technique based on difference equations has been developed and its effectiveness proven theoretically. The algorithms have been successfully tested and proven on experimental data from a rig that produces cyclic temperature variations. These tests highlighted that the separation of the thermocouple junctions must be very small to ensure that both sensors are subjected to the same gas temperatures. Exhaust gas temperatures were recorded by an array of thermocouples during transient operation of a high performance two-stroke engine. The results show that the increase in bandwidth arising from the dual sensor technique allowed accurate measurement of exhaust gas temperature with relatively robust thermocouples. Finally, an array of very fine thermocouples (12.5 - 50 microns) was used to measure the in-cycle temperature variation in the exhaust.

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In this work we present the theoretical framework for the solution of the time-dependent Schrödinger equation (TDSE) of atomic and molecular systems under strong electromagnetic fields with the configuration space of the electron’s coordinates separated over two regions; that is, regions I and II. In region I the solution of the TDSE is obtained by an R-matrix basis set representation of the time-dependent wave function. In region II a grid representation of the wave function is considered and propagation in space and time is obtained through the finite-difference method. With this, a combination of basis set and grid methods is put forward for tackling multiregion time-dependent problems. In both regions, a high-order explicit scheme is employed for the time propagation. While, in a purely hydrogenic system no approximation is involved due to this separation, in multielectron systems the validity and the usefulness of the present method relies on the basic assumption of R-matrix theory, namely, that beyond a certain distance (encompassing region I) a single ejected electron is distinguishable from the other electrons of the multielectron system and evolves there (region II) effectively as a one-electron system. The method is developed in detail for single active electron systems and applied to the exemplar case of the hydrogen atom in an intense laser field.

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The Rapid Oscillations in the Solar Atmosphere instrument reveals solar atmospheric fluctuations at high frequencies. Spectra of variations of the G-band intensity (IG ) and Ca II K-line intensity (IK ) show correlated fluctuations above white noise to frequencies beyond 300 mHz and 50 mHz, respectively. The noise-corrected G-band spectrum for f = 28-326 mHz shows a power law with exponent -1.21 ± 0.02, consistent with the presence of turbulent motions. G-band spectral power in the 25-100 mHz ("UHF") range is concentrated at the locations of magnetic bright points in the intergranular lanes and is highly intermittent in time. The intermittence of the UHF G-band fluctuations, shown by a positive kurtosis ?, also suggests turbulence. Combining values of IG , IK , UHF power, and ? reveals two distinct states of the solar atmosphere. State 1, including almost all the data, is characterized by low IG , IK , and UHF power and ? ˜ 6. State 2, including only a very small fraction of the data, is characterized by high IG , IK , and UHF power and ? ˜ 3. Superposed epoch analysis shows that the UHF power peaks simultaneously with spatio-temporal IG maxima in either state. For State 1, IK shows 3.5 minute chromospheric oscillations with maxima occurring 21 s after IG maxima implying a 150-210 km effective height difference. However, for State 2 the IK and IG maxima are simultaneous; in this highly magnetized environment sites of G-band and K-line emission may be spatially close together.

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Objectives: Men have higher incidence and mortality rates for nearly all cancers. They are less likely than women to utilise cancer information services and other social support services. The aim of this study was to explore and compare the experience and coping behaviour of men and women after treatment for colorectal cancer (CRC). Methods: A longitudinal qualitative study was conducted involving 38 individuals (24 men and 14 women) with CRC. Data were generated using semi-structured interviews at four time points over an 18-month period, post-diagnosis. Interviews focused on participant's experience of CRC and on how gender affected their coping. This paper reports the findings of interviews 3 and 4 which examined the participant's experience after chemotherapy. Results: Three themes emerged from the interviews ('new normal', living with uncertainty and support needs). Many men and women reacted similarly; however, there was some variation evident between and within sexes. The main difference was with regard to the long-term physical side effects of the illness. Many women admitted to still experiencing side effects, whereas many men indicated that they had no problems. These men engaged in practices that aligned with their gender identity and view of masculinity. It must be noted that some men and women were still experiencing an impact. Conclusions: Recovery from the physical and psychological effects of CRC does not occur simultaneously. Healthcare professionals should be aware that not all men (or women) conform to the social stereotypes of masculinity (or femininity). Copyright © 2010 John Wiley & Sons, Ltd.

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The generalized KP (GKP) equations with an arbitrary nonlinear term model and characterize many nonlinear physical phenomena. The symmetries of GKP equation with an arbitrary nonlinear term are obtained. The condition that must satisfy for existence the symmetries group of GKP is derived and also the obtained symmetries are classified according to different forms of the nonlinear term. The resulting similarity reductions are studied by performing the bifurcation and the phase portrait of GKP and also the corresponding solitary wave solutions of GKP
equation are constructed.

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The physics of the plume-induced shock and separation, particularly at high plume to exit pressure ratios with and without shock-turbulent boundary-layer control methods, were studied using computational techniques. Mass-averaged Navier-Stokes equations with a two-equation turbulence model were solved by using a fully implicit finite volume scheme and time.marching algorithm. The control methodologies for shock interactions included a porous tail and a porous extension attached at the nozzle exit or trailing edge. The porous tail produced a weaker shock and fixed the shock position on the control surface. The effect of the porous extension on shock interactions was mainly to restrain the plume from strongly underexpanding during a change in flight conditions. These techniques could give an additional dimension to the design and control of supersonic missiles.

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Dissociative electron attachment to cyanoacetylene (propiolonitrile) HCCCN has been observed in the electron energy range 0-12 eV. Negative ions are formed in two main bands with maxima at similar to 1.6 eV (CCCN-) and similar to 5.3 eV (CCCN-, CN-, HCC- and CC-). There are also weaker resonances which lead to dissociative electron attachment to form CN-, HCC- and CC- with a maximum intensity at similar to 8.1 eV and CCCN-, CN- and CC- at similar to 11.2 eV. A trace of CCN- is observed at similar to 9.1 eV. The positions of the main dissociative attachment bands observed are close to positions of pi* resonances recently calculated by Sommerfeld and Knecht. Calculations have also been performed in this work, which confirm the position of the p* orbitals. The electron affinity of the CCCN radical is determined as 4.59 +/- 0.25 eV from the threshold for CCCN- formation at 1.32 +/- 0.15 eV. Dissociative electron attachment to this molecule will act as a source of negative ions in extraterrestrial environments where electrons are present with more than 1.3 eV energy.

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We extend the semiclassical description of two-state atomic collisions to low energies for which the impact parameter treatment fails. The problem reduces to solving a system of first-order differential equations with coefficients whose semiclassical asymptotes experience the Stokes phenomenon in the complex coordinate plane. Primitive semiclassical and uniform Airy approximations are discussed.

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A two-dimensional mathematical model for evaluating the simultaneous heat and moisture migration in porous building materials was proposed. Vapor content and temperature were chosen as the principal driving potentials. The numerical solution was based on the control volume finite difference technique with fully implicit scheme in time. Two validation experiments were developed in this study. The evolution of transient moisture distributions in both one-dimensional and two-dimensional cases was measured. A comparison between experimental results and those obtained by the numerical model proves that they are fully consistent with each other. The model can be easily integrated into a whole building heat, air and moisture transfer model. Another main advantage of the present numerical method lies in the fact that the required moisture transport properties are comparatively simple and easy to determine.

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The photomineralisation of 4-chlorophenol (4-CP) sensitised by Degussa P25 TiO2 in O2-saturated solution represents a possible standard test system in semiconductor-sensitised photomineralisation studies. As part of a detailed examination of this photosystem, the results of the temporal variations in the concentrations of 4-CP, CO2, Cl- and the major organic intermediates, namely, 4-chlorocatechol (4-CC), hydroquinone (HQ), benzoquinone and 4-chlororesorcinol, are reported. The observed variations in [4-CP], [4-CC], [HQ] and [CO2] fit those predicted by a kinetic model which utilises kinetic equations with a Langmuir-Hinshelwood form and assumes that there are three major possible routes in which the photogenerated hydroxyl radicals can react with 4-CP, ie. 4-CP --> 4-CC, 4-CP --> HQ and 4-CP --> (unstable intermediate) --> CO2 and that these routes have the following probabilities of occurring: 48%, 10% and 42%.

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Belfast, with its history of communal violence, is normally seen as lying outside the mainstream of nineteenth-century British urban development. The visit of Queen Victoria in 1849 suggests a more complex, less linear picture. What emerges is an urban identity in transition, in which aspirations to conform to an ideal of civic harmony temporarily overrode acute sectarian and political divisions, where pride in recent economic achievement sat uneasily alongside an awareness of the town’s newcomer status, and where an emerging sense of regional difference competed with a continuing assumption of Irish identity.