88,735 research outputs found
Ky Fan Inequality and Bounds for Differences of Means
Full text linkWe prove an equivalent relation between Ky Fan-typed inequalities and certain bounds for the differences of means. We also generalize a result of H. Alzer, S. Ruscheweyh and L. Salinas
On the Ky Fan Inequality
No full textSome inequalities related to the Ky Fan and C.-L. Wang inequalities for weighted arithmetic and geometric means are given
Using performance assessment in secondary school mathematics: an empirical study in a Singapore classroom
No full textThis article reports an exploratory study on using performance assessment in mathematics instruction in a high-performing secondary school in Singapore. An intact mathematics class participated in the study, and received chapter-based performance tasks as intervention during regular mathematics lessons for about one and a half school years. The performance tasks used included authentic and/or open-ended tasks. The students’ academic achievements and attitudes in mathematics were compared with a comparison class that did not receive the intervention. Both quantitative and qualitative data were collected, mainly through questionnaire surveys, performance task tests, conventional school exams, and interviews with students and teachers. The results suggest that the students receiving the intervention performed significantly better than their counterparts in solving conventional exam problems, and in general they also showed more positive changes in attitudes towards mathematics and mathematics learning. The students from the experimental class also expressed positive views about the benefits of using performance tasks in promoting their ability in higher order thinking, though no statistically significant difference was detected between the two classes of students in solving unconventional tasks before and after intervention. Overall, the results appear to support teachers’ using contextualised problems in real life situations and open-ended investigations in students’ learning of mathematic
Richardson, Barbauld, and the construction of an early modern fan club
No full textMPhilMuch has been written about the life and long works of the eighteenth century epistolary novelist, Samuel Richardson, but the prospect of his position as the first celebrity novelist – responsible for courting his own fame as well as initiating his own fan club – has largely been ignored. The body of manuscripts housed at the National Art Library in the Victoria and Albert Museum in London provides the modern scholar with evidence of the skeletal beginnings of an early fan club. This thesis aims to show how these manuscripts were turned into a saleable commodity by the publisher and entrepreneur Richard Phillips, while under the guiding hand of another, slightly later, literary celebrity, Anna Laetitia Barbauld. In order to restore Richardson’s reputation amongst a new nineteenth century audience, Barbauld was required to construct her own idea of him as an eighteenth century celebrity author, and in doing so the insecurities of a self-professed, apparently diffident man, are revealed. Barbauld’s capacious, but heavily edited selection of letters is analyzed in this thesis, providing ample evidence that Richardson’s correspondents were more than just eager letter writers. By using Barbauld’s biography of Richardson this thesis aims to show how she manipulates the genre of life writing in her construction of him.
This thesis offers an alternative reading of how the Richardson manuscripts are viewed, redefining them as not simply a collection of letters, but as a collective entity, deliberately selected and archived as evidence of an early modern fan club, and its celebrity managing director
Experimental study of blade rigidity effects on the global and the local performances of a thick blades axial-flow fan
Full text linkAn experimental investigation on the aerodynamic performances of thick blades axial-flow fans was carried out in this study. Two fans are considered, the first one is rotomoulded (in plastic) and the second one is milled (in aluminium). Both have exactly the same shape, excepting that the rotomoulded fan has hollow blades. They were designed from an existing fan (manufactured by plastic injection process) used in the cooling system of an automotive vehicle power unit. As far as shape is concerned, the only difference between the two first fans and the traditional injected fan is the blade thickness, whereas as far as rigidity is concerned, the only difference between the rotomoulded and the milled fans is the ability of the rotomoulded fan to be deformed easier than the milled fan. The aim of this study is to determine on the one hand the influence of the blade thickness and on the other hand the way the deformation of the hollow blades may affect the global and the local performances. The global performances of the fans were measured in a test bench designed according to the ISO 5801 standards. The curve of the aerodynamics characteristics (pressure head versus flow rate) and of the global efficiency are slightly lower for the rotomoulded fan. The wall pressure fluctuations were also investigated for three flow rates: one corresponding to the maximum efficiencies of both fans and two others corresponding to an under-flow and an over-flow rate. The power spectral density (PSD) levels, estimated by the Welch method, are between six and nine times higher for the rotomoulded fan at nominal flow rate. At partial flow rate, however, the PSD levels are close for both fans
Experimental study of blade thickness effects on the global and local performances of a Controlled Vortex Designed axial-flow fan
Full text linkThe purpose of this work is to study the effects of blade thickness on the performances of an axial-flow fan. Two fans that differ only in the thickness of their blades were studied. The first fan was designed to be part of the cooling system of an automotive vehicle power unit and has very thin blades. The second fan has much thicker blades compatible with the rotomoulding conception process. The global performances of the fans were measured in a test bench designed according to the ISO-5801 standard. The curve of aerodynamics characteristics (pressure head versus ow-rate) is slightly steeper for the fan with thick blades, and the nominal point is shifted towards lower flow-rates. The efficiency of the thick blades fan is lower than the efficiency of the fan with thin blades but remains high on a wider flow-rate range. The mean velocity field downstream of the rotors are very similar at nominal points with less centrifugation for the thick blades fan. The thick blades fan moreover maintains an axial exit-flow on a wider range of flow-rates. The main dierences concern local properties of the flow: Phase-averaged velocities and wall pressure fluctuations strongly differ at the nominal flow-rates. The total level of fluctuations is lower for the thick blades fan that for the thin blades fan and the spectral decomposition of the wall fluctuations and velocity signals reveal more harmonics for the thick blades fan, with less correlation between the different signals. For this kind of turbomachinery, the use of thick blades could lead to a good compromise between aerodynamic and acoustic performances, on a wider operating range
A Note on the Ky Fan Inequality
No full textThe Ky Fan inequality is essentially the assertion that t/(1−t) is log-concave. We study its weighted form in the context of signed weights
The performance and application of cross flow fans for automotive engine cooling systems
Full text linkThe work reported centres on the application of cross flow fan units to provide forced air flow over the radiator used for engine cooling. It is shown that a cooling system in which the airflow is ducted through the vehicle would lead to a significant reduction in vehicle drag. A ducted system allows more exact prediction of performance, and can be more easily designed in conjunction with across flow fan, that has rectangular inlet and outlet sections, and an ability to form 'S', 'L' and 'U' airflow geometries. This shape advantage of the cross flow fan also allows the use of radiators with a higher aspect ratio that could in turn permit lower bonnet lines on vehicles with a further reduction in aerodynamic drag. At higher vehicle speeds adequate cooling is usually provided by ram airflow through the cooling system. An airflow by-pass arrangement controlled by a balance valve has been devised and tested. The operation of this valve was found to be stable and smooth, and extremely beneficial in reducing the total system resistance and increasing fan performance under ram airflow conditions. A computer model has been developed and a programme produced to facilitate matching of the air circuit, fan and motor. Examples illustrate the use of this in the design of a system for a 1,6 litre passenger vehicle, with maximum b.h.p. in second gear being taken as the most critical engine condition for cooling performance
Are Bayesian Fan Charts Useful for Central Banks? Uncertainty, Forecasting, and Financial Stability Stress Tests
Full text linkThis paper shows how fan charts generated from Bayesian vector autoregression (BVAR) models can be useful for assessing 1) the forecasting accuracy of central banks’ prediction models and 2) the credibility of stress tests carried out to evaluate financial stability. Using unique data from the Czech National Bank (CNB), we compare our BVAR fan charts for inflation, GDP growth, interest rate and the exchange rate to those of the CNB, which are based on past forecasting errors. Our results suggest that in terms of the Kullback-Leibler Information Criterion, BVAR fan charts typically do not outperform those of the CNB, providing a useful cross-check of their accuracy. However, we show how BVAR fan charts can rigorously deal with the non-negativity constraint on the nominal interest rate and usefully complement the official fan charts. Finally, we put forward how BVAR fan charts can be useful for assessing financial stability and propose a simple method for evaluating whether the assumptions of banks’ stress tests about the macroeconomic outlook are sufficiently adverse.Bayesian vector autoregression, fan chart, inflation targeting, stress tests, uncertainty.
Use of fan rig data for the understanding and prediction of fan broadband noise and noise changes due to a variable area nozzle
No full textThis thesis presents the results of the research component of this EngD, entitledUse of fan rig data for the understanding and prediction of fan broadband noise and noisechanges due to a variable area nozzleAs suggested by the title, fan rig noise measurements form an integral part of this thesis. Theanalysis of a database of rig noise measurements forms the first section of this thesis, in twoparts. The first part describes the analysis of a set of fan rig noise measurements, including thevariation of fan broadband and tone noise in forward and rearward arcs. The second partexamines a large database of fan rig noise measurements, and attempts to derive correlationsof fan broadband noise and fan performance parameters. Cluster Analysis, PrincipleComponent Analysis, and Regression Analysis are used to understand and describe theunderlying physics of broadband noise generation and the relationships between thesepredictors.The second section of this thesis uses a cascade broadband noise model to investigate rotorstatorbroadband noise. Predictions of the broadband noise from this noise model arecompared to rig measurements, showing good accuracy. The underlying physics of rotorstatorbroadband noise generation is investigated by performing two parametric studies usingthe broadband noise model. The first parametric study investigates the effect on broadbandnoise of simple flow and geometric parameters, namely number of vanes, vane chord, vanestagger angle, and rotor wake turbulence intensity, turbulent length scale, and flow Machnumber onto the cascade. These results are used to derive scaling power laws for theprediction of changes in broadband noise due to changes in these parameters. The secondparametric study expands upon this by investigating the effect on broadband noise of the fandesign parameters shaft speed, pressure ratio, and efficiency, at approach, cutback and cruiseconditions. The variation in broadband noise due to these design parameters is explained byconsidering the underlying flow and geometric parameters such as number of vanes and Machnumber, and the scaling power laws based on these simple parameters are used to predict thechange in broadband noise between different performance points.The final section of this thesis investigates the effect of varying exhaust nozzle area on totalengine noise. A new method is presented that allows the transfer of changes in fan rig noise toEugene P. Deane EngD Thesis September 2009 2engine noise predictions, to estimate the change in fan noise due to the pressure ratio changesbrought about by a variable area nozzle. Changes in engine noise are investigated forapproach, cutback, and sideline conditions, and the application of the new method assessed.As the research displayed in this thesis is closely linked to industry, the foundation of workpresented in several chapters is dependent on data or figures that are commercially sensitive.It has therefore been necessary to create a confidential appendix (Appendix X) to includethese commercially sensitive items. These additional results and figures in Appendix X aresupplementary in nature, and sufficient results are presented in the public thesis to illustratethe results of the various chapters. Where supplementary information and results are available,this is clearly indicated at the pertinent point in the published thesis, along with the section ofAppendix X where the information can be found
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