Statnote 20: non-linear regression: fitting a general polynomial curve

In some circumstances, there may be no scientific model of the relationship between X and Y that can be specified in advance and indeed the objective of the investigation may be to provide a ‘curve of best fit’ for predictive purposes. In such an example, the fitting of successive polynomials may be the best approach. There are various strategies to decide on the polynomial of best fit depending on the objectives of the investigation.

The steady performance of a porous and compliant aerostatic thrust bearing

Recent developments in aerostatic thrust bearings have included: (a) the porous aerostatic thrust bearing containing a porous pad and (b) the inherently compensated compliant surface aerostatic thrust bearing containing a thin elastomer layer. Both these developments have been reported to improve the bearing load capacity compared to conventional aerostatic thrust bearings with rigid surfaces. This development is carried one stage further in a porous and compliant aerostatic thrust bearing incorporating both a porous pad and an opposing compliant surface. The thin elastomer layer forming the compliant surface is bonded to a rigid backing and is of a soft rubber like material. Such a bearing is studied experimentally and theoretically under steady state operating conditions. A mathematical model is presented to predict the bearing performance. In this model is a simplified solution to the elasticity equations for deflections of the compliant surface. Account is also taken of deflections in the porous pad due to the pressure difference across its thickness. The lubrication equations for flow in the porous pad and bearing clearance are solved by numerical finite difference methods. An iteration procedure is used to couple deflections of the compliant surface and porous pad with solutions to the lubrication equations. Comparisons between experimental results and theoretically predicted bearing performance are in good agreement. However these results show that the porous and compliant aerostatic thrust bearing performance is lower than that of a porous aerostatic thrust bearing with a rigid surface in place of the compliant surface. This discovery is accounted to the recess formed in the bearing clearance by deflections of the compliant surface and its effect on flow through the porous pad.

Evaluating the environmental Kuznets curve

We examine the empirical evidence for an environmental Kuznets curve using a semiparametric smooth coefficient regression model that allows us to incorporate flexibility in the parameter estimates, while maintaining the basic econometric structure that is typically used to estimate the pollution-income relationship. This allows us to assess the sensitivity to parameter heterogeneity of typical parametric models used to estimate the relationship between pollution and income, as well as identify why the results from such models are seldom found to be robust. Our results confirm that the resulting relationship between pollution and income is fragile; we show that the estimated pollution-income relationship depends substantially on the heterogeneity of the slope coefficients and the parameter values at which the relationship is evaluated. Different sets of parameters obtained from the semiparametric model give rise to many different shapes for the pollution-income relationship that are commonly found in the literature.

Laminar distribution of the pathological changes in sporadic frontotemporal lobar degeneration with transactive response (TAR) DNA-binding protein of 43kDa (TDP-43) proteinopathy:a quantitative study using polynomial curve fitting

Aims: Previous data suggest heterogeneity in laminar distribution of the pathology in the molecular disorder frontotemporal lobar degeneration (FTLD) with transactive response (TAR) DNA-binding protein of 43kDa (TDP-43) proteinopathy (FTLD-TDP). To study this heterogeneity, we quantified the changes in density across the cortical laminae of neuronal cytoplasmic inclusions, glial inclusions, neuronal intranuclear inclusions, dystrophic neurites, surviving neurones, abnormally enlarged neurones, and vacuoles in regions of the frontal and temporal lobe. Methods: Changes in density of histological features across cortical gyri were studied in 10 sporadic cases of FTLD-TDP using quantitative methods and polynomial curve fitting. Results: Our data suggest that laminar neuropathology in sporadic FTLD-TDP is highly variable. Most commonly, neuronal cytoplasmic inclusions, dystrophic neurites and vacuolation were abundant in the upper laminae and glial inclusions, neuronal intranuclear inclusions, abnormally enlarged neurones, and glial cell nuclei in the lower laminae. TDP-43-immunoreactive inclusions affected more of the cortical profile in longer duration cases; their distribution varied with disease subtype, but was unrelated to Braak tangle score. Different TDP-43-immunoreactive inclusions were not spatially correlated. Conclusions: Laminar distribution of pathological features in 10 sporadic cases of FTLD-TDP is heterogeneous and may be accounted for, in part, by disease subtype and disease duration. In addition, the feedforward and feedback cortico-cortical connections may be compromised in FTLD-TDP. © 2012 The Authors. Neuropathology and Applied Neurobiology © 2012 British Neuropathological Society.

Effect of fluid contaminant on the behaviour of a hydrostatic thrust bearing

DUE TO COPYRIGHT RESTRICTIONS ONLY AVAILABLE FOR CONSULTATION AT ASTON UNIVERSITY LIBRARY AND INFORMATION SERVICES WITH PRIOR ARRANGEMENT

A shape-based decomposition of the yield adjustment term in the arbitrage-free Nelson and Siegel (AFNS) model of the yield curve

The appealing feature of the arbitrage-free Nelson-Siegel model of the yield curve is the ability to capture movements in the yield curve through readily interpretable shifts in its level, slope or curvature, all within a dynamic arbitrage-free framework. To ensure that the level, slope and curvature factors evolve so as not to admit arbitrage, the model introduces a yield-adjustment term. This paper shows how the yield-adjustment term can also be decomposed into the familiar level, slope and curvature elements plus some additional readily interpretable shape adjustments. This means that, even in an arbitrage-free setting, it continues to be possible to interpret movements in the yield curve in terms of level, slope and curvature influences. © 2014 © 2014 Taylor & Francis.

Integer Points Close to a Smooth Curve

∗ This research is partially supported by the Bulgarian National Science Fund under contract MM-403/9

Structural Analysis of Contours as the Sequences of the Digital Straight Segments and of the Digital Curve Arcs

Recognition of the object contours in the image as sequences of digital straight segments and/or digital curve arcs is considered in this article. The definitions of digital straight segments and of digital curve arcs are proposed. The methods and programs to recognize the object contours are represented. The algorithm to recognize the digital straight segments is formulated in terms of the growing pyramidal networks taking into account the conceptual model of memory and identification (Rabinovich [4]).

Key Agreement Protocol Using Elliptic Curve Matrix Power Function

* Work is partially supported by the Lithuanian State Science and Studies Foundation.

Weierstrass Points with First Non-Gap Four on a Double Covering of a Hyperelliptic Curve

2000 Mathematics Subject Classification: Primary 14H55; Secondary 14H30, 14H40, 20M14.