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Functional Relation (functional + relation)
Selected AbstractsComputational form-finding of tension membrane structures,Non-finite element approaches: Part 1.INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2003Use of cubic splines in finding minimal surface membranes Abstract This paper, presented in three parts, discusses a computational methodology for form-finding of tension membrane structures (TMS), or fabric structures, used as roofing forms. The term ,form-finding' describes a process of finding the shape of a TMS under its initial tension. Such a shape is neither known a priori, nor can it be described by a simple mathematical function. The work is motivated by the need to provide an efficient numerical tool, which will allow a better integration of the design/analysis/manufacture of TMS. A particular category of structural forms is considered, known as minimal surface membranes (such as can be reproduced by soap films). The numerical method adopted throughout is dynamic relaxation (DR) with kinetic damping. Part 1 describes a new form-finding approach, based on the Laplace,Young equation and cubic spline fitting to give a full, piecewise, analytical description of a minimal surface. The advantages arising from the approach, particularly with regard to manufacture of cutting patterns for a membrane, are highlighted. Part 2 describes an alternative and novel form-finding approach, based on a constant tension field and faceted (triangular mesh) representation of the minimal surface. It presents techniques for controlling mesh distortion and discusses effects of mesh control on the accuracy and computational efficiency of the solution, as well as on the subsequent stages in design. Part 3 gives a comparison of the performance of the initial method (Part 1) and the faceted approximations (Part 2). Functional relations, which encapsulate the numerical efficiency of each method, are presented. Copyright © 2002 John Wiley & Sons, Ltd. [source] Computational form-finding of tension membrane structures,Non-finite element approaches: Part 2.INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2003Triangular mesh discretization, control of mesh distortion in modelling minimal surface membranes Abstract This paper, presented in three parts, discusses a computational methodology for form-finding of tension membrane structures (TMS), or fabric structures, used as roofing forms. The term ,form-finding' describes a process of finding the shape of a TMS under its initial tension. Such a shape is neither known a priori, nor can it be described by a simple mathematical function. The work is motivated by the need to provide an efficient numerical tool, which will allow a better integration of the design/analysis/manufacture of TMS. A particular category of structural forms is considered, known as minimal surface membranes (such as can be reproduced by soap films). The numerical method adopted throughout is dynamic relaxation (DR) with kinetic damping. Part 1 gave a background to the problem of TMS design, described the DR method, and presented a new form-finding methodology, based on the Laplace,Young equation and cubic spline fitting to give a full, piecewise, analytical description of the surface. Part 2 describes an alternative and novel form-finding method, based on a constant tension field and faceted (triangular mesh) representation of the minimal surface. Techniques for controlling mesh distortion are presented, and their effects on the accuracy and computational efficiency of the solution, as well as on the subsequent stages in design, are examined. Part 3 gives a comparison of the performance of the initial method (Part 1) and the faceted approximations (Part 2). Functional relations, which encapsulate the numerical efficiency of each method, are presented. Copyright © 2002 John Wiley & Sons, Ltd. [source] Hierarchy of equations in the generalized density functional theoryINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 5 2006Į. NagyArticle first published online: 28 NOV 200 Abstract Functional relations and equations of hierarchy in the generalized density functional theory (DFT) are derived from coordinate scaling and adiabatic connection. Local and nonlocal solutions for the noninteracting kinetic energy, exchange energy, correlation energy, and the kinetic energy correction functionals are presented. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006 [source] A Parametric Approach to Flexible Nonlinear InferenceECONOMETRICA, Issue 3 2001James D. Hamilton This paper proposes a new framework for determining whether a given relationship is nonlinear, what the nonlinearity looks like, and whether it is adequately described by a particular parametric model. The paper studies a regression or forecasting model of the form yt=,(xt)+,t where the functional form of ,(,) is unknown. We propose viewing ,(,) itself as the outcome of a random process. The paper introduces a new stationary random field m(,) that generalizes finite-differenced Brownian motion to a vector field and whose realizations could represent a broad class of possible forms for ,(,). We view the parameters that characterize the relation between a given realization of m(,) and the particular value of ,(,) for a given sample as population parameters to be estimated by maximum likelihood or Bayesian methods. We show that the resulting inference about the functional relation also yields consistent estimates for a broad class of deterministic functions ,(,). The paper further develops a new test of the null hypothesis of linearity based on the Lagrange multiplier principle and small-sample confidence intervals based on numerical Bayesian methods. An empirical application suggests that properly accounting for the nonlinearity of the inflation-unemployment trade-off may explain the previously reported uneven empirical success of the Phillips Curve. [source] Effect of degree of fluid saturation on transport coefficients in disturbed soilsEUROPEAN JOURNAL OF SOIL SCIENCE, Issue 1 2004A. Tuli Summary To improve the predictive capability of transport models in soils we need experimental data that improve their understanding of properties at the scale of pores, including the effect of degree of fluid saturation. All transport occurs in the same soil pore space, so that one may intuitively expect a link between the different transport coefficients and key geometrical characteristics of the pores such as tortuosity and connectivity, and pore-size distribution. To understand the combined effects of pore geometry and pore-size distribution better, we measured the effect of degree of water saturation on hydraulic conductivity and bulk soil electrical conductivity, and of degree of air saturation on air conductivity and gaseous diffusion for a fine sand and a sandy loam soil. To all measured data were fitted a general transport model that includes both pore geometry and pore-size distribution parameters. The results show that both pore geometry and pore-size distribution determine the functional relations between degree of saturation, hydraulic conductivity and air conductivity. The control of pore size on convective transport is more for soils with a wider pore-size distribution. However, the relative contribution of pore-size distribution is much larger for the unsaturated hydraulic conductivity than for gaseous phase transport. For the other transport coefficients, their saturation dependency could be described solely by the pore-geometry term. The contribution of the latter to transport was much larger for transport in the air phase than in the water phase, supporting the view that connectivity dominates gaseous transport. Although the relation between effective fluid saturation and all four relative transport coefficients for the sand could be described by a single functional relation, the presence of a universal relationship between fluid saturation and transport for all soils is doubtful. [source] Orientational analysis of planar fibre systems observed as a Poisson shot-noise processJOURNAL OF MICROSCOPY, Issue 1 2007SALME KÄRKKÄINEN Summary We consider two-dimensional fibrous materials observed as a digital greyscale image. The problem addressed is to estimate the orientation distribution of unobservable thin fibres from a greyscale image modelled by a planar Poisson shot-noise process. The classical stereological approach is not straightforward, because the point intensities of thin fibres along sampling lines may not be observable. For such cases, Kärkkäinen et al. (2001) suggested the use of scaled variograms determined from grey values along sampling lines in several directions. Their method is based on the assumption that the proportion between the scaled variograms and point intensities in all directions of sampling lines is constant. This assumption is proved to be valid asymptotically for Boolean models and dead leaves models, under some regularity conditions. In this work, we derive the scaled variogram and its approximations for a planar Poisson shot-noise process using the modified Bessel function. In the case of reasonable high resolution of the observed image, the scaled variogram has an approximate functional relation to the point intensity, and in the case of high resolution the relation is proportional. As the obtained relations are approximative, they are tested on simulations. The existing orientation analysis method based on the proportional relation is further experimented on images with different resolutions. The new result, the asymptotic proportionality between the scaled variograms and the point intensities for a Poisson shot-noise process, completes the earlier results for the Boolean models and for the dead leaves models. [source] On the relation between the association strength and other similarity measuresJOURNAL OF THE AMERICAN SOCIETY FOR INFORMATION SCIENCE AND TECHNOLOGY, Issue 7 2010Leo Egghe A graph in van Eck and Waltman [JASIST, 60(8), 2009, p. 1644], representing the relation between the association strength and the cosine, is partially explained as a sheaf of parabolas, each parabola being the functional relation between these similarity measures on the trajectories , a constant. Based on earlier obtained relations between cosine and other similarity measures (e.g., Jaccard index), we can prove new relations between the association strength and these other measures. [source] A boundary value problem for the spherically symmetric motion of a pressureless gas with a temperature-dependent viscosityMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 16 2009Bernard Ducomet Abstract We consider an initial-boundary value problem for the equations of spherically symmetric motion of a pressureless gas with temperature-dependent viscosity µ(,) and conductivity ,(,). We prove that this problem admits a unique weak solution, assuming Belov's functional relation between µ(,) and ,(,) and we give the behaviour of the solution for large times. Copyright © 2009 John Wiley & Sons, Ltd. [source] Response to cutting of Larrea divaricata and L. cuneifolia in ArgentinaAPPLIED VEGETATION SCIENCE, Issue 1 2002E. Martinez Carretero Abstract. The response of Larrea divaricata and L. cuneifolia to cutting stems 0,20 cm above the ground was studied in the arid piedmont area west of Mendoza, Argentina. The species occur at different elevations and in vegetation zones: L. cuneifolia < 1250 m; L. divaricata between 1250 and 2500 m. Four treatments with 10 replicates were analysed in randomly chosen plants: cut at ground level with lopping shears; cut at ground level with a pick; cut at 10 cm with lopping shears; and cut at 20 cm with lopping shears. The initial and final height, volume, and dry matter (above- and below-ground) were determined. The relation between volume and initial and final dry matter and height was analysed through a factorial MANOVA (p < 0,05), and the functional relation between volume, dry matter and height was estimated by adjusting a regression model. In both species, maximum recovery was reached when cut with shears, and predicted recovery (turnover) was 17-18 yr. In the two last treatments height was a useful predictor of dry matter. L. divaricata -dominated plots have a lower biomass, growth rate, and allocation to stems and root than L. cuneifolia -dominated plots. Regrowth following clipping on an area of 3,10 ha, is sufficient to support the annual needs (cooking and heating) of one family. [source] Combining descriptive and functional analyses to assess and treat screamingBEHAVIORAL INTERVENTIONS, Issue 2 2003G. Tracey Galiatsatos This study systematically examined the functional relation between screaming and environmental events in a 13-year-old boy diagnosed with autism and PDD-NOS. A functional analysis of screaming was conducted in study 1, with six conditions (attention, demand, play, alone, tangible,toy, and tangible,edible). Highest rates of screaming were observed during the tangible,toy and tangible,edible conditions. The analog assessment was followed by a descriptive assessment, which revealed the participant was most likely to scream when teacher attention was diverted to other students. Additionally, items found to maintain screaming during the analog assessment were never delivered contingent upon screaming in the participant's natural environment. The results of the descriptive assessment suggested that the analog assessment might have produced a false-positive outcome. A treatment based upon the results of the combined assessments led to a 50% reduction in screaming within four weeks. Two-year follow-up data indicated that screaming occurred at near-zero rates. Copyright © 2003 John Wiley & Sons, Ltd. [source] Decreasing rumination using a starchy food satiation procedureBEHAVIORAL INTERVENTIONS, Issue 1 2002Laura L. Dudley A starchy food satiation procedure was evaluated in an ABAB withdrawal design on the post-meal rumination of a nine-year-old girl with autism. During treatment unlimited quantities of starchy foods were provided following each meal. High rates of rumination occurred during baseline conditions, followed by an immediate decrease in rumination during treatment. Rumination decreased to 82 and 97% of baseline during the first and second treatment conditions, respectively. In addition, follow-up probes were conducted at irregular intervals for 4 years following treatment, during which zero or near-zero rates of rumination were sustained. This study extends the literature on the functional relation between increased starchy food quantity and rumination in adults to rumination with a young child, and demonstrates maintenance of the treatment effect for 4 years. Copyright © 2002 John Wiley & Sons, Ltd. [source] Effect of degree of fluid saturation on transport coefficients in disturbed soilsEUROPEAN JOURNAL OF SOIL SCIENCE, Issue 1 2004A. Tuli Summary To improve the predictive capability of transport models in soils we need experimental data that improve their understanding of properties at the scale of pores, including the effect of degree of fluid saturation. All transport occurs in the same soil pore space, so that one may intuitively expect a link between the different transport coefficients and key geometrical characteristics of the pores such as tortuosity and connectivity, and pore-size distribution. To understand the combined effects of pore geometry and pore-size distribution better, we measured the effect of degree of water saturation on hydraulic conductivity and bulk soil electrical conductivity, and of degree of air saturation on air conductivity and gaseous diffusion for a fine sand and a sandy loam soil. To all measured data were fitted a general transport model that includes both pore geometry and pore-size distribution parameters. The results show that both pore geometry and pore-size distribution determine the functional relations between degree of saturation, hydraulic conductivity and air conductivity. The control of pore size on convective transport is more for soils with a wider pore-size distribution. However, the relative contribution of pore-size distribution is much larger for the unsaturated hydraulic conductivity than for gaseous phase transport. For the other transport coefficients, their saturation dependency could be described solely by the pore-geometry term. The contribution of the latter to transport was much larger for transport in the air phase than in the water phase, supporting the view that connectivity dominates gaseous transport. Although the relation between effective fluid saturation and all four relative transport coefficients for the sand could be described by a single functional relation, the presence of a universal relationship between fluid saturation and transport for all soils is doubtful. [source] A new high-order finite volume element method with spectral-like resolutionINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3-4 2002F. Sarghini Abstract In this work, a new high-order finite volume element method with good spatial resolution characteristics is presented. The method is based on a functional representation of the unknowns based on the finite element method, a balance of physical quantities in weak formulation obtained by using the finite volume method, and an implicit reduction of some of the unknowns obtained by enforcing functional relations between some of them. Applications to hyperbolic and elliptic operators in 1D and 2D, as well as to Navier,Stokes equations for incompressible flows are presented. Copyright © 2002 John Wiley & Sons, Ltd. [source] New relations between similarity measures for vectors based on vector normsJOURNAL OF THE AMERICAN SOCIETY FOR INFORMATION SCIENCE AND TECHNOLOGY, Issue 2 2009Leo Egghe The well-known similarity measures Jaccard, Salton's cosine, Dice, and several related overlap measures for vectors are compared. While general relations are not possible to prove, we study these measures on the "trajectories" of the form , where a > 0 is a constant and ||·|| denotes the Euclidean norm of a vector. In this case, direct functional relations between these measures are proved. For Jaccard, we prove that it is a convexly increasing function of Salton's cosine measure, but always smaller than or equal to the latter, hereby explaining a curve, experimentally found by Leydesdorff. All the other measures have a linear relation with Salton's cosine, reducing even to equality, in case a = 1. Hence, for equally normed vectors (e.g., for normalized vectors) we, essentially, only have Jaccard's measure and Salton's cosine measure since all the other measures are equal to the latter. [source] | |||||||||||||