Search results for "collocation"
showing 10 items of 58 documents
ΔP as a measure of collocation strength
2018
AbstractThis paper explores the proposed benefits of ΔP (delta P) as a measure of collocation strength. Its focus is on contrasting ΔP with other, more commonly used, association measures, particularly transitional probabilities, but also mutual information and Lexical Gravity G. To this end, first the strong correlation between ΔP and transitional probability is illustrated with the help of two exemplary corpora. This is followed by an analysis of hesitation placement in spontaneous spoken English, based on the assumption that hesitations will not be placed within strong collocations. Results show that, despite their strong similarity, in some contexts ΔP is more predictive of hesitation p…
Multiplicity results for a class of asymmetric weakly coupled systems of second order ordinary differential equations
2005
We prove the existence and multiplicity of solutions to a two-point boundary value problem associated to a weakly coupled system of asymmetric second-order equations. Applying a classical change of variables, we transform the initial problem into an equivalent problem whose solutions can be characterized by their nodal properties. The proof is developed in the framework of the shooting methods and it is based on some estimates on the rotation numbers associated to each component of the solutions to the equivalent system.
Oscillation criteria for even-order neutral differential equations
2016
Abstract We study oscillatory behavior of solutions to a class of even-order neutral differential equations relating oscillation of higher-order equations to that of a pair of associated first-order delay differential equations. As illustrated with two examples in the final part of the paper, our criteria improve a number of related results reported in the literature.
Domain decomposition in the symmetric boundary element analysis
2002
Recent developments in the symmetric boundary element method (SBEM) have shown a clear superiority of this formulation over the collocation method. Its competitiveness has been tested in comparison to the finite element method (FEM) and is manifested in several engineering problems in which internal boundaries are present, i.e. those in which the body shows a jump in the physical characteristics of the material and in which an appropriate study of the response must be used. When we work in the ambit of the SBE formulation, the body is subdivided into macroelements characterized by some relations which link the interface boundary unknowns to the external actions. These relations, valid for e…
Consistency between GRUAN sondes, LBLRTM and IASI
2017
Abstract. Radiosonde soundings from the GCOS Reference Upper-Air Network (GRUAN) data record are shown to be consistent with Infrared Atmospheric Sounding Instrument (IASI)-measured radiances via LBLRTM (Line-By-Line Radiative Transfer Model) in the part of the spectrum that is mostly affected by water vapour absorption in the upper troposphere (from 700 hPa up). This result is key for climate data records, since GRUAN, IASI and LBLRTM constitute reference measurements or a reference radiative transfer model in each of their fields. This is specially the case for night-time radiosonde measurements. Although the sample size is small (16 cases), daytime GRUAN radiosonde measurements seem to h…
Blow-up collocation solutions of nonlinear homogeneous Volterra integral equations
2011
In this paper, collocation methods are used for detecting blow-up solutions of nonlinear homogeneous Volterra-Hammerstein integral equations. To do this, we introduce the concept of "blow-up collocation solution" and analyze numerically some blow-up time estimates using collocation methods in particular examples where previous results about existence and uniqueness can be applied. Finally, we discuss the relationships between necessary conditions for blow-up of collocation solutions and exact solutions.
Collocation Method for Linear BVPs via B-spline Based Fuzzy Transform
2018
The paper is devoted to an application of a modified F-transform technique based on B-splines in solving linear boundary value problems via the collocation method. An approximate solution is sought as a composite F-transform of a discrete function (which allows the solution to be compactly stored as the values of this discrete function). We demonstrate the effectiveness of the described technique with numerical examples, compare it with other methods and propose theoretical results on the order of approximation when the fuzzy partition is based on cubic B-splines.
A Generalised RBF Finite Difference Approach to Solve Nonlinear Heat Conduction Problems on Unstructured Datasets
2011
Radial Basis Functions have traditionally been used to provide a continuous interpolation of scattered data sets. However, this interpolation also allows for the reconstruction of partial derivatives throughout the solution field, which can then be used to drive the solution of a partial differential equation. Since the interpolation takes place on a scattered dataset with no local connectivity, the solution is essentially meshless. RBF-based methods have been successfully used to solve a wide variety of PDEs in this fashion. Such full-domain RBF methods are highly flexible and can exhibit spectral convergence rates Madych & Nelson (1990). However, in their traditional implementation the fu…
A comparison analysis between unsymmetric and symmetric radial basis function collocation methods for the numerical solution of partial differential …
2002
Abstract In this article, we present a thorough numerical comparison between unsymmetric and symmetric radial basis function collocation methods for the numerical solution of boundary value problems for partial differential equations. A series of test examples was solved with these two schemes, different problems with different type of governing equations, and boundary conditions. Particular emphasis was paid to the ability of these schemes to solve the steady-state convection-diffusion equation at high values of the Peclet number. From the examples tested in this work, it was observed that the system of algebraic equations obtained with the symmetric method was in general simpler to solve …
Geometry/Time Measurement/Sundials Graphical Resolution via Algorithmic and Parametric Processes
2018
Every people, in every historical period, developed methods to measure Time both at a daily scale and at a yearly scale. Some of them constructed sundials to represent the apparent trajectory of the Sun around the Earth, by using and developing tools from descriptive and projective Geometry, mainly. This subject acquired a great multidisciplinary interest since ancient times, also for Science of Representation applications. This study presents the first results of an ongoing research concerning some aspects related to Time Measurement. The geometric-spatial setting of the Sun-Earth system is described and is structured parametrically via algorithms, following the known conventions shared an…