Search results for "Spline"

Datorzinātne un informācijas tehnoloģijas

2011

Periodic Discrete Splines

2014

Periodic discrete splines with different periods and spans were introduced in Sect. 3.4. In this chapter, we discuss families of periodic discrete splines, whose periods and spans are powers of 2. As in the polynomial splines case, the Zak transform is extensively employed. It results in the Discrete Spline Harmonic Analysis (DSHA). Utilization of the Fast Fourier transform (FFT) enables us to implement all the computations in a fast explicit way.

A remarkable equality referring to spline functions in Hilbert spaces

2010

In the introduction of this paper is presented the definition of the generalized spline functions as solutions of a variational problem and are shown some theorems regarding to the existence and uniqueness. The main result of this article consists in a remarkable equality verified by the generalized spline elements, based on the properties of the spaces, operator and interpolatory set involved, which can be used as a characterization theorem of the generalized spline functions in Hilbert spaces.

Biorthogonal Multiwavelets Originated from Hermite Splines

2015

This chapter presents multiwavelet transforms that manipulate discrete-time signals. The transforms are implemented in two phases: 1. Pre (post)-processing, which transforms a scalar signal into a vector signal (and back). 2. Wavelet transforms of the vector signal. Both phases are performed in a lifting way. The cubic interpolating Hermite splines are used as a predicting aggregate in the vector wavelet transform. Pre(post)-processing algorithms which do not degrade the approximation accuracy of the vector wavelet transforms are presented. A scheme of vector wavelet transforms and three pre(post)-processing algorithms are described. As a result, we get fast biorthogonal algorithms to trans…

A new calculation procedure for non-uniform residual stress analysis by the hole-drilling method

1998

The hole-drilling method is one of the most used semi-destructive techniques for residual stress analysis in mechanical parts. In the presence of non-uniform residual stress, the stress field can be determined from the measured relaxed strains using several calculation methods, but the most used one is the so-called integral method. This method is characterized by some simplifications that lead to approximate results, especially when the residual stress varies abruptly. In this paper a new calculation procedure called the spline methods is proposed, which allows these drawbacks to be overcome. Numerical simulations and an experimental test have corroborated the best performance of the prop…

Prediction of BOD5 content of the inflow to the treatment plant using different methods of black box - the case study

2020

The publication presents the possibility of modeling in a 1 d advance of the content of organic compounds in the influent wastewater to the treatment plant, where the content of these compounds is determined by both the biochemical and chemical oxygen demand. To predict the quality of the wastewater at the inflow a set of indicators where used to make measurements on a daily basis. In order to develop statistical models 3 methods where used, namely: multivariate adaptive regression splines (MARS), boosted trees (BT), and genetic programming (GP). The carried-out calculations showed that, to calculate the BOD5 there can only be used models developed on the basis of the value of daily wastewa…

Assessment of Gully Erosion Susceptibility Using Multivariate Adaptive Regression Splines and Accounting for Terrain Connectivity

2017

In this work, we assessed gully erosion susceptibility in two adjacent cultivated catchments of Sicily (Italy) by employing multivariate adaptive regression splines (MARS) and a set of geo-environmental variables. To explore the influence of hydrological connectivity on gully occurrence we measured the changes of performance occurred when adding one by one nine predictors reflecting terrain connectivity to a base model that included contributing area and slope gradient. Receiver operating characteristic (ROC) curves and the area under the ROC curve (AUC) were used to evaluate models performance. Gully predictive models were trained in both the catchments and submitted to internal (in the ca…

Real-time image rotation using B-spline interpolation on FPGA's board

1998

The aim of our work is to realize the implementation of a real-time high-quality image rotation on FPGA's board. The method we used is based on M. Unser's work and consists in applying a B-spline interpolator. The difficulty of this problem is due to the relatively weak integration capacity of FPGAs. To solve this problem we have searched for determining the minimum number of bits to code the filter while keeping a good accuracy of filtering output. In this article, we remind a few definitions about B-spline functions and we present how we use B- spline interpolation for the image rotation problem. Then, we describe the way we calculate probability density function of the output error in or…

On mathematical modelling of the solid-liquid mixtures transport in porous axial-symmetrical container with Henry and Langmuir sorption kinetics

2018

In this paper we study diffusion and convection filtration problem of one substance through the pores of a porous material which may absorb and immobilize some of the diffusing substances. As an example we consider round cylinder with filtration process in the axial direction. The cylinder is filled with sorbent i.e. absorbent material that passed through dirty water or liquid solutions. We can derive the system of two partial differential equations (PDEs), one expressing the rate of change of concentration of water in the pores of the sorbent and the other - the rate of change of concentration in the sorbent or kinetical equation for absorption. The approximation of corresponding initial b…

ECONOMIC ACTIVITY, CREDIT MARKET CONDITIONS, AND THE HOUSING MARKET

2017

In this paper, we assess the characteristics of the housing market and its main determinants. Using data for 20 industrial countries over the period 1970Q1–2012Q2 and a discrete-time Weibull duration model, we find that the likelihood of the end of a housing boom or a housing bust increases over time. Additionally, we show that the different phases of the housing market cycle are strongly dependent on the economic activity, but credit market conditions are particularly important in the case of housing booms. The empirical findings also indicate that although housing booms have similar lengths in European and non-European countries, housing busts are typically shorter in European countries. …