Search results for "basis"
showing 10 items of 760 documents
Timed Sets, Functional Complexity, and Computability
2012
AbstractThe construction of various categories of “timed sets” is described in which the timing of maps is considered modulo a “complexity order”. The properties of these categories are developed: under appropriate conditions they form discrete, distributive restriction categories with an iteration. They provide a categorical basis for modeling functional complexity classes and allow the development of computability within these settings. Indeed, by considering “program objects” and the functions they compute, one can obtain models of computability – i.e. Turing categories – in which the total maps belong to specific complexity classes. Two examples of this are introduced in some detail whi…
Locally Supported Wavelets on the Sphere
1998
We construct explicitly wavelets on the sphere that provide a locally supported and stable basis for the Sobolev spaces H2,0 ⩽ s < 1. We get at hand at fast wavelet transform with almost optimal complexity. This basis can be easily implemented in numerical schemes. We apply the wavelet transform to singularity detection and data compression. This contribution summarizes the results of [1].
Periodic Spline Wavelets and Wavelet Packets
2014
This chapter presents wavelets and wavelet packets in the spaces of periodic splines of arbitrary order, which, in essence, are the multiple generators for these spaces. The SHA technique provides explicit representation of the wavelets and wavelet packets and fast implementation of the transforms in one and several dimensions.
Discrete-mathematical approach to formal description of measurement procedure
1996
The discrete-mathematical model of measurement procedure is developed for facilitating the description of measurements in both quantitative and qualitative scales. On the basis of this model the Measurement Problem is formulated. It is shown that the problem can be considered, in the general case, as one of the discrete optimization problems. The suggested approach brings closer the concepts of a computing algorithm and measurement procedure so that it permits the application of similar tools for the analysis and development of both of them.
Optimization of a Sea Wave Energy Harvesting Electromagnetic Device
2008
This paper presents the optimization of a permanent magnet linear generator directly coupled to sea waves. In order to maximize energy extraction, the stochastic features of the energy source is included in the mathematical model of the system in order to satisfactorily tackle the problem. An optimization procedure which includes the stochastic features of the model is presented and a machine built on the basis of the results of this procedure is shown.
An Advanced Numerical Model in Solving Thin-Wire Integral Equations by Using Semi-Orthogonal Compactly Supported Spline Wavelets
2003
Abstract—In this paper, the semi-orthogonal compactly sup- ported spline wavelets are used as basis functions for the efficient solution of the thin-wire electric field integral equation (EFIE) in frequency domain. The method of moments (MoM) is used via the Galerkin procedure. Conventional MoM directly applied to the EFIE, leads to dense matrix which often becomes computation- ally intractable when large-scale problems are approached. To overcome these difficulties, wavelets can be used as a basis set so obtaining the generation of a sparse matrix; this is due to the local supports and the vanishing moments properties of the wavelets. In the paper, this technique is applied to analyze elec…
Highly efficient full-wave electromagnetic analysis of 3-D arbitrarily shaped waveguide microwave devices using an integral equation technique
2015
A novel technique for the full-wave analysis of 3-D complex waveguide devices is presented. This new formulation, based on the Boundary Integral-Resonant Mode Expansion (BI-RME) method, allows the rigorous full-wave electromagnetic characterization of 3-D arbitrarily shaped metallic structures making use of extremely low CPU resources (both time and memory). The unknown electric current density on the surface of the metallic elements is represented by means of Rao-Wilton-Glisson basis functions, and an algebraic procedure based on a singular value decomposition is applied to transform such functions into the classical solenoidal and nonsolenoidal basis functions needed by the original BI-RM…
A molecular electron density theory study of the chemo- and regioselective [3 + 2] cycloaddition reactions between trifluoroacetonitrile N-oxide and …
2018
Abstract The [3 + 2] cycloaddition (32CA) reaction between trifluoroacetonitrile N-oxide (NO 7) and 2,2,4,4-tetramethyl-3-thioxocyclobutan-1-one (THK 12) as well as the self-dimerization of NO 7 as a competitive pathway were studied within the Molecular Electron Density Theory (MEDT) using several DFT functionals together with def2-TZVP basis set. Taking CCSD(T)/TZVP activation energies as reference, among the employed functionals, just the B2PLYP-D3(BJ) one is able to portray complete predominance of 32CA reaction over self-dimerization process in excellent agreement with the experimental outcomes. Analysis of the global reactivity indices permits to characterize NO 7 and THK 12 as a stron…
Comparative density-functional LCAO and plane-wave calculations ofLaMnO3surfaces
2005
We compare two approaches to the atomic, electronic, and magnetic structures of LaMnO3 bulk and the (001), (110) surfaces—hybrid B3PW with optimized LCAO basis set (CRYSTAL-2003 code) and GGA-PW91 with plane-wave basis set (VASP 4.6 code). Combining our calculations with those available in the literature, we demonstrate that combination of nonlocal exchange and correlation used in hybrid functionals allows to reproduce the experimental magnetic coupling constants Jab and Jc as well as the optical gap. Surface calculations performed by both methods using slab models show that the antiferromagnetic (AF) and ferromagnetic (FM) (001) surfaces have lower surface energies than the FM (110) surfac…
Computational modeling of isotropic electron paramagnetic resonance spectra of doublet state main group radicals
2007
The combined use of theoretical and mathematical methods in the analysis of electron paramagnetic resonance data has greatly increased the ability to interpret even the most complex spectra reported for doublet state inorganic main group radicals. This personal account summarizes the theoretical basis of such an approach and provides an in-depth discussion of some recent illustrative examples of the utilization of this methodology in practical applications. The emphasis is on displaying the enormous potential embodied within the approach. peerReviewed