In a series of papers, we suggested non-statistical method for the detection structural breaks in time series. It is based on applications special fuzzy modeling methods, namely Fuzzy transform (F-transform) and selected methods Natural Logic (FNL). this paper, combine our with principles classical Chow test, which well-known statistical testing presence break. The idea to construct statistics ...

We propose a novel direct sampling method (DSM) for the effective and stable inversion of Radon transform. The DSM is based on generalization important almost orthogonality property in classical DSMs to fractional order Sobolev duality products new family probing functions. product proves be able greatly enhance robustness reconstructions some practically but severely ill-posed inverse problems...

In the present work, we report on synthesis of EuSO4 powders by two different methods using EuS as starting material. The compound contains divalent europium and crystallizes in orthorhombic crystal system, space group Pnma with parameters close to SrSO4. exhibits near isotropic thermal expansion over temperature range 300–700 K. was examined Raman, Fourier-transform infrared absorption lumines...

This paper describes an implementation of the Discrete Fourier Transform (DFT) and the Inverse Discrete Fourier Transform (IDFT). We show how the computation of the DFT and IDFT may be performed in Java and show why such operations are typically considered slow. This is a multi-part paper, in part 2, we discuss a speed up of the DFT and IDFT using a class of algorithms known as the FFT (Fast Fo...

The necessary conditions to transform hydroxyamide (1) and 2-oxazolines (2, 3) into 3- or 4-methyl benzo[f] isoquinolines (4, 5) has been established. The mechanism of these reactions has been proposed claiming the existence of the protonated 2-oxazoline (6) and the styrylamides (7) as intermediates.

[08.3] Compute e−πx 2 ∗ e−πx2 and sinx x ∗ sinx x . (Be careful what you assert: sin x x is not in L (R).) Discussion: The idea is to invoke f ∗ g = (f̂ · ĝ)̂ for even functions f, g ∈ L, since for even functions the inverse Fourier transform is the same as the forward Fourier transform. Conveniently, Gaussians are in L ∩ L, and have Fourier transforms which are again Gaussians: ̂ e−πax(ξ) = 1 √ a...

Harmonic analysis is at the heart of much of signal and image processing. This is mainly the harmonic analysis of abelian groups, and ultimately, after sampling, and quantizing, finite abelian groups. Nevertheless, this general group theoretic viewpoint has proved fruitful, yielding a natural group-based multiresolution framework as well as some new and potentially useful nonabelian examples. T...

Let (M, g) be a simple Riemannian manifold. Under the assumption that the metric g is real-analytic, it is shown that if the geodesic ray transform of a function f ∈ L(M) vanishes on an appropriate open set of geodesics, then f = 0 on the set of points lying on these geodesics. Using this result, a version of Helgason’s support theorem for the geodesic ray transform is proven. The approach is b...

The need to evaluate expressions of the form f(A) or f(A)b, where f is a nonlinear function, A is a large sparse n × n matrix, and b is an n-vector, arises in many applications. This paper describes how the Faber transform applied to the field of values of A can be used to determine improved error bounds for popular polynomial approximation methods based on the Arnoldi process. Applications of ...