In this study nano-crystalline ZnO particles were synthesized by microwave-assisted solution combustion method. Zinc nitrate and urea were used as oxidizer and fuel, respectively. The effect of fuel to oxidizer (F/O) ratio on ZnO powder properties was investigated by using different urea/nitrate ratios. X-ray diffractometer, scanning electron microscopy and fourier transform infra-red were used...

The Fuzzy transform is applied mainly to 1-D signals and 2-D data organized as a regular grid (e.g., images), thus, limiting its potential application arbitrary in terms of dimensionality structure. This article defines analyzes the properties data-driven F-transform, with focus on construction class membership functions, which are multiscale, local, linearly independent, intrinsic, robust disc...

The classical Shannon sampling theorem states that a signal f with Fourier transform F ∈ L(R) having its support contained in (−π, π) can be recovered from the sequence of samples (f(n))n∈Z via f(t) = ∑ n∈Z f(n) sin(π(t− n)) π(t− n) (t ∈ R). In this article we prove a generalization of this result under the assumption that F ∈ E (R) has support contained in (−π, π).

zero), and a single object (N=1) is situated at a known objThe problem of detecting, locating and charaprojectioerizing location; see [1-3] for a discussion of ML localization of objects in a 2D cross-section from noisy projection data an object from noisy projection measurements. has been considered recently [1-3], in which objects are characterized by a finite number of parameters, which In t...

It is known that if the support of a function $f \in L^{1}(\mathbb{R}^{n})$ and its Fourier transform have finite measure then $f=0$ almost everywhere. We study generalizations this property for semisimple Lie groups.

A propagation of pulse generated by an electric dipole is studied. A general formula for the electric field, which is uniformly valid for large distance and time, is presented. Fourier transform, stationary phase and simple contour integration methods are applied. 1. CURRENT PULSE AND FOURIER TRANSFORM Electric dipole is excited by a current I(t) = I0f(t) where f(t) is a pulse. The Fourier tran...

Abstract. We have combined the Laplace transform and the Stieltjes transform of the form f̂(x) = R∞ 0 f(t) (xm+tm)ρ dt, m, ρ > 0 and applied it to an ordered vector space of generalized functions to which the topology of bounded convergence is assigned. Some of the order properties of the transform and its inverse are studied. Also we solve an initial value problem and compare different solution...

The most commonly applied technique to obtain an estimated power spectrum ) ( ˆ f S of a sampled time series ) (t x of finite length N, is to compute the Fourier transform ) 2 ( f j X  , followed by multiplication by its complex conjugate and scaling by the length of the finite observation, i.e. N f j X f j X f S / ) 2 ( ) 2 ( ) ( ˆ *     (see Chapter 7 in van Drongelen, 2007). The reliabi...

In this paper we study Hyers-Ulam stability of Euler’s equation in the calculus variations two special cases: when F=F(x,y′) and F=F(y,y′). For first case use direct method for second Laplace transform. Theorem Example corresponding estimations Jyx−Jy0x are given. We mention that it is time problem Ulam-stability extremals functionals represented integral form studied.

Glossary WT1D The one-dimensional Wavelet Transform as defined in [1]. See also [2] in this volume. WT2D The two-dimensional Wavelet Transform. Discrete Ridgelet Trasnform (DRT) The discrete implementation of the continuous Ridgelet transform. Fast Slant Stack (FSS) An algebraically exact Radon transform of data on a Cartesian grid. First Generation Discrete Curvelet Transform (DCTG1) The discr...