Spectral expansion

Unexpected routes to synthesize functionalized benzoxocinones and heteroannulated pyranochromenes were achieved via transformations of the γ -pyrone ring in chromone-3-carboxylic acid throughout its reactions with some acyclic and cyclic carbon nucleophiles. A key part of the reaction mechanisms is discussed. Structures of the new synthesized products were established on the basis of elemental analysis and spectral data (IR, MS, and 1H and 13C NMR).

14p langthannam 29-12-2021 5 0   Download

Formulae expressing explicitly the q-difference derivatives and the moments of the polynomials Pn(x ; q) ∈ T (T ={Pn(x ; q) ∈ Askey–Wilson polynomials: Al-Salam-Carlitz I, Discrete q-Hermite I, Little (Big) q-Laguerre, Little (Big) q-Jacobi, q-Hahn, Alternative q-Charlier) of any degree and for any order in terms of Pi(x ; q) themselves are proved. We will also provide two other interesting formulae to expand the coefficients of general-order q-difference derivatives Dp q f (x), and for the moments xDp q f (x), of an arbitrary function f(x) in terms of its original expansion coefficients.

15p kethamoi1 20-11-2019 14 0   Download

The analysis of the spectral properties and dynamic evolution of a CME/shock event observed on November 1st 2003 in white-light by the LASCO coronagraph and in the ultraviolet by the UVCS instrument operating aboard SOHO, has been performed to compute the properties of some important plasma parameters in the middle corona below about 2Rx. Simultaneous observations obtained with the MLSO/Mk4 white-light coronagraph, providing both the early evolution of the CME expansion in the corona and the pre-shock electron density profile along the CME front, were also used to study this event.

4p kethamoi1 17-11-2019 14 0   Download

Matrix-Assisted Laser Desorption Ionization Time-Of-Flight Mass Spectrometry (MALDI-TOF MS) has become one of the most popular methods for the rapid, cost-effective and accurate classification and characterization of cultivable microorganisms. Due to its simple sample preparation and short measurement time, MALDI-TOF MS is an excellent choice for the high-throughput study of microbial isolates from rhizospheres or plants grown under diverse environmental conditions.

6p caygaocaolon1 13-11-2019 11 1   Download

In this work, we study the one-dimensional Dirac system on a whole line with impulsive conditions. We construct a spectral function of this system. Using the spectral function, we establish a Parseval equality and spectral expansion formula for such a system.

19p nutifooddau 21-01-2019 17 2   Download

In this paper we show how one can deduce the Titchmarsh expansion formula in eigenfunctions of Hill’s operator from the Gel’fand expansion formula.

15p tuongvidanh 06-01-2019 13 2   Download

This intuitive yet rigourous introduction derives the core results of digital communication from first principles. Theory, rather than industry standards, motivates the engineering approaches, and key results are stated with all the required assumptions. The book emphasizes the geometric view, opening with the inner product, the matched filter for its computation, Parseval's theorem, the sampling theorem as an orthonormal expansion, the isometry between passband signals and their baseband representation, and the spectral-efficiency optimality of quadrature amplitude modulation (QAM).

0p ringphone 06-05-2013 59 6   Download

V an isometry, as in the theorem of Plancherel, is not just a weighted L2-norm on some measure space. This is due to the fact that the back transformation Z has a different expression on each branch, and this is caused by the ramification of the domain. It is not clear to us how one could find a family of generalized eigenfunctions leading to a spectral representation of A.

0p camchuong_1 04-12-2012 62 3   Download

The splitting point b must be chosen large enough that the remaining integral over (b, ∞) is small. Successive terms in its asymptotic expansion are found by integrating by parts. The integral over (a, b) can be done using dftint.

16p babyuni 17-08-2010 62 10   Download

The past 20 years witnessed an expansion of power spectrum estimation techniques, which have proved essential in many applications, such as communications, sonar, radar, speech/image processing, geophysics, and biomedical signal processing [13, 11, 7].

16p nguyen4 17-11-2009 67 7   Download