We present theoretical arguments and strong phenomenological evidence that hadronic Regge trajectories are essentially nonlinear and can be well approximated, for phenomenological purposes, by a specific square-root form.

The Fourier and Fourier-Stieltjes algebras A(G) and B(G) of a locally compact group G are introduced and studied in 60’s by Piere Eymard in his PhD thesis. If G is a locally compact abelian group, then A(G) ≃ L(Ĝ), and B(G) ≃ M(Ĝ), via the Fourier and Fourier-Stieltjes transforms, where Ĝ is the Pontryagin dual of G. Recently these algebras are defined on a (topological or measured) groupoid an...

Editor’s note: This Commentary is a companion to Refractory Depression, Fatigue, Irritable Bowel Syndrome, and Chronic Pain: A Functional Medicine Case Report on page 104 (available at: www.thepermanentejournal.org/ issues/2016/fall/6239-ibs.html). Also note that material describing the foundation and practice of Functional Medicine has been excerpted, with permission, from Introduction to Func...

A method is described for validating fast Fourier transforms (FFTs) based on the use of simple input fiinctions whose discrete Fourier transforms can be evaluated in closed form. Explicit analytical results are developed for one-dimensional and two-dimensional discrete Fourier transforms. The analytical results are easily generalized to higher dimensions. The results offer a means for validatin...

Dirichlet series and Fourier series can both be used to encode sequences of complex numbers an , n ∈ N. Dirichlet series do so in a manner adapted to the multiplicative structure of N, whereas Fourier series reflect the additive structure of N. Formally at least, the Mellin transform relates these two ways of representing sequences. In this paper, we make sense of the Mellin transform of period...

In this study, Santa Barbara Amorphous (SBA-15) mesoporous silica has been functionalized with aminopropyl groups that were converted to propargyl-bearing moieties through the reaction with propargyl bromide. The material then underwent an efficient Cu(I)-catalyzed azide alkyne click reaction with sodium azide in order to obtain the corresponding triazole products. The covalent modification of ...

In present study we used five green plants for microwave assisted synthesis of Alumina nanoparticles from Aluminum nitrate. Structural characterization was studied using x-ray diffraction that showed semi- crystalline and possibly, amorphous structure. Fourier infrared spectroscopy was used to determine Al-O bond and functional groups responsible for synthesis of nanoparticles. FTIR confirmed e...

Toluene and benzene were eliminated using multi-walled carbon nanotubes (MWCNTs). In order to investigate influence of acid treatment on the MWCNTs adsorption capacities, the MWCNTs were functionalized by nitric acid (10 M) under reflux conditions for 2 h. Fourier transform infrared (FTIR) and Raman spectroscopy were employed to confirm the formation of functional groups on the nanotubes su...

We present a Fourier space density functional approach for hard particles with attractive interactions, which is based on a previously developed two-dimensional approach [S. Hlushak, W. Rżysko, and S. Sokołowski, J. Chem. Phys. 131, 094904 (2009)] for hard-sphere chains. The interactions are incorporated by means of a three-dimensional Fourier image of the direct correlation function that is ob...