Trapezoidal intuitionistic fuzzy numbers (TrIFNs) express abundant and flexible information in a suitable manner and  are very useful to depict the decision information in the procedure of decision making. In this paper, some new aggregation operators, such as, trapezoidal intuitionistic fuzzy weighted power harmonic mean (TrIFWPHM) operator, trapezoidal intuitionistic fuzzy ordered weighted po...

Dynamical quantum groups were recently introduced by Etingof and Varchenko as an algebraic framework for studying the dynamical Yang–Baxter equation, which is precisely the Yang–Baxter equation satisfied by 6j-symbols. We investigate one of the simplest examples, generalizing the standard SU(2) quantum group. The matrix elements for its corepresentations are identified with Askey–Wilson polynom...

This is an introduction to some fundamental ideas of harmonic analysis. It assumes that the reader knows the basics of measure theory and the Lebesgue integral, and knows a little (not much more than the definitions) about Banach and Hilbert spaces. Some of this is reviewed in Section 2.1.

Motivated by Wiener's work on generalized harmonic analysis, we consider the Marcinkiewicz space 6XP(R) of functions of bounded upper averagep power and the space St(R) of functions of bounded upper p variation. By identifying functions whose difference has norm zero, we show that St(R), 1 <p < oo, is a Banach space. The proof depends on the result that each equivalence class in cVP(R) contains...

high harmonic generation is a useful tool for the generation of short, intense attosecond pulses. In order to simulate high harmonic generation, we performed a numerical solution to the time dependent Schr&ouml;dinger equation. by considering dipole approximation, we predicted generation of a 53 attosecond pulse. In order to see the time and frequency of emission of attosecond pulse, we exploit...

I spent most of my research time this summer studying the basic methods of harmonic analysis. My goal was to write an explanation and elaboration of Fefferman’s 1973 paper, Pointwise Convergence of Fourier Series. I was attempting to fill in the details and clarify things to the degree that the paper would be accessible at the level of a beginning graduate student, and to add enough background ...

This article contains an expanded version of the material covered by the author in two 90-minute lectures at the 9th international school on Nonlinear Analysis, Function spaces, and Applications, held in Třešt’, Czech Republic during the period September 11 to September 17, 2010. In memory of Nigel Kalton