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In this paper, we propose a numerical method of computing an integral whose integrand is a slowly decaying oscillatory function. In the proposed method, we consider a complex analytic function in the upper-half complex plane, which is…

Numerical Analysis · Mathematics 2019-09-12 Hidenori Ogata

Superoscillations have roots in various scientific disciplines, including optics, signal processing, radar theory, and quantum mechanics. This intriguing mathematical phenomenon permits specific functions to oscillate at a rate surpassing…

Complex Variables · Mathematics 2024-03-12 F. Colombo , I. Sabadini , D. C. Struppa , A. Yger

Provided a special function of one variable and some of its derivatives can be accurately computed over a finite range, a method is presented to build a series of polynomial approximations of the function with a defined relative error over…

Computational Physics · Physics 2007-05-23 C. Semay

The aim of this paper is to study generating functions for the coefficients of the classical superoscillatory function associated with weak measurements. We also establish some new relations between the superoscillatory coefficients and…

Classical Analysis and ODEs · Mathematics 2023-04-03 Fabrizio Colombo , Rolf Soeren Krausshar , Irene Sabadini , Yilmaz Simsek

The increasing difficulty in continued development of digital electronic logic has led to a renewed interest in alternative approaches. Oscillatory computing is one such approach that leverages alternative physical systems and computation…

Dynamical Systems · Mathematics 2024-12-02 Wilkie Olin-Ammentorp

A notion of band limited functions is considered in the case of the hyperbolic plane in its Poincare upper half-plane $\mathbb{H}$ realization. The concept of band-limitedness is based on the existence of the Helgason-Fourier transform on…

Functional Analysis · Mathematics 2011-05-17 Hans Feichtinger , Isaac Pesenson

Superoscillating signals are band--limited signals that oscillate in some region faster their largest Fourier component. While such signals have many scientific and technological applications, their actual use is hampered by the fact that…

Quantum Physics · Physics 2013-08-01 Eytan Katzav , Moshe Schwartz

In this paper, a technique on constructing nonlinear resilient Boolean functions is described. By using several sets of disjoint spectra functions on a small number of variables, an almost optimal resilient function on a large even number…

Information Theory · Computer Science 2009-11-18 WeiGuo Zhang , GuoZhen Xiao

This letter proposes an analytical approach to formulate the power system oscillation frequency under a large disturbance. A fact is revealed that the oscillation frequency is only the function of the oscillation amplitude when the system's…

Systems and Control · Computer Science 2015-03-27 Bin Wang , Kai Sun

An astonishingly simple analytical frequency approximation formula for a class of strongly nonlinear oscillators is derived and applied to various example systems yielding useful quick estimates.

Other Condensed Matter · Physics 2016-04-15 Kevin Rapedius

In this note unbounded hyperexpansive weighted composition operators are investigated. AS a consequence unbounded hyperexpansive multiplication and composition operators are characterized.

Functional Analysis · Mathematics 2014-02-21 Yousef Estaremi

The work is devoted to the construction of a new interval arithmetic which would combine algorithmic efficiency and high quality estimation of the ranges of expressions.

Numerical Analysis · Mathematics 2022-04-21 Dmitry A. Skorik

An algorithm is presented which generates pairs of oscillatory random time series which have identical periodograms but differ in the number of oscillations. This result indicate the intrinsic limitations of spectral methods when it comes…

Data Analysis, Statistics and Probability · Physics 2007-05-23 A. G. Rossberg

It is shown that a band-limited function bounded by 1 for negative x can grow arbitrarily fast for positive x.

Classical Analysis and ODEs · Mathematics 2025-01-03 Lloyd N. Trefethen

In the last decade there has been a growing interest in superoscillations in various fields of mathematics, physics and engineering. However, while in applications as optics the local oscillatory behaviour is the important property, some…

Mathematical Physics · Physics 2023-01-19 Jussi Behrndt , Fabrizio Colombo , Peter Schlosser , Daniele C. Struppa

Coupled distinct arrays of nonlinear oscillators have been shown to have a regime of high frequency, or ultra-harmonic, oscillations that are at multiples of the natural frequency of individual oscillators. The coupled array architectures…

Pattern Formation and Solitons · Physics 2007-05-23 Alexandra S. Landsman , Ira B. Schwartz

We further develop the concept of supergrowth [Jordan, Quantum Stud.: Math. Found. $\textbf{7}$, 285-292 (2020)], a phenomenon complementary to superoscillation, defined as the local amplitude growth rate of a function being higher than its…

A new approach for upper bounding the channel reliability function using the code spectrum is described. It allows to treat in a unified way both a low and a high rate cases. In particular, the earlier known upper bounds are improved, and a…

Information Theory · Computer Science 2007-07-16 Marat V. Burnashev

Abstrct: In this note, by considering fractionally linear functions over a finite field and consequently developing an abstract sequence, we study some of its properties.

Discrete Mathematics · Computer Science 2007-05-23 V. M. Siddlenikov , R. N. Mohan , Moon Ho Lee

Let R be a ring. A construction method for flexible quadratic algebras with scalar involution over R is presented which unifies various classical constructions in the literature, in particular those to construct composition algebras.

Rings and Algebras · Mathematics 2007-05-23 S. Pumpluen