Related papers: Analyticity, superoscillations and supershifts in …
Superstatistics is a widely employed tool of non-equilibrium statistical physics which plays an important role in analysis of hierarchical complex dynamical systems. Yet, its "canonical" formulation in terms of a single nuisance parameter…
We report a method for constructing bandpass functions that approximate a given analytic function with arbitrary accuracy over a finite interval. A corollary is that bandpass functions can be obtained that oscillate arbitrarily slower than…
The phenomenon of superoscillation, where band limited signals can oscillate over some time period with a frequency higher than the band limit, is not only very interesting but it also seems to offer many practical applications. The first…
A thermodynamic-like formalism is developed for superstatistical systems based on conditional entropies. This theory takes into account large-scale variations of intensive variables of systems in nonequilibrium stationary states. Ordinary…
Band-limited functions can oscillate locally at an arbitrarily fast rate through an interference phenomenon known as superoscillations. Using an optical pulse with a superoscillatory envelope we experimentally break the temporal…
Higher dimensional super symmetry has been analyzed in terms of quaternion variables and the theory of quaternion harmonic oscillator has been analyzed. Supersymmertization of quaternion Dirac equation has been developed for…
A natural connection between rational functions of several real or complex variables, and subspace collections is explored. A new class of function, superfunctions, are introduced which are the counterpart to functions at the level of…
Oscillons, extremely long-living localized oscillations of a scalar field, are studied in theories with quartic and sine-Gordon potentials in two spatial dimensions. We present qualitative results concentrating largely on a study in…
Analytic approximations of functions of Cayley-Dickson variables are investigated. The case of functions of complexified Cayley-Dickson variables is also encompassed. Moreover, extensions of functions of Cayley-Dickson variables are…
The changes in brightness of an astronomical source as a function of time are key probes into that source's physics. Periodic and quasi-periodic signals are indicators of fundamental time (and length) scales in the system, while stochastic…
In this paper we investigate new results on the theory of superoscillations using time-frequency analysis tools and techniques such as the short-time Fourier transform (STFT) and the Zak transform. We start by studying how the short-time…
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…
In this work we present an introduction to Supersymmetry in the context of 1-dimensional Quantum Mechanics. For that purpose we develop the concept of hamiltonians factorization using the simple harmonic oscillator as an example, we…
In this paper, particle physics concepts are blended into a field theory for macroscopic phenomena: Fluid mechanics is enhanced by anticommuting Grassmann variables to describe vorticity, while an additional interaction for the Grassmann…
We describe recent nonlinear analytic approximation tools in the classical setting of Hardy spaces in the upper half plane and show how to transfer them to the higher dimensional real setting of harmonic functions in upper half spaces. It…
Recently, motivated by certain loop quantum gravity inspired corrections, it was shown that for spherically symmetric midisuperspace models infinitely many second derivative theories of gravity exist (as revealed by the presence of three…
Superpositions of different statistics on different time or spatial scales (in short, superstatistics) can naturally lead to an effective description by nonextensive statistical mechanics. We first discuss the role of escort distributions…
Frequency is a central concept in Mathematics, Physics, and Signal Processing. It is the main tool for describing the oscillatory behavior of signals, which is usually argued to be the manifestation of some of their key features, depending…
The analysis of time variability, whether fast variations on time scales well below the second or slow changes over years, is becoming more and more important in high-energy astronomy. Many sophisticated tools are available for data…
A recipe is presented for constructing band-limited superoscillating functions that exhibit arbitrarily high frequencies over arbitrarily long intervals.