Related papers: Basic Functional Analysis Puzzles of Spectral Flow
By an appropriate definition, we divide the irregular set into level sets. Then we characterize the multifractal spectrum of these new pieces by calculating their entropies. We also compute the entropies of various intersections of the…
This paper describes various approaches to modeling a random process with a given rational power spectral density. The main attention is paid to the spectral form of mathematical description, which allows one to obtain a relation for the…
A workflow describes the entirety of processing steps in an analysis, such as employed in many fields of physics. Workflow management makes the dependencies between individual steps of a workflow and their computational requirements…
Due to existence of periodic windows, chaotic systems undergo numerous bifurcations as system parameters vary, rendering it hard to employ an analytic continuation, which constitutes a major obstacle for its effective analysis or…
We derive renormalised finite functional flow equations for quantum field theories in real and imaginary time that incorporate scale transformations of the renormalisation conditions, hence implementing a flowing renormalisation. The flows…
The question in the title is ambiguous. At least the understanding of words essentially different and function theory should be clarified. We discuss approaches to do that. We also present a new framework for analytic function theories…
Total variation gradient flows are important in several applied fields, including image analysis and materials science. In this paper, we review a few basic topics including definition of a solution, explicit examples and the notion of…
We present a general theory of fractal transformations and show how it leads to a new type of method for filtering and transforming digital images. This work substantially generalizes earlier work on fractal tops. The approach involves…
Expository notes about spectral sequences, filtered spectra, and synthetic spectra. We focus on the $\tau$-formalism as it arises in filtered spectra.
For centuries, bubbles have fascinated artists, engineers, and scientists alike. In spite of century-long research on them, new and often surprising bubble phenomena, features, and applications keep popping up. In this paper I sketch my…
Equations arising in General Relativity are usually too complicated to be solved analytically and one has to rely on numerical methods to solve sets of coupled partial differential equations. Among the possible choices, this paper focuses…
Many slope filtrations occur in algebraic geometry, asymptotic analysis, ramification theory, p-adic theories, geometry of numbers... These functorial filtrations, which are indexed by rational (or sometimes real) numbers, have a lot of…
These informal notes are concerned with spaces of functions in various situations, including continuous functions on topological spaces, holomorphic functions of one or more complex variables, and so on.
We present in this paper the motivation and theory of nonlinear spectral representations, based on convex regularizing functionals. Some comparisons and analogies are drawn to the fields of signal processing, harmonic analysis and sparse…
Polymorphic circuits are a special kind of circuits which possess multiple build-in functions, and these functions are activated by environment parameters, like temperature, light and VDD. The behavior of a polymorphic circuit can be…
We calculate the two-loop and one-loop/one-emission contributions required for soft gluon evolution at the next-to-leading order. The colour structures are expressed in the colour flow basis, and the kinematic dependence and loop integrals…
Dimensional analysis provides many simple and useful tools for various situations in science. The objective of this paper is to investigate its relations to functions, i.e., the dimensions for functions that yield physical quantities and…
Streamflow, as a natural phenomenon, is continuous in time and so are the meteorological variables which influence its variability. In practice, it can be of interest to forecast the whole flow curve instead of points (daily or hourly). To…
Knowledge flow analysis offers a simple and flexible way to find flaws in security protocols. A protocol is described by a collection of rules constraining the propagation of knowledge amongst principals. Because this characterization…
A Compact Introduction to Fractional Calculus is presented including basic definitions, fractional differential equations and special functions.