Related papers: Taylor Series as Wide-sense Biorthogonal Wavelet D…
We construct directional wavelet systems that will enable building efficient signal representation schemes with good direction selectivity. In particular, we focus on wavelet bases with dyadic quincunx subsampling. In our previous work, We…
We consider series of the form $\sum a_n \{n\cdot x\}$, where $n\in\Z^{d}$ and $\{x\}$ is the sawtooth function. They are the natural multivariate extension of Davenport series. Their global (Sobolev) and pointwise regularity are studied…
We extend many theorems from the context of solid angle sums over rational polytopes to the context of solid angle sums over real polytopes. Moreover, we consider any real dilation parameter, as opposed to the traditional integer dilation…
It is the purpose of this article to outline a course that can be given to engineers looking for an understandable mathematical description of the foundations of distribution theory and the necessary functional analytic methods. Arguably,…
We analyze the perturbative cusp and closed polygons of Wilson lines for massless gauge theories in coordinate space, and express them as exponentials of two-dimensional integrals. These integrals have geometric interpretations, which link…
The results obtained by analyzing signals with the Square Wave Method (SWM) introduced previously can be presented in the frequency domain clearly and precisely by using the Square Wave Transform (SWT) described here. As an example, the SWT…
Chiral perturbation theory is extended to nonrelativistic systems with spontaneously broken symmetry. In the effective Lagrangian, order parameters associated with the generators of the group manifest themselves as effective coupling…
The usual prescription for constructing gauge-invariant Lagrangian is generalized to the case where a Lagrangian contains second derivatives of fields as well as first derivatives. Symmetric tensor fields in addition to the usual vector…
We prove a factorization formula for the Taylor series coefficients of a zero of a polynomial as a function of the polynomial's coefficients. This result extends to more general functions which we call "complex-exponent polynomials". To…
The problem of two coupled scalar fields, one with mass much lighter than the other is analysed by means of Wilson's renormalization group approach. Coupled equations for the potential and the wave function renormalization are obtained by…
This paper presents new analytic solutions to the Dirac equation employing a recently introduced method that is based on the formulation of spinorial fields and their driving electromagnetic fields in terms of geometric algebras. A first…
From the perspective of asymptotic stability at high Reynolds numbers, Taylor-Couette flow, as a typical rotating shear flow, exhibits rich decay behaviors. Previously, for the extensively studied Couette flow or the Taylor-Couette flow in…
The robustness of two widespread multifractal analysis methods, one based on detrended fluctuation analysis and one on wavelet leaders, is discussed in the context of time-series containing non-uniform structures with only isolated…
We introduce an equation named matrix Dirac equation which can be considered as a generalization of Dirac equation for an electron. The liaison between matrix Dirac equation and standard Dirac equation is discussed. We write a lagrangian…
We demonstrate that the Dirac representation theory can be effectively adjusted and applied to signal theory. The main emphasis is on orthogonality as the principal physical requirement. The particular role of the identity and projection…
In the context of data-driven control of nonlinear systems, many approaches lack of rigorous guarantees, call for nonconvex optimization, or require knowledge of a function basis containing the system dynamics. To tackle these drawbacks, we…
Particle Flow Filters perform the measurement update by moving particles to a different location rather than modifying the particles' weight based on the likelihood. Their movement (flow) is dictated by a drift term, which continuously…
In this paper we consider the problem of defining transforms for signals on directed graphs, with a specific focus on defective graphs where the corresponding graph operator cannot be diagonalized. Our proposed method is based on the Schur…
This report aims to present my research updates on distance function wavelets (DFW) based on the fundamental solutions and the general solutions of the Helmholtz, modified Helmholtz, and convection-diffusion equations, which include the…
The wavelet spectra is a common starting point for estimating the Hurst exponent of a self-similar signal using wavelet-based techniques. The decay of the $\log_2$ average energy of the detail wavelet coefficients as a function of the level…