Related papers: Normalized Gompertz wavelets and their application
In this paper, we study the generalized gapped k-mer filters and derive a closed form solution for their coefficients. We consider nonnegative integers $\ell$ and $k$, with $k\leq \ell$, and an $\ell$-tuple $B=(b_1,\ldots,b_{\ell})$ of…
In this paper, we generalize finite depth wavelet scattering transforms, which we formulate as $\Lb^q(\mathbb{R}^n)$ norms of a cascade of continuous wavelet transforms (or dyadic wavelet transforms) and contractive nonlinearities. We then…
In this paper we treat statistical inference for an intrinsic wavelet estimator of curves of symmetric positive definite (SPD) matrices in a log-Euclidean manifold. This estimator preserves positive-definiteness and enjoys…
We consider two-dimensional steady periodic gravity waves on water of finite depth with a prescribed but arbitrary vorticity distribution. The water surface is allowed to be overhanging and no assumptions regarding the absence of stagnation…
We propose a novel scheme to normalize scattering modes of the electromagnetic field. By relying on analytical solutions for Maxwell's equations in the homogenous medium outside the scatterer, we derive normalization conditions that only…
Most finite element methods for solving time-harmonic wave-propagation problems lead to a linear system with a non-normal coefficient matrix. The non-normality is due to boundary conditions and losses. One way to solve these systems is to…
We introduce and study several combinatorial properties of a class of symmetric polynomials from the point of view of integrable vertex models in finite lattice. We introduce the $L$-operator related with the $U_q(sl_2)$ $R$-matrix, and…
We investigate the Helmholtz equation with suitable boundary conditions and uncertainties in the wavenumber. Thus the wavenumber is modeled as a random variable or a random field. We discretize the Helmholtz equation using finite…
Two-direction multiscaling functions $\boldsymbol{\phi}$ and two-direction multiwavelets $\boldsymbol{\psi}$ associated with $\boldsymbol{\phi}$ are more general and more flexible setting than one-direction multiscaling functions and…
We prove new, sharp, wavenumber-explicit bounds on the norms of the Helmholtz single- and double-layer boundary-integral operators as mappings from $L^2(\partial \Omega)\rightarrow H^1(\partial \Omega)$ (where $\partial\Omega$ is the…
In this work we present the study of the renormalizability of the Generalized Quantum Electrodynamics ($GQED_{4}$). We begin the article by reviewing the on-shell renormalization scheme applied to $GQED_{4}$. Thereafter, we calculate the…
We revisit the Einstein-Gauss-Bonnet theory in view of the GW170817 event, which compels that the gravitational wave speed is equal to $c_T^2=1$ in natural units. We use an alternative approach compared to one previous work of ours, which…
We introduce a one parameter deformation of the Zwegers' $\mu$-function as the image of $q$-Borel and $q$-Laplace transformations of a fundamental solution for the $q$-Hermite-Weber equation. We further give some formulas for our…
Regularization methods improve the stability of ill-posed inverse problems by introducing some a priori characteristics for the solution such as smoothness or sharpness. In this contribution, we propose a multidimensional, scale-dependent…
We establish system of equations for single function normalized tight frame wavelets with compact supports associated with $2\times 2$ expansive integral matrices in $L^2(\R^2)$.
The functional determinants of the GJMS scalar operators, P_{2k}, on even-dimensional spheres are computed via Barnes multiple gamma functions relying on the numerical availability of the digamma function. For the critical k=d/2 case, it is…
In this note, we extend the characterization of dyadic Lipschitz regularity of functions to non-atomic probability spaces, using generalized Haar systems.
We construct the Generalized Monodromy matrix $\mathcal{\hat{M}}(\omega)$ of two dimensional string effective action by introducing the T-duality group properties.The integrability conditions with general solutions depending on spectral…
We propose a generic, phenomenological approach to modifying the dispersion of gravitational waves, independent of corrections to the generation mechanism. This model-independent approach encapsulates all previously proposed…
We introduce generalized hypergeometric Bernoulli numbers for Dirichlet characters. We study their properties, including relations, expressions and determinants. At the end in Appendix we derive first few expressions of these numbers.