相关论文: Unitary Representations of Wavelet Groups and Enco…

Terms in arithmetic of the form s in the formula s=t(< s >), with t a term with one free variable and < s > a numeral denoting the G\"odel number of s, are examined by writing the explicit definition of the encoding functions whose…

In this article, we introduce and study the concept of $\textit{spherical-vectors}$, which can be perceived as a natural extension of the arguments of complex numbers in the context of quaternions. We initially establish foundational…

Recent work introduced a unified framework for steerable and directional wavelets in two and three dimensions that ensures many desirable properties, such as a multi-scale structure, fast transforms, and a flexible angular localization. We…

Learning representations of geographical space is vital for any machine learning model that integrates geolocated data, spanning application domains such as remote sensing, ecology, or epidemiology. Recent work embeds coordinates using sine…

We introduce an harmonic analysis for iterated function systems (IFS) (X, mu) which is based on a Markov process on certain paths. The probabilities are determined by a weight function W on X. From W we define a transition operator R_W…

We consider representation learning on periodic graphs encoding crystal materials. Different from regular graphs, periodic graphs consist of a minimum unit cell repeating itself on a regular lattice in 3D space. How to effectively encode…

The representation theory of tensor functions is a powerful mathematical tool for constitutive modeling of anisotropic materials. A major limitation of the traditional theory is that many point groups require fourth- or sixth-order…

In this article, we continue the investigation of hep-th 1611.02179 regarding iterative properties of dual conformal integrals in higher dimensions. In d=4, iterative properties of four and five point dual conformal integrals manifest…

Given an infinite iterated function system (IFS) $\mathcal{F}$, we define its dimension spectrum $D(\mathcal{F})$ to be the set of real numbers which can be realised as the dimension of some subsystem of $\mathcal{F}$. In the case where…

Let $\Lambda$ be a countable index set and $S=\{\phi_i: i\in \Lambda\}$ be a conformal iterated function system on $[0,1]^d$ satisfying the open set condition. Denote by $J$ the attractor of $S$. With each sequence $(w_1,w_2,...)\in…

We construct a wavelet and a generalised Fourier basis with respect to some fractal measures given by one-dimensional iterated function systems. In this paper we will not assume that these systems are given by linear contractions…

An extensive group-theoretical treatment of linear relativistic field equations on Minkowski spacetime of arbitrary dimension D>2 is presented in these lecture notes. To start with, the one-to-one correspondence between linear relativistic…

The Eigendecomposition of quadratic forms (symmetric matrices) guaranteed by the spectral theorem is a foundational result in applied mathematics. Motivated by a shared structure found in inferential problems of recent interest---namely…

In this work, we investigate the interval generalized Sylvester matrix equation ${\bf{A}}X{\bf{B}}+{\bf{C}}X{\bf{D}}={\bf{F}}$ and develop some techniques for obtaining outer estimations for the so-called united solution set of this…

We establish a connection between certain unique models, or equivalently unique functionals, for representations of p-adic groups and linear characters of their corresponding Hecke algebras. This allows us to give a uniform evaluation of…

A linear constraint system is specified by linear equations over the group $\ZZ_d$ of integers modulo $d$. Their operator solutions play an important role in the study of quantum contextuality and non-local games. In this paper, we use the…

Let $(X,d)$ be a compact metric space, and let an iterated function system (IFS) be given on $X$, i.e., a finite set of continuous maps $\sigma_{i}$: $ X\to X$, $i=0,1,..., N-1$. The maps $\sigma_{i}$ transform the measures $\mu $ on $X$…

Let $q$ be a $2N$th root of unity where $N$ is odd. Let $U_q(sl_2)$ denote the quantum group with large center corresponding to the lie algebra $sl_2$ with generators $E,F,K$, and $K^{-1}$. A semicyclic representation of $U_q(sl_2)$ is an…

In the paper we study a class $F$ of multiparameter functions defined in terms of a polybasic $s$-adic $Q^{*}_{s}$-representation of numbers by \begin{equation*} f_a\bigl(x=\Delta^{Q^{*}_s}_{\alpha_1\alpha_2\ldots\alpha_n\ldots}\bigr) =…

Let $\psi$ and $F$ be positive definite forms with integral coefficients of equal degree. Using the circle method, we establish an asymptotic formula for the number of identical representations of $\psi$ by $F$, provided $\psi$ is…