相关论文: A Generalised Hadamard Transform
We present an overview of some recent developments in the theory of generalized formal series, grounded in diffeological geometric framework. These constructions aim to offer new tools for understanding infinite-dimensional phenomena in…
The tensor train decomposition decomposes a tensor into a "train" of 3-way tensors that are interconnected through the summation of auxiliary indices. The decomposition is stable, has a well-defined notion of rank and enables the user to…
The analysis and visualization of tensor fields is a very challenging task. Besides the cases of zeroth- and first-order tensors, most techniques focus on symmetric second-order tensors. Only a few works concern totally symmetric tensors of…
A novel method to obtain parametrizations of complex inverse orthogonal matrices is provided. These matrices are natural generalizations of complex Hadamard matrices which depend on non zero complex parameters. The method we use is via…
In this paper, we investigate the joint generalized channel estimation and device identification problem in Internet of Things (IoT) networks {under multipath propagation}. To fully utilize the received signal, we decompose the generalized…
Matrices over the ring of formal power series are considered. Normal forms with respect to various sub-groups of the two-sided transformations are constructed. The construction is based on the special property of the action: it induces a…
We extend the counting of generalized form factors presented in PRD63(2000) by Ji and Lebed to the axial vector and the tensor operator at twist-2 level. Following this, a parameterization of all higher moments in x of the tensor (helicity…
By a generalized Delsarte polynomial we mean a Laurent polynomial whose exponent vectors are linearly independent. We consider certain monomial deformations of generalized Delsarte polynomials and study their associated differential…
The Fractional Fourier Transform is a ubiquitous signal processing tool in basic and applied sciences. The Fractional Fourier Transform generalizes every property and application of the Fourier Transform. Despite the practical importance of…
In this article, we report, for the first time, broadband multifunctional metasurfaces with more than four distinct functionalities. The constituent meta-atoms combine two different phase change materials, $\mathrm{VO_2}$ and…
We study the thermodynamics of the one-dimensional extended Hubbard model at half-filling using a density-matrix renormalization group method applied to transfer matrices. We show that the various phase transitions in this system can be…
We give the converse to Dirichlet's theorem on primes in arithmetic progressions by generalizing an old result of Guinand.
A brief survey of the theory of soliton perturbations is presented. The focus is on the usefulness of the so-called Generalised Fourier Transform (GFT). This is a method that involves expansions over the complete basis of `squared olutions`…
In this paper we provide an analytical procedure which leads to a system of $(n-2)^2$ polynomial equations whose solutions give the parameterisation of the complex $n\times n$ Hadamard matrices. It is shown that in general the Hadamard…
The intended purpose of this work is to provide the reader with a comprehensive, state-of-the art presentation of the theory of complex Hadamard matrices, or at least report on the very recent advances. This manuscript consists of three…
Convolutions or Hadamard products of analytic functions is a well explored area of research and many nice results are available in literature. On the other hand, very little is known in general about the convolutions of univalent harmonic…
We present a novel Fourier camera, an in-hardware optical compression of high-speed frames employing pixel-level sign-coded exposure where pixel intensities temporally modulated as positive and negative exposure are combined to yield…
We introduce several possible generalizations of tomography for quadratic surfaces. We analyze different types of elliptic, hyperbolic and hybrid tomograms. In all cases it is possible to consistently define the inverse tomographic map. We…
As an appropriate analog of the Euclidean short-time Fourier transform, we study a windowed version of the Helgason-Fourier transform on the complex unit ball and translate the theory of modulation/coorbit spaces. As a result, atomic…
A complex Hadamard matrix is a square matrix H with complex entries of absolute value 1 satisfying $HH^*= nI$, where $*$ stands for the Hermitian transpose and I is the identity matrix of order $n$. In this paper, we first determine the…