Related papers: Angular decomposition of tensor products of a vect…
For commuting linear operators $P_0,P_1,..., P_\ell$ we describe a range of conditions which are weaker than invertibility. When any of these conditions hold we may study the composition $P=P_0P_1... P_\ell$ in terms of the component…
Let $\mathbb R_t[\theta]$ be the ring generated over $\mathbb R$ by $\cos\theta$ and $\sin\theta$, and $\mathbb R_t(\theta)$ be its quotient field. In this paper we study the ways in which an element p of $\mathbb R_t[\theta]$ can be…
The Poincare invariant coupled-channel formalism for two-particle systems interacting via one-particle exchange, which has been developed and applied to vector mesons in Ref. [1] is applied to axial vector mesons. We thereby extend the…
The widespread use of multi-sensor technology and the emergence of big datasets has highlighted the limitations of standard flat-view matrix models and the necessity to move towards more versatile data analysis tools. We show that…
The transverse momentum spectra of identified particles produced in high energy proton-proton ($p+p$) collisions are empirically described by a new method with the framework of participant quark model or the multisource model at the quark…
We present a novel nonnegative tensor decomposition method, called Legendre decomposition, which factorizes an input tensor into a multiplicative combination of parameters. Thanks to the well-developed theory of information geometry, the…
We considered the electro- and photoproduction of \rho and other vector mesons with moderately large transverse momentum in the scattering of unpolarized electrons on unpolarized nucleons and nuclei. For these processes we have analyzed how…
The decomposition locus of a tensor is the set of rank-one tensors appearing in a minimal tensor-rank decomposition of the tensor. For tensors lying on the tangential variety of any Segre variety, but not on the variety itself, we show that…
This work introduces a mathematical approach to analysing the polymer dynamics in turbulent viscoelastic flows that uses a new geometric decomposition of the conformation tensor, along with associated scalar measures of the polymer…
We propose a new operator defined between two tensors, the broadcast product. The broadcast product calculates the Hadamard product after duplicating elements to align the shapes of the two tensors. Complex tensor operations in libraries…
A vector composition of a vector $\mathbf{\ell}$ is a matrix $\mathbf{A}$ whose rows sum to $\mathbf{\ell}$. We define a weighted vector composition as a vector composition in which the column values of $\mathbf{A}$ may appear in different…
We derive transformation formulas for the generalized polarization tensors under rigid motions and scaling in three dimensions, and use them to construct an infinite number of invariants under those transformations. These invariants can be…
In this article, we consider the tensor product of two simple modules of quanum $GL_2$ over a field of characteristic $p\neq 0$. We show that it can be expressed as a direct sum of indecomposable twisted tilting modules. This problem has…
We examine the transverse momentum $Q_\perp$ dependence of the helicity structure functions for massive vector bosons of mass $Q$ in hadron reactions. We demonstrate that large logarithmic terms of the form $\ln(Q/Q_\perp)$ in the helicity…
We introduce a simple algorithm that efficiently computes tensor products of Pauli matrices. This is done by tailoring the calculations to this specific case, which allows to avoid unnecessary calculations. The strength of this strategy is…
Decompositions of tensors into factor matrices, which interact through a core tensor, have found numerous applications in signal processing and machine learning. A more general tensor model which represents data as an ordered network of…
Exploiting particular features of classical groups, simple constructions are given for the irreducible constituents of the tensor square of the adjoint modules and the leading terms in higher tensor powers. This provides an independent…
We present a new approach to the reduction of one-loop amplitudes obtained by reconstructing the tensorial expression of the scattering amplitudes. The reconstruction is performed at the integrand level by means of a sampling in the…
Recently, the concept of generating function has been employed in one-loop reduction. For one-loop integrals encompassing arbitrary tensor ranks and higher-pole contributions, the generating function can be decomposed into a tensor part and…
Finding the rank of a tensor is a problem that has many applications. Unfortunately it is often very difficult to determine the rank of a given tensor. Inspired by the heuristics of convex relaxation, we consider the nuclear norm instead of…