Related papers: Factorization of the transition matrix for the gen…
In continuation to our recent work on noncommutative polynomial factorization, we consider the factorization problem for matrices of polynomials and show the following results. (1) Given as input a full rank $d\times d$ matrix $M$ whose…
We introduce the notion of quantum duplicates of an (associative, unital) algebra, motivated by the problem of constructing toy-models for quantizations of certain configuration spaces in quantum mechanics. The proposed (algebraic) model…
We present a simple proof of the factorization of (complex) symmetric matrices into a product of a square matrix and its transpose, and discuss its application in establishing a uniqueness property of certain antilinear operators.
This paper provides a framework for investigations in fluctuation theory for L\'evy processes with matrix-exponential jumps. We present a matrix form of the components of the infinitely divisible factorization. Using this representation we…
Graded rings provide a natural algebraic framework for encoding symmetry via decompositions into homogeneous components indexed by a group, together with multiplication rules reflecting the group operation. Among graded rings, strongly…
In my textbook on Quantum Field Theory \cite{tpqft} and in a recent paper \cite{tpejc2018}, I advocated a lattice regularization procedure for defining the path integral for the relativistic particle, using the non-quadratic action…
In this paper we obtain, by our method of crossbreeding in certain set of $\zeta$-factorization formulas, the corresponding complete hybrid formulas. These are playing the role of criterion for selection of new families of $\zeta$-kindred…
A typical system of k difference (or differential) equations can be compressed, or folded into a difference (or ordinary differential) equation of order k. Such foldings appear in control theory as the canonical forms of the controllability…
Recent works have discussed the violation of factorization and universality in hadronic hard scattering processes aimed at measurements of T-odd distributions. We use simple arguments to show that it is possible to restore an approximate…
In this note we prove that the factorization theorem for dominated polynomials previously proved by the authors is equivalent to an alternative factorization scheme that uses classical linear techniques and a linearization process. However,…
We use the well-known observation that the solutions of Jacobi's differential equation can be represented via non-oscillatory phase and amplitude functions to develop a fast algorithm for computing multi-dimensional Jacobi polynomial…
This paper provides a general proof of a relationship theorem between nonlinear analogue polynomial equations and the corresponding Jacobian matrix, presented recently by the present author. This theorem is also verified generally effective…
We demonstrate a factorization formula for semi-inclusive deep-inelastic scattering with hadrons in the current fragmentation region detected at low transverse momentum. To facilitate the factorization, we introduce the transverse-momentum…
In this paper we show how gauge symmetries in an effective theory can be used to simplify proofs of factorization formulae in highly energetic hadronic processes. We use the soft-collinear effective theory, generalized to deal with…
We obtain closed-form solutions of several inhomogeneous Lienard equations by the factorization method. The two factorization conditions involved in the method are turned into a system of first-order differential equations containing the…
It has recently been shown that periodic layered media can reflect strongly for all incident angles and polarizations in a given frequency range. The standard treatment gets these band gaps from an eigenvalue equation for the Bloch factor…
Recently, a factorization theorem was proposed for partonic flavor evolution as defined by the net flavor of the Winner-Take-All axis of a jet. We validate the factorization theorem through explicit calculation at two-loop order, and in the…
Many known models, which generally use a factorization hypothesis, give a poor account of the decays B into J/psi + K(*). Usually there is a free overall factor, which is fit to the data, so that tests of the models rely upon ratios. The…
Matrix factorization exploits the idea that, in complex high-dimensional data, the actual signal typically lies in lower-dimensional structures. These lower dimensional objects provide useful insight, with interpretability favored by sparse…
In this paper we use Jacob's ladders together with fundamental Hardy-Littlewood formula (1921) to prove the so-called $\zeta$-factorization formula on the critical line. Simultaneously, we obtain a set of control parameters of metamorphosis…