Related papers: Unitary loops and factorization
This paper shows how to obtain a simple closed form for the elements of a triangular matrix raised to the nth power.
This paper is dedicated to the problem of verification of matrices for unitary similarity. For the case of nonderogatory matrices, we have been able to present the new solution for this problem based on geometric approach. The main…
In this talk, I reviewed the role of factorization in diffraction hard scattering.
Cylindrical Algebraic Decomposition (CAD) by projection and lifting requires many iterated univariate resultants. It has been observed that these often factor, but to date this has not been used to optimise implementations of CAD. We…
We study in detail the factorization of the newly obtained two-loop four-particle amplitude in superstring theory. In particular some missing factors from the scalar correlators are obtained correctly, in comparing with a previous study of…
In this work, we prove that any symplectic matrix can be factored into no more than 9 unit triangular symplectic matrices. This structure-preserving factorization of the symplectic matrices immediately reveals two well-known features that,…
We give a new expression for the number of factorizations of a full cycle into an ordered product of permutations of specified cycle types. This is done through purely algebraic means, extending work of Biane. We deduce from our result a…
A new mathematical notation is proposed for the iteration of functions. It facilitates the application of the iteration of functions in mathematical and logical expressions, definitions of sets, and formulations of algorithms. Illustrations…
In addition to the diagonalization of a normal matrix by a unitary similarity transformation, there are two other types of diagonalization procedures that sometimes arise in quantum theory applications -- the singular value decomposition…
We give an elementary proof for new strict upper and lower bounds for the correction term in Ramanujan's approximation for the factorial function
We give a combinatorial proof of the factorization formula of modified Macdonald polynomials when the parameter t is specialized at a primitive root of unity. Our proof is restricted to the special case of partitions with 2 columns. We…
We describe in detail the constrained procedure of differential renormalization and develop the techniques required for one-loop calculations. As an illustration we renormalize Scalar QED and show that the two-, three- and four-point Ward…
In contrast to the situation in classical linear algebra, not every tropically non-singular matrix can be factored into a product of tropical elementary matrices. We do prove the factorizability of any tropically non-singular 2x2 matrix…
A method is presented in which matrix elements for some processes are calculated recursively. This recursive calculational technique is based on the method of basis spinors.
We extend a factorization due to Krein to arbitrary analytic functions from the upper half-plane to itself. The factorization represents every such function as a product of fractional linear factors times a function which, generally, has…
This is the second one in a series of papers classifying the factorizations of almost simple groups with nonsolvable factors. In this paper we deal with almost simple unitary groups.
A summary of the calculation of the color-planar and complete light quark contributions to the massive three-loop form factors is presented. Here a novel calculation method for the Feynman integrals is used, solving general uni-variate…
We prove recursive formulas involving sums of divisors and sums of triangular numbers and give a variety of identities relating arithmetic functions to divisor functions providing inductive identities for such arithmetic functions.
This is a short review of some recent results obtained by the author. These results are related the problem of obtaining polynomial identities (computational formulas) for some matrix functions by means of the known polarization theorem,…
We continue studying the problem of analytic approximation of matrix functions. We introduce the notion of a partial canonical factorization of a badly approximable matrix function $\Phi$ and the notion of a canonical factorization of a…