Related papers: Computing the Fr\'echet Derivative of the Polar De…
We investigate the degree of the polar transformations associated to a certain class of multi-valued homogeneous functions. In particular we prove that the degree of the pre-image of generic linear spaces by a polar transformation…
This paper extends the classical Ostrogradsky-Hermite reduction for rational functions to more general functions in primitive extensions of certain types. For an element $f$ in such an extension $K$, the extended reduction decomposes $f$ as…
We present a new closed form for the interpolating polynomial of the general univariate Hermite interpolation that requires only calculation of polynomial derivatives, instead of derivatives of rational functions. This result is used to…
If a function $f:\mathbb{R}\to\mathbb{R}$ can be represented as the sum of $n$ periodic functions as $f=f_1+\dots+f_n$ with $f(x+\alpha_j)=f(x)$ ($j=1,\dots,n$), then it also satisfies a corresponding $n$-order difference equation…
Formal expressions are derived for the multipole expansion of the structure functions of a general polarization observable of exclusive electrodisintegration of the deuteron using a longitudinally polarized beam and/or an oriented target.…
In this thesis we study when a homogeneous polynomial $f$ decomposes or "splits" additively. Up to base change this means that it is possible to write $f = g + h$ where $g$ and $h$ are polynomials in independent sets of variables. This…
An algorithm for numerically computing the exponential of a matrix is presented. We have derived a polynomial expansion of $e^x$ by computing it as an initial value problem using a symbolic programming language. This algorithm is shown to…
We propose a new method to compute the unipotent radical $R_u(H)$ of the differential Galois group $H$ associated to a parameterized second-order homogeneous linear differential equation of the form \[\tfrac{\partial^2}{\partial…
We establish new explicit zero-free regions for the Dedekind zeta-function. Two key elements of our proof are a non-negative, even, trigonometric polynomial and explicit upper bounds for the explicit formula of the so-called differenced…
The partition function of a factor graph and the partition function of the dual factor graph are related to each other by the normal factor graph duality theorem. We apply this result to the classical problem of computing the partition…
Misprints in the C_F^2 part of the splitting function \Delta P_{gq}^(1) Eq. (3.29) are corrected. Due to a minus sign error between the C_F^2- 1/2 C_A C_F piece and the remaining part of Eq. (A.4), Eq. (3.46) is changed. Finally…
In this paper, we present numerical procedures to compute solutions of partial differential equations posed on fractals. In particular, we consider the strong form of the equation using standard graph Laplacian matrices and also weak forms…
We study factorizations of rational matrix functions with simple poles on the Riemann sphere. For the quadratic case (two poles) we show, using multiplicative representations of such matrix functions, that a good coordinate system on this…
Following several decades of successive algorithmic improvements, works from the 2010s have showed how to compute the Hermite normal form (HNF) of a univariate polynomial matrix within a complexity bound which is essentially that of…
The Cholesky decomposition plays an important role in finding the inverse of the correlation matrices. As it is a fast and numerically stable for linear system solving, inversion, and factorization compared to singular valued decomposition…
We study categories of matrix factorizations. These categories are defined for any regular function on a suitable regular scheme. Our paper has two parts. In the first part we develop the foundations; for example we discuss derived direct…
We calculate the deuteron electromagnetic form factors in a modified version of Weinberg's chiral effective field theory approach to the two-nucleon system. We derive renormalizable integral equations for the deuteron without partial wave…
A partial fraction decomposition of the Fermi function resulting in a finite sum over simple poles is proposed. This allows for efficient calculations involving the Fermi function in various contexts of electronic structure or electron…
A univariate polynomial f over a field is decomposable if it is the composition f = g(h) of two polynomials g and h whose degree is at least 2. We determine the dimension (over an algebraically closed field) of the set of decomposables, and…
We consider a function $U=e^{-f_0}\prod_j^N f_j^{\alpha_j}$ on a real affine space, here $f_0,..,f_N$ are linear functions, $\alpha_1, ...,\alpha_N$ complex numbers. The zeros of the functions $f_1, ..., f_N$ form an arrangement of…