Related papers: Space-time dimensionality D as complex variable: c…
An approach to infinite dimensional integration which unifies the case of oscillatory integrals and the case of probabilistic type integrals is presented. It provides a truly infinite dimensional construction of integrals as linear…
Hybrid spectral-spatial representations are introduced to rapidly calculate periodic scalar and dyadic Green's functions of the Helmholtz equation for 2D and 3D configurations with a 1D (linear) periodicity. The presented schemes work…
In this work the authors use their contour integral method to derive a double integral connected to the modified Bessel function of the second kind and express it in terms of the Lerch function. There are some useful results relating double…
Quantitative recurrence indicators are defined by measuring the first entrance time of the orbit of a point $x$ in a decreasing sequence of neighborhoods of another point $y$. It is proved that these recurrence indicators are a.e. greater…
To entirely determine the resulting functions of one-loop integrals it is necessary to find the correct analytic continuation to all relevant kinematical regions. We argue that this continuation procedure may be performed in a general and…
Multiple Mellin-Barnes integrals are often used for perturbative calculations in particle physics. In this context, the evaluation of such objects may be performed through residues calculations which lead to their expression as multiple…
Fourier transformations of several functions of one and two variables are evaluated and then used to derive some integral and series identities. It is shown that certain double Mordell integrals can be reduced to a sum of products of…
A dynamical system with discrete time is studied by means of algebraic geometry. The system admits a reduction that is interpreted as a classical field theory in 2+1-dimensional wholly discrete space-time. The integrals of motion of a…
We introduce a two-dimensional metric (interval) temporal logic whose internal and external time flows are dense linear orderings. We provide a suitable semantics and a sequent calculus with axioms for equality and extralogical axioms. Then…
Dimensional analysis provides many simple and useful tools for various situations in science. The objective of this paper is to investigate its relations to functions, i.e., the dimensions for functions that yield physical quantities and…
Ab initio predictions of two-loop electroweak contributions to observables are increasingly essential for precision collider experiments, yet their evaluation remains very challenging. We connect recurrence techniques and dispersive method…
We present an algorithm to calculate the linear response of periodic systems in the time-dependent density functional thoery, using a real-space representation of the electron wave functions and calculating the dynamics in real time. The…
We study the local Dirichlet integral of distance functions and their behavior within the harmonic Dirichlet space. We provide estimates for the local Dirichlet integral of distance functions, which allow us to study their membership in the…
Recently considerable efforts have been devoted to computing cosmological correlators and the corresponding wavefunction coefficients, as well as understanding their analytical structures. In this note, we revisit the computation of these…
The period is a classical complex analytic invariant for a compact Riemann surface defined by integration of differential 1-forms. It has a strong relationship with the complex structure of the surface. In this chapter, we review another…
Windowed recurrences are sliding window calculations where a function is applied iteratively across the window of data, and are ubiquitous throughout the natural, social, and computational sciences. In this monograph we explore the…
We consider binomial and inverse binomial sums at infinity and rewrite them in terms of a small set of constants, such as powers of $\pi$ or $\log(2)$. In order to perform these simplifications, we view the series as specializations of…
We apply the structure theory of finite dimensional algebras in order to deduce dimension formulas for spaces of period numbers, i.e., complex numbers defined by integrals of algebraic nature. We get a complete and conceptually clear answer…
The main way of analyzing the complexity of a program is that of extracting and solving a recurrence that expresses its running time in terms of the size of its input. We develop a method that automatically extracts such recurrences from…
In this paper, we propose a new method for evaluating scalar one-loop Feynman integrals in generalized D-dimension. The calculations play an important building block for two-loop and higher-loop corrections to the processes at future…