Related papers: Extension of HPL to complex arguments
We prove multi-parameter Leibniz rules corresponding to flag paraproducts of arbitrary complexity in mixed-norm spaces, including endpoint estimates. The proof relies on multi-linear harmonic analysis techniques and a quantitative treatment…
The energy spectra of two different quantum systems are paired through supersymmetric algorithms. One of the systems is Hermitian and the other is characterized by a complex-valued potential, both of them with only real eigenvalues in their…
The paper advocates for LLMs to enhance the accessibility, usage and explainability of rule-based legal systems, contributing to a democratic and stakeholder-oriented view of legal technology. A methodology is developed to explore the…
The polylogarithm function is one of the constellation of important mathematical functions. It has a long history, and many connections to other special functions and series, and many applications, for instance in statistical physics.…
This paper deals with exploiting symmetry for solving linear and integer programming problems. Basic properties of linear representations of finite groups can be used to reduce symmetric linear programming to solving linear programs of…
The explicit formulas expressing harmonic sums via alternating Euler sums (colored multiple zeta values) are given, and some explicit evaluations are given as applications.
A generalization of the classical Lipschitz summation formula is proposed. It involves new polylogarithmic rational functions constructed via the Fourier expansion of certain sequences of Bernoulli--type polynomials. Related families of…
We review the results of several of our papers about the procedure of extension of Hamiltonians, allowing the construction of families of superintegrable systems with non-trivial polynomial first integrals (or symmetry operators) of…
We continue the study of the construction of analytical coefficients of the epsilon-expansion of hypergeometric functions and their connection with Feynman diagrams. In this paper, we show the following results: Theorem A: The multiple…
We discuss possible discretizations of complex analysis and some of their applications to probability and mathematical physics, following our recent work with Dmitry Chelkak, Hugo Duminil-Copin and Cl\'ement Hongler.
The integration of Large Language Models (LLMs) into optimization has created a powerful synergy, opening exciting research opportunities. This paper investigates how LLMs can enhance existing optimization algorithms. Using their…
Complex and Hermitian structures on hom-Lie algebras are introduced and some examples of these structures are presented. Also, it is shown that there not exists a proper complex (Hermitian) home-Lie algebra of dimension two. Then using a…
We present two open-source (BSD) implementations of ellipsoidal harmonic expansions for solving problems of potential theory using separation of variables. Ellipsoidal harmonics are used surprisingly infrequently, considering their…
Polynomial optimization problems over binary variables can be expressed as integer programs using a linearization with extra monomials in addition to those arising in the given polynomial. We characterize when such a linearization yields an…
In this note we announce Lp multiplier theorems for invariant and non-invariant operators on compact Lie groups in the spirit of the well-known Hormander-Mikhlin theorem on Rn and its variants on tori Tn. Applications are given to the…
A large class of Feynman integrals, like e.g., two-point parameter integrals with at most one mass and containing local operator insertions, can be transformed to multi-sums over hypergeometric expressions. In this survey article we present…
In this paper, we begin by reviewing the calculus induced by the framework of [10]. In there, we extended Polylogarithm functions over a subalgebra of noncommutative rational power series, recognizable by finite state (multiplicity)…
We introduce the Mathematica package SummerTime for arbitrary-precision computation of sums appearing in the results of DRA method. So far these results include the following families of the integrals: 3-loop onshell massless vertices,…
In terms of the derivative operator and three hypergeometric series identities, several interesting summation formulas involving generalized harmonic numbers are established.
Harmonic sums and their generalizations are extremely useful in the evaluation of higher-order perturbative corrections in quantum field theory. Of particular interest have been the so-called nested sums,where the harmonic sums and their…