Related papers: Harmonic sums and polylogarithms at non-positive m…
This paper presents a noncommutative theory of symmetric functions, based on the notion of quasi-determinant. We begin with a formal theory, corresponding to the case of symmetric functions in an infinite number of independent variables.…
A well-known ansatz (`trace method') for soliton solutions turns the equations of the (noncommutative) KP hierarchy, and those of certain extensions, into families of algebraic sum identities. We develop an algebraic formalism, in…
In this paper we describe the right-sided combinatorial Hopf structure of three Hopf algebras appearing in the context of renormalization in quantum field theory: the non-commutative version of the Fa\`a di Bruno Hopf algebra, the…
In this paper, we introduce an iterative process which converges strongly to a common element of sets of solutions of finite family of generalized equilibrium problems, sets of fixed points of finite family of continuous relatively…
In this paper, we explore the merits of various algorithms for polynomial optimization problems, focusing on alternatives to sum of squares programming. While we refer to advantages and disadvantages of Quantifier Elimination, Reformulation…
The two-dimensional harmonic polylogarithms $\G(\vec{a}(z);y)$, a generalization of the harmonic polylogarithms, themselves a generalization of Nielsen's polylogarithms, appear in analytic calculations of multi-loop radiative corrections in…
The role of coalgebras as well as algebraic groups in non-commutative probability has long been advocated by the school of von Waldenfels and Sch\"urmann. Another algebraic approach was introduced more recently, based on shuffle and pre-Lie…
In this paper we propose and analyze three parallel hybrid extragradient methods for finding a common element of the set of solutions of equilibrium problems involving pseudomonotone bifunctions and the set of fixed points of nonexpansive…
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…
In \cite{IKLNDP23} we presented a systematic study of algebra structures of multiple zeta values in positive characteristic introduced by Thakur as analogues of classical multiple zeta values of Euler. In this paper we construct algebra and…
We review the appearance of Hopf algebras in the renormalization of quantum field theories and in the study of diffeomorphisms of the frame bundle important for index computations in noncommutative geometry.
Using the theory of noncommutative symmetric functions, we introduce the higher order peak algebras, a sequence of graded Hopf algebras which contain the descent algebra and the usual peak algebra as initial cases (N = 1 and N = 2). We…
We introduce a family of periods of mixed Tate motives called dissection polylogarithms, that are indexed by combinatorial objects called dissection diagrams. The motivic coproduct on the former is encoded by a combinatorial Hopf algebra…
We develop the theory of weighted P-partitions, which generalises the theory of P-partitions from labelled posets to weighted labelled posets. We define the related generating functions in the natural way and compute their product,…
We show that the shuffle algebras for polylogarithms and regularized MZVs in the sense of Ihara, Kaneko and Zagier are both free commutative nonunitary Rota-Baxter algebras with one generator. We apply these results to show that the full…
We develop new closed form representations of sums of (n + {\alpha})th shifted harmonic numbers and reciprocal binomial coefficients in terms of {\alpha}th shifted harmonic numbers. Some interesting new consequences and illustrative…
We give systematic method to evaluate a large class of one-dimensional integral relating to multiple zeta values (MZV) and colored MZV. We also apply the technique of iterated integrals and regularization to elucidate the nature of some…
Many applications modeled by polynomial systems have positive dimensional solution components (e.g., the path synthesis problems for four-bar mechanisms) that are challenging to compute numerically by homotopy continuation methods. A…
We introduce new bases for the Hopf algebra of quasisymmetric functions that refine the symmetric powersum basis. These bases are expanded in terms of quasisymmetric monomial functions by using fillings of matrices. We define the analog of…
We show that various identities from [1] and [3] involving Gould-Hopper polynomials can be deduced from the real but also complex orthogonal invariance of multivariate Gaussian distributions. We also deduce from this principle a useful…