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We combine continuous and integral logics and found a logical framework for metric measure spaces equipped with a family of continuous relations and operations. We prove the ultraproduct theorem and deduce compactness and other usual…
We extend the work of M.Borovoi on the nonabelian Galois cohomology of linear reductive algebraic groups over number fields to a general base scheme. As an application, we obtain new results on the arithmetic of such groups over global…
We develop a new method that improves the efficiency of equation-by-equation algorithms for solving polynomial systems. Our method is based on a novel geometric construction, and reduces the total number of homotopy paths that must be…
Let $\underline{\mathcal F}$ be a $\tau$-sheaf. Building on previous work of Drinfeld, Anderson, Taguchi, and Wan, B\"ockle and Pink \cite{bp1} develop a cohomology theory for $\underline{\mathcal F}$. In \cite{boc1} B\"ockle uses this…
We introduce the multivariable connected sum which is a generalization of Seki-Yamamoto's connected sum and prove the fundamental identity for these sums by series manipulation. This identity yields explicit procedures for evaluating…
It is known that the Lyapunov exponent of analytic 1-frequency quasiperiodic cocycles is continuous in cocycle and, when the frequency is irrational, jointly in cocycle and frequency. In this paper, we extend a result of Bourgain to show…
We present the Matlab toolbox MacaulayLab, which implements numerical linear algebra algorithms for solving multivariate polynomial systems and rectangular multiparameter eigenvalue problems. Its structure and functionality are the result…
We determine the product structure on Hochschild cohomology of commutative algebras in low degrees, obtaining the answer in all degrees for complete intersection algebras. As applications, we consider cyclic extension algebras as well as…
Following Bridgeman, we demonstrate several families of infinite dilogarithm identities associated with Fibonacci numbers, Lucas numbers, convergents of continued fractions of even periods, and terms arising from various recurrence…
We shall define the q-analogs of multiple zeta functions and multiple polylogarithms in this paper and study their properties, based on the work of Kaneko et al. and Schlesinger, respectively.
Combinatorial harmonic analysis techniques are used to develop new functional analysis methods based on Bogoliubov functionals. Concrete applications of the methods are presented, namely, the study of a non-equilibrium stochastic dynamics…
In this article, a new approach based on linear algebra is adopted to study a hybrid Sheffer polynomial sequences. The recurrence relations and differential equation for these polynomials are derived by using the properties and…
We propose and study a generalized continued fraction algorithm that can be executed in an arbitrary imaginary quadratic field, the novelty being a non-restriction to the five Euclidean cases. Many hallmark properties of classical continued…
Bihom-associative algebras have been recently introduced in the study of group hom-categories. In this paper, we introduce a Hochschild type cohomology for bihom-associative algebras with suitable coefficients. The underlying cochain…
We evaluate binomial series with harmonic number coefficients, providing recursion relations, integral representations, and several examples. The results are of interest to analytic number theory, the analysis of algorithms, and…
We study the analytic continuation of Feynman integrals from the kite family, expressed in terms of elliptic generalisations of (multiple) polylogarithms. Expressed in this way, the Feynman integrals are functions of two periods of an…
We describe an algorithm for computing Macaulay dual spaces for multi-graded ideals. For homogeneous ideals, the natural grading is inherited by the Macaulay dual space which has been leveraged to develop algorithms to compute the Macaulay…
This article introduces an algorithm to compute the persistent homology of a filtered complex with various coefficient fields in a single matrix reduction. The algorithm is output-sensitive in the total number of distinct persistent…
Our constructions provide a systematic way to study cohomology tri-dendriform algebra via classical cohomology, simplifying computations and enabling the use of established techniques.
We study cylindric partitions with two-element profiles using MacMahon's partition analysis. We find explicit formulas for the generating functions of the number of cylindric partitions by first finding the recurrences using partition…