Related papers: Regularized Products over arithmetic Schemes
This paper is concerned with recovering the solution of a final value problem associated with a parabolic equation involving a non linear source and a non-local term, which to the best of our knowledge has not been studied earlier. It is…
We define the notion of infinite friezes of positive integers as a variation of Conway-Coxeter frieze patterns and study their properties. We introduce useful gluing and cutting operations on infinite friezes. It turns out that…
Ihara, Kaneko, and Zagier defined two regularizations of multiple zeta values and proved the regularization theorem that describes the relation between those regularizations. We show that the regularization theorem can be generalized to…
We exhibit a probabilistic algorithm which computes a rational point of an absolutely irreducible variety over a finite field defined by a reduced regular sequence. Its time--space complexity is roughly quadratic in the logarithm of the…
We investigate the complexity of computing the Zariski closure of a finitely generated group of matrices. The Zariski closure was previously shown to be computable by Derksen, Jeandel, and Koiran, but the termination argument for their…
We introduce a family of mathematical objects called $\mathcal{P}$-schemes, where $\mathcal{P}$ is a poset of subgroups of a finite group $G$. A $\mathcal{P}$-scheme is a collection of partitions of the right coset spaces $H\backslash G$,…
We deal with non-smooth differential systems $\dot{z}=X(z), z\in R^{n},$ with discontinuity occurring in a codimension one smooth surface $\Sigma$. A regularization of $X$ is a 1-parameter family of smooth vector fields…
We describe a framework for systematic enumeration of families combinatorial structures which possess a certain regularity. More precisely, we describe how to obtain the differential equations satisfied by their generating series. These…
We study the problem of approximation of 2D set of points. Such type of problems always occur in physical experiments, econometrics, data analysis and other areas. The often problems of outliers or spikes usually make researchers to apply…
We generalize the zig-zag product construction to produce infinite families of regular graphs of any constant degree. We analyze the second largest eigenvalue of this new zig-zag product to show that the modified zig-zag product of good…
We examine two central regularization strategies for monotone variational inequalities, the first a direct regularization of the operative monotone mapping, and the second via regularization of the associated dual gap function. A key link…
In recent decades, a growing number of discoveries in fields of mathematics have been assisted by computer algorithms, primarily for exploring large parameter spaces that humans would take too long to investigate. As computers and…
In this paper we give bounds on the Castelnuovo-Mumford regularity of products of ideals and ideal sheaves. In particular, we show that the regularity of a product of ideals is bounded by the sum of the regularities of its factors if the…
The main goal of this paper is to relate the topologically relevant stationary points of a cardinality-constrained optimization problem and its continuous reformulation up to their type. For that, we focus on the nondegenerate M- and…
There is growing body of learning problems for which it is natural to organize the parameters into matrix, so as to appropriately regularize the parameters under some matrix norm (in order to impose some more sophisticated prior knowledge).…
We derive residue formulas for the regularized integrals (introduced by Li-Zhou) on configuration spaces of elliptic curves. Based on these formulas, we prove that the regularized integrals satisfy holomorphic anomaly equations, providing a…
Variational regularization and the quasisolutions method are justified for unbounded closed, possibly nonlinear, operators. The argument is quite simple and yields general results.
We study some infinite products of absolute zeta functions. Especially, we consider the convergence and the rationality of them.
In this technical report, certain interesting classification of arithmetical functions is proposed. The notion of additively decomposable and multiplicatively decomposable arithmetical functions is proposed. The concepts of arithmetical…
The finite Dirichlet series from the title are defined by the condition that they vanish at as many initial zeroes of the zeta function as possible. It turned out that such series can produce extremely good approximations to the values of…