Related papers: A Wallis Product on Clovers
In 1655, John Wallis whilst at the University of Oxford discovered the famous and beautiful formula for pi, now known as Wallis' Product. Since then, several analogous formulae have been discovered generalising the original. One more modern…
Inspired by the definition of generalized wreath product of permutation groups, we define the generalized wreath product of graphs, containing the classical Cartesian and wreath product of graphs as particular cases. We prove that the…
A special formula for the total mean curvature of an ovaloid is derived. This formula allows us to extend the notion of the mean curvature to the class of boundaries of strictly convex sets. Moreover, some integral formula for ovaloids is…
A new generalization of the classical separate algebraicity theorem is suggested and proved.
We survey the extensions of a group by a group using crossed products instead of exact sequences of groups. The approach has various advantages, one of them being that the crossed product is an universal object. Several new applications are…
This paper studies the moduli space of stable surfaces of general type. The moduli space component containing the moduli point of a product of smooth curves of general type is proved to be the product of the moduli spaces of the curves,…
We generalize Wallis's 1655 infinite product for $\pi/2$ to one for $(\pi/K)\csc(\pi/K)$, as well as give new Wallis-type products for $\pi/4, 2, \sqrt{2+\sqrt2}, 2\pi/3\sqrt3,$ and other constants. The proofs use a classical infinite…
We aim to present two new generalized integral formulae involving product of generalized Struve function $\mathcal{W}_{p,b,c}\left( z\right)$, which are expressed in terms of the generalized Lauricella functions. The main results presented…
In this note we consider a question related to the high-dimensional generalization of the classical Severi's finiteness theorem for curves. We will introduce some background and then state the main result. The proof of the main result is…
Using the short time existence of the Calabi flow, we prove that any extremal Kaehler metric on a product toric variety is a product extremal Kaehler metric.
In this paper, we propose a generalization of a congruence due to Carlitz.
We prove all conjectures from chapter 7 of Yves Andr\'e's book on motives in the case of products of elliptic curves. The proofs given here are simpler and more uniform than the previous proofs in known cases.
We propose an algebraic method for the classification of branched Galois covers of a curve $X$ focused on studying Galois ring extensions of its geometric adele ring $\A_{X}$. As an application, we deal with cyclic covers; namely, we…
We prove some identities for the squares of generalized Tribonacci numbers. Various summation identities involving these numbers are derived.
In arXiv:2205.02920 a variant of the classical elastic flow for closed curves in $\mathbb{R}^{n}$ was introduced, that is more suitable for numerical purposes. Here we investigate the long-time properties of such evolution demonstrating…
We show that the existence of disintegration for cylindrical measures follows from a general disintegration theorem for countably additive measures.
In the present article, real number representations, that are generalizations of classical positive and alternating representations of numbers, are introduced and investigated. The main metric relation, properties of cylinder sets are…
Generalizing work of Schoen, we prove that the Chow group modulo $\ell$ of a product of $3$ or more very general complex elliptic curves is infinite.
We prove that every curve on a rationally connected variety is algebraically equivalent to a (non-effective) integral sum of rational curves.
Motivated by the reduction techniques involving character triples for the local-global conjectures, we show that a blockwise relation between module triples is a consequence of a derived equivalence with additional properties. Moreover, we…