Expression of Farhi's integral in terms of known mathematical constants

JC Pain - arxiv preprint arxiv:2408.14835, 2024 - arxiv.org
In an interesting article entitled" A curious formula related to the Euler Gamma function",
Bakir Farhi posed the open question of whether it was possible to obtain an expression of …

Asymptotically optimal communication for torus-based cryptography

M van Dijk, D Woodruff - Annual International Cryptology Conference, 2004 - Springer
We introduce a compact and efficient representation of elements of the algebraic torus. This
allows us to design a new discrete-log based public-key system achieving the optimal …

On asymptotic constants related to products of Bernoulli numbers and factorials

BC Kellner - 2009 - degruyter.com
We discuss the asymptotic expansions of certain products of Bernoulli numbers and
factorials, eg, for integers k≥ 1 and r≥ 0. Our main interest is to determine exact …

How Far Might We Walk at Random?

SR Finch - arxiv preprint arxiv:1802.04615, 2018 - arxiv.org
This elementary treatment first summarizes extreme values of a Bernoulli random walk on
the one-dimensional integer lattice over a finite discrete time interval. Both the symmetric …

Maximum queue length for traffic light with Bernoulli arrivals

SR Finch - arxiv preprint arxiv:1802.04621, 2018 - arxiv.org
Cars arrive at an intersection with a stoplight, which is either red or green. The cars all travel
in the same direction, that is, we ignore cross-traffic & oncoming traffic. Assume that the …

Correlation between angle and side

SR Finch - arxiv preprint arxiv:1012.0781, 2010 - arxiv.org
Let alpha be an arbitrary angle in a random spherical triangle Delta and a be the side
opposite alpha.(The sphere has radius 1; vertices of Delta are independent and uniform.) If …

Another look at AR (1)

SR Finch - arxiv preprint arxiv:0710.5419, 2007 - arxiv.org
Given a stationary first-order autoregressive process X_t (with lag-one correlation rho
satisfying| rho|< 1), we examine the Central Limit Theorem for (1/n)* ln| X_1... X_n| and …

[PDF][PDF] Cusped hyperbolic 3-manifolds from some regular polyhedra

A Cavicchioli, F Spaggiari, AI Telloni - Houston J. Math, 2013 - Citeseer
We illustrate some topological properties and give surgery descriptions of the cusped
hyperbolic orientable 3–manifolds obtained by face pairings of the regular octahedron and …

Idempotents and nilpotents modulo n

S Finch - arxiv preprint math/0605019, 2006 - arxiv.org
arxiv:math/0605019v2 [math.NT] 18 Nov 2017 Page 1 arxiv:math/0605019v2 [math.NT] 18
Nov 2017 Idempotents and Nilpotents Modulo n Steven Finch November 18, 2017 Abstract …

Rank-3 projections of a 4-cube

SR Finch - arxiv preprint arxiv:1204.3468, 2012 - arxiv.org
The orthogonal projection of a 4-cube onto a uniform random 3-subspace in R^ 4 is a
convex 3-polyhedron P with 14 vertices almost surely. Three numerical characteristics of P …