Related papers: Estimation of $\pi$ via experiment
A measurement of the ratio of the branching fractions of the B[0,s] meson to J/psi f0(980) and to J/psi phi(1020) is presented. The J/psi, f0(980), and phi(1020) are observed through their decays to mu+ mu-, pi+ pi-, and K+ K-,…
This article studies statistical estimation of $\pi$ based on the fact that the ratio of the volumes of a $d$-dimensional hypersphere and a $d$-dimensional hypercube is a certain function of $\pi$, and the function depends on the dimension…
We review the binding and energy level alignment of $\pi$-conjugated systems on metals, a field which during the last two decades has seen tremendous progress both in terms of experimental characterization as well as in the depth of…
A systematic study of the $\pi^-/\pi^+$ ratio in heavy-ion collisions with the same neutron/proton ratio but different masses can help single out effects of the nuclear mean field on pion production. Based on simulations using the IBUU04…
A partial wave analysis of the of the $\pi ^0\pi ^0$ system produced in the charge exchange reaction: $\pi ^-p\to \pi ^0\pi ^0n$ at an incident momentum of $18.3 GeV/c$ is presented as a function of ${\pi ^0\pi ^0}$ invariant mass,…
We study one-dimensional elastic collisions of three point masses on a line under vacuum, with no triple collisions. We express momentum conservation in matrix form and analyze the composite map $D=D_{BC}D_{AB}$ and its powers $D^k$, which…
The main task of this work is to find a fast and robust way to determine pp-collision time t0 at the SPD experiment. Using physics motivations, from the input flux of reconstructed particles' tracks we identify a subset of pions which is…
We describe how to compute very far decimals of $$\pi$$ and how to provide formal guarantees that the decimals we compute are correct. In particular, we report on an experiment where 1 million decimals of $$\pi$$ and the billionth…
As a complement to experimental and theoretical approaches, numerical modeling has become an important component to study asteroid collisions and impact processes. In the last decade, there have been significant advances in both…
In many modern astronomical facilities, multi-object telescopes are crucial instruments. Most of these telescopes have thousands of robotic fiber positioners(RFPs) installed on their focal plane, sharing an overlapping workspace. Collisions…
This paper proposes a novel contact and wearable sensing system for estimating the upper body posture and joint angles (ankle, knee, and hip) of the human body using foot pressure distribution information obtained from a sensor attached to…
Accurately modeling local surface properties of objects is crucial to many robotic applications, from grasping to material recognition. Surface properties like friction are however difficult to estimate, as visual observation of the object…
We consider the motion of a finite though large number of particles in the whole space R n. Particles move freely until they experience pairwise collisions. We use our recent theory of divergence-controlled positive symmetric tensors in…
The experiment consists of counting and measuring the size of the many fragments observed after the fall of a mercury drop on the floor. The size distribution follows a power-law for large enough fragments. We address the question of a…
With the aim of generalizing histogram statistics to higher dimensional cases, density estimation via discrepancy based sequential partition (DSP) has been proposed to learn an adaptive piecewise constant approximation defined on a binary…
We present a method for guaranteed collision detection with toleranced motions. The basic idea is to consider the motion as a curve in the 12-dimensional space of affine displacements, endowed with an object-oriented Euclidean metric, and…
\begin{abstract} $\pi$, the ratio between a circumference and is radius, is an irrational transcendental number. Fractal analysis is used here to show that $\pi$\textquoteright{s} digit sequence corresponds to a uniformly distributed random…
In this work, we develop a new iterative method for computing the digits of $\pi$ by argument reduction of the tangent function. This method combines a modified version of the iterative formula for $\pi$ with squared convergence that we…
As robots are being increasingly used in close proximity to humans and objects, it is imperative that robots operate safely and efficiently under real-world conditions. Yet, the environment is seldom known perfectly. Noisy sensors and…
We use geometric scaling invariant quantities to measure the approach, or not, of the imaginary and real parts of the elastic scattering amplitude, to the black disk limit, in $pp$ collisions at very high energy.