Related papers: Another (wrong) construction of $\pi$
We compute the p-widths, $\{\omega_p\}$, for the real projective plane with the standard metric.
A construction is presented that allows to produce subspace codes of long length using subspace codes of shorter length in combination with a rank metric code. The subspace distance of the resulting code, called linkage code, is as good as…
We consider interval estimation of the difference between two binomial proportions. Several methods of constructing such an interval are known. Unfortunately those confidence intervals have poor coverage probability: it is significantly…
The statistical precision of a chord method for estimating fractal dimension from a correlation integral is derived. The optimal chord length is determined, and a comparison is made to other estimators. These calculations use the…
In this paper we propose a general ternary construction of lattices from three rows and ternary codes. Most laminated lattices and Kappa lattices in ${\bf R}^n$, $n\leq 24$ can be recovered from our tenary construction naturally. This…
Use of the effective Lagrangian incorporating both the scalar and pseudoscalar mesons gives a possibility to calculate the $\pi \pi$-scattering lengths without attraction of the ChPT theory.
We improve $O(p^4)$ calculation in $U(2)_L\times U(2)_R$ chiral theory of mesons by resummation calculation for vector mesons physics and restudy decay $\rho\to\pi\pi$. A complete and compact expression for $f_{\rho\pi\pi}(p^2)$ (up to…
We prove that if a set is `large' in the sense of Erd\H{o}s, then it approximates arbitrarily long arithmetic progressions in a strong quantitative sense. More specifically, expressing the error in the approximation in terms of the gap…
We will discuss about a possible method of using the cubit rod by the architects and the surveyors of Ancient Egypt to measure and draw lengths, comparing it with the other interpretations present in Literature. Instead of the modern…
We present a comprehensive survey of constructions of the real numbers (from either the rationals or the integers) in a unified fashion, thus providing an overview of most (if not all) known constructions ranging from the earliest attempts…
Using techniques from calculus, we combine classical identities for $\pi$, $\operatorname{ln}2$, and harmonic numbers, to arrive at a nice infinite series formula for $\pi/3$ that does not appear to be well known. In addition, we give…
This Letter provides a new determination of the ten real coefficients that describe the structure of the $K \to \pi\pi\pi$ amplitudes in the limit where isospin is conserved and complex phases, due to either CP violation or final-state…
Near threshold pion production experiments have been recently carried out and used to extract S--wave $\pi\pi$ scattering lengths. We emphasize here that at present these processes are related only at the tree level (and its first…
A short proof is given that the graphs with proper interval representations are the same as the graphs with unit interval representations.
Subtraction is a powerful technique for creating new bijections from old. Let's reinvent it! While we're at it, let's reinvent division as well.
Given a finite metric, one can construct its tight span, a geometric object representing the metric. The dimension of a tight span encodes, among other things, the size of the space of explanatory trees for that metric; for instance, if the…
We consider the problem of estimating the distance, or range, between two locations by measuring the phase of a sinusoidal signal transmitted between the locations. This method is only capable of unambiguously measuring range within an…
We describe a method of integration to obtain identities of the arctangent function and show how this method can be applied to the high-accuracy computation of the constant pi using the equation $\pi = 4 \arctan \left( 1 \right)$. Our…
This note presents an analytic technique for proving the linear independence of certain small subsets of real numbers over the rational numbers. The applications of this test produce simple linear independence proofs for the subsets of…
We introduce a simple expression for the map of Asplund's distances with the multiplicative Logarithmic Image Processing (LIP) law. It is a difference between a morphological dilation and a morphological erosion with an additive structuring…