Related papers: New 5-designs---revisited

In this article we will represent some ideas and a lot of new theorems in Euclidean plane geometry.

This is an addendum to a previous article, which aims to provide the proofs of some results in that paper (Theorem 7.5 and Proposition 9.15) which were removed from its final version. The reason for such omission is that these proofs follow…

We present a reply to the objections raised by M. J. W. Hall against our extension of Gleason's theorem.

We give a new example for a proper scoring rule motivated by the form of Anderson--Darling distance of distribution functions and Example 5 in Brehmer and Gneiting (2020).

In this note, the correction to the proof of one theorem in some our previous paper [arXiv:1302.0589] will be given.

This article provides a new perspective on the geometry of a projective line, which helps clarify and illuminate some classical results about projective plane. As part of the same train of ideas, the article also provides a proof of the…

In this note, we show that a part of [5, Remark 2.2] is not correct. Some conditions are given under which the same holds.

New cases of the multiplicity conjecture are considered.

We study the new ``gauge'' theories in 5+1 dimensions, and their non-commutative generalizations. We argue that the $\theta$-term and the non-commutative torus parameters appear on an equal footing in the non-critical string theories which…

The following article is one of introduction to additive frieze patterns, linking the subject to multiplicative frieze patterns. We also add two new theorems about additive frieze patterns (see theorem 2 and 5) and a conjecture about…

We construct a new type of geometric knot theory, plumbers' knots, and solve the problems of distinguishing and enumerating such knots at a fixed level of complexity. (v2) Minor edits, added theorem 3.18. (v3) Substantial revisions,…

The study of combinatorial designs has a rich history spanning nearly two centuries. In a recent breakthrough, the notorious Existence Conjecture for Combinatorial Designs dating back to the 1800s was proved in full by Keevash via the…

An elementary geometric proof for the existence of Witt's 5-(12,6,1) design is given.

We use Pixton's relations to prove a reconstruction theorem for genus 2 Gromov-Witten invariants in the style of Kontsevich-Manin (genus 0) and Getzler (genus 1). We also calculate genus 2 (descendant) Gromov-Witten invariants of…

Bhabha scattering is one of the processes at the ILC where high precision data will be expected. The complete NNLO corrections include radiative loop corrections, with contributions from Feynman diagrams with five external legs. We take…

We discuss the claims of the comment at arXiv.org:physics/0609234. We show that A.V. Kildishev et al. misread our method of extracting of optical constants of nanostructured films. The theoretical calculations performed in the comment…

An technically interesting proof of a known theorem.

We obtain a global version and a twisted version (in the sense of \cite{bp05}) of the main theorem of \cite{bkr}.

A novel approach to an old symmetry problem is developed. A new proof is given for the following symmetry problem, studied earlier.

The purpose of this letter is to point out an argument which may ultimately lead to a rigorous proof of the Penrose inequality in the general case. The argument is a variation of Geroch's original proposal for a proof of the positive energy…