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This article reviews several recent proposed redefinitions of the kilogram, and compares them with respect to practical realizations, uncertainties (estimated standard deviations), and educational aspects.

Data Analysis, Statistics and Probability · Physics 2015-05-19 Theodore P. Hill , Ronald F. Fox , Jack Miller

Some observations on the Wu-Sprung potential.

Classical Analysis and ODEs · Mathematics 2007-05-23 Diego Dominici

A sketch of some of the fundamental notions related to the nature of knowledge is offered, with special focus on the role of mathematics and my own opinions. No single idea exposed here is entirely original; indeed, this topic has been…

History and Overview · Mathematics 2023-10-23 Daniel Canarutto

This work is a continuation of [1]. As in the previous article, here we will describe some interesting ideas and a lot of new theorems in plane geometry related to them.

History and Overview · Mathematics 2018-02-13 A. Skutin

We collect here various conjectures on congruences made by the author in a series of papers, some of which involve binary quadratic forms and other advanced theories. Part A consists of 100 unsolved conjectures of the author while…

Number Theory · Mathematics 2015-03-13 Zhi-Wei Sun

Various versions of club are shown to be different. A question of Soukup, Fuchino and Juhasz, is it consistent to have a stick without club, is answered as a consequence. The more detailed version of the paper, which is coming up, also…

Logic · Mathematics 2009-09-25 Mirna Džamonja , Saharon Shelah

I exemplify part of my recent work on the upper halfplane.

Representation Theory · Mathematics 2009-10-21 Bernhard Kroetz

We highlight some facts about continued fractions of real cubic irrationalities. This may be thought as a small section in a textbook on continued fractions.

Number Theory · Mathematics 2023-11-29 Wadim Zudilin

A survey of work on motivic integration.

Algebraic Geometry · Mathematics 2007-05-23 Eduard Looijenga

This note discusses an interesting matrix factorization called the CUR Decomposition. We illustrate various viewpoints of this method by comparing and contrasting them in different situations. Additionally, we offer a new characterization…

Numerical Analysis · Mathematics 2019-09-05 Keaton Hamm , Longxiu Huang

The Halting Problem is ill-conceived and ill-defined.

Logic in Computer Science · Computer Science 2016-06-29 Eric C. R. Hehner

A quick overview of category theory and topos theory including slice categories, monics, epics, isos, diagrams, cones, cocones, limits, colimits, products and coproducts, pushouts and pullbacks, equalizers and coequalizers, initial and…

Category Theory · Mathematics 2024-07-01 Eric Schmid

This is a Comment on "Universal Fluctuations in Correlated Systems".

Statistical Mechanics · Physics 2009-11-07 B. Zheng , S. Trimper

I present a few new and recent ideas of the multiloop calculations.

High Energy Physics - Phenomenology · Physics 2014-05-23 Roman N. Lee

An introduction to circle valued Morse theory and Novikov homology, from an algebraic point of view.

Algebraic Topology · Mathematics 2007-05-23 Andrew Ranicki

We provide the first information on diffeotopy groups of exotic smoothings of R^4: For each of uncountably many smoothings, there are uncountably many isotopy classes of self-diffeomorphisms. We realize these by various explicit group…

Geometric Topology · Mathematics 2018-12-03 Robert E. Gompf

We give characterizations of the separability of the induction and ad-induction functors associated to a coring morphism.

Rings and Algebras · Mathematics 2007-05-23 J. Gomez-Torrecillas

A brief account of interesting moments in the genesis of the quark paradigm is presented.

History and Philosophy of Physics · Physics 2014-12-31 Vladimir A. Petrov

We establish bounds on the probability that two different agents, who share an initial opinion expressed as a probability distribution on an abstract probability space, given two different sources of information, may come to radically…

Probability · Mathematics 2019-03-20 Krzysztof Burdzy , Jim Pitman

Gompf showed that for $K$ in a certain family of double-twist knots, the swallow-follow operation makes $1/n$-surgery on $K \# -K$ into a cork boundary. We derive a general Floer-theoretic condition on $K$ under which this is the case. Our…

Geometric Topology · Mathematics 2024-09-04 Irving Dai , Abhishek Mallick , Ian Zemke