This is a review on infinite non-abelian symmetries in two-dimensional field theories. We show how any integrable QFT enjoys the existence of infinitely many {\bf conserved} charges. These charges {\bf do not commute} between them and satisfy a Yan...
A class of optimal three-weight cyclic codes of dimension 3 over any finite field was presented by Vega [Finite Fields Appl., 42 (2016) 23-38]. Shortly thereafter, Heng and Yue [IEEE Trans. Inf. Theory, 62(8) (2016) 4501-4513] generalized this result...
Axial algebras are non-associative algebras generated by semisimple idempotents, known as axes, that all obey a fusion rule. Axial algebras were introduced by Hall, Rehren and Shpectorov as a generalisation of the axioms of Majorana theory, which was...
Axial algebras are non-associative algebras generated by semisimple idempotents whose adjoint actions obey a fusion law. Axial algebras that are generated by two such idempotents play a crucial role in the theory. We classify all primitive 2-generate...
A key inequality which underpins the regularity theory of optimal transport for costs satisfying the Ma--Trudinger--Wang condition is the Pogorelov second derivative bound. This translates to an apriori interior $C^1$ estimate for smooth optimal maps...
Dabura’s curse technique is actually an unknown level of "light" manipulation, with all the cool things that stem from that, and his Deskunte trait [——-] allows him to form physical objects from that light as well.
We investigate planetary accretion that starts from equal-mass planetesimals using an analytic theory and numerical simulations. We particularly focus on how the planetary mass $M_{\rm oli}$ at the onset of oligarchic growth depends on the initial ma...
We investigate the eigenstate thermalization hypothesis (ETH) of highly excited descendant states in two-dimensional large central charge $c$ conformal field theory. We use operator product expansion of twist operators to calculate the short interval...
Within the framework of complex supergeometry and motivated by two-dimensional genus-zero holomorphic N=2 superconformal field theory, we define the moduli space of N=2 super-Riemann spheres with oriented and ordered half-infinite tubes (or equival...
We study the electronic structure of finite armchair graphene nanoribbons using density-functional theory and the Hubbard model, concentrating on the states localized at the zigzag termini. We show that the energy gaps between end-localized states ar...
We present a dynamical theory of statistical convergence in which the law of large numbers arises from outcome-outcome feedback rather than assumed independence. Defining the convergence field and its derivative, we show that empirical frequencies ev...
In classical probability theory, the convergence of empirical frequencies to theoretical probabilities: as captured by the Law of Large Numbers (LLN): is treated as axiomatic and emergent from statistical assumptions such as independence and identica...
When a steady-state cylindrical plasma discharge is centrally fuelled, the collisionless radial electron flux is canonically coupled to an axial current. The identification and analysis of this transport driven current, previously reported in collisi...
The inelastic scanning tunneling microscopy (STM) has been shown recently (Loth et al. Science 329, 1628 (2010)) to be extendable as to access the nanosecond, spin-resolved dynamics of magnetic adatoms and molecules. Here we analyze theoretically thi...
The 1919 Eclipse Expedition to test the light-bending prediction of General Relativity remains one of the most famous physics experiments of the 20th century. However, in recent decades it has been increasingly often alleged that the data-analysis...
The Global Positioning System (GPS) provides an excellent educational example as to how the theory of general relativity is put into practice and becomes part of our everyday life. This paper gives a short and instructive derivation of an important...
We describe an explicit version of Hilbert's irreducibility theorem using a generalization of Gallagher's larger sieve. We give applications to the Galois theory of random polynomials, and to the images of the adelic representation associated to elli...
The Dirichlet series $L_m(s)$ are of fundamental importance in number theory. Shanks defined the generalized Euler and class numbers in connection with these Dirichlet series, denoted by $\{s_{m,n}\}_{n\geq 0}$. We obtain a formula for the exponentia...
Laplace's views on randomness and determinism. The paper was written for "Cahiers rationalistes" and addresses a rather wide audience. It contains large quotations of Laplace, most of them coming from his introduction to the book "Analytical theory...
We assess the potential of nuclear starburst disks to obscure the Seyfert-like AGN that dominate the hard X-ray background at z~1. Over 1200 starburst disk models, based on the theory developed by Thompson et al., are calculated for five input para...