The problem of finding the asymptotic behavior of the maximal density of sphere packings in high Euclidean dimensions is one of the most fascinating and challenging problems in discrete geometry. One century ago, Minkowski obtained a rigorous lower...
We analyse and clarify the finite-size scaling of the weakly-coupled hierarchical $n$-component $|\varphi|^4$ model for all integers $n \ge 1$ in all dimensions $d\ge 4$, for both free and periodic boundary conditions. For $d>4$, we prove that for a...
We obtain precise plateau estimates for the two-point function of the finite-volume weakly-coupled hierarchical $|\varphi|^4$ model in dimensions $d \ge 4$, for both free and periodic boundary conditions, and for any number $n \ge 1$ of components of...
We show that, in contrast to the real analytic case, quasianalytic ultradifferentiability can never be tested in lower dimensions. Our results are based on a construction due to Jaffe....
We study the stability of the O(N) fixed point in three dimensions under perturbations of the cubic type. We address this problem in the three cases $N=2,3,4$ by using finite size scaling techniques and high precision Monte Carlo simulations. It is...
A recently developed method has been extended to a nonlocal equation arising in steady water wave propagation in two dimensions. We obtain analyic approximation of steady water wave solution in two dimensions with rigorous error bounds for a set of p...
The Bañados, Teitelboim and Zanelli\cite{BTZ} solution corresponding to the exterior space-time of a black hole in $(2+1)$ dimensions has been found to be very useful to understand various aspects relating to the gravitational field of a black hole....
For systems of partial differential equations in three spatial dimensions, dynamical conservation laws holding on volumes, surfaces, and curves, as well as topological conservation laws holding on surfaces and curves, are studied in a unified framewo...
Sep 29, 2020 · This article delves into the meaning of governance, explores its core dimensions, and provides an in-depth explanation of the 6 types of governance that drive the modern world.
can lead to new innovations and help to make operations more efficient. The SECI model distinguishes four knowledge dimensions (forming the "SECI" acronym):
Although they do not address the hierarchy problem, models with Universal Extra Dimensions have attracted a lot of attention as simple benchmark models characterized by small mass splittings and a dark matter WIMP played by the Lightest Kaluza-Klein...
We present Michel Kervaire work on knots in higher dimensions....
Nous nous intéressons à la reconstruction parcimonieuse d'images à l'aide du problème d'optimisation régularisé LASSO. Dans de nombreuses applications pratiques, les grandes dimensions des objets à reconstruire limitent, voire empêchent, l'ut...
N=2 supergravity in four dimensions, or equivalently N=1 supergravity in five dimensions, has an interesting set of BPS solutions that each correspond to a number of charged centers. This set contains black holes, black rings and their bound states...
The invaded cluster algorithm is used to study the XY model in two and three dimensions up to sizes 2000^2 and 120^3 respectively. A soft spin O(2) model, in the same universality class as the 3D XY model, is also studied. The static critical prope...
Jump into a new dimension of math. Have you ever felt like two dimensions isn't quite enough? The Desmos 3D Calculator lets you explore curves, surfaces, and points in all three dimensions.
We express Alltop's construction of mutually unbiased bases as orbits under the Weyl-Heisenberg group in prime dimensions and find a related construction in dimensions 2 and 4. We reproduce Alltop's mutually unbiased bases using abelian subgroups of...
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Jan 29, 2015 · I am having a difficult time researching the height/length/width dimensions of a 26' boat when sitting on a trailer (or any similar boat for that matter). We are thinking about moving up from a …
The dimer model is a classical statistical mechanics model which is exactly solvable in two dimensions, but about which little is known in higher dimensions. In analogy with large $N$ limits in lattice gauge theory, we study a large $N$ limit of the...