Related papers: Exploring Collatz Dynamics with Human-LLM Collabor…
A recast of the standard residue-class analysis of the 3x+1 (Collatz) map in terms of two elementary operators on arithmetic progressions. The resulting calculus (i) splits any progression into its even and odd subsequences in a single…
A new coercivity estimate on the spectral gap of the linearized Boltzmann collision operator for multiple species is proved. The assumptions on the collision kernels include hard and Maxwellian potentials under Grad's angular cut-off…
Initially, we derive a nonlinear integral equation for the vacuum counting function of the spin 1/2-XYZ chain in the {\it disordered regime}, thus paralleling similar results by Kl\"umper \cite{KLU}, achieved through a different technique…
We study continuous wavelet transforms associated to matrix dilation groups giving rise to an irreducible square-integrable quasi-regular representation on ${\rm L}^2(\mathbb{R}^d)$. We first prove that these representations are integrable…
Over an algebraically closed field $\mathbb{K}$ with any characteristic, on an $N$-dimensional smooth projective $\mathbb{K}$-variety $\mathbf{P}$ equipped with $c\geqslant N/2$ very ample line bundles $\mathcal{L}_1,\dots,\mathcal{L}_c$,…
Logic programming (LP) is a programming language based on first-order Horn clause logic that uses SLD-resolution as a semi-decision procedure. Finite SLD-computations are inductively sound and complete with respect to least Herbrand models…
We develop a neutrino transfer code for core-collapse simulations, that directly solves the multidimensional Boltzmann equations in full general relativity. We employ the discrete ordinate method, which discretizes the six dimensional phase…
We show that there exists a universal mechanism of long-range soliton attraction in three-dimensional solids and, therefore, of discontinuity of any commensurate-incommensurate (C-IC) phase transition. This mechanism is due to the strain…
A generalisation of Takens' delay-coordinate embedding theorem to stochastic systems, the Stochastic Embedding Sufficiency Theorem, is an inverse methodology enabling non-parametric recovery of both drift and diffusion fields from scalar…
Introduced in 2006 by Japaridze, cirquent calculus is a refinement of sequent calculus. The advent of cirquent calculus arose from the need for a deductive system with a more explicit ability to reason about resources. Unlike the more…
A theoretical framework supported by literature reported experimental evidence (Homes, Harshman along with Voyager, Hubble and EGRET space platforms and others) is presented which indicates that superconductivity is a self energy phenomenon…
Kadison's transitivity theorem implies that, for irreducible representations of C*-algebras, every invariant linear manifold is closed. It is known that CSL algebras have this propery if, and only if, the lattice is hyperatomic (every…
Lipton's reduction theory provides an intuitive and simple way for deducing the non-interference properties of concurrent programs, but it is difficult to directly apply the technique to verify linearizability of sophisticated fine-grained…
We show that by integrating out the electric field and incorporating proper boundary conditions, a semiclassical Boltzmann equation can describe electron transport properties, continuously from the diffusive to ballistic regimes. General…
Data-aware modal logics offer a powerful formalism for reasoning about semi-structured queries in languages such as DataGL, XPath, and GQL. In brief, these logics can be viewed as modal systems capable of expressing both reachability…
In this paper we prove new constructive coercivity estimates for the Boltzmann collision operator without cutoff, that is for long-range interactions. In particular we give a generalized sufficient condition for the existence of a spectral…
We study a system composed of two parallel totally asymmetric simple exclusion processes with open boundaries, where the particles move in the two lanes in opposite directions and are allowed to jump to the other lane with rates inversely…
The Collatz conjecture states that repeated steps of $n\mathrm{\to }\mathrm{3}n\mathrm{+1}$ at odd numbers and $n\mathrm{\to }n\mathrm{/2}$ at even numbers amount to walks over root paths to the branching number $c=4$ in the `trivial'…
We introduce a sound and complete coinductive proof system for reachability properties in transition systems generated by logically constrained term rewriting rules over an order-sorted signature modulo builtins. A key feature of the…
It has been conjectured that transport in integrable one-dimensional (1D) systems is necessarily ballistic. The large diffusive response seen experimentally in nearly ideal realizations of the S=1/2 1D Heisenberg model is therefore puzzling…