Related papers: Topological models of arithmetic
Let $\mathbb{A}$ be an annulus in the plane $\mathbb R^2$ and $g:\mathbb{A}\rightarrow \mathbb{A}$ be a boundary components preserving homeomorphism which is distal and has no periodic points. In \cite{SXY}, the authors show that there is a…
We consider small nonlinear perturbations of linear systems on a time scale with the phase space being finite or infinite-dimensional. For $\Delta$-differential operators, corresponding to linear dynamic systems we consider their…
We establish conditions for nonexistence of global solutions for a class of quasilinear parabolic problems with a potential on complete, non-compact Riemannian manifolds, including the Porous Medium Equation and the p-Laplacian with a…
In this paper, a study of topological and algebraic properties of two families of functions from the unit interval $I$ into the plane $\mathbb{R}^2$ is performed. The first family is the collection of all Peano curves, that is, of those…
An alternative mathematics based on qualitative plurality of finiteness is developed to make non-standard mathematics independent of infinite set theory. The vague concept "accessibility" is used coherently within finite set theory whose…
Erd\H{o}s space $\mathfrak{E}$ and complete Erd\H{o}s space $\mathfrak{E}_c$ have been previously shown to have topological characterizations. In this paper, we provide a topological characterization of the topological space…
Enumerative invariants in Algebraic Geometry 'count' $\tau$-(semi)stable objects $E$ with fixed topological invariants $[E]=a$ in some geometric problem, using a virtual class $[{\cal M}_a^{\rm ss}(\tau)]_{\rm virt}$ in homology, for the…
We introduce a tool for analysing models of $\textnormal{CT}^-$, the compositional truth theory over Peano Arithmetic. We present a new proof of Lachlan's theorem that arithmetical part of models of $\textnormal{PA}$ are recursively…
We prove that for any homogeneous structure $\mathbf{K}$ in a language with finitely many relation symbols of arity at most two satisfying SDAP$^+$ (or LSDAP$^+$), there are spaces of subcopies of $\mathbf{K}$, forming subspaces of the…
We revisit the algebraic description of shape invariance method in one-dimensional quantum mechanics. In this note we focus on four particular examples: the Kepler problem in flat space, the Kepler problem in spherical space, the Kepler…
Given an infinite-dimensional Banach space $X$ and a Banach space $Y$ with no finite cotype, we determine whether or not every continuous linear operator from $X$ to $Y$ is absolutely $(q;p)$-summing for almost all choices of $p$ and $q$,…
Let $A$ be a partial *-algebra endowed with a topology $\tau$ that makes it into a locally convex topological vector space $A[\tau]$. Then $A$ is called a topological partial *-algebra if it satisfies a number of conditions, which all…
We study mapping properties of operators with kernels defined via a combination of continuous and discrete orthogonal polynomials, which provide an abstract formulation of quantum (q-) Fourier type systems. We prove Ismail conjecture…
The nonstandard approach to program semantics has successfully resolved the completeness problem of Floyd-Hoare logic. The known versions of nonstandard semantics, the Hungary semantics and axiomatic semantics, are so general that they are…
We hope to see how much for a model M of some completion T of PA (Peano Arithmetic) does M restriction {<} determine M, say up to isomorphism. We advance in characterizing for non-standard models M of PA the "minimal" set {(a,b):n < a < b…
Rational maps on the Riemann sphere occupy a distinguished niche in the general theory of smooth dynamical systems. First, rational maps are complex-analytic, so a broad spectrum of techniques can contribute to their study (quasiconformal…
We prove that for each sufficiently complicated orientable surface $S$, there exists an infinite image linear representation $\rho$ of $\pi_1(S)$ such that if $\gamma\in\pi_1(S)$ is freely homotopic to a simple closed curve on $S$, then…
Quantum contextuality, a fundamental feature distinguishing quantum theory from classical models, is investigated via algebraic and topological structures inherent in modular tensor categories. This work rigorously demonstrates that braid…
A well-known conjecture of Orlov asks whether the existence of a full exceptional collection implies rationality of the underlying variety. We prove this conjecture for arithmetic toric varieties over general fields. We also investigate a…
Let A be a local conformal net of factors on the circle with the split property. We provide a topological construction of soliton representations of the tensor product of n copies of A, that restrict to true representations of subnet…