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We provide a compactness criterion for the set of laws $\mathfrak{P}^{ac}_{sem}(\Theta)$ on the Skorokhod space for which the canonical process $X$ is a semimartingale having absolutely continuous characteristics with differential…

Probability · Mathematics 2018-05-11 Chong Liu , Ariel Neufeld

We verified that the existence of a maximal ideal of height 0 in a p-adic algebra in a certain class is independent of the axiom of ZFC. We established the theory on a P-point in the boundary of a topological space in the universal totally…

Number Theory · Mathematics 2013-03-12 Tomoki Mihara

We study the emergence of Minkowski space-time from a causal network. Differently from previous approaches, we require the network to be topologically homogeneous, so that the metric is derived from pure event-counting. Emergence from…

General Relativity and Quantum Cosmology · Physics 2016-01-26 Giacomo Mauro D'Ariano , Alessandro Tosini

We provide a short introduction to the field of topological data analysis and discuss its possible relevance for the study of complex systems. Topological data analysis provides a set of tools to characterise the shape of data, in terms of…

Data Analysis, Statistics and Probability · Physics 2018-12-05 Vsevolod Salnikov , Daniele Cassese , Renaud Lambiotte

We analyse the structure of the quotient $\mathrm{A}_\sim(\Gamma,X,\mu)$ of the space of measure-preserving actions of a countable discrete group by the relation of weak equivalence. This space carries a natural operation of convex…

Dynamical Systems · Mathematics 2016-01-06 Peter Burton

Time-dependent conformal maps are used to model a class of growth phenomena limited by coupled non-Laplacian transport processes, such as nonlinear diffusion, advection, and electro-migration. Both continuous and stochastic dynamics are…

Statistical Mechanics · Physics 2007-05-23 Martin Z. Bazant , Jaehyuk Choi , Benny Davidovitch

We introduce and study the framework of compact metric structures and their associated notions of isomorphisms such as homeomorphic and bi-Lipschitz isomorphism. This is subsequently applied to model various classification problems in…

Logic · Mathematics 2016-10-04 Christian Rosendal , Joseph Zielinski

We give a systematic account of iterated function systems (IFS) of weak contractions of different types (Browder, Rakotch, topological). We show that the existence of attractors and asymptotically stable invariant measures, and the validity…

Dynamical Systems · Mathematics 2020-04-24 Krzysztof Leśniak , Nina Snigireva , Filip Strobin

This paper presents a study of the inherent structural properties of Krylov subspaces, in particular for the self-adjoint class of operators, and how they relate with the important phenomenon of `Krylov solvability' of linear inverse…

Functional Analysis · Mathematics 2024-10-31 Noè Angelo Caruso

Given a compact metric space $X$, we associate to it an inverse sequence of finite $T_0$ topological spaces. The inverse limit of this inverse sequence contains a homeomorphic copy of $X$ that is a strong deformation retract. We provide a…

Geometric Topology · Mathematics 2022-03-14 Pedro J. Chocano , Manuel A. Morón , Francisco R. Ruiz del Portal

Topological data analysis is a powerful tool for describing topological signatures in real world data. An important challenge in topological data analysis is matching significant topological signals across distinct systems. In geometry and…

Algebraic Topology · Mathematics 2025-02-19 Stephen Y Zhang , Michael P H Stumpf , Tom Needham , Agnese Barbensi

We introduce a topology-preserving discretization for coupling incompressible fluids with thin deformable structures, achieving guaranteed leakproofness through preservation of fluid domain connectivity. Our approach leverages a stitching…

Computational Physics · Physics 2026-02-05 Jonathan Panuelos , Eitan Grinspun , David Levin

Let $E$ be a Banach space such that $E'$ has the Radon-Nikod\'ym property. The aim of this work is to connect relative weak compactness in the $E$-valued martingale Hardy space $H^{1}(\mu,E)$ to a convex compactness criterion in a weaker…

Functional Analysis · Mathematics 2024-10-21 Vasily Melnikov

We prove an "abelian, locally compact" Whitehead theorem in fine shape: A fine shape morphism between locally connected finite-dimensional locally compact separable metrizable spaces with trivial $\pi_0$ and $\pi_1$ is a fine shape…

Algebraic Topology · Mathematics 2022-11-22 Sergey A. Melikhov

We provide a unified analysis of a posteriori and a priori error bounds for a broad class of discontinuous Galerkin and $C^0$-IP finite element approximations of fully nonlinear second-order elliptic Hamilton--Jacobi--Bellman and Isaacs…

Numerical Analysis · Mathematics 2021-03-24 Ellya L. Kawecki , Iain Smears

We discuss the asymptotic structure of spacetimes, presenting a new construction of ideal points at infinity and introducing useful topologies on the completed space. Our construction is based on structures introduced by Geroch, Kronheimer,…

General Relativity and Quantum Cosmology · Physics 2009-11-10 Donald Marolf , Simon F. Ross

Weak topologies that yield weak convergence for bounded sequences and nets in CAT($0$) spaces have been studied in the past. We are here concerned with weak topologies that yield weak convergence of unbounded sequences and nets. We analyze…

Metric Geometry · Mathematics 2022-04-05 Philip Miller , Arian Berdellima , Max Wardetzky

It is a well-known result in pointfree topology that every locally compact frame is spatial. Whether this result extends to MT-algebras (McKinsey-Tarski algebras) was an open problem. We resolve it in the negative by constructing a locally…

General Topology · Mathematics 2025-08-05 G. Bezhanishvili , S. D. Melzer , R. Raviprakash , A. L. Suarez

In this paper, we prove that the iterates of the accelerated Nesterov's algorithm in the critical regime do converge in the weak topology to a global minimizer of an $L$-smooth function in a real Hilbert space, hence answering positively a…

Optimization and Control · Mathematics 2025-11-03 Radu Ioan Bot , Jalal Fadili , Dang-Khoa Nguyen

In this work, we develop an adaptive nonconforming finite element algorithm for the numerical approximation of phase-field parameterized topology optimization governed by the Stokes system. We employ the conforming linear finite element…

Numerical Analysis · Mathematics 2026-04-20 Bangti Jin , Jing Li , Yifeng Xu , Shengfeng Zhu
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