In the language of L∞-modules proposed by Gigli, we introduce a first order calculus on a topological Lusin measure space (M , m) carrying a quasi-regular, strongly local Dirichlet form. Furthermore, we develop a second order calculus if (M ,E, m) is tamed by a signed measure in the extended Kato class in the sense of Erbar, Rigoni, Sturm and Tamanini.

Uploaded April 2025

Vector and tensor calculus offers an elegant language for expressing the way things behave in space and time, and Arianrhod shows how this enabled physicists and mathematicians to think in a brand-new way. In exploring the evolution of vectors and tensors, Arianrhod shows the genius required to reimagine the world—and how a clever mathematical construct can dramatically change discovery’s direction.

Uploaded April 2025

Time parallel time integration, also known as PinT (Parallel-in-Time) methods, aims to predict the near and far future simultaneously. In this self-contained book, the first on the topic, readers will find a comprehensive and up-to-date description of methods and techniques that have been developed to do just this.

Uploaded April 2025

In this paper we first study well-posedness in the natural energy space and give regularity results. Hence we give precise qualitative results for solutions when Ω is bounded and r = 2, ρ is constant, κ, δ ≥ 0. These results motivate a detailed discussion of the derivation of the problem in Theoretical Acoustics and the consequent proposal of adding to the model.

Uploaded April 2025

We verify the inductive blockwise Alperin weight condition in odd characteristic for the finite exceptional Chevalley groups F4(q) for q not divisible by.

Uploaded April 2025

This article investigates the asymptotics of G₂-monopoles. First, we prove that when the underlying G₂-manifold is nonparabolic (i.e. admits a positive Green's function), finite intermediate energy monopoles with bounded curvature have finite mass. The second main result restricts to the case when the underlying G₂-manifold is asymptotically conical.

Uploaded April 2025

When first published in 2005, Matrix Mathematics quickly became the essential reference book for users of matrices in all branches of engineering, science, and applied mathematics. In this fully updated and expanded edition, the author brings together the latest results on matrix theory to make this the most complete, current, and easy-to-use book on matrices.

Uploaded April 2025

This work is devoted to the study of integral p-adic Hodge theory in the context of Artin stacks. For a Hodge-proper stack, using the formalism of prismatic cohomology, we establish a version of p-adic Hodge theory with the étale cohomology of the Raynaud generic fiber as an input.

Uploaded March 2025

On the Problem of Infinite Spin in Total Collisions of the Planar N-body Problem solves the problem for almost every choice of the masses of the four-body problem.

Uploaded March 2025

Methods of Graph Decompositions discusses some state-of-the-art decomposition methods of graph theory, which are highly instrumental when dealing with a number of fundamental concepts such as unigraphs, isomorphism, reconstruction conjectures, k-dimensional graphs, degree sequences, line graphs and line hypergraphs.

Uploaded March 2025