A forgotten episode of mathematical resistance reveals the rise of modern mathematics and its cornerstone, mathematical purity, as political phenomena.

Uploaded June 2025

Provides both an overview of the state of the art of nonlocal modeling and discretization and novel analyses for a class of nonstandard nonlocal models.

Uploaded June 2025

This monograph presents an interpretive essay on the foundations of Leibniz's calculus, accompanied by key texts in English translation. The essay examines Leibniz's evolving views on infinitesimals and infinite numbers, tracing their development from his early metaphysical ideas to his mature justifications of the calculus.

Uploaded June 2025

This text was produced for the second part of a two-part sequence on advanced calculus, whose aim is to provide a firm logical foundation for analysis. The first part treats analysis in one variable, and the text at hand treats analysis in several variables. After a review of topics from one-variable analysis and linear algebra, the text treats in succession multivariable differential calculus, including systems of differential equations, and multivariable integral calculus.

Uploaded June 2025

This book provides the mathematical foundations needed for designing practical controllers for linear time-invariant systems. The authors accomplish this by incorporating intentional time delays into measurements with the goal of achieving anticipation capabilities, reduction in noise sensitivity, and a fast response. The benefits of these types of delay-based controllers have long been recognized, but designing them based on an analytical approach became possible only recently.

Uploaded June 2025

Using material from many different sources in a systematic and unified way, this self-contained book provides both rigorous mathematical theory and practical numerical insights while developing a framework for determining the convergence rate of discretizations to optimal control problems. Elements of the framework include the reference point, the truncation error, and a stability theory for the linearized first-order optimality conditions.

Uploaded June 2025

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