The present paper is devoted to the investigation of the properties of the space of distributions with discontinuous test functions of several variables. The consideration of discontinuous test ...

The continuity hypothesis (1) posits that there is continuity, of some form, between waking and dreaming mentation. A recent body of work has provided convincing evidence for different aspects of ...

Abstract: We propose a novel characterization of piecewise-defined barrier functions for certifying forward invariant sets of piecewise continuous dynamical systems. Forward invariance is established ...

Abstract: The reliability of a learning model is key to the successful deployment of machine learning in various applications. Creating a robust model, particularly one unaffected by adversarial ...

Some of the dynamic stall models have "switches" or portions of the model that turn on under certain conditions. One example is the Beddoes-Leishman type models. I'm not certain of the continuity of ...

Perhaps nothing in mathematics is more useful for physics, chemistry, biology and engineering than differential equations. Isaac Newton had to invent calculus so he could write down the first such ...

This example illustrates some properties of splines. Splines are curves, which are usually required to be continuous and smooth. Splines are usually defined as piecewise polynomials of degree n with ...

The human brain is a marvel of nature, capable of engaging in continuous and spontaneous thought processes that shape cognitive functions. As artificial intelligence (AI) and large language models ...