Unpack the meaning of "crypto terminology for ∇" while considering its significance in vector calculus, illustrating its role in mathematical expressions and data transformation. The symbol ∇, known ...

Analytic functions, defined by the property of being locally expressible as convergent power series, form a cornerstone of complex analysis. Differential operators, which act on these functions by ...

In this paper, we investigate under what circumstances the Laplace-Beltrami operator on a pseudo-Riemannian manifold can be written as a sum of squares of vector fields, as is naturally the case in ...

The remarkable potentials of Artificial Intelligence (AI) and Deep Learning have paved the way for a variety of fields ranging from computer vision and language modeling to healthcare, biology, and ...