Extension of Darbo’s fixed point theorem via shifting distance functions and its application

In this paper, we discuss solvability of infinite system of fractional integral equations (FIE) of mixed type. To achieve this goal, we first use shifting distance function to establish a new generalization of Darbo’s fixed point theorem, and then apply it to the FIEs to establish the existence of solution on tempered sequence space. Finally, we verify our results by considering a suitable example.

Partial Regularity for Harmonic Maps into Spheres at a Singular or Degenerate Free Boundary

We prove partial regularity of weakly stationary harmonic maps with (partially) free boundary data on manifolds where the domain metric may degenerate or become singular along the free boundary at the rate $$d^\alpha $$ d α for the distance function d from the boundary.

Numerical computation of the cut locus via a variational approximation of the distance function

We propose a new method for the numerical computation of the cut locus of a compact submanifold of R3 without boundary. This method is based on a convex variational problem with conic constraints, with proven convergence. We illustrate the versatility of our approach by the approximation of Voronoi cells on embedded surfaces of R3.

Artificial Intelligence from Colonial India: Race, Statistics, and Facial Recognition in the Global South

This article examines the history of a similarity measure—the Mahalanobis Distance Function—and its movement from colonial India into contemporary artificial intelligence technologies, including facial recognition, and its reapplication into postcolonial India. The article identifies how the creation of the Distance Function was connected to the colonial “problem” of caste and ethnic classification for British bureaucracy in 1920-1930s India. This article demonstrates that the Distance Function is a statistical method, originating to make anthropometric caste distinctions in India, that became both a technical standard and a mobile racialized technique, utilized in machine learning applications. The creation of the Distance Function as a measure of “similitude” at a particular period of colonial state-making helped to model wider categories of classification which have proliferated in facial recognition technology. Overall, we highlight how a measurement function that operates in recognition technologies today can be traced across time and space to other racialized contexts.