Several important multivariate probability inequalities can be formulated in terms of multivariate convolutions of the form ∫ $f_{1}(x)f_{2}(x-\theta )dx$, where ...

At the University of Vaasa in Finland, mathematician Yosra Barkaoui has successfully generalized a fundamental theorem that had remained confined to “bounded” systems for more than 40 years.

For more than 350 years, a mathematics problem whose solution was considered the Holy Grail to the greatest mathematician minds had remained unsolved. Now, a team of mathematicians led by a prominent ...

Yosra Barkaoui’s doctoral dissertation in mathematics at the University of Vaasa, Finland, has successfully generalised a fundamental theorem that has been limited to the bounded case. The research ...

The minimax inequality $\min_x \sup_y f(x, y) \leqslant \sup_x f(x, x)$, proved by K. Fan for convex spaces, is proved here for certain contractible and acyclic spaces. Some variational inequality and ...

During my time as an eager undergraduate mathematician, I’d often wonder what it would feel like to prove a truly new result and have my name immortalised in the mathematical history books. I thought ...

Convergence theorems form the backbone of probability theory and statistical inference, ensuring that sequences of random variables behave in a predictable manner as their index grows. These theorems, ...