ABSTRACT: This extensive research paper provides a thorough investigation of the algebraic structure of complex products in groups, with comprehensive analysis of both commutative and non-commutative ...

In the third century BCE, Apollonius of Perga asked how many circles one could draw that would touch three given circles at exactly one point each. It would take 1,800 years to prove the answer: eight ...

Although computers are overwhelmingly digital today, there’s a good point to be made that analog computers are the more efficient approach for specific applications. The authors behind a recent paper ...

For centuries prime numbers have captured the imaginations of mathematicians, who continue to search for new patterns that help them identify primes and the way they are distributed among other ...

Princeton mathematician Noga Alon has received the 2024 Wolf Prize in Mathematics “for pioneering contributions to mathematical cryptography, combinatorics, and the theory of computer science.” He ...

A framework based on advanced AI techniques can solve complex, computationally intensive problems faster and in a more more scalable way than state-of-the-art methods, according to a new study. A ...

The proposed algorithm combines variational scheduling with post-processing to achieve near-optimal solutions to combinatorial optimization problems with constraints within the operation time of ...

The traveling salesman problem is considered a prime example of a combinatorial optimization problem. Now a Berlin team led by theoretical physicist Prof. Dr. Jens Eisert of Freie Universität Berlin ...

Consider this sequence of numbers: 5, 7, 9. Can you spot the pattern? Here’s another with the same pattern: 15, 19, 23. One more: 232, 235, 238. “Three equally spaced things,” says Raghu Meka, a ...