The proof resolves a nearly 80-year-old problem known as the Duffin-Schaeffer conjecture. In doing so, it provides a final answer to a question that has preoccupied mathematicians since ancient times: ...

Fuzzy number approximations provide a robust framework for representing and managing uncertainty in quantitative analyses. By generating simplified yet accurate representations of fuzzy ...

Earlier this summer, we posted about a study that revealed that monkeys could listen to a series of beeps and then equate it to a visual representation of the same number. One of the researchers ...

The ancient Greeks wondered when “irrational” numbers can be approximated by fractions. By proving the longstanding Duffin-Schaeffer conjecture, two mathematicians have provided a complete answer. The ...

Around 250 B.C., the Greek mathematician Archimedes calculated the ratio of a circle's circumference to its diameter. A precise determination of pi, as we know this ratio today, had long been of ...

In this paper, we reveal a new connection between approximation numbers of periodic Sobolev type spaces, where the smoothness weights on the Fourier coefficients are ...

Journal of Applied Probability, Vol. 47, No. 3 (SEPTEMBER 2010), pp. 826-840 (15 pages) A random intersection graph G(n, m, p) is defined on a set 𝓥 of n vertices. There is an auxiliary set 𝓦 ...

The circumference of a sphere is measured to be 24 cm, with a possible error of 0.25 cm. Use the differential \(dV\) to estimate the maximum error in the calculated ...