Various classes of analytic, quasi-analytic and other infinitely differentiable functions of a real variable are studied. The paper gives a self-contained treatment by means of an elementary real ...

https://doi.org/10.4169/amer.math.monthly.120.06.566 https://www.jstor.org/stable/10.4169/amer.math.monthly.120.06.566 Abstract We construct an example of a monotonic ...

The Uncertainty-Aware Fourier Ptychography (UA-FP) framework marks a transformative milestone in computational imaging, revolutionizing the way we address system uncertainties. This innovative ...

In the late 19th century, Karl Weierstrass invented a fractal-like function that was decried as nothing less than a “deplorable evil.” In time, it would transform the foundations of mathematics.

The original version of this story appeared in Quanta Magazine. Calculus is a powerful mathematical tool. But for hundreds of years after its invention in the 17th century, it stood on a shaky ...

If \(f\) is differentiable on \([-1,1]\) then \(f\) is continuous at \(x=0\text{.}\) If \(f'(x)\lt 0\) and \(f"(x)>0\) for all \(x\) then \(f\) is concave down ...