Abstract: In this note, we discuss a generalization of the well-known implicit function theorem to the time-delay case. We show that the latter problem is closely related to the bicausal changes of ...

Mathematician Kevin Buzzard of Imperial College London is training computers how to prove one of the most famous problems in math history: Fermat’s last theorem. Resolving the problem isn’t the point.

GPT-5.4 Pro cracked a conjecture in number theory that had stumped generations of mathematicians, using a proof strategy that ...

A Chinese artificial intelligence system has solved a decade-old problem proposed by an American mathematician, according to a new study. The algebra conjecture was first posed in 2014 by then ...

\item $x^2 + xy + y^2 = 7$, 在 $(2, 1)$ 处. \item $x \cos xy = 0$, 在 $(1, \uppi/2)$ 处. 令 $F(x, y) = x^2 + xy + y^2 - 7$。显然 $F(2, 1) = 4 + 2 + 1 - 7 = 0 ...

Nootropics are a category of supplements or drugs linked with beneficial effects on brain function. Supporters of nootropics say they can boost memory, motivation, creativity, alertness, general ...

Over the last several years, fusion power has gone from the butt of jokes — always a decade away! — to an increasingly tangible and tantalizing technology that has drawn investors off the sidelines.

Abstract: In scene text detection, the effective fusion of the detail information and the semantic information is crucial for the accurate results. However, the upsampling operation used in existing ...

Today is the anniversary of the founding of the North Atlantic Treaty Organization. NATO has long been misunderstood, under-discussed, and marketed to the American people as a force for peace and ...

We proposes a new ODI-SR model characterized by its capacity to perform Fast and Arbitrary-scale ODI-SR processes, denoted as FAOR. The key innovation lies in adapting the implicit image function from ...