We introduce templates for exponential-asymptotic expansions that, in contrast to matched asymptotic approaches, enable the simultaneous satisfaction of both boundary values in classes of linear and ...

Researchers now say OpenAI’s GPT-5 has helped prove strict limits on QMA. The model suggested a mathematical expression that led to a breakthrough on how far error reduction can go. The study may be ...

\({\log _a}a = 1\) (since \({a^1} = a\)) so \({\log _7}7 = 1\) \({\log _a}1 = 0\) (since \({a^0} = 1\)) so \({\log _{20}}1 = 0\) \({\log _a}p + {\log _a}q = {\log _a ...

Timothy Li is a consultant, accountant, and finance manager with an MBA from USC and over 15 years of corporate finance experience. Timothy has helped provide CEOs and CFOs with deep-dive analytics, ...