This is a preview. Log in through your library . Abstract We generalize the Newton polygon procedure for algebraic equations to generate solutions of polynomial differential equations of the form ∑∞ ...

\({\log _a}a = 1\) (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 ...

We study a nonlinear elliptic equation with measurable nonlinearity in a nonsmooth domain when the righthand side is a measure. A global Calderón-Zygmund type estimate in variable exponent spaces is ...

For centuries, mathematicians have tried to prove that Euler’s fluid equations can produce nonsensical answers. A new approach to machine learning has researchers betting that “blowup” is near. For ...

Whenever we use ‘mathematical statements’ to convert verbal information with an aim to describe relationships between things that vary with circumstances and time etc, we end up writing verbal ...

When you cut yourself, a mass migration begins inside your body: Skin cells flood by the thousands toward the site of the wound, where they will soon lay down fresh layers of protective tissue. In a ...

Banner image: Skin cells as seen under the microscope. (Credit: Eric Bunker/Liu Lab) When you cut yourself, a mass migration begins inside your body: Skin cells flood by the thousands toward the site ...