4 citations · 8 across the 10 of their papers we have counts for
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Real-Analyticity of Generalized Sine Functions with Two Parameters
Pisheng Ding
We identify the maximal real interval on which is real-analytic for any real number and any integer . We achieve this by first proving that is…
A Fundamental Theorem of Calculus for Second-order Directional Derivative
Pisheng Ding
Given a two-variable function without critical points and a compact region bounded by two level curves of , this note proves that the integral over of the second-ord…
On the Gradient of Harmonic Functions
Pisheng Ding
For a harmonic function u on Euclidean space, this note shows that its gradient is essentially determined by the geometry of its level hypersurfaces. Specifically, the factor by wh…
Several Metric Properties of Level Curves
Pisheng Ding
This article establishes several remarkably simple identities relating certain metric invariants of level curves of real and complex functions. In particular, we relate lengths of…