This paper presents a conceptual analysis for students' images of graphs and their extension to graphs of two-variable functions. We use the conceptual analysis, based on quantitative and ...

Annals of Mathematics, Second Series, Vol. 176, No. 3 (November, 2012), pp. 1783-1826 (44 pages) We prove generalizations of Löwner's results on matrix monotone functions to several variables. We give ...

WHAT is the theory of functions about? This question may be heard now and again from a mathematical student; and if, by way of a pattial reply, it be said that the elements of the theory of functions ...

Harmonic functions, defined as twice continuously differentiable functions satisfying Laplace’s equation, have long been a subject of intense study in both pure and applied mathematics. Their ...