We relate two parameter solutions of the sixth Painlevé equation and finite-gap solutions of the Heun equation by considering monodromy on a certain class of Fuchsian differential equations. In the appendix, we present formulae on differentials of elliptic modular functions, and obtain the ellitic form of the sixth Painlevé equation directly.

Manjula Tiwari, Karen A. Bjorndal,* Alan B. Bolten and Benjamin M. Bolker Archie Carr Center for Sea Turtle Research and Department of Zoology, University of Florida, PO Box 118525, Gainesville, FL 32611, USA *Correspondence: E-mail: [email protected] Abstract The mid-domain effect (MDE) model was developed to evaluate patterns of species richness. We applied the MDE model to intraspecific di...

{The Internet is experiencing an explosion in the number of connected users. Beyond simple mechanisms of FTP and electronic mail, distributed information services provided by WAIS, Gopher, Archie, WWW, etc. are rapidly changing the operating view of the Internet. This change is further expedited by the falling costs associated with terminal equipment that can handle continuous media such as aud...

The Internet is experiencing an explosion in the number of connected users. Beyond simple mechanisms of FTP and electronic mail, distributed information services provided by WAIS, Gopher, Archie, WWW, etc. are rapidly changing the operating view of the Internet. This change is further expedited by the falling costs associated with terminal equipment that can handle continuous media such as audi...

in this paper we have solved analytically the schrödinger equation for a microscopic particle in a one-dimensional box with two infinite walls, which the potential function inside it, has a linear form. based on the solutions of this special quantum mechanical system, we have shown that as the quantum number approaches infinity the expectation values of microscopic particle position and square ...