Mathematics, Volume 1, Issue 1

Let C₁ and C₂ be algebraic plane curves in ${ℂ}^2$ such that the curves intersect in d₁ · d₂ points where d₁, d₂ are the degrees of the curves respectively. Oka and Sakamoto proved that π1(${ℂ}^2$ C₁ U C₂)) ≅ π1 (${ℂ}^2$ C₁) × π1 (${ℂ}^2$...

Following Ramanujan's work on modular equations and approximations of $\pi$, there are formulas for $1/\pi$ of the form Following Ramanujan's work on modular equations and approximations of $\pi$, there are formulas for $1/\pi$ of the form $\sum _{k=}^{}$...

In his 1984 Ph.D. thesis, J. Greene defined an analogue of the Euler integral transform for finite field hypergeometric series. Here we consider a special family of matrices which arise naturally in the study of this transform and prove a conjecture...

As is widely known, mathematics plays a unique role in all natural sciences as a refined scientific language and powerful research tool. Indeed, most of the fundamental laws of nature are written in mathematical terms and we study their consequences...