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A circle that in internally tangent to two sides of a triangle and to the circumcircle is called a mixtilinear incircle. There are three mixtilinear incircles, one ...

Consider a set A_n={a_1,a_2,...,a_n} of n positive integer-denomination postage stamps sorted such that 1=a_1<a_2<...<a_n. Suppose they are to be used on an envelope with ...

A projective module generalizes the concept of the free module. A module M over a nonzero unit ring R is projective iff it is a direct summand of a free module, i.e., of some ...

The Rhind papyrus is a famous document from the Egyptian Middle Kingdom that dates to 1650 BC. It was purchased by Henry Rhind in Egypt in 1858, and placed in the British ...

Find the minimum size square capable of bounding n equal squares arranged in any configuration. The first few cases are illustrated above (Friedman). The only packings which ...

Adomian polynomials decompose a function u(x,t) into a sum of components u(x,t)=sum_(n=0)^inftyu_n(x,t) (1) for a nonlinear operator F as F(u(x,t))=sum_(n=0)^inftyA_n. (2) ...

The quantum electrodynamical law which applies to spin-1/2 particles and is the relativistic generalization of the Schrödinger equation. In 3+1 dimensions (three space ...

Given a system of ordinary differential equations of the form d/(dt)[x; y; v_x; v_y]=-[0 0 -1 0; 0 0 0 -1; Phi_(xx)(t) Phi_(yx)(t) 0 0; Phi_(xy)(t) Phi_(yy)(t) 0 0][x; y; ...

The partial differential equation 3/4U_y+W_x=0, (1) where W_y+U_t-1/4U_(xxx)+3/2UU_x=0 (2) (Krichever and Novikov 1980; Novikov 1999). Zwillinger (1997, p. 131) and Calogero ...

The Lotka-Volterra equations describe an ecological predator-prey (or parasite-host) model which assumes that, for a set of fixed positive constants A (the growth rate of ...