Numerical methods for ordinary differential equationsNumerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their use is also known as "numerical integration", although this term can also refer to the computation of integrals. Many differential equations cannot be solved exactly. For practical purposes, however – such as in engineering – a numeric approximation to the solution is often sufficient. The algorithms studied here can be used to compute such an approximation.
Stable manifoldIn mathematics, and in particular the study of dynamical systems, the idea of stable and unstable sets or stable and unstable manifolds give a formal mathematical definition to the general notions embodied in the idea of an attractor or repellor. In the case of hyperbolic dynamics, the corresponding notion is that of the hyperbolic set. The gravitational tidal forces acting on the rings of Saturn provide an easy-to-visualize physical example. The tidal forces flatten the ring into the equatorial plane, even as they stretch it out in the radial direction.
Linear complementarity problemIn mathematical optimization theory, the linear complementarity problem (LCP) arises frequently in computational mechanics and encompasses the well-known quadratic programming as a special case. It was proposed by Cottle and Dantzig in 1968. Given a real matrix M and vector q, the linear complementarity problem LCP(q, M) seeks vectors z and w which satisfy the following constraints: (that is, each component of these two vectors is non-negative) or equivalently This is the complementarity condition, since it implies that, for all , at most one of and can be positive.
Online gamblingOnline gambling is any kind of gambling conducted on the internet. This includes virtual poker, casinos, and sports betting. The first online gambling venue opened to the general public was ticketing for the Liechtenstein International Lottery in October 1994. Today, the market is worth around $40 billion globally each year, according to various estimates. Many countries restrict or ban online gambling. However, it is legal in some states of the United States, some provinces in Canada, most countries of the European Union, and several nations in the Caribbean.
Online pokerOnline poker is the game of poker played over the Internet. It has been partly responsible for a huge increase in the number of poker players worldwide. Christiansen Capital Advisors stated online poker revenues grew from 82.7millionin2001to2.4 billion in 2005, while a survey carried out by DrKW and Global Betting and Gaming Consultants asserted online poker revenues in 2004 were at $1.4 billion. 