7 (seven) is the natural number following 6 and preceding 8. It is the only prime number preceding a cube. As an early prime number in the series of positive integers, the number seven has greatly symbolic associations in religion, mythology, superstition and philosophy. The seven Classical planets resulted in seven being the number of days in a week. It is often considered lucky in Western culture and is often seen as highly symbolic. Unlike Western culture, in Vietnamese culture, the number seven is sometimes considered unlucky.
In mathematics, stability theory addresses the stability of solutions of differential equations and of trajectories of dynamical systems under small perturbations of initial conditions. The heat equation, for example, is a stable partial differential equation because small perturbations of initial data lead to small variations in temperature at a later time as a result of the maximum principle. In partial differential equations one may measure the distances between functions using Lp norms or the sup norm, while in differential geometry one may measure the distance between spaces using the Gromov–Hausdorff distance.
In the theory of ordinary differential equations (ODEs), Lyapunov functions, named after Aleksandr Lyapunov, are scalar functions that may be used to prove the stability of an equilibrium of an ODE. Lyapunov functions (also called Lyapunov’s second method for stability) are important to stability theory of dynamical systems and control theory. A similar concept appears in the theory of general state space Markov chains, usually under the name Foster–Lyapunov functions.
Series 7 of the ITV programme Foyle's War first aired in 2013, beginning Sunday 24 March; comprising three episodes, it is set in the period from August–September 1946. Foyle returns from a trip to the US, during which he pursued former industrialist and subsequently senator Howard Paige ("Fifty Ships"). It is revealed that Paige committed suicide, allegedly after being hounded by Foyle, although Foyle was unaware of Paige's suicide.
The seventh series of the British science fiction television programme Doctor Who was broadcast concurrently on BBC One in the United Kingdom, and was split into two parts as the previous series had been. Following its premiere on 1 September 2012, the series aired weekly with five episodes until 29 September. The remaining eight episodes were broadcast between 30 March and 18 May 2013. The 2012 Christmas special, "The Snowmen", aired separately from the main series and introduced a new TARDIS interior, title sequence, theme tune, and outfit for the Doctor.
