Smooth structureIn mathematics, a smooth structure on a manifold allows for an unambiguous notion of smooth function. In particular, a smooth structure allows one to perform mathematical analysis on the manifold. A smooth structure on a manifold is a collection of smoothly equivalent smooth atlases. Here, a smooth atlas for a topological manifold is an atlas for such that each transition function is a smooth map, and two smooth atlases for are smoothly equivalent provided their union is again a smooth atlas for This gives a natural equivalence relation on the set of smooth atlases.
JudgeA judge is a person who presides over court proceedings, either alone or as a part of a panel of judges. A judge hears all the witnesses and any other evidence presented by the barristers or solicitors of the case, assesses the credibility and arguments of the parties, and then issues a ruling in the case based on their interpretation of the law and their own personal judgment. A judge is expected to conduct the trial impartially and, typically, in an open court.
SmoothnessIn mathematical analysis, the smoothness of a function is a property measured by the number of continuous derivatives it has over some domain, called differentiability class. At the very minimum, a function could be considered smooth if it is differentiable everywhere (hence continuous). At the other end, it might also possess derivatives of all orders in its domain, in which case it is said to be infinitely differentiable and referred to as a C-infinity function (or function).
Bachelor of LawsBachelor of Laws (Legum Baccalaureus; LL.B.) is an undergraduate law degree in the United Kingdom, Europe and most common law jurisdictions. It is awarded by universities in Europe, Australia, the People's Republic of China, Hong Kong S.A.R., Macau S.A.R., Malaysia, Bangladesh, India, Japan, Pakistan, Uganda, Kenya, Ghana, New Zealand, Nigeria, Singapore, South Africa, Botswana, Israel, Brazil, Tanzania, Zambia, and other jurisdictions. In the United States, the Bachelor of Laws was the primary law degree until the 1960s, when it was phased out in favour of the Juris Doctor.
Backward compatibilityBackward compatibility (sometimes known as backwards compatibility) is a property of an operating system, software, real-world product, or technology that allows for interoperability with an older legacy system, or with input designed for such a system, especially in telecommunications and computing. Modifying a system in a way that does not allow backward compatibility is sometimes called "breaking" backward compatibility. Such breaking usually incurs various types of costs, such as switching cost.
