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Model theory is a general theory of interpretations of axiomatic set theory. It is the branch of logic studying mathematical structures by considering first-order sentences ...

A second-order partial differential equation of the form Hr+2Ks+Lt+M+N(rt-s^2)=0, (1) where H, K, L, M, and N are functions of x, y, z, p, and q, and r, s, t, p, and q are ...

A morphism is a map between two objects in an abstract category. 1. A general morphism is called a homomorphism, 2. A morphism f:Y->X in a category is a monomorphism if, for ...

cos(20 degrees)cos(40 degrees)cos(80 degrees)=1/8. An identity communicated to Feynman as a child by a boy named Morrie Jacobs (Gleick 1992, p. 47). Feynman remembered this ...

"Neighborhood" is a word with many different levels of meaning in mathematics. One of the most general concepts of a neighborhood of a point x in R^n (also called an ...

A diagram lemma also known as 3×3 lemma. According to its most general statement, the commutative diagram illustrated above with exact rows and columns can be completed by ...

The word "normal form" is used in a variety of different ways in mathematics. In general, it refers to a way of representing objects so that, although each may have many ...

Numerical differentiation is the process of finding the numerical value of a derivative of a given function at a given point. In general, numerical differentiation is more ...

Let S be a subset of a metric space. Then the set S is open if every point in S has a neighborhood lying in the set. An open set of radius r and center x_0 is the set of all ...

The catacaustic of a parabola (t,t^2) opening upward is complicated for a general radiant point (x,y). However, the equations simplify substantially in the case x=infty ...