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Let f:A->B be a map between sets A and B. Let Y subset= B. Then the preimage of Y under f is denoted by f^(-1)(Y), and is the set of all elements of A that map to elements in ...

The Randić index of a graph is defined as half the sum of the matrix elements of its Randić matrix. While the index was introduced to model the branching of the carbon-atom ...

Given a commutative unit ring R and a filtration F:... subset= I_2 subset= I_1 subset= I_0=R (1) of ideals of R, the Rees ring of R with respect to F is R_+(F)=I_0 direct sum ...

The Reynolds transport theorem, also called simply the Reynolds theorem, is an important result in fluid mechanics that's often considered a three-dimensional analog of the ...

Let the minimal length of an addition chain for a number n be denoted l(n). Then the Scholz conjecture, also called the Scholz-Brauer conjecture or Brauer-Scholz conjecture, ...

A sheaf is a presheaf with "something" added allowing us to define things locally. This task is forbidden for presheaves in general. Specifically, a presheaf F on a ...

Let delta=z>=z_(observed). A value 0<=alpha<=1 such that P(delta)<=alpha is considered "significant" (i.e., is not simply due to chance) is known as an alpha value. The ...

Abstract Algebra

The adjective "affine" indicates everything that is related to the geometry of affine spaces. A coordinate system for the n-dimensional affine space R^n is determined by any ...

An equation representing a locus L in the n-dimensional Euclidean space. It has the form L:f(x_1,...,x_n)=0, (1) where the left-hand side is some expression of the Cartesian ...