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Flag algebras are an important computational tool in the field of graph theory which have a wide range of applications in homomorphism density and related topics. Roughly, they formalize the notion of adding and multiplying homomorphism densities and set up a framework to solve graph homomorphism inequalities with computers by reducing them to semidefinite programming problems.
The Unicode Standard encodes almost all standard characters used in mathematics. [1] Unicode Technical Report #25 provides comprehensive information about the character repertoire, their properties, and guidelines for implementation. [1]
While base ten is normally used for scientific notation, powers of other bases can be used too, [25] base 2 being the next most commonly used one. For example, in base-2 scientific notation, the number 1001 b in binary (=9 d) is written as 1.001 b × 2 d 11 b or 1.001 b × 10 b 11 b using binary numbers (or shorter 1.001 × 10 11 if binary ...
The stabilizer subgroup of the standard flag is the group of invertible upper triangular matrices.. More generally, the stabilizer of a flag (the linear operators on V such that () < for all i) is, in matrix terms, the algebra of block upper triangular matrices (with respect to an adapted basis), where the block sizes .
Random variables are usually written in upper case Roman letters, such as or and so on. Random variables, in this context, usually refer to something in words, such as "the height of a subject" for a continuous variable, or "the number of cars in the school car park" for a discrete variable, or "the colour of the next bicycle" for a categorical variable.
In abstract algebra, given a magma with binary operation ∗ (which could nominally be termed multiplication), left division of b by a (written a \ b) is typically defined as the solution x to the equation a ∗ x = b, if this exists and is unique. Similarly, right division of b by a (written b / a) is the solution y to the equation y ∗ a = b ...
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