Search Results for ""

The q-binomial coefficient is a q-analog for the binomial coefficient, also called a Gaussian coefficient or a Gaussian polynomial. A q-binomial coefficient is given by [n; ...

The figure eight knot, also known as the Flemish knot and savoy knot, is the unique prime knot of four crossings 04-001. It has braid word ...

The trefoil knot 3_1, also called the threefoil knot or overhand knot, is the unique prime knot with three crossings. It is a (3, 2)-torus knot and has braid word sigma_1^3. ...

A (p,q)-torus knot is obtained by looping a string through the hole of a torus p times with q revolutions before joining its ends, where p and q are relatively prime. A ...

One of the symbols { and } used in many different contexts in mathematics. Braces are used 1. To denote grouping of mathematical terms, usually as the outermost delimiter in ...

One of the symbols ( or ) used to denote grouping. Parentheses have a great many specialized meanings in mathematics. A few of these are described below. 1. Parentheses are ...

The l^2-norm (also written "l^2-norm") |x| is a vector norm defined for a complex vector x=[x_1; x_2; |; x_n] (1) by |x|=sqrt(sum_(k=1)^n|x_k|^2), (2) where |x_k| on the ...

A linear real-valued function omega^1 of vectors v such that omega^1(v)|->R. Vectors (i.e., contravariant vectors or "kets" |psi>) and one-forms (i.e., covariant vectors or ...

Let A^~, B^~, ... be operators. Then the commutator of A^~ and B^~ is defined as [A^~,B^~]=A^~B^~-B^~A^~. (1) Let a, b, ... be constants, then identities include [f(x),x] = 0 ...

A piecewise function is a function that is defined on a sequence of intervals. A common example is the absolute value, |x|={-x for x<0; 0 for x=0; x for x>0. (1) Piecewise ...