Search Results for ""

The series z=ln(e^xe^y) (1) for noncommuting variables x and y. The first few terms are z_1 = x+y (2) z_2 = 1/2(xy-yx) (3) z_3 = 1/(12)(x^2y+xy^2-2xyx+y^2x+yx^2-2yxy) (4) z_4 ...

In general, an extremal graph is the largest graph of order n which does not contain a given graph G as a subgraph (Skiena 1990, p. 143). Turán studied extremal graphs that ...

Find the shape of the curve down which a bead sliding from rest and accelerated by gravity will slip (without friction) from one point to another in the least time. The term ...

The self-intersection of a one-sided surface. The word "cross-cap" is sometimes also written without the hyphen as the single word "crosscap." The cross-cap can be thought of ...

There are a number of point processes which are called Hawkes processes and while many of these notions are similar, some are rather different. There are also different ...

The biconjugate gradient method often displays rather irregular convergence behavior. Moreover, the implicit LU decomposition of the reduced tridiagonal system may not exist, ...

Bertelsen's number is an erroneous name erroneously given to the erroneous value of pi(10^9)=50847478, where pi(x) is the prime counting function. This value is 56 lower than ...

The degree to which a given quantity is correct and free from error. For example, a quantity specified as 100+/-1 has an (absolute) accuracy of +/-1 (meaning its true value ...

An angle bracket is the combination of a bra and ket (bra+ket = bracket) which represents the inner product of two functions or vectors (or 1-forms), <f|g>=intf(x)g^|(x)dx in ...

The Buchstab function omega(u) is defined by the delay differential equation {uomega(u)=1 for 1<=u<=2; (uomega(u))^'=omega(u-1) for u>2 (1) (Panario 1998). It approaches the ...