Where is a path encircling 0 in the positive direction, beginning at and returning to positive infinity with respect for the branch cut along the positive real axis.
42.
The station is built on the west side of Fourth Avenue due to plans for a possible extension of the express tracks south of LIRR Bay Ridge Branch cut.
43.
As we know from complex analysis, this is a multi-valued function that requires a branch cut from the origin to \ infty to be defined in a continuous manner.
44.
The utility's attempts to collect its bills grabbed national attention last week when one of its local branches cut off power to a missile base that owed $ 683, 000.
45.
The bank said the sale of the branches cut the number of its employees by 600, and that another 600 are expected to go through early retirement and other inducements.
46.
So the \ theta you get depends on what values you restrict \ theta to be ( i . e . where you place your branch cuts for the logarithm ).
47.
A single valued version called the principal value of the logarithm can be defined which is discontinuous on the negative x axis and equals the multivalued version on a single branch cut.
48.
Using the first ( last ) branch cut the principal square root \ scriptstyle \ sqrt z maps \ scriptstyle z to the half plane with non-negative imaginary ( real ) part.
49.
The tale can be interpreted as symbolic of the power of nature ( to heal itself )-the knights head reattaches itself just as a branch cut of a tree will sprout new leaves.
50.
The left one shows a tree with its branches cut but sprouting new shoots and containing a caterpillar spinning its cocoon, while the right one shows the metamorphosis of the caterpillar into a moth.
