Search Results for ""

The complex structure of a point x=x_1,x_2 in the plane is defined by the linear map J:R^2->R^2 J(x_1,x_2)=(-x_2,x_1), (1) and corresponds to a counterclockwise rotation by ...

Analysis of data ordered by the time the data were collected (usually spaced at equal intervals), called a time series. Common examples of a time series are daily temperature ...

The degree (or relative degree, or index) of an extension field K/F, denoted [K:F], is the dimension of K as a vector space over F, i.e., [K:F]=dim_FK. If [K:F] is finite, ...

A foliation F of dimension p on a manifold M is transversely orientable if it is integral to a p-plane distribution D on M whose normal bundle Q is orientable. A p-plane ...

There are several closely related results that are variously known as the binomial theorem depending on the source. Even more confusingly a number of these (and other) ...

A point lattice is a regularly spaced array of points. In the plane, point lattices can be constructed having unit cells in the shape of a square, rectangle, hexagon, etc. ...

The first example discovered of a map from a higher-dimensional sphere to a lower-dimensional sphere which is not null-homotopic. Its discovery was a shock to the ...

A graph whose nodes are sequences of symbols from some alphabet and whose edges indicate the sequences which might overlap. The above figures show the first few n-dimensional ...

The area Delta (sometimes also denoted sigma) of a triangle DeltaABC with side lengths a, b, c and corresponding angles A, B, and C is given by Delta = 1/2bcsinA (1) = ...

A finite set of contraction maps w_i for i=1, 2, ..., N, each with a contractivity factor s<1, which map a compact metric space onto itself. It is the basis for fractal image ...