Search results
Results from the WOW.Com Content Network
Polytopal flip graphs are, by this property, connected. As shown by Klaus Wagner in the 1930s, the flip graph of the topological sphere is connected. [7] Among the connected flip graphs, one also finds the flip graphs of any finite 2-dimensional set of points. [8] In higher dimensional Euclidean spaces, the situation is much more complicated.
For triangulations of a point set in dimension 5 or above, there exists examples where the flip graph is disconnected and a triangulation cannot be obtained from other triangulations via flips. [ 6 ] [ 3 ] Whether all flip graphs of finite 3- or 4-dimensional point sets are connected is an open problem.
A sigmoid function is any mathematical function whose graph has a characteristic S-shaped or sigmoid curve. A common example of a sigmoid function is the logistic function, which is defined by the formula: [1] = + = + = ().
A point P has coordinates (x, y) with respect to the original system and coordinates (x′, y′) with respect to the new system. [1] In the new coordinate system, the point P will appear to have been rotated in the opposite direction, that is, clockwise through the angle . A rotation of axes in more than two dimensions is defined similarly.
Even functions are those real functions whose graph is self-symmetric with respect to the y-axis, and odd functions are those whose graph is self-symmetric with respect to the origin. If the domain of a real function is self-symmetric with respect to the origin, then the function can be uniquely decomposed as the sum of an even function and an ...
showing on a horizontal axis and on a vertical axis, where is a phase space trajectory. Scatterplot : A scatter graph or scatter plot is a type of display using variables for a set of data. The data is displayed as a collection of points, each having the value of one variable determining the position on the horizontal axis and the value of the ...
The edges and vertices of these six regions form Tietze's graph, which is a dual graph on this surface for the six-vertex complete graph but cannot be drawn without crossings on a plane. Another family of graphs that can be embedded on the Möbius strip, but not on the plane, are the Möbius ladders , the boundaries of subdivisions of the ...
If we condense the skew entries into a vector, (x,y,z), then we produce a 90° rotation around the x-axis for (1, 0, 0), around the y-axis for (0, 1, 0), and around the z-axis for (0, 0, 1). The 180° rotations are just out of reach; for, in the limit as x → ∞ , ( x , 0, 0) does approach a 180° rotation around the x axis, and similarly for ...