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Quadrature amplitude modulation is based on packing circles into circles within a phase-amplitude space. A modem transmits data as a series of points in a two-dimensional phase-amplitude plane. The spacing between the points determines the noise tolerance of the transmission, while the circumscribing circle diameter determines the transmitter ...
Symmetry breaking in pitchfork bifurcation as the parameter ε is varied. ε = 0 is the case of symmetric pitchfork bifurcation.. In a dynamical system such as ¨ + (;) + =, which is structurally stable when , if a bifurcation diagram is plotted, treating as the bifurcation parameter, but for different values of , the case = is the symmetric pitchfork bifurcation.
A tree fork is a bifurcation in the trunk of a tree giving rise to two roughly equal diameter branches. These forks are a common feature of tree crowns. The wood grain orientation at the top of a tree fork is such that the wood's grain pattern most often interlocks to provide sufficient mechanical support.
If 0 < p / q < 1 then the Ford circles that are tangent to C[p/q] are precisely the Ford circles for fractions that are neighbours of p / q in some Farey sequence. Thus C[2/5] is tangent to C[1/2], C[1/3], C[3/7], C[3/8], etc. Ford circles appear also in the Apollonian gasket (0,0,1,1). The picture below illustrates this ...
Illustration of the dining philosophers problem. Each philosopher has a bowl of spaghetti and can reach two of the forks. In computer science, the dining philosophers problem is an example problem often used in concurrent algorithm design to illustrate synchronization issues and techniques for resolving them.
Circle packing in a circle is a two-dimensional packing problem with the objective of packing unit circles into the smallest possible larger circle. Table of solutions, 1 ≤ n ≤ 20 [ edit ]
In bifurcation theory, a field within mathematics, a pitchfork bifurcation is a particular type of local bifurcation where the system transitions from one fixed point to three fixed points.
The tangent lines must be equal in length for any point on the radical axis: | | = | |. If P, T 1, T 2 lie on a common tangent, then P is the midpoint of ¯.. In Euclidean geometry, the radical axis of two non-concentric circles is the set of points whose power with respect to the circles are equal.