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In graph theory, a branch of combinatorial mathematics, a block graph or clique tree [1] is a type of undirected graph in which every biconnected component (block) is a clique. Block graphs are sometimes erroneously called Husimi trees (after Kôdi Husimi ), [ 2 ] but that name more properly refers to cactus graphs , graphs in which every ...
In the center of mass frame the kinetic energy is the lowest and the total energy becomes = ˙ + The coordinates x 1 and x 2 can be expressed as = = and in a similar way the energy E is related to the energies E 1 and E 2 that separately contain the kinetic energy of each body: = = ˙ + = = ˙ + = +
The natural outcome of this requirement is a wing design that is thin and wide, which has a low thickness-to-chord ratio. At lower speeds, undesirable parasitic drag is largely a function of the total surface area, which suggests using a wing with minimum chord, leading to the high aspect ratios seen on light aircraft and regional airliners ...
A different area rule, known as the supersonic area rule, developed by NACA aerodynamicist Robert Jones in "Theory of wing-body drag at supersonic speeds", [2] is applicable at speeds beyond transonic, and in this case, the cross-sectional area requirement is established with relation to the angle of the Mach cone for the design speed.
A partially balanced incomplete block design with n associate classes (PBIBD(n)) is a block design based on a v-set X with b blocks each of size k and with each element appearing in r blocks, such that there is an association scheme with n classes defined on X where, if elements x and y are ith associates, 1 ≤ i ≤ n, then they are together ...
The structure of the blocks and cutpoints of a connected graph can be described by a tree called the block-cut tree or BC-tree. This tree has a vertex for each block and for each articulation point of the given graph. There is an edge in the block-cut tree for each pair of a block and an articulation point that belongs to that block. [8]
In order to reduce the maximum force on the motor mounts as the motor operates over a range of speeds, a smaller mass, m 2, is connected to m 1 by a spring and a damper, k 2 and c 2. F 1 is the effective force on the motor due to its operation. Response of the system excited by one unit of force, with (red) and without (blue) the 10% tuned mass ...
Since the velocity of the object is the derivative of the position graph, the area under the line in the velocity vs. time graph is the displacement of the object. (Velocity is on the y-axis and time on the x-axis. Multiplying the velocity by the time, the time cancels out, and only displacement remains.)