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Initially the second moment of area increases as the surface area increases, increasing BM, so Mφ moves to the opposite side, thus increasing the stability arm. When the deck is flooded, the stability arm rapidly decreases. The centre of buoyancy is at the centre of mass of the volume of water that the hull displaces.
A graph is locally cyclic if every neighbourhood is a cycle. For instance, the octahedron is the unique connected locally C 4 graph, the icosahedron is the unique connected locally C 5 graph, and the Paley graph of order 13 is locally C 6. Locally cyclic graphs other than K 4 are exactly the underlying graphs of Whitney triangulations ...
In Cartesian coordinates, the divergence of a continuously differentiable vector field = + + is the scalar-valued function: = = (, , ) (, , ) = + +.. As the name implies, the divergence is a (local) measure of the degree to which vectors in the field diverge.
If () = = and () () for all x in an open interval that contains c, except possibly c itself, =. This is known as the squeeze theorem . [ 1 ] [ 2 ] This applies even in the cases that f ( x ) and g ( x ) take on different values at c , or are discontinuous at c .
A unit distance graph with 16 vertices and 40 edges. In mathematics, particularly geometric graph theory, a unit distance graph is a graph formed from a collection of points in the Euclidean plane by connecting two points whenever the distance between them is exactly one.
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.)
The points P 1, P 2, and P 3 (in blue) are collinear and belong to the graph of x 3 + 3 / 2 x 2 − 5 / 2 x + 5 / 4 . The points T 1, T 2, and T 3 (in red) are the intersections of the (dotted) tangent lines to the graph at these points with the graph itself. They are collinear too.
A homomorphism from the flower snark J 5 into the cycle graph C 5. It is also a retraction onto the subgraph on the central five vertices. Thus J 5 is in fact homomorphically equivalent to the core C 5. In the mathematical field of graph theory, a graph homomorphism is a mapping between two graphs that respects their structure