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A stable isolated (i.e., solitary) traveling nonlinear wave solution to a set of equations that obeys a superposition-like principle (i.e., solitons passing through one ...

Solomon's seal knot is the prime (5,2)-torus knot 5_1 with braid word sigma_1^5. It is also known as the cinquefoil knot (a name derived from certain herbs and shrubs of the ...

A curve which may pass through any region of three-dimensional space, as contrasted to a plane curve which must lie in a single plane. Von Staudt (1847) classified space ...

The space groups in two dimensions are called wallpaper groups. In three dimensions, the space groups are the symmetry groups possible in a crystal lattice with the ...

The Spearman rank correlation coefficient, also known as Spearman's rho, is a nonparametric (distribution-free) rank statistic proposed by Spearman in 1904 as a measure of ...

Let two spheres of radii R and r be located along the x-axis centered at (0,0,0) and (d,0,0), respectively. Not surprisingly, the analysis is very similar to the case of the ...

A spherical cap is the region of a sphere which lies above (or below) a given plane. If the plane passes through the center of the sphere, the cap is a called a hemisphere, ...

A spherical ring is a sphere with a cylindrical hole cut so that the centers of the cylinder and sphere coincide, also called a napkin ring. Let the sphere have radius R and ...

A spherical segment is the solid defined by cutting a sphere with a pair of parallel planes. It can be thought of as a spherical cap with the top truncated, and so it ...

In a rectangular room (a cuboid) with dimensions 30^'×12^'×12^', a spider is located in the middle of one 12^'×12^' wall one foot away from the ceiling. A fly is in the ...