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The multiplicative identity of R[x] is the polynomial x 0; that is, x 0 times any polynomial p(x) is just p(x). [2] Also, polynomials can be evaluated by specializing x to a real number. More precisely, for any given real number r, there is a unique unital R-algebra homomorphism ev r : R[x] → R such that ev r (x) = r. Because ev r is unital ...
The quantity 206 265 ″ is approximately equal to the number of arcseconds in a circle (1 296 000 ″), divided by 2π, or, the number of arcseconds in 1 radian. The exact formula is = (″) and the above approximation follows when tan X is replaced by X.
Thus if N = 300,000,000 (90% of the US population, with 10% of population being too young to participate) and K = 30 then Degrees of Separation = APL = 19.5 / 3.4 = 5.7 and if N = 7,200,000,000 (90% of the world population, with 10% of population being too young to participate) and K = 30 then Degrees of Separation = APL = 22.7 / 3.4 = 6.7.
When the rays are lines of sight from an observer to two points in space, it is known as the apparent distance or apparent separation. Angular distance appears in mathematics (in particular geometry and trigonometry ) and all natural sciences (e.g., kinematics , astronomy , and geophysics ).
When =, =, we can easily see the separatrix and the two basins of attraction by solving for the trajectories backwards in time.. In the FitzHugh–Nagumo model, when the linear nullcline pierces the cubic nullcline at the left, middle, and right branch once each, the system has a separatrix.
On the other hand, when X is fixed but T is allowed to vary within certain boundaries, to force T to be T 0 may be inconvenient, since non-T 0 topologies are often important special cases. Thus, it can be important to understand both T 0 and non-T 0 versions of the various conditions that can be placed on a topological space.
for some non-zero constants a and b and a given function g defined on ∂Ω. Here, u is the unknown solution defined on Ω and ∂u / ∂n denotes the normal derivative at the boundary. More generally, a and b are allowed to be (given) functions, rather than constants.
A ray trace through a prism with apex angle α. Regions 0, 1, and 2 have indices of refraction, , and , and primed angles ′ indicate the ray's angle after refraction.. Ray angle deviation and dispersion through a prism can be determined by tracing a sample ray through the element and using Snell's law at each interface.