# Arbitrary constant

Related to Arbitrary constant: Arbitrary function
 (Math.) a quantity of function that is introduced into the solution of a problem, and to which any value or form may at will be given, so that the solution may be made to meet special requirements. an undetermined constant in a differential equation having the same value during all changes in the values of the variables.

Webster's Revised Unabridged Dictionary, published 1913 by G. & C. Merriam Co.
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Let (X, [[sigma].sub.b]) be a b-metric-like space with parameter s [greater than or equal to] 1, and let f, g : X [right arrow] X and [alpha] : X x X [right arrow] [0, [infinity]) be given mappings and arbitrary constant p such that p [greater than or equal to] 2.
(b) By the first equation of (7), we easily obtain the fact that [r.sub.1]u(1-u/K)-[rho][u.sup.[alpha]]v [less than or equal to] [r.sub.1]u(1-u/K) in [0, +[infinity])x[OMEGA]; the first result follows easily from the simple comparison argument for parabolic problems, and thus there exists T [member of] (0, +[infinity]) such that u(t, x) [less than or equal to] K + [epsilon] in [T, +[infinity]) x [OMEGA] for an arbitrary constant [epsilon] > 0.
where [c.sub.0] is an arbitrary constant. From (4), we have
For arbitrary constant values, [[alpha].sub.2] = [[alpha].sub.1] = l, [[alpha].sub.7] = -1, [[alpha].sub.6] = 1, [[alpha].sub.10] = 0, [[alpha].sub.11] = 1, and [[alpha].sub.8] = 5.
Proof If f is a constant function, say f(x) = c for all x [member of] G, then using the functional equation (10) we have g(x) = c(2c- 1) for any arbitrary constant c [member of] C.
Here, we note, for rigid body displacement field, that [u.sub.r] = a + b x r, where a and b are arbitrary constant vectors, and, for constant electric potential, [[phi].sub.r] [tau]([u.sub.r], [[phi].sub.r]) = 0.
Here we propose [f.sub.2](T) = T + [epsilon][T.sup.2], where e is an arbitrary constant. For this model, manipulation of (13)-(15) yields
with l [right arrow] -3p[mu]/(4[[pi].sup.2][p.sup.3] - 2[rho]), as [alpha] = [e.sup.[pi]i[tau]] [right arrow] 0, where [[??].sub.0] is an arbitrary constant.
After integration we get [[lambda].sub.2]g' = [c.sup.2][phi](g') + [c.sub.1], where [c.sub.1] is an arbitrary constant. Suppose that [lim.sub.x[right arrow][infinity]]([partial derivative]u/[partial derivative]x)(x, 0) = A.
Optical band gap is denoted as Eg for the crystal and 'A' is the arbitrary constant. Plank's constant is denoted by 'h' and frequency of incident photons is denoted by 'Y'.
where m is an arbitrary constant. These values of (eq.) and (eq.) are define the famous Schwarzschild spacetime.
Later, inhomogeneous ODE (17) is solved uniformly in all three cases using method of arbitrary constant variation .

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