The phrase "an unknown coefficient" is correct and usable in written English.
It can be used in mathematical or scientific contexts when referring to a coefficient that is not specified or determined.
Example: "In the equation, we need to solve for an unknown coefficient that affects the outcome."
Alternatives: "an unspecified coefficient" or "a variable coefficient".
Each ensemble member, and thus each curve feature, is weighted by an unknown coefficient.
A method is presented for reconstructing an unknown coefficient in a linear diffusion equation from measured data.
In addition, (boldsymbol {w} (in mathcal {F})) is an unknown coefficient for ϕ(x).
where a i is an unknown coefficient (0 ≤ i ≤ z, z ∈ Z+).
In [23], the authors considered the problem of identifying an unknown coefficient in a nonlinear diffusion equation.
K is the number of Poisson wavelets, β i is an unknown coefficient, which should be estimated from the data.
First, we approximate (D^{nu}x t)) by the shifted Jacobi orthonormal polynomials (grave{P}^{(alpha,beta)}_{T,j}(t)) as D^{nu}x t) simeqmathbf{C}^{T} Psi_{T,N}(t), (31) where C is an unknown coefficients matrix that can be written as mathbf{C} =left ( begin{array}c@ c_{ 0} c_{ 1} vdots c_{ N} end{array} right ). (32).
By solving the equation for a ( 0, 0 ), the following explicit formula for the value a ( 0, 0 ) of the unknown coefficient a ( x, t ) is obtained: a ( 0, 0 ) = g ″ ( 0 ) g ( 0 ).
By solving the equation for a x ( 0, 0 ), the following explicit formula for the value a x ( 0, 0 ) of the unknown coefficient a ( x, t ) is obtained: a x ( 0, 0 ) = g ‴ ( 0 ) g ( 0 ) − g ″ ( 0 ) f ( 0 ) + f ′ ( 0 ) g ( 0 ) g 2 ( 0 ).
For this, we first need to show that T ( s ) u t ( x, t ) = u t ( x, s + t ). by using the well-known property of the semigroup of the linear operators T ( s ) u ( x, t ) = u ( x, s + t ), which leads us to the determination of the unknown coefficient a = a ( x, t ) analytically.
This lemma leads us to the solution of the parabolic problem (1) without knowing the unknown coefficient a ( x, t ), but knowing a ( 0, 0 ) and a x ( 0, 0,).
