are called the normalizing numbers of problem (1.1 - 1.2 1.1 - 1.2that f ( x, λ noticee thateigenfunctions of problem (1.1)-(1.2) corresponding to the eigenvalues λ n ).
These results not only generalize the results of [13, 19, 22] but also give some new uniqueness results for the inverse Sturm-Liouville problems through normalizing constants instead of eigenvalues.
The function (Delta(lambda)) is called the characteristic function and numbers ({ mu_{n} } _{nin mathbb{Z} }) are called the normalizing constants of the problem (1 - 7).
In our uniqueness results to be given further, the known eigenvalues and normalizing constants are of problem (1.1 - 1.3) where a countable number of different boundary conditions at (x=0) may be involved.
Hence, the normalizing factor β n for problem (62) can be written as β n = ∑ l ∈ L ( n ) m ~ l = ∑ l ∈ L ( n ) ( 1 0 0.1 × γ l ) / ∥ h ll ∥ 2 2. Furthermore, we find β = max n ∈ N { β n }, and set ρ = β for Algorithm 1. Below are the links to the authors' original submitted files for images.
Let λ n and α n ( n ∈ Z ) be, respectively, eigenvalues and normalizing numbers of the boundary value problem (1), (2).
Then, we give some uniqueness theorems by using Weyl function and spectral data, which are called eigenvalues and normalizing constants for solution of inverse problem.
where λ n 0 and α n 0 are, respectively, eigenvalues and normalizing numbers of the boundary value problem (1), (2) when Ω ( x ) ≡ 0. Proof According to (3) we have S 0 ( x, λ ) = S ( x, λ ) − ∫ 0 μ ( x ) A ( x, t ) ( sin λ t − cos λ t ) d t. (16).
If dye signal from sleep-like signals shows bleaching kinetics distinct from epileptiform signal, this would imply that the biophysical sources of these two signals are distinct, and that normalizing with the epileptiform signal would entail a new set of problems distinct from the problems associated with ΔF/F.
Moveover, we also investigate the problem of missing both eigenvalues and normalizing constants in the situation where the potential q is (C^{2k-1}) near a suitable point.
