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Let the approximation basis consist of radial basis functions (7) centred in grid points x i ∈ [0, h,2 h,…300], where h is the grid step.
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With LR, the basis B is transformed into a new basis consisting of roughly orthogonal vectors.
Moreover, (L^2(mathbb R^d)) has an orthonormal basis consisting of eigenfunctions of (overline{A}).
Therefore has a complete orthonormal basis consisting of the eigenfunctions of.
The experimental basis consists of measurements of pressure fluctuations and gas mixing by tracer-gas injection.
A probability measure in Rd is called a spectral measure if it has an orthonormal basis consisting of exponentials.
The other solution, designed for the class of graphs with cycle basis consisting of cycles of length at most l, leads to O |F|Δ⌈l/2⌉log(|F|Δ⌊l/2⌋)) running time.
Public education was dependent on an institutional basis consisting of a number of institutions: schools, museums and other places holding public exhibitions, and periodicals (Neurath 1931/1973, 222).
A Hermitean operator is an operator which has the property that there is an orthonormal basis consisting of its eigenvectors and those eigenvalues are all real.
We define the Bell basis as a basis consisting of two Bell states begin{array}rcl@ |Psi^{mp}rangle=frac{1}{sqrt{2}}(|Hrangle_{1}|V ranglend{arrayrangle_{1}|Hrangle_{2}), end{array} (1).
The minimum set of sub-models for simulating stand dynamics on an individual-tree basis consists of tree-level models for diameter increment and survival.
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