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A moving source whose spatial support is contained within a ball with a given radius is treated by Kusiak and Weatherwax [7].
Let μ be a regular Borel measure whose support is contained in a unit cube Q in Rn and let Kj be the singular integral operator on L2(Rn,μ) with the kernel function (xj−yj)/∣∣x−y∣∣2, 1⩽j⩽n.
Main question: For a given Ω ⊆ R d (containing 0, open and symmetric with respect to 0 ) and a continuous positive definite function f : R d → C which vanishes off Ω, when can we approximate f uniformly by continuous positive definite functions whose support is contained in Ω ?
One then takes a cut-off function (chi (|z_n|)), whose support is contained in ({|z_n|
The solid support is contained in columns whose dimensions depend on the scale of synthesis and may vary between 0.05 mL and several liters.
More recently, high-throughput oligonucleotide synthesis where the solid support is contained in the wells of multi-well plates (most often, 96 or 384 wells per plate) became a method of choice for parallel synthesis of oligonucleotides on small scale.
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where the supremum is taken over all nonnegative measures such that (the support of ) is contained in and for every.
Through the paper, we let be a standard mollifier sequence in, such that the support of is contained in the interval.
The values of (varPhi^0) at the integers are obtained by finding the 1-eigenvector of the matrix D. Since the symbol function H is a matrix polynomial of degree 3, the support((varPhi^0 )) is contained in [0,3].
We may assume that the support of g is contained in the ball (B 0,R)), where R is a positive number.
Then a characterization theorem that ensures that the measurable support of Λ is contained in S′ is proved.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.
Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com