We study nonuniform sampling in shift-invariant spaces and the construction of Gabor frames with respect to the class of totally positive functions whose Fourier transform factors as ĝ(ξ) = ∏n j=1(1 + 2πiδjξ) −1 e 2 for δ1, . . . , δn ∈ R, c > 0 (in which case g is called totally positive of Gaussian type). In analogy to Beurling’s sampling theorem for the Paley-Wiener space of entire functions...

Abstract:  The precision of conventional sampling designs is not usually satisfactory for estimating parameters of clump and rare populations. Many of fish species live in school and disperse all over a vast area like a sea so that they are rare compare to their habitats. Theory of a class of sampling designs called adaptive sampling designs has rapidly grown during last decade which solv...

The classical WKS sampling theorem has been extended to the case of nonuniform sampling by numerous authors. For detailed information on the theory and its numerous applications, we refer to the book [15]. Most known irregular sampling results deal with Paley–Wiener functions which have L2(R) restrictions on the real line. It seems that the best known nonuniform WKS sampling results for entire ...

We study nonuniform sampling in shift-invariant spaces and the construction of Gabor frames with respect to the class of totally positive functions whose Fourier transform factors as ĝ(ξ) = ∏n j=1(1 + 2πiδjξ) −1 e 2 for δ1, . . . , δn ∈ R, c > 0 (in which case g is called totally positive of Gaussian type). In analogy to Beurling’s sampling theorem for the Paley-Wiener space of entire functions...

In the Big Data era, sampling remains a central theme. This paper investigates characteristics of inverse on two different datasets (real and simulated) to determine when big data become too small for be used examine impact rate subsamples. We find that method, using appropriate subsample size both mean proportion parameters, performs well with smaller dataset than through simulation study real...

Acceptance sampling (AS), as one of the main fields of statistical quality control (SQC),involves a system of principles and methods to make decisions about accepting or rejecting alot or sample. For attributes, the design of a single AS plan generally requires determination ofsample size, and acceptance number. Numerous approaches have been developed foroptimally selection of design parameters...

In biological monitoring, deploying an effective standardised quantitative sampling method, optimised by trap design and sampling effort, is an essential consideration. To exemplify this using dung beetle (Coleoptera: Scarabaeidae: Scarabaeinae and Aphodiinae) communities, three pitfall trap designs (un-baited (TN), baited at ground level (flat trap, TF), and baited above the trap (hanging trap...