In this paper, we identify univariate prewavelets on spaces spanned by translates of multiquadric functions and other radial basis functions with nonequally spaced centers (or "knots"). Although the multiquadric function and its relations are our prime examples, the theory is sufficiently broad to admit prewavelets from other radial basis function spaces as well.

Background and Aims Ramularia collo-cygni is an ascomycete fungus that colonizes barley primarily as a benign endophyte, although this interaction can become pathogenic, causing the disease Ramularia leaf spot (RLS). Factors, particularly reactive oxygen species, that resulted in the transition of the fungus from endophyte to necrotrophic parasite and the development of disease symptoms were in...

1 Stochastic collocation In a stochastic simulation, one is typically interested in the relationship between the variables that drive the system (inputs) and the system response (outputs). For the “forward problem,” the inputs Z = (Z1, . . . , Zd) are random variables with distributions that we assume to be known. The outputs are some known functions g of the simulation state u = u(x, t;Z), whi...

Multiquadric method is employed for solving the two dimensional depth-integrated water quality model and the eutrophication model in marine environments. The models simulate the spatial and temporal variations of nutrients in the Tolo Harbour of Hong Kong by taking considerations of the tidal current, wind stress, growth dynamics of phytoplankton and the transformation rate of nutrients. The ph...

Radial Basis Function networks with linear output are often used in regression problems because they can be substantially faster to train than Multi-layer Perceptrons. We show how radial base Cauchy, multiquadric and Inverse multiquadric type functions can be used to approximate a rapidly changing continuous test function. In this paper, the performance of the reduced matrix design by QLP decom...

A treecode is presented for evaluating sums defined in terms of the multiquadric radial basis function (RBF), φ(x) = (|x|2 + c2)1/2, where x ∈ R3 and c ≥ 0. Given a set of N nodes, evaluating an RBF sum directly requires CPU time that scales like O(N2). For a given level of accuracy, the treecode reduces the CPU time to O(N logN) using a far-field expansion of φ(x). We consider two options for ...

NAC proteins are plant transcription factors that are involved in tolerance to abiotic and biotic stresses, as well as in many developmental processes. Stress-responsive NAC1 (SNAC1) transcription factor is involved in drought tolerance in barley and rice, but has not been shown previously to have a role in disease resistance. Transgenic over-expression of HvSNAC1 in barley cv. Golden Promise r...

Ramularia collo-cygni is a barley pathogen of increasing importance in Northern and Central Europe, New Zealand and South America. Accurate visual and microscopic identification of the pathogen from diseased tissue is difficult. A nested PCR-based diagnostic test has been developed as part of an initiative to map the distribution of the pathogen in Scotland. The entire nuclear ribosomal interna...

Les pŽtroles bruts contiennent de nombreux constituants Ñ dont les asphaltnes Ñ qui peuvent tre adsorbŽs sur les surfaces minŽrales et modifier leurs caractŽristiques de mouillage. Ce qui distingue les asphaltnes des autres constituants de l'huile est leur tendance ˆ s'agrŽger et mme ˆ se sŽparer du pŽtrole en rŽaction ˆ des modifications du pouvoir solvant du pŽtrole. Du fait qu'ils change...