we present a method for  the construction of compactlysupported $left (begin{array}{lll}1 & 0 & -11 & 1 & 0 1 &  0 & 1end{array}right )$-wavelets  under a mild condition. wavelets inherit thesymmetry of the corresponding scaling function and satisfies thevanishing moment condition originating in the symbols of the scalingfunction. as an application, an  example is  provided.

Let φ be an orthonormal scaling function with approximation degree p−1, and let Bn be the B-spline of order n. Then, spline type scaling functions defined by f̄n = f ∗Bn (n = 1, 2, . . . ) possess higher approximation order, p+n−1, and compact support. The corresponding biorthogonal wavelet functions are also constructed. This technique is extended to the case of biorthogonal scaling function sy...

Corrosion in general is a complex interaction between water and metal surfaces and materials in which the water is stored or transported. Water quality monitoring in terms of corrosion and scaling is crucial, and a key element of preventive maintenance, given the economic and health hurts caused by corrosion and scaling in water utilities. The aim of this study is to determine the best model fo...

We consider the mathematical properties of the generating and partition functions in the two variable scaling region about the tricritical point in some models of polymer collapse. We concentrate on models that have a similar behaviour to that of interacting partially-directed self-avoiding walks (IPDSAW) in two dimensions. However, we do not restrict the discussion to that model. After describ...

Fitness sharing has been used widely in genetic algorithms for multi-objective function optimization and machine learning. It is often implemented with a scaling function, which adjusts an individual's raw tness to improve the performance of the genetic algorithm. However, choosing a scaling function is an ad hoc a air that lacks su cient theoretical foundation, and which often gives results th...