fractalinterpolation techniques provide good deterministic representations of complex phenomena. This paper approaches the Hermite, interpolation using fractal procedures. This problem prescribes at each support absc...
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fractalinterpolation techniques provide good deterministic representations of complex phenomena. This paper approaches the Hermite, interpolation using fractal procedures. This problem prescribes at each support abscissa not only the value of a function but also its first p derivatives. It is shown here that the proposed fractalinterpolation function and its first p derivatives are good approximations of the corresponding derivatives of the original function. According to the theorems, the described method allows to interpolate, with arbitrary accuracy, a smooth function with derivatives prescribed on a set of points. The functions solving this problem generalize the Hermite osculatory polynomials. (C) 2004 Elsevier Inc. All rights reserved.
fractal interpolation functions are used to construct a compactly supported continuous, orthogonal wavelet basis spanning L(2) (lR). The wavelets share many of the properties normally associated with spline wavelets, ...
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fractal interpolation functions are used to construct a compactly supported continuous, orthogonal wavelet basis spanning L(2) (lR). The wavelets share many of the properties normally associated with spline wavelets, in particular, they have linear phase.
The present paper studies the influence of adhesives on the behaviour of cracks in deformable bodies. Especially the delamination and debonding effects are studied. The adhesive material is assumed to introduce nonmon...
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The present paper studies the influence of adhesives on the behaviour of cracks in deformable bodies. Especially the delamination and debonding effects are studied. The adhesive material is assumed to introduce nonmonotone possibly multivalued laws which can be described via nonconvex superpotentials. Cracks of fractal geometry are considered. Approximating the fractal crack by a sequence of smooth surfaces or curves and combining this procedure with an algorithm based on the optimization of the potential and of the complementary energy for each approximation of the fractal crack, we get the solution of the problem. Numerical examples, using singular elements for the consideration of the crack singularity, illustrate the theory.
Solutions to the equation (I-S)g = f include Weierstrass functions and fractal interpolation functions of Barnsley. Closure of the range of I - S in C and L(r) is characterized when \\S\\ = 1 and solutions g are repre...
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Solutions to the equation (I-S)g = f include Weierstrass functions and fractal interpolation functions of Barnsley. Closure of the range of I - S in C and L(r) is characterized when \\S\\ = 1 and solutions g are represented as weak Abel-like limits.
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