in this paper, boundary value problems of fractional order are converted into an optimal control problems. then an approximate solution is constructed from translations and dilations of a b-spline function such that the exact boundary conditions are satisfied. the fractional differential operators are taken in the riemann-liouville and caputo sense. several example are given and the optimal err...

Various results on constructing wavelets, multiwavelets and wavelet frames for periodic functions are reviewed. The orthonormal and Riesz bases as well as frames are constructed from sequences of subspaces called multiresolution analyses. These studies employ general frequency-based approaches facilitated by functions known as orthogonal splines and polyphase splines. While the focus is on the ...

| In applications using multiwavelets, there is a necessary step of associating a given discrete signal with a function in the scaling function space V 0. This association is equivalent to including a preelter and a posttlter for the lterbank determined by the underlying multiwavelets. We give a construction for orthogonal (paraunitary) FIR pre-lters that preserve the approximation order of a g...

By using affine-invariant shape descriptors, it is possible to recognize an unknown planar object from an image taken from an arbitrary view when standard view images of candidate objects exist in a database. In a previous study, an affine-invariant function calculated from the wavelet coefficients of the object boundary has been proposed. In this work, the invariant is constructed from the mul...

this study aims to numerically investigate on the crashworthiness of thin-walled square tubes by consideration of 3-d oblique loading. in this type of loading, direction of loading is defined by using two spatial angles relative to the position of the tube. to this aim, finite element (fe) analysis is employed to simulate the loading for 8 different numerical models with different loading orien...

(Bi)orthogonal (multi)wavelets on the real line have been extensively studied and employed in applications with success. A lot of problems are defined bounded intervals or domains. Therefore, it is important both theory application to construct all possible wavelets some desired properties from (bi)orthogonal line. Vanishing moments compactly supported key property for sparse wavelet representa...