Abstract: A new approach to fabricating regularly patterned nano-scale structures, by self assembly of the structures is disclosed, where a pattern of nano-lines are deposited on a substrate and nano-structures are grown by self assembly in regions between the lines to form regular or patterned nano-scale structures, which are ideally suited for the construction nano-scale materials, nano-scale electronic devices and other nano-scale objects, apparatuses or devices. The invention also relates to methods of making and using same.

Abstract: A non-separable multiresolution structure based on frames by radial scaling functions is disclosed, which are minimally supported in the frequency. Resulting frame multiwavelets are also disclosed which can be isotropic. The construction can be carried out in any number of dimensions and for a variety of dilation matrices.

Abstract: A method and system for solving the inverse acoustic scattering problem using an iterative approach with consideration of half-off-shell transition matrix elements (near-field) information, where the Volterra inverse series correctly predicts the first two moments of the interaction, while the Fredholm inverse series is correct only for the first moment and that the Volterra approach provides a method for exactly obtaining interactions which can be written as a sum of delta functions.

Abstract: A method for padding, filtering, denoising, image enhancing and increased time-frequency acquisition is described for digitized data of a data set where unknown data is estimated using real data by adding unknown data points in a manner that the padding routine can estimate the interior data set including known and unknown data to a given accuracy on the known data points. The method also provides filtering using non-interpolating, well-tempered distributed approximating functional (NIDAF)-low-band-pass filters. The method also provides for symmetric and/or anti-symmetric extension of the data set so that the data set may be better refined and can be filtered by Fourier and other type of low frequency or harmonic filters.

Abstract: A method for padding, filtering, denoising, image enhancing and increased time-frequency acquisition is described for digitized data of a data set is described where unknown data is estimated using real data by adding unknown data points in a manner that the padding routine can estimate the interior data set including known and unknown data to a given accuracy on the known data points. The method also provides filtering using non-interpolating, well-tempered distributed approximating functional (NIDAF)-low-band-pass filters. The method also provides for symmetric and/or anti-symmetric extension of the data set so that the data set may be better refined and can be filtered by Fourier and other type of low frequency or harmonic filters.