A construction of multiwavelets

AbstractA class of r-regular multiwavelets, depending on the smoothness of the multiwavelet functions, is introduced with the appropriate notation and definitions. Oscillation properties of orthonormal systems are obtained in Lemma 1 and Corollary 1 without assuming any vanishing moments for the scaling functions, and in Theorem 1 the existence of r-regular multiwavelets in L2(Rn) is established. In Theorem 2, a particular r-regular multiresolution analysis for multiwavelets is obtained from an r-regular multiresolution analysis for uniwavelets. In Theorem 3, an r-regular multiresolution analysis of split-type multiwavelets, which are perhaps the simplest multiwavelets, is easily obtained by using an r-regular multiresolution analysis for uniwavelets and a (2n − 1)-fold regular multiresolution analysis for uniwavelets. For some split-type multiwavelets, the support or width of the wavelets is shorter than the support or width of the scaling functions without loss of regularity nor of vanishing moments. Examples of split-type multiwavelets in L2(R) are constructed and illustrated by means of figures. Symmetry and antisymmetry are preserved in the case of infinite support

Representation of differential operators in wavelet basis

AbstractExisting work on the representation of operators in one-dimensional, compactly-supported, orthonormal wavelet bases is extended to two dimensions. The nonstandard form of the representation of operators is given in separable two-dimensional, periodic, orthonormal wavelet bases. The matrix representation of the partial-differential operators ∂x and ∂y are constructed and a closed form formula for the matrix representation of a general partial-differential operator g(∂x, ∂y) is derived, where g is an analytic function

Convolution Theorems for Clifford Fourier Transform and Properties

The non-commutativity of the Clifford multiplication gives different aspects from the classical Fourier analysis.We establish main properties of convolution theorems for the Clifford Fourier transform. Some properties of these generalized convolutionsare extensions of the corresponding convolution theorems of the classical Fourier transform.DOI : http://dx.doi.org/10.22342/jims.20.2.143.125-14

Smooth tight frame wavelets and image microanalyis in the fourier domain

AbstractGeneral results on microlocal analysis and tight frames in R2 are summarized. To perform microlocal analysis of tempered distributions, orthogonal multiwavelets, whose Fourier transforms consist of characteristic functions of squares or sectors of annuli, are constructed in the Fourier domain and are shown to satisfy a multiresolution analysis with several choices of scaling functions. To have good localization in both the x and Fourier domains, redundant smooth tight wavelet frames, with frame bounds equal to one, called Parseval wavelet frames, are obtained in the Fourier domain by properly tapering the above characteristic functions. These nonorthogonal frame wavelets can be generated by two-scale equations from a multiresolution analysis. A natural formulation of the problem is by means of pseudodifferential operators. Singularities, which are added to smooth images, can be localized in position and direction by means of the frame coefficients of the filtered images computed in the Fourier domain. Using Plancherel's theorem, the frame expansion of the filtered images is obtained in the x domain. Subtracting this expansion from the scarred images restores the original images

Origins of the 1/4 keV Soft X-Ray Background

Snowden and coworkers have presented a model for the 1/4 keV soft X-ray diffuse background in which the observed flux is dominated by a ~ 10^6 K thermal plasma located in a 100-300 pc diameter bubble surrounding the Sun, but has significant contributions from a very patchy Galactic halo. Halo emission provides about 11% of the total observed flux and is responsible for half of the H I anticorrelation. The remainder of the anticorrelation is presumably produced by displacement of disk H I by the varying extent of the local hot bubble (LHB). The ROSAT R1 and R2 bands used for this work had the unique spatial resolution and statistical precision required for separating the halo and local components, but provide little spectral information. Some consistency checks had been made with older observations at lower X-ray energies, but we have made a careful investigation of the extent to which the model is supported by existing sounding rocket data in the Be (73-111 eV) and B bands (115-188 eV) where the sensitivities to the model are qualitatively different from the ROSAT bands. We conclude that the two-component model is well supported by the low-energy data. We find that these combined observations of the local component may be consistent with single-temperature thermal emission models in collisional ionization equilibrium if depleted abundances are assumed. However, different model implementations give significantly different results, offering little support for the conclusion that the astrophysical situation is so simple.Comment: 17 pages, 6 figures, accepted by the Astrophysical Journa

Cutter Assembly for Microscope and Related Method

A low-profile cutter assembly for use on a microscope and related cutting method are provided. The cutter assembly includes a support subassembly having a mounting ring for receiving and engaging the objective of a microscope. A cutter subassembly carried by the support subassembly is displaceable between a home and a forward position in response to actuation. Upon reaching the forward position, additional actuation causes the front end of the cutter subassembly to pivot toward the stage, thereby placing a cutter adjacent to or in contact with the specimen. By selectively actuating the cutter subassembly, multiple cuts may be performed, as necessary or desired for cutting a spore or isolating a particular specimen

On the Stability of Oscillatory Pipe Flows

The linear stability of pure oscillatory pipe flow is investigated by solving the linearized disturbance equations as an initial value problem. The importance of the initial conditions on transient dynamics of the flow is analyzed. It is shown that transient growth can play an important role in the development of flow instability. The accuracy of the quasi-steady assumption is assessed. It is shown that the growth rates obtained with this assumption deviate considerably from the results obtained with a direct numerical solution of the linearized initial value problem

Foragebeef.ca Web Site: A Model for Technology Transfer

We live in an age of information overload. As budgets for technology transfer of scientific information and extension education continue to fall, new ways to disseminate agricultural knowledge are needed. Research findings, published in many scientific journals and reports, are seldom readily available to extension agents and farmers. Over time some of this material is lost. This program aimed to locate the best information on various forage and beef topics relative to Canada and the Northern USA and to summarise them in condensed form and in scientific review papers for a web-based site