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

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

Two-dimensional quaternion wavelet transform

In this paper we introduce the continuous quaternion wavelet transform (CQWT). We\ud express the admissibility condition in terms of the (right-sided) quaternion Fourier transform.\ud We show that its fundamental properties, such as inner product, norm relation, and\ud inversion formula, can be established whenever the quaternion wavelets satisfy a particular\ud admissibility condition. We present several examples of the CQWT. As an application\ud we derive a Heisenberg type uncertainty principle for these extended wavelets

18F-Labeling of 1, 2-Diacylglycerol

開始ページ、終了ページ: 冊子体のページ付

Windowed Fourier transform of two-dimensional quaternionic signals

In this paper, we generalize the classical windowed Fourier transform (WFT) to quaternion-\ud valued signals, called the quaternionic windowed Fourier transform (QWFT). Using\ud the spectral representation of the quaternionic Fourier transform (QFT), we derive several\ud important properties such as reconstruction formula, reproducing kernel, isometry, and\ud orthogonality relation. Taking the Gaussian function as window function we obtain quaternionic\ud Gabor filters which play the role of coefficient functions when decomposing\ud the signal in the quaternionic Gabor basis. We apply the QWFT properties and the\ud (right-sided) QFT to establish a Heisenberg type uncertainty principle for the QWFT.\ud Finally, we briefly introduce an application of the QWFT to a linear time-varying system

Boundedness of Pseudodifferential Operators on Banach Function Spaces

We show that if the Hardy-Littlewood maximal operator is bounded on a separable Banach function space $X(\mathbb{R}^n)$ and on its associate space $X'(\mathbb{R}^n)$, then a pseudodifferential operator $\operatorname{Op}(a)$ is bounded on $X(\mathbb{R}^n)$ whenever the symbol $a$ belongs to the H\"ormander class $S_{\rho,\delta}^{n(\rho-1)}$ with $0<\rho\le 1$, $0\le\delta<1$ or to the the Miyachi class $S_{\rho,\delta}^{n(\rho-1)}(\varkappa,n)$ with $0\le\delta\le\rho\le 1$, $0\le\delta0$. This result is applied to the case of variable Lebesgue spaces $L^{p(\cdot)}(\mathbb{R}^n)$.Comment: To appear in a special volume of Operator Theory: Advances and Applications dedicated to Ant\'onio Ferreira dos Santo

Nanoelectromechanical coupling in fullerene peapods probed via resonant electrical transport experiments

Fullerene peapods, that is carbon nanotubes encapsulating fullerene molecules, can offer enhanced functionality with respect to empty nanotubes. However, the present incomplete understanding of how a nanotube is affected by entrapped fullerenes is an obstacle for peapods to reach their full potential in nanoscale electronic applications. Here, we investigate the effect of C60 fullerenes on electron transport via peapod quantum dots. Compared to empty nanotubes, we find an abnormal temperature dependence of Coulomb blockade oscillations, indicating the presence of a nanoelectromechanical coupling between electronic states of the nanotube and mechanical vibrations of the fullerenes. This provides a method to detect the C60 presence and to probe the interplay between electrical and mechanical excitations in peapods, which thus emerge as a new class of nanoelectromechanical systems.Comment: 7 pages, 3 figures. Published in Nature Communications. Free online access to the published version until Sept 30th, 2010, see http://www.nature.com/ncomms/journal/v1/n4/abs/ncomms1034.htm

Discrete structure of ultrathin dielectric films and their surface optical properties

The boundary problem of linear classical optics about the interaction of electromagnetic radiation with a thin dielectric film has been solved under explicit consideration of its discrete structure. The main attention has been paid to the investigation of the near-zone optical response of dielectrics. The laws of reflection and refraction for discrete structures in the case of a regular atomic distribution are studied and the structure of evanescent harmonics induced by an external plane wave near the surface is investigated in details. It is shown by means of analytical and numerical calculations that due to the existence of the evanescent harmonics the laws of reflection and refraction at the distances from the surface less than two interatomic distances are principally different from the Fresnel laws. From the practical point of view the results of this work might be useful for the near-field optical microscopy of ultrahigh resolution.Comment: 25 pages, 16 figures, LaTeX2.09, to be published in Phys.Rev.

Calcium-dependent release of adenosine and uridine nucleotides from A549 cells

Extracellular nucleotides play an important role in lung defense, but the release mechanism and relative abundance of different nucleotide species secreted by lung epithelia are not well defined. In this study, to minimize cell surface hydrolysis, we used a low-volume, flow-through chamber and examined adenosine and uridine nucleotide concentrations in perfusate aliquots of human lung A549 cells challenged by 50% hypotonic shock. Adenosine triphosphate (ATP), adenosine diphosphate (ADP), adenosine monophosphate (AMP), and adenosine (Ado) were quantified in high-performance liquid chromatography (HPLC) analysis of fluorescent etheno derivatives, and uridine triphosphate (UTP) and uridine diphosphate (UDP) were measured using HPLC-coupled radioenzymatic assays. After the onset of hypotonic shock, ATP, ADP, UTP, and UDP in the perfusates increased markedly and peaked at approximately 2.5 min, followed by a gradual decay in the next 15–20 min; peak changes in Ado and AMP were relatively minor. The peak concentrations and fold increment (in parentheses) were: 34 ± 13 nM ATP (5.6), 11 ± 5 nM ADP (3.7), 3.3 ± 1.2 nM AMP (1.4), 23 ± 7 nM Ado (2.1), 21 nM UTP (>7), and 11 nM UDP (27). Nucleotide release was almost completely abolished from cells loaded with the calcium chelator 1,2-bis(2-aminophenoxy)ethane-N,N,N',N'-tetraacetic acid (BAPTA). Under isotonic conditions, elevation of intracellular calcium with the calcium ionophore ionomycin (5 μM, 3 min) also released nucleotides with kinetics and relative abundance as above, albeit less robust. ADP:ATP (1:3) and UDP:UTP (1:2) ratios in perfusates from stimulated cells were markedly higher than the cytosolic ratios of these species, suggesting that a nucleotide diphosphate (NDP)-rich compartment, e.g., the secretory pathway, contributed to nucleotide release. Laser confocal microscopy experiments illustrated increased FM1-43 uptake into the plasma membrane upon hypotonic shock or ionomycin treatment, consistent with enhanced vesicular exocytosis under these conditions. In summary, our results strongly suggest that calcium-dependent exocytosis is responsible, at least in most part, for adenosine and uridine nucleotide release from A549 cells