We proved that for any matrix dilation and for any positive integer n, there exists a compactly supported tight wavelet frame with approximation order n. Explicit methods for construction of dual and tight wavelet frames with a given number of vanishing moments are suggested.

BACKGROUND Pulmonary hypertension (PH) and collagen metabolism abnormalities are prevalent in patients with heart failure with preserved ejection fraction (HFpEF). Peripheral endothelial dysfunction (PED) has been described in HF and in pulmonary arterial hypertension. Our aim is to determine whether PH is associated with PED and impaired collagen metabolism in patients with HFpEF.; METHODS A...

We consider systems of unitary operators on the complex Hilbert space L(R) of the form U :=UDA , v1 ..., vn :=[DT l1 v1 } } } T ln vn : m, l1 , ..., ln # Z], where DA is the unitary operator corresponding to dilation by an n_n real invertible matrix A and Tv1 , ..., Tvn are the unitary operators corresponding to translations by the vectors in a basis [v1 , ..., vn] for R. Orthonormal wavelets a...

Lower-extremity veins have efficient wall structure and function and competent valves that permit upward movement of deoxygenated blood toward the heart against hydrostatic venous pressure. Matrix metalloproteinases (MMPs) play an important role in maintaining vein wall structure and function. MMPs are zinc-binding endopeptidases secreted as inactive pro-MMPs by fibroblasts, vascular smooth mus...

BACKGROUND Development of thoracic aortic aneurysms is the most significant clinical phenotype in patients with Marfan syndrome. An inflammatory response has been described in advanced stages of the disease. Because the hallmark of vascular inflammation is local interleukin-6 (IL-6) secretion, we explored the role of this proinflammatory cytokine in the formation of aortic aneurysms and rupture...

background achalasia is the most recognized motor disorder of the esophagus.because it is an uncommon disease, most studies have reviewed small numbers of patients. here, we report demographic, clinical features and treatment outcomes in 700 achalasia patients. methods in all patients, diagnosis was established based on clinical, radiological, endoscopic and manometric criteria. a questionnaire...

K.-H. Grr ochenig and A. Haas asked whether for every expanding integer matrix A 2 M n (Z) there is a Haar-type orthonormal wavelet basis having dilation factor A and translation lattice Z n. They proved that this is the case when the dimension n = 1. This paper shows that this is also the case when the dimension n = 2.

Matrix fields are becoming increasingly important in digital imaging. In order to perform shape analysis, enhancement or segmentation of such matrix fields, appropriate image processing tools must be developed. This paper extends fundamental morphological operations to the setting of matrices, in the literature sometimes referred to as tensors despite the fact that matrices are only rank two te...

BACKGROUND Arterial remodeling after balloon angioplasty has been recognized as a major determinant of restenosis. Perturbation of collagen metabolism might be important. After balloon injury, matrix metalloproteinase (MMP) expression is upregulated. We investigated the effect of Batimastat, a nonspecific MMP inhibitor, on late lumen loss, arterial remodeling, and neointima formation after ball...

A general form of the double porosity model of single phase flow in a naturally fractured reservoir is derived from homogenization theory. The microscopic model consists of the usual equations describing Darcy flow in a reservoir, except that the porosity and permeability coefficients are highly discontinuous. Over the matrix domain, the coefficients are scaled by a parameter representing the s...