In this paper, we exploit the relation between the regularity of refinable functions with non-integer dilations and the distribution of powers of a fixed number modulo 1, and show the nonexistence of a non-trivial C∞ solution of the refinement equation with non-integer dilations. Using this, we extend the results on the refinable splines with non-integer dilations and construct a counterexample...

In the present paper we give a self-contained proof of Imprimitivity theorem for systems of covariance, or generalised imprimitivity systems, based on transitive spaces. The theorem holds for locally compact groups and non-normalised positive operator valued (POV) measures. For projective valued measures, the theorem was proven by Mackey, [21], for separable groups, and by Blattner, [4], in ful...

We study some basic morphological operators acting on the lattice of all subgraphs of an arbitrary (unweighted) graph G. To this end, we consider two dual adjunctions between the edge set and the vertex set of G. This allows us (i) to recover the classical notion of a dilation/erosion of a subset of the vertices of G and (ii) to extend it to subgraphs of G. Afterward, we propose several new ope...

Background Adverse outcomes are increasingly common in patients after the Fontan operation as they approach adulthood. Right ventricular (RV) morphology, ventricular dilation, and diminished ventricular strain have all been independently associated with death or heart transplant. The aim of this study was to assess the impact of ventricular morphology on ventricular stress/strain relationship i...

Performing morphological operations such as dilation and erosion of binary images, using very long line structuring elements is computationally expensive when performed brute-force following definitions. We present two-pass algorithms that run at constant time for obtaining binary dilations and erosions with all possible length line structuring elements, simultaneously. The algorithms run at co...

INTRODUCTION A simple technique to dilate urethral stricture using guide wire and sheath dilator has been described in pediatric urology. The aim of this study was to report the long-term outcome of the children who underwent dilation of the urethral stricture using guide wire and sheath dilator. MATERIALS AND METHODS From 1999 to 2004, a total of 52 children with documented urethral strictur...

In this paper, we evaluate the performance of morphological operations in central processing unit (CPU) and graphics processing unit (GPU) on various sizes of image and structuring element. The languages selected for algorithm implementation are C++, Matlab for CPU and CUDA for GPU. The parallel programming approach using threads for image analysis is done on basic entities of images. The morph...

OBJECTIVE Here we present the first video demonstration of reduction corporoplasty in the management of phallic disfigurement in a 17 year old man with a history sickle cell disease and priapism. INTRODUCTION Surgical management of aneurysmal dilation of the corpora has yet to be defined in the literature. MATERIALS AND METHODS We preformed bilateral elliptical incisions over the lateral co...