An irregular assignment is a k -labeling of the edges : {1, 2, , } f E k → ... such that the vertex weights (label sums of edges incident with the vertex) are different for all vertices of G . The smallest k for which there is an irregular assignment is the irregularity strength. The notion of irregularity strength was introduced by Chartrand et al. [8] and studied by numerous authors, see [6,1...

We investigate how the regularity of nonharmonic Fourier series is related to the spacing of their frequencies. This is obtained by using a transform which simultaneously captures the advantages of the Gabor and Wavelet transforms. Applications to the everywhere irregularity of solutions of some PDEs are given. We extend these results to the anisotropic setting in order to derive directional ir...

OBJECTIVES The aim of this study was to define the morphological features of coronary artery spasm sites using optical coherence tomography (OCT) in patients with vasospastic angina (VSA). BACKGROUND Plaque characteristics at coronary artery spasm sites have not been investigated systematically. METHODS Sixty-nine consecutive patients (80 spasm sites) presenting with VSA who underwent OCT i...

Subjects observed a random dot pattern that moved horizontally with modulated velocity within an invisible aperture. The velocity contrast, (V2-V1)/V1, was 2/3. Two different percepts occurred while observing this stimulus. At lower modulation frequencies, between 2 and 12 Hz, velocity changes were clearly seen; this percept is called "motion irregularity". At frequencies higher than 20 Hz velo...

PURPOSE To evaluate the association between degree of retinal abnormalities and uncorrected visual acuity (UCVA) in idiopathic epiretinal membrane (ERM) patients with a small amount of refractive error. METHODS We retrospectively reviewed 49 eyes (37 patients) of idiopathic ERM patients. We investigated the association between visual acuity and macular status (central macular thickness [CMT],...

We describe the Gevrey series solutions at singular points of the irregular hypergeometric system (GKZ system) associated with an affine plane monomial curve. We also describe the irregularity complex of such a system with respect to its singular support and in particular we prove, using elementary methods, that this irregularity complex is a perverse sheaf as assured by a theorem of Z. Mebkhout.

Two new graph characteristics, the total vertex irregularity strength and the total edge irregularity strength, are introduced. Estimations on these parameters are obtained. For some families of graphs the precise values of these parameters are proved. © 2006 Elsevier B.V. All rights reserved.

a vertex irregular total k-labeling of a graph g with vertex set v and edge set e is an assignment of positive integer labels {1, 2, ..., k} to both vertices and edges so that the weights calculated at vertices are distinct. the total vertex irregularity strength of g, denoted by tvs(g)is the minimum value of the largest label k over all such irregular assignment. in this paper, we study the to...