In this work, we have estimated nodal points and nodal lengths for the diffusion operator. Furthermore, by using these new spectral parameters, we have shown that the potential function of the diffusion operator can be established uniquely. An analogous inverse problem was solved for the Sturm–Liouville problem in recent years. c © 2005 Elsevier Ltd. All rights reserved.

Let X be a smooth projective surface. Here we study the postulation of a general union Z of fat points of X, when most of the connected components of Z have multiplicity 2. This problem is related to the existence of ”good” families of curves on X, with prescribed singularities, most of them being nodes, and to the cohomology of suitable line bundles on blowing ups of X. More precise statements...

LetX denote the rational curve with n+1 nodes obtained from the Riemann sphere by identifying 0 with∞ and ζj with −ζj for j = 0, 1, . . . , n−1, where ζ is a primitive (2n)th root of unity. We show that if n is even, then X has no smooth Weierstrass points, while if n is odd, then X has 2n smooth Weierstrass points. C. Widland [14] showed that the rational curve with three nodes obtained from P...

The Lady Maisry ballads afford us a framework within which to segment a storyline into its major components. Segments and as a consequence nodal points are discussed for nine different variants of the Lady Maisry story of a (young) woman being burnt to death by her family, on account of her becoming pregnant by a foreign personage. We motivate the importance of nodal points in textual and liter...

BACKGROUND The purpose of this study was to investigate if nodal ratio has a prognostic role in the survival of patients with recurrent nasopharyngeal carcinoma (NPC) in the neck. METHODS Patients with recurrent NPC in the neck who were treated in Queen Mary Hospital from 2000 to 2011 were identified. Clinical data, pathological results, and survival outcome were analyzed. RESULTS Only noda...

This paper reports on an ongoing research project on an "nonpencil" approach in generating architectural forms using nontraditional geometries. Space curves are investigated to determine nodal points in 3D space, which are then interpreted into common architectural elements. The nodal points are used in a variety of ways to generate walls, columns, floors, and volumes. The determination of form...

This paper presents an application of a flexible model-based template matching algorithm named "deformable template matching." The template which models the shape of objects consists of some nodal points and segments that connect the nodal points sequentially. The template holds information about the known deformation of the object's shape, and it makes the shape recognition flexible. The match...