background haemorrhoids are cushions of submucosal vascular tissue located in the anal canal starting just distal to the dentate line. haemorrhoidal disease is a common anorectal disorder which has symptoms of bleeding, prolapse, pain, thrombosis, mucus discharge, and pruritus. haemorrhoidectomy is one of most frequently performed anorectal operation worldwide. objectives the aim of this study ...

A graph G= (V,E) with p vertices and q edges is called a Harmonic mean graph if it is possible to label the vertices xV with distinct labels f(x) from 1,2,....,q+1 in such a way that when each edge e=uv is labeled with f(uv)= ( ) ( ) ( ) ( ) (or) ( ) ( ) ( ) ( ) , then the edge labels are distinct. In this case, f is called Harmonic mean labeling of G. In this paper we prove that Double Triang...

Motivated by a problem in learning theory, we are led to study the dominant eigenvalue of a class of random matrices. This turns out to be related to the roots of the derivative of random polynomials (generated by picking their roots uniformly at random in the interval [0, 1], although our results extend to other distributions). This, in turn, requires the study of the statistical behavior of t...

In classical differential geometry, surfaces of constant mean curvature (CMC surfaces) have been studied extensively [1]. As a generalization of CMC surfaces, Bobenko [2] introduced the notion of surface with harmonic inverse mean curvature (HIMC surface). He showed that HIMC surfaces admit Lax representation with variable spectral parameter. In [5], Bobenko, Eitner and Kitaev showed that the G...

We give conditions on the functions σ and u on R such that if u is given by the convolution of σ and u, then u is harmonic on R.