In this paper, we establish a proof for  a  necessary condition for  multiple objective fractional programming. In order to derive the set of necessary conditions, we employ an equivalent parametric problem. Also, we  present the related semi parametric model.

In this work, we introduce $H^*$-condition on the set of submodules of a module. Let $M$ be a module. We say $M$ satisfies $H^*$ provided that for every submodule $N$ of $M$, there is a direct summand$D$ of $M$ such that $(N+D)/N$ and $(N+D)/D$ are cosingular. We show that over a right perfect right $GV$-ring,a homomorphic image of a $H^*$ duo module satisfies $H^*$.

Endometriosis is a condition that is characterized by the presence of endometrial tissue implants that are outside the uterine lining. It is presented in 10–15% of women in the reproductive age group, 2–5% of postmenopausal women, 25–30% of infertile women and 40–70% of women with chronic pelvic pain. The natural course of endometriosis starts with ectopic tissue implantation and bleeding occur...

We introduce a cross eigenvalue condition matrix for measuring the sensitivity of eigenvalue computations. A fundamental difference between this new object and traditional eigenvalue condition numbers is that cross interactions between eigenvectors that are not associated with the same eigenvalue are taken into account. We develop an abstract formulation that makes it possible to define continu...

If Γ is a 2-Moufang generalized n-gon for n ≤ 6, then Γ is Moufang. © 2004 Elsevier Ltd. All rights reserved. MSC: 20E42; 51E12; 05C25