5 Area of Intersecting Ellipses 5 5.1 No Intersection Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 5.2 One Intersection Point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 5.3 Two Intersection Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 5.4 Three Intersection Points . . . ....

This paper focuses on the relationship between an $L$-subset and the system of level-elements induced by it, where the underlying lattice $L$ is a complete residuated lattice and the domain set of $L$-subset is an $L$-partially ordered set $(X,P)$. Firstly, we obtain the sufficient and necessary condition that an $L$-subset is represented by its system of level-elements. Then, a new representat...

Let $R$ be a commutative ring with identity and $M$ be an unitary $R$-module. The intersection graph of an $R$-module $M$, denoted by $Gamma(M)$, is a simple graph whose vertices are all non-trivial submodules of $M$ and two distinct vertices $N_1$ and $N_2$ are adjacent if and only if $N_1cap N_2neq 0$. In this article, we investigate the concept of a planar intersection graph and maximal subm...

The minimal prime decomposition for semiprime ideals is defined and studied on z-ideals of C(X). The necessary and sufficient condition for existence of the minimal prime decomposition of a z-ideal / is given, when / satisfies one of the following conditions: (i) / is an intersection of maximal ideals. (ii) I is an intersection of O , s, when X is basically disconnected. (iii) I=O , when x X h...

This paper presents two feature extraction methods and two decision methods to retrieve images having some section in them that is like the user input image. The features used are variances of gray level co-occurrences and lineangle-ratio statistics constituted by a 2-D histogram of angles between two intersecting lines and ratio of mean gray levels inside and outside the regions spanned by tho...