This paper presents circular polar coordinates transformation of periodic fuzzy membership function. The purpose is identification of domain of periodic membership functions in consequent part of IF-THEN rules. Proposed methods in this paper remove complicatedness concerning domain of periodic membership function from defuzzification in fuzzy approximate reasoning. Defuzzification on circular p...

Visual Servoing is generally contained of control and feature tracking. Study of previous methods shows that no attempt has been made to optimize these two parts together. In kernel based visual servoing method, the main objective is to combine and optimize these two parts together and to make an entire control loop. This main target is accomplished by using Lyapanov theory. A Lyapanov candidat...

The volume of the polar body of a symmetric convex set K of Rd is investigated. It is shown that its reciprocal is a convex function of the time t along movements, in which every point of K moves with constant speed parallel to a fixed direction. This result is applied to find reverse forms of the Lp-Blaschke-Santaló inequality for two-dimensional convex sets.

In this research paper, we present a novel frame work for handling $m$-polar information by combining the theory of $m-$polar fuzzy  sets with graphs. We introduce certain types of edge regular $m-$polar fuzzy graphs and edge irregular $m-$polar fuzzy graphs. We describe some useful properties of edge regular, strongly edge irregular and strongly edge totally irregular $m-$polar fuzzy graphs. W...

fringe encodes a glycosyltransferase that modulates the ability of the Notch receptor to be activated by its ligands. We describe studies of fringe function during early stages of Drosophila oogenesis. Animals mutant for hypomorphic alleles of fringe contain follicles with an incorrect number of germline cells, which are separated by abnormally long and disorganized stalks. Analysis of clones o...

We prove that the reciprocal of the volume of the polar bodies, about the Santaló point, of a shadow system of convex bodies Kt, is a convex function of t. Thus extending to the non-symmetric case a result of Campi and Gronchi. The case that the reciprocal of the volume is an affine function of t is also investigated and is characterized under certain conditions. We apply these results to prove...

This paper proves some results concerning the polar factorisation of an integrable vector-valued function u into the composition u = u ◦ s, where u = ∇ψ almost everywhere for some convex function ψ, and s is a measure-preserving mapping. Not every integrable function has a polar factorisation; we extend the class of counterexamples. We introduce a generalisation: u has a polar inclusion if u(x)...