This paper defines and establishes properties of a class of normalized radial visualizations (NRVs) that includes the RadViz mapping onto the two-dimensional unit disk. A NRV normalizes data to map highdimensional records into lower dimensional space, where records’ images are convex combinations of points called dimensional anchors. NRVs are radial visualizations because dimensional anchors ar...

In this paper we study an eigenvalue boundary value problem which arises when seeking radial convex solutions of the Monge-Ampère equations. We shall establish several criteria for the existence, multiplicity and nonexistence of strictly convex solutions for the boundary value problem with or without an eigenvalue parameter.

The problem is trivially positive in R2. However, a surprising negative answer for n ≥ 12 was given by Larman and Rogers [LR] in 1975. Subsequently, a series of contributions were made to reduce the dimensions to n ≥ 5 by a number of authors (see [Ba], [Bo], [G2], [Gi], [Pa], and [Z1]). That is, the problem has a negative answer for n ≥ 5. See [G3] for a detailed description. It was proved by G...

We establish two criteria for the existence of convex solutions for a boundary value problem arising from the study of the existence of convex radial solutions for the Monge–Ampère equations. We shall use fixed point theorems in a cone. © 2005 Elsevier Inc. All rights reserved.

background: there is little information about blood supply of the carpal joint in one- humped camel, while there is extensive data about cow and equine species. in order to perform surgeries and diagnostic techniques in carpal region, information about the elements of the joint such as its arteries is necessary. objectives: this study aims at describing the origins, arrangements, and branches o...

We extend the canonical cell decomposition due to Epstein and Penner of a hyperbolic manifold with cusps to the strictly convex setting. It follows that a sufficiently small deformation of the holonomy of a finite volume strictly convex real projective manifold is the holonomy of some nearby projective structure with radial ends, provided the holonomy of each maximal cusp has a

Many simulation algorithms (chemical reaction systems, differential systems arising from the modeling of transient behavior in the process industries and etc.) contain the numerical solution of systems of differential equations. For the efficient solution of the above mentioned problems, linear multistep methods or Runge-Kutta technique are used. For the simulation of chemical procedures the ra...

the analysis of flow in water-distribution networks with several pumps by the content model may be turned into a non-convex optimization uncertain problem with multiple solutions. newton-based methods such as gga are not able to capture a global optimum in these situations. on the other hand, evolutionary methods designed to use the population of individuals may find a global solution even for ...

Computing the exact ideal and nadir criterion values is a very ‎important subject in ‎multi-‎objective linear programming (MOLP) ‎problems‎‎. In fact‎, ‎these values define the ideal and nadir points as lower and ‎upper bounds on the nondominated points‎. ‎Whereas determining the ‎ideal point is an easy work‎, ‎because it is equivalent to optimize a ‎convex function (linear function) over a con...

The parabolic partial differential equation arises in many application of technologies. In this paper, we propose an approximate method for solution of the heat and advection-diffusion equations using Laguerre-Gaussians radial basis functions (LG-RBFs). The results of numerical experiments are compared with the other radial basis functions and the results of other schemes to confirm the validit...