Local and Global Frames of Reference: Last time we introduced the basic elements of affine and Euclidean geometry: points and (free) vectors. However, as of yet we have no mechanism for representing these objects. Recall that points are to be thought of as locations in space and (free) vectors represent direction and magnitude, but are not tied down to a particular location in space. We seek a ...

An interactive multiobjective fuzzy inventory problem with two resource constraints is presented in this paper. The cost parameters and index parameters, the storage space, the budgetary cost, and the objective and constraint goals are imprecise in nature. These parameters and objective goals are quantified by linear/nonlinear membership functions. A compromise solution is obtained by geometric...

Abstract The maxentropic reconstruction is a technique for finding an unknown probability distribution from some known information. In this paper we obtain the maxentropic reconstruction of some probability distributions from the knowledge of a prior distribution and of some lower and upper bounds for the mean values of some random variables. For this we use the Csiszár’s I-projection theorems ...

This paper undergoes quantitative analyses on fundamental properties of ad hoc networks including estimating the number of hiddenterminal pairs and the number of exposed-terminal sets. To obtain these results, we propose a paradigm to systematically derive exact formulas for a great deal of subgraph probabilities of random geometric graphs. In contrast to previous work, which established asympt...

Coordination and harmony between different departments of a company can be an important factor in achieving competitive advantage if the company corrects alignment between strategies of different departments. This paper presents an integrated decision model based on recent advances of geometric programming technique. The demand of a product considers as a power function of factors such as produ...

The motion rotors, or motors, are used to model Euclidean motion in 3D conformal geometric algebra. In this chapter we present a technique for estimating the motor which best transforms one set of noisy geometric objects onto another. The technique reduces to an eigenrotator problem and has some advantages over matrix formulations. It allows motors to be estimated from a variety of geometric da...

Random geometric graphs (RGG) contain vertices whose points are uniformly distributed in a given plane and an edge between two distinct nodes exists when their distance is less than a given positive value. RGGs are appropriate for modeling multi-hop wireless networks consisting of n mobile devices with transmission radius r unit length that are independently and uniformly distributed randomly i...

Local and Global Frames of Reference: Last time we introduced the basic elements of affine and Euclidean geometry: points and (free) vectors. However, as of yet we have no mechanism for representing these objects. Recall that points are to be thought of as locations in space and (free) vectors represent direction and magnitude, but are not tied down to a particular location in space. We seek a ...