We discuss external and internal graphical and linguistic representational systems. We argue that a cognitive theory of peoples' reasoning performance must account for (a) the logical equivalence of inferences expressed in graphical and linguistic form; and (b) the implementational di erences that a ect facility of inference. Our theory proposes that graphical representations limit abstraction ...

where a, b, c are rational parameters. By specialization of the parameters, Euler obtained the various classical functions that were around at that time. For example, taking b = c = 1 gives us Newton’s binomial series for (1 − z)−a and taking a = b = 1/2, c = 3/2 gives us arcsin(√z)/√z. Finally, taking all parameters equal to 1 recovers the ordinary geometric series, which more or less explains...

Three and four parameter representations of 3x3 orthogonal matrices are extended to the general case of proper NxN orthogonal matrices. These developments generalize the classical Rodrigues parameter, the Euler parameters, and the recently introduced modified Rodrigues parameters to higher dimensions. The developments presented generalize and extend the classical result known as the Cayley tran...

The aim of this paper is to construct generating functions, related to nonnegative real parameters, for q-Eulerian type polynomials and numbers (or q-Apostol type Frobenius–Euler polynomials and numbers). We derive some identities for these polynomials and numbers based on the generating functions and functional equations. We also give multiplication formula for the generalized Apostol type Fro...

In this paper, coordination between a spacecraft and its several manipulators is investigated, during a capture maneuver of a moving object in space. Using a general Lagrangian formulation, the dynamics model of the system is derived, and the results are summarized in an explicit dynamics model of multiple manipulator space free-flyers. The system dynamics is also formulated on the basis of cho...

We describe an empirical investigation into some of the layout criteria that may facilitate the comprehension of Euler diagrams. The three criteria under investigation were: smoothness, zone area equality and edge closeness. Subjects were asked to interpret diagrams that had good and bad levels of each criterion. The goal of this research is an initial step into using empirical evidence to supp...

This paper presents algorithms for identifying parameters of an N degrees-of-freedom robotic manipulator. First, we outline the fundamental properties of the Newton-Euler formulation of robot dynamics from the view point of parameter identification. We then show that the Newton-Euler model which is nonlinear in the dynamic parameters can be transformed into an equivalent modified model which is...

The mathematical model of an industrial robot is usually described in the form of Lagrange-Euler equations, Newton-Euler equations or generalized d’Alambert equations. However, these equations require the physical parameters of a robot that are difficult to obtain. In this paper, two methods for calculation of a Lagrange-Euler model of robot using neural networks are presented and compared. The...

In the present paper, we introduce Eulerian polynomials with parameters a and b and give the definition of them. By using the definition of generating function for our polynomials, we derive some new identities in Analytic Numbers Theory. Also, we give relations between Eulerian polynomials with parameters a and b, Bernstein polynomials, Poly-logarithm functions, Bernoulli and Euler numbers. Mo...