In this paper some properties of quadratic forms whose base points lie in the point set F Π , the fundamental domain of the modular group, and transforming these forms into the reduced forms with the same discriminant ∆ < 0 are given.

Fixed mobile convergence (FMC) will be one of the strongest trends in telecommunications in the near future. Given the choice, most consumers would want to use a single handset yet do not want to pay the premium when at home or in the office. Even though seamless network integration will still take some time to become reality, there are many convergence opportunities that are currently being ex...

For the last 15 years cosmologists believe that something like inflation is necessary in order to construct an internally consistent cosmological theory. For more than 20 years the best hopes for the theory of all fundamental interactions are related to supersymmetry. Unfortunately it is not that simple to combine these two ideas. The main problem is that the effective potential for the inflato...

Recent observation of supernovae type Ia show clearly that there is a large scale repulsive force in the Universe. Neither of the four known fundamental interactions can account for this repulsive force. Gravity is known to be the interaction responsible for the large scale structure and evolution of the Universe. The problem with gravity is that it gives rise to a force which is attractive onl...

Though parts of the present paper perfectly look like abstract general nonsense, its origin is a rather concrete question. Given a simply connected almost simple Chevalley group G and a field k, what is a fundamental domain (in an appropriate sense) for the action of G(k[t, t−1]) on the product ∆+ × ∆− of the two associated Bruhat–Tits buildings ∆+ = ∆(G(k((t−1)))) and ∆− = ∆(G(k((t)))) ? The s...

We prove that the symbolic dynamical system generated by a purely substitutive Arnoux-Rauzy sequence is measurably conjugate to a toral translation. The proof is based on an explicit construction of a fundamental domain with fractal boundary (a Rauzy fractal) for this toral translation. Communicated by Pierre Liardet Dedicated to the memory of Gérard Rauzy

Although the grasp-task interplay in our daily life is unquestionable, very little research has addressed this problem in robotics. In order to fill the gap between the grasp and the task, we adopt the most successful approaches to grasp and task specification, and extend them with additional elements that allow to define a grasp-task link. We propose a global sensor-based framework for the spe...

Consider two views of a multi-body scene consisting of k planar bodies moving in pure translation one relative to the other. We show that the fundamental matrices, one per body, live in a 3-dimensional subspace, which when represented as a step-3 extensor is the common transversal on the collection of extensors defined by the homography matrices H1; :::; Hk of the moving planes. We show that as...

This paper reports the exploratory study’s finding based on the participants’ behaviors while interacting with Augmented Reality based system in group learning environment. Technology has long been used to enhance group learning, often known as Computer-Supported Collaborative Learning (CSCL). Recent research in this area showed that technology somehow hinders the communication and interaction ...

A 0 3 3 C v 2 C v C O-Attempts to understand the fundamental physical limits of computation have been under way for over a quarter century. We discuss this field, with B e 3 3 3 S 3 S 0 emphasis on the central notion of reversible computation, and emphasis on the relationship to the ultimate nature of physical law. A brief discussion of the generation of information is included. In ordinary com...