We discuss the occurrence of Bose-Einstein condensation in systems of noninteracting charged particles in three and one dimensions and in presence of an external magnetic eld. In the one dimensional, as well as in the magnetic eld cases, although not a critical temperature, a characteristic temperature can be found, corresponding to the case in which the ground state density becomes a macroscop...

In this paper we present suucient conditions for the controllability of the reduced dynamics of a class of mechanical systems with symmetry. We prove conditions (boundedness of coadjoint orbits and existence of a radially unbounded Lyapunov function) under which the drift vector eld (of the reduced system) is weakly positively Poisson stable (WPPS). The WPPS nature of the drift vector eld along...

Rigorous upper and lower bounds for the e€ective moduli are obtained for heterogeneous piezoelectric materials, by generalizing the Hashin±Shtrikman variational principle to the coupled problems of piezoelectricity. The key in obtaining these bounds is the choice of the ®eld variables used in the variational principles, i.e., the strain tensor and the electric displacement vector or the stress ...

The traditional concept of the receptive eld (e.g., [4, 6]) holds that each portion of the receptive eld (RF), in response to a stimulus element, has unitary (excitatory or inhibitory) in uence on neuronal response. Here, we argue: i) receptive eld components naturally have dual or vector (both excitatory and inhibitory) in uence; ii) neuronal integration is better understood in terms of local ...

Foveated, log-polar, or space-variant image architectures provide a high resolution and wide eld workspace, while providing a small pixel computation load. These characteristics are ideal for mobile robotic and active vision applications. A common problem in these application areas is image blur and motion artifact. Recently, there has been described a generalization of the Fourier Transform (t...

We describe classical solutions to the Minkowski space equations of motion of SU(2) gauge theory coupled to a Higgs eld in the spatial spherical ansatz. We show how to reduce the equations to four equations for four gauge invariant degrees of freedom which correspond to the massive gauge bosons and the Higgs particle. The solutions typically dissipate at very early and late times. To describe t...

In this paper we describe a method to construct invariant grey scale features of 3D images. Invariant features remain constant if the images are transformed according to the action of a transformation group. The paper considers only the Euclidean transformation group. In many applications scanned 3D objects underlie translations or rotations which makes it diicult to compare them. Our invariant...

This is the third of three papers about the Compression Theorem: if M m is embedded in Q q R with a normal vector eld and if q ? m 1, then the given vector eld can be straightened (ie, made parallel to the given R direction) by an isotopy of M and normal eld in Q R. The theorem can be deduced from Gromov's theorem on directed em-beddings 3; 2.4.5 (C 0)] and the rst two parts gave proofs. Here w...