This work presents the minimal length paths, for a robot that maintains risibility of a landmark. The robot is a differential drive system and has limited sensing capabilities (range and angle of view). The optimal paths are eomposed of straight liner and curves that saturate L e Camera pan angle.

In this paper we revisit the formulation of scalar field theories on de Sitter backgrounds subject to the generalized uncertainty principle (GUP). The GUP arises in several contexts in string theory, but is most readily thought of as resulting from using strings as effective probes of geometry, which suggests an uncertainty relation incorporating the string scale ls. After reviewing the string ...

The length and complexity of a linear equalizer filter is highly dependent on the nature of the channel effects it must mitigate. The governing design rules are typically stated in terms of the channel's temporal characteristics, i.e. impulse response duration. Equalizer implementational complexity is a principal limiting factor for high bandwidth data communication applications, and consequent...

Studies in string theory and quantum gravity suggest the existence of a finite lower limit ∆x0 to the possible resolution of distances, at the latest on the scale of the Planck length of 10−35m. Within the framework of the euclidean path integral we explicitly show ultraviolet regularisation in field theory through this short distance structure. Both rotation and translation invariance can be p...

Candidate theories of quantum gravity predict the presence a minimal measurable length at high energies. Such feature is in contrast with Heisenberg Uncertainty Principle. Therefore, phenomenological approaches to introduced models spelled as modifications mechanics including length. The effects such modification are expected be relevant large energies/small lengths. One first consequence that ...

We propose a new approach to calculate perturbatively the effects of a particular deformed Heisenberg algebra on energy spectrum. We use this method to calculate the harmonic oscillator spectrum and find that corrections are in agreement with a previous calculation. Then, we apply this approach to obtain the hydrogen atom spectrum and we find that splittings of degenerate energy levels appear. ...

We study the effects of the existence of a minimal observable length in the phase space of classical and quantum de Sitter (dS) and Anti de Sitter (AdS) cosmology. Since this length has been suggested in quantum gravity and string theory, its effects in the early universe might be expected. Adopting the existence of such a minimum length results in the Generalized Uncertainty Principle (GUP), w...