This paper reviews recent academic work on the spatial concentration of entrepreneurship and innovation in the United States. We discuss rationales for the agglomeration of these activities and the economic consequences of clusters. We identify and discuss policies that are being pursued in the United States to encourage local entrepreneurship and innovation. While arguments exist for and again...

We study the evolution of strings in the equatorial plane of a Kerr-Newmann black hole. Writing the equations of motion and the constraints resulting from Hamilton’s principle, three classes of exact solutions are presented, for a closed string, encircling the black-hole. They all depend on two arbitrary, integration functions and two constants. A process for extracting energy is examined for t...

The probability density function of Kerr effect phase noise, often called the Gordon-Mollenauer effect, is derived analytically. The Kerr effect phase noise can be accurately modeled as the summation of a Gaussian random variable and a noncentral chi-square random variable with two degrees of freedom. Using the received intensity to correct for the phase noise, the residual Kerr effect phase no...

We report the measurement of Kerr nonlinearity of thin films of GaN by using the eclipsing Z-scan technique. The measurement was performed using 100 fs pulses at 800 nm. We measured a pure refractive signal, whose associated nonlinear Kerr coefficient was n2 = (−7.3 ± 0.4)× 10−14 cm2 W−1.

Nonlinear magneto-optical diffraction from periodically structured samples has been studied using magnetization-induced second harmonic generation ~MSHG!. Several orders of diffraction were clearly observable in MSHG, along with a strong dependence on the magnetization. Sizeable asymmetry between the MSHG signal measured in positive and negative diffraction peaks, especially visible in second o...

The fast contraction, or pinching, of optical vortices in both thermal and Kerr self-defocusing media is investigated by numerical techniques. For the thermal case, heat diffusion across the vortex core is described, and the heretofore unexplained stability of optical-vortex solitons in thermal media is explained. © 2001 Optical Society of America OCIS codes: 190.4420, 190.5940, 190.3270, 160.4...

We present a simple proof, using the conservation equations, that any quantum stress tensor on Kerr space-time which is isotropic in a frame which rotates rigidly with the angular velocity of the event horizon must be divergent at the velocity of light surface. We comment on our result in the light of the absence of a ‘true Hartle-Hawking’ vacuum for Kerr.

The equation of cosmic string loops in Kerr-de Sitter spacetimes is derived. Having solved the equation numerically, we find that the loops can evolve except for too small ones in the spacetimes.

Using the energy momentum complex given by Møller in 1978 based on the absolute parallelism, the energy distribution in Kerr spacetime is evaluated. The energy with this spacetime is found to be the same as it was earlier evaluated using different definitions mainly based on the metric tensor.