The Hausdorff dimension of fractal sets and fractional quantum Hall effect

We consider Farey series of rational numbers in terms of fractal sets labeled by the Hausdorff dimension with values defined in the interval 1<h<2 and associated with fractal curves. Our results come from the observation that the fractional quantum Hall effect-FQHE occurs in pairs of dual topological quantum numbers, the filling factors. These quantum numbers obey some properties of the Farey series and so we obtain that the universality classes of the quantum Hall transitions are classified in terms of h. The connection between Number Theory and Physics appears naturally in this context.     

On the probability distribution of data at points in real complete intersection varieties

We show several estimates on the probability distribution of some data at points in real complete intersection varieties: norms of real affine solutions, condition number of real solution of real systems of multi-variate polynomial equations and convergence radius of Newton's operator for under-determined system of multi-variate polynomial equations.     

A study of the self-injected laser for subnanosecond pulse generation

We present a detailed analysis of the self-injected Nd:YAG laser which is capable of generating subnanosecond duration pulses with peak powers as high as 200 MW. The model predicts that pulses with durations much shorter than the electrical rise time of the electrooptical switch driver can be obtained. Application of this technique to a conventionally Q-switched Nd:YAG laser allowed us to obtain 550 ps pulses with 120 mJ in a very stable and reliable way.     

Determination of the saturation parameter of electronic transition in a uranium-neon hollow-cathode discharge by optogalvanic spectroscopy

Summary The optogalvanic signal (OGS) induced in a uranium-neon hollow-cathode discharge was measured as a function of the laser power density for the 0→16900 cm⁻¹ (591.5 nm) uranium transition. Theoretical relations derived by solving a two-level system rate equations showed the OGS dependence on the laser photon flux, for a modulated c.w. light and for stimulated transitions starting from the ground state. A fitting of the theoretical relations to the experimental measurements allowed the determination of the σ₀ τ product, that is, the saturation parameter of the transition. The results showed good agreement between the σ₀ τ values obtained by the optogalvanic and the usual optical absorption processes.     

Quark fragmentation and trigger side momentum distributions in high-p T processes

It has been widely argued that the experimental evidence concerning the momentum accompanying highp T triggers is a grave problem for models which take the trigger hadron to be a quark fragment. It is claimed that the trigger hadron takes much too large a fraction (z _c ) of the jet momentum for the trigger side jet to be a quark. The jet momentum is not directly measured, but deduced from the derivative of the momentum (p _x ) accompanying the trigger with respect to the trigger transverse momentum-p _T ^t . This argument is shown to be unsafe. Using both an approximate analytic approach to illustrate the physics and subsequently a full numerical computation it is proved that the deduction of the fractional momentum accompanying the trigger, 1/z _c ?1, fromdp _x /dp _T ^t is not correct. Further we show that models—specifically that of Feynman and Field—which do take the trigger to be a quark fragment are essentially in agreement with the data on trigger side momentum distributions. A surprising prediction of our analysis is thatp _x should be approximately constant forp _T ^t ≧6GeV/c.     

Additional aspects of the Stackelberg strategy in nonzero-sum games

The Stackelberg strategy in nonzero-sum games is a reasonable solution concept for games where, either due to lack of information on the part of one player about the performance function of the other, or due to different speeds in computing the strategies, or due to differences in size or strength, one player dominates the entire game by imposing a solution which is favorable to himself. This paper discusses some properties of this solution concept when the players use controls that are functions of the state variables of the game in addition to time. The difficulties in determining such controls are also pointed out. A simple two-stage finite state discrete game is used to illustrate these properties.This work was supported in part by the U.S. Air Force under Grant No. AFOSR-68-1579D, in part by NSF under Grant No. GK-36276, and in part by the Joint Services Electronics Program under Contract No. DAAB-07-72-C-0259 with the Coordinated Science Laboratory, University of Illinois, Urbana, Illinois.     

Reversible magnetization of surface superconductivity

Direct measurements of the surface superconducting magnetization of the PbTl system shows that this state is a thermodynamic reversible one.     

Electrical resistivity of amorphous Zr70Cu30 and the Kondo like model

Electrical resistivity measurements of amorphous Zr₇₀Cu₃₀ as a function of the concentrations of two level systems show that a Kondo like theory cannot explain the observed temperature dependence.