Non-idempotent Intersection Types in Logical Form

Intersection types are an essential tool in the analysis of operational and denotational properties of lambda-terms and functional programs. Among them, non-idempotent intersection types provide precise quantitative information about the evaluation of terms and programs. However, unlike simple or second-order types, intersection types cannot be considered as a logical system because the application rule (or the intersection rule, depending on the presentation of the system) involves a condition stipulating that the proofs of premises must have the same structure. Using earlier work introducing an indexed version of Linear Logic, we show that non-idempotent typing can be given a logical form in a system where formulas represent hereditarily indexed families of intersection types.

M2- and M5-branes in E11 current algebra formulation of M-theory

Equations of motion for M2- and M5-branes are written down in the [Formula: see text] current algebra formulation of M-theory. These branes correspond to currents of the second and the fifth rank antisymmetric tensors in the [Formula: see text] representation, whereas the electric and magnetic fields (coupled to M2- and M5-branes) correspond to currents of the third and the sixth rank antisymmetric tensors, respectively. We show that these equations of motion have solutions in terms of the coordinates on M2- and M5-branes. We also discuss the geometric equations, and show that there are static solutions when M2- or M5-brane exists alone and also when M5-brane wraps around M2-brane. This situation is realized because our Einstein-like equation contains an extra term which can be interpreted as gravitational energy contributing to the curvature, thus avoiding the usual intersection rule.

MEASUREMENTS OF FRACTAL SCALING OF A PASSIVE SCALAR IN UNIFORMLY SHEARED TURBULENCE

Statistics and scaling properties of temperature traces in a uniformly sheared, nearly homogeneous turbulent flow have been investigated experimentally. Heat was injected continuously from an electrically heated, thin ribbon and the fluctuating temperature was measured with a cold wire. By virtue of Taylor's "frozen flow" approximation, the temperature time series was interpreted as a linear section through the heated/unheated fluid interface. The box-counting method was used to reveal the possible fractal scaling of this interface. The results are somewhat mixed. Temperature traces taken away from the centerline of the heated wake appear to exhibit some scaling over a limited range, with a fractal dimension of 0.38 ± 0.05, which, according to the intersection rule, would imply a fractal dimension of about 2.38 for the scalar interface. In contrast, temperature traces taken near the centerline did not show any scaling, but this may be due to the high "density" of such traces, which renders the use of the box-counting algorithm questionable.