We construct perturbation series for the qth moment of eigenfunctions of various critical random-matrix ensembles in the strong multifractality regime close to localization. Contrary to previous investigations, our results are valid in the region q<1/2. Our findings allow one to verify, at first leading orders in the strong multifractality limit, the symmetry relation for anomalous fractal dime...

We demonstrate the nontrivial scaling behavior of Ising models defined on (i) a donut-shaped surface and (ii) a curved surface with a constant negative curvature. By performing Monte Carlo simulations, we find that the former model has two distinct critical temperatures at which both the specific heat C(T) and magnetic susceptibility χ(T) show sharp peaks. The critical exponents associated with...

We present criteria of Hille-Nehari type for the half-linear dynamic equation (r(t)Φ(y∆))∆+p(t)Φ(yσ) = 0 on time scales. As a particular important case we get that there is a a (sharp) critical constant which may be different from what is known from the continuous case, and its value depends on the graininess of a time scale and on the coefficient r. As applications we state criteria for strong...

In this paper, a set of operators suitable for digit-serial FIR filtering is presented. The canonical and inverted forms are studied. In each of these structures both the symmetrical and antisymmetrical particular cases are also covered. In last two decades, many efficient algorithms and architectures have been introduced for the design of low complexity bit-parallel Multiple Constant Multiplic...

A solution to the ranking and selection problem of determining a subset of size m containing at least c of the v best from k normal distributions has been developed. The best distributions are those having, for example, i the smallest means, or ii the smallest variances. This paper reviews various applicable algorithms and supplies the operating constants needed to apply these solutions. The co...

Long wavelength optical phonons of quartz were analyzed by a Born-Von Karman model not previously used. It was found that only one force constant associated with the turning of the Si-0 bonds has a critical effect on the softmode frequency and the a-p transition in quartz. The square of the soft-mode frequency was found to depend linearly on this force constant which has the temperature depende...

1. With constant temperature and light intensity, the rate of elongation of a sporangiophore of Phycomyces is constant for many hours. 2. With constant light intensity, values of micro, the "critical thermal increment," have been computed for the elongation of different sporangiophores. These values group themselves closely about the modes 11,000, 16,000, 20,000, 26,000, and 33,000 calories. Sp...

This is a talk given at the conference Critical Dialogues in Cosmology at Princeton University, June 24–27, 1996. It gives a brief summary of our present theoretical understanding regarding the value of the cosmological constant, and describes how to calculate the probability distribution of the observed cosmological constant in cosmological theories with a large number of subuniverses (i. e., ...