This paper is an expository survey of results on integral representations and discrete sum expansions of functions in L(R) in terms of coherent states. Two types of coherent states are considered: Weyl–Heisenberg coherent states, which arise from translations and modulations of a single function, and affine coherent states, called “wavelets,” which arise as translations and dilations of a singl...

A formula for the fission fragment yield area in the coordinate system of the fragment total kinetic energy and of the fragment mass is presented. It was deduced along the lines of the multiexit-channel model of fission elaborated by Brosa, Grossmann and Müller. This formula was fitted to the fragment mass-, average total kinetic energy-, and variance distributions of the thermal neutron induce...

We present measurements of the Nusselt number N as a function of the Rayleigh number R and the Prandtl number sigma in cylindrical cells with aspect ratios gamma = 0.5 and 1.0. We used acetone, methanol, ethanol, and 2-propanol with Prandtl numbers sigma = 4.0, 6.5, 14.2, and 34.1, respectively, in the range 3x10(7) less, similarR less, similar10(11). At constant R, N(R,sigma) varies with sigma...

The Rayleigh-Bénard theory by Grossmann and Lohse [J. Fluid Mech. 407, 27 (2000)] is extended towards very large Prandtl numbers Pr. The Nusselt number Nu is found here to be independent of Pr. However, for fixed Rayleigh numbers Ra a maximum in the Nu(Pr) dependence is predicted. We moreover offer the full functional dependences of Nu(Ra,Pr) and Re(Ra,Pr) within this extended theory, rather th...

The finiteness of black hole entropy suggest that spacetime is fundamentally discrete, and hints at an underlying relationship between geometry and ”information”. The foundation of this relationship is yet to be uncovered, but should manifest itself in a theory of quantum gravity. We review recent attempts to define a microscopic measure for black hole entropy and for the maximum entropy of sph...

In the 12th Marcel Grossmann Meeting, July 17, 2009, the author raised the issue of whether early graviton production could affect non-Gaussian contributions to DM density profiles. Non gaussianity of evolving cosmological states is akin to asking if there is a way to get quantum contributions due to squeezed initial vacuum states which act highly non classically. If particle counting algorithm...

This paper provides a historical perspective and an overview of the pioneering work that Manfred Morari developed in the area of resiliency for chemical processes. Motivated by unique counter-intuitive examples, we present a review of the early mathematical formulations and solution methods developed by Grossmann and co-workers for quantifying Static Resiliency (Flexibility). We also give a bri...

We measured Reynolds numbers Re of turbulent Rayleigh-Bénard convection over the Rayleighnumber range 2×10 <∼ R <∼ 10 11 and Prandtl-number range 3.3 <∼ σ <∼ 29 for cylindrical samples of aspect ratio Γ = 1. For R <∼ Rc ≃ 3× 10 9 we found Re ∼ R βeff with βeff ≃ 0.46 < 1/2. Here both the σand R-dependences are quantitatively consistent with the Grossmann-Lohse (GL) prediction. For R > Rc we fou...

This paper summarizes the contribution presented at the IX Marcel Grossmann Meeting (Rome, July 2000). It is stressed, in particular, that a non-relativistic background of ultra-light dilatons, produced in the context of string cosmology, could represent today a significant fraction of cold dark matter. If the dilaton mass lies within the resonant band of present gravitational antennas, a stoch...