Almost isometric embeddings into configuration-compacta

We show that a Polish metric space X which has ‘compact configuration spaces’ is free of almost isometric embeddings, i.e. given such an embedding into X one gets an isometric embedding. By assuming a continuous version of ℵ₀-homogeneity we get the converse statement, and also prove almost isometry uniqueness.     

Nonlinear wave interactions in patterned Silica and AlGaAs waveguides

We study nonlinear interactions between discrete optical solitons that propagate in different regimes of diffraction, and the nonlinear scattering of dispersive waves by local optical potentials. It is well known in optics that when linear coherent waves meet, they interfere without interactions. Linear waves also scatter through local optical structures not exchanging any power with the guided modes of these structures. As a focusing Kerr nonlinearity is present, such linearly-inhibited phenomena can exist. Our studies are performed in silica and AlGaAs nonlinear waveguides, excited by ultra-short pulses in the near infrared. Presented at 9-th International Workshop on Nonlinear Optics Applications, NOA 2007, May 17–20, 2007, Świnoujście, Poland     

Multi-parameter evaluation of fast sol–gel process by terahertz measurements

We present a feasibility study to apply terahertz (THz) spectroscopy and THz imaging as non-destructive diagnostic tools for sol–gel analysis, manufacturing and quality control. By performing THz spectroscopy on liquid and solid samples we were able to follow several key parameters during the sol–gel formation process and of the final product. Sol–gel transformations were monitored by THz absorption, whereas density changes have been observed through changes in refractive indices. Time domain spectroscopy (TDS), both in transmission and reflection geometries, was used to monitor the properties of fast sol–gel resins. THz imaging of gold coated, thin-film sol–gel enables us to determine inhomogeneities and defects in their internal structure. We demonstrated that THz spectroscopy can be implemented as an online analytical tool for multi-parameter evaluation of the sol–gel process during fabrication, and of the final product.     

Special Moufang sets, their root groups and their {micro}-maps

We prove Timmesfeld's conjecture that special abstract rankone groups are quasisimple. We give two characterizations ofthe root groups in special Moufang sets: a normal subgroup ofthe point stabilizer is a root group if it is either regular,or nilpotent and transitive. We prove that if a root group ofa special Moufang set contains an involution, then it is ofexponent 2. We also show that the root groups are abelian ifand only if the so-called µ-maps are involutions.     

Lubricated squeezing flow of a Newtonian liquid between elastic and rigid plates

Theoretical force-time relationships were derived for squeezing flow of a Newtonian liquid between lubricated rigid and elastic plates. It is shown how the elastic number, representing the ratio between the elastic plate's rigidity and the specimen's viscosity, affects the force-time curve and under what circumstances the fluid specimen's thickness becomes a significant factor. Potential implications of the analysis in oral sensory evaluations of viscous foods are also considered.     

Swelling of dextran gel and osmotic pressure of soluble dextran in the presence of salts

The swelling of dextran gels (Sephadex) in salt solutions with a water activity of 0.937, compared with the swelling in pure water, exhibited anion specificity as evidenced by an increased swelling ratio in the following order: Na₂SO₄ < H₂O < NaCl < NaSCN. The swelling ratio showed a good linear correlation with the osmotic pressure of dextran (500 kD) in these solutions. The salt‐concentration difference (imbalance) between the polymer‐solution side of the membrane and the polymer‐free permeate side during the osmotic‐pressure measurements positively correlated with the effect of the salt on the polymer osmotic pressure. These phenomena conform to Hofmeister‐type (or lyotropic) behavior. The diminishing augmentation of dextran osmotic pressure and the change in the salt‐concentration imbalance with rising NaSCN concentration imply a positive preferential interaction and adsorption of the salt onto the polymer. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2740–2750, 2001     

Randomized broadcast in networks

In this paper we study the rate at which a rumor spreads through an undirected graph. This study has two important applications in distributed computation: in simple, robust and efficient broadcast protocols, and in the maintenance of replicated databases.     

On balking from an empty queue

The intuition while observing the economy of queueing systems, is that one’s motivation to join the system, decreases with its level of congestion. Here we present a queueing model where sometimes the opposite is the case. The point of departure is the standard first-come first-served single server queue with Poisson arrivals. Customers commence service immediately if upon their arrival the server is idle. Otherwise, they are informed if the queue is empty or not. Then, they have to decide whether to join or not. We assume that the customers are homogeneous and when they consider whether to join or not, they assess their queueing costs against their reward due to service completion. As the whereabouts of customers interact, we look for the (possibly mixed) join/do not join Nash equilibrium strategy, a strategy that if adopted by all, then under the resulting steady-state conditions, no one has any incentive not to follow it oneself. We show that when the queue is empty then depending on the service distribution, both ‘avoid the crowd’ (ATC) and ‘follow the crowd’ (FTC) scenarios (as well as none-of-the-above) are possible. When the queue is not empty, the situation is always that of ATC. Also, we show that under Nash equilibrium it is possible (depending on the service distribution) that the joining probability when the queue is empty is smaller than it is when the queue is not empty. This research was supported by The Israel Science Foundation Grant No. 237/02.